{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_26408/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_26408","id":"gutenberg_26408","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/26408","summary":null,"tags":["Category: Humour","Category: Mathematics","Category: Philosophy & Ethics","Circle-squaring","Perpetual motion","Science -- Miscellanea","Trisection of angle"],"text":"E-text prepared by David Starner, Keith Edkins, and the Project Gutenberg\nOnline Distributed Proofreading Team (http://www.pgdp.net)\n\n\n\nTranscriber's note:\n\n      A few typographical errors have been corrected: they are\n      listed at the end of the text.\n\n      In mathematical formulae the carat (^) and underscore (_)\n      introduce superscripts or subscripts respectively, of one\n      character or a group enclosed in curly braces ({xyz}).\n      Elsewhere underscores delimit italics in the text, and\n      braces enclose the original page numbers thus {123}.\n\n\n\n\n\nBY AUGUSTUS DE MORGAN\n\nA BUDGET OF\nPARADOXES\n\nREPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM\n\nSECOND EDITION EDITED BY DAVID EUGENE SMITH\n\nWITH A NEW INTRODUCTION BY ERNEST NAGEL\n\nPROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY\n\nUNABRIDGED EDITION--TWO VOLUMES BOUND AS ONE\n\nVolume II\n\n\n\n\n\n\n\nDOVER PUBLICATIONS, INC., NEW YORK\n\n       *       *       *       *       *\n\n_This new Dover Edition, published in 1954,\nis an unabridged republication of the Second Edition\nof 1915, with a new introduction by Professor Ernest Nagel._\n\n_Copyright 1954 by Dover Publications, Inc.\nManufactured in the United States of America_\n\n       *       *       *       *       *\n\n\n{1}\n\nA BUDGET OF PARADOXES.\n\nVOLUME II.\n\nON SOME PHILOSOPHICAL ATHEISTS.\n\nWith the general run of the philosophical atheists of the last century the\nnotion of a God was an hypothesis. There was left an admitted possibility\nthat the vague somewhat which went by more names than one, might be\npersonal, intelligent, and superintendent. In the works of Laplace,[1] who\nis sometimes called an atheist from his writings, there is nothing from\nwhich such an inference can be drawn: unless indeed a Reverend Fellow of\nthe Royal Society may be held to be the fool who said in his heart, etc.,\netc., if his contributions to the _Philosophical Transactions_ go no higher\nthan _nature_. The following anecdote is well known in Paris, but has never\nbeen printed entire. Laplace once went in form to present some edition of\nhis \"Systeme du Monde\" to the First Consul, or Emperor. Napoleon, whom some\nwags had told that this book contained no mention of the name of God, and\nwho was fond of putting embarrassing questions, received it with--\"M.\nLaplace, they tell me you have written this large book on the system of the\nuniverse, and have never even mentioned its Creator.\" Laplace, who, though\nthe most supple of politicians, was as stiff as a martyr on every point of\nhis philosophy or religion (e. g., even under Charles X he never concealed\nhis dislike of the priests), drew himself up and answered {2} bluntly, \"Je\nn'avais pas besoin de cette hypothese-la.\"[2] Napoleon, greatly amused,\ntold this reply to Lagrange, who exclaimed, \"Ah! c'est une belle hypothese;\nca explique beaucoup de choses.\"[3]\n\nIt is commonly said that the last words of Laplace were, \"Ce que nous\nconnaissons est peu de chose; ce que nous ignorons est immense.\"[4] This\nlooks like a parody on Newton's pebbles:[5] the following is the true\naccount; it comes to me through one remove from Poisson.[6] After the\npublication (in 1825) of the fifth volume of the _Mecanique Celeste_,\nLaplace became gradually weaker, and with it musing and abstracted. He\nthought much on the great problems of existence, and often muttered to\nhimself, _Qu'est ce que c'est que tout cela!_[7] After many alternations,\nhe appeared at last so permanently prostrated that his family applied to\nhis favorite pupil, M. Poisson, to try to get a word from him. Poisson paid\na visit, and after a few words of salutation, said, \"J'ai une bonne\nnouvelle a vous annoncer: on a recu au Bureau des Longitudes une lettre\nd'Allemagne annoncant que M. Bessel a verifie par l'observation vos\ndecouvertes theoriques sur les satellites de Jupiter.\"[8] Laplace opened\nhis eyes and answered with deep {3} gravity, \"_L'homme ne poursuit que des\nchimeres_.\"[9] He never spoke again. His death took place March 5, 1827.\n\nThe language used by the two great geometers illustrates what I have said:\na supreme and guiding intelligence--apart from a blind rule called _nature\nof things_--was an _hypothesis_. The absolute denial of such a ruling power\nwas not in the plan of the higher philosophers: it was left for the smaller\nfry. A round assertion of the non-existence of anything which stands in the\nway is the refuge of a certain class of minds: but it succeeds only with\nthings subjective; the objective offers resistance. A philosopher of the\nappropriative class tried it upon the constable who appropriated _him_: I\ndeny your existence, said he; Come along all the same, said the\nunpsychological policeman.\n\nEuler[10] was a believer in God, downright and straightforward. The\nfollowing story is told by Thiebault,[11] in his _Souvenirs de vingt ans de\nsejour a Berlin_,[12] published in his old age, about 1804. This volume was\nfully received as trustworthy; and Marshall Mollendorff[13] told the Duc de\nBassano[14] in 1807 that it was the most veracious of books written by the\nmost honest of men. Thiebault says that he has no personal knowledge of the\ntruth of the story, but {4} that it was believed throughout the whole of\nthe north of Europe. Diderot[15] paid a visit to the Russian Court at the\ninvitation of the Empress. He conversed very freely, and gave the younger\nmembers of the Court circle a good deal of lively atheism. The Empress was\nmuch amused, but some of her councillors suggested that it might be\ndesirable to check these expositions of doctrine. The Empress did not like\nto put a direct muzzle on her guest's tongue, so the following plot was\ncontrived. Diderot was informed that a learned mathematician was in\npossession of an algebraical demonstration of the existence of God, and\nwould give it him before all the Court, if he desired to hear it. Diderot\ngladly consented: though the name of the mathematician is not given, it was\nEuler. He advanced towards Diderot, and said gravely, and in a tone of\nperfect conviction: _Monsieur,_ (a + b^{n}) / n = x, _donc Dieu existe;\nrepondez!_[16] Diderot, to whom algebra was Hebrew, was embarrassed and\ndisconcerted; while peals of laughter rose on all sides. He asked\npermission to return to France at once, which was granted.\n\n\n\nROTATION OF THE MOON.\n\n    An examination of the Astronomical doctrine of the Moon's rotation. By\n    J. L.[17] Edinburgh, 1847, 8vo.\n\nA systematic attack of the character afterwards made with less skill and\nmore notice by Mr. Jellinger Symons.\n\nJuly 1866, J. L. appears as Mr. James Laurie, with a new pamphlet \"The\nAstronomical doctrines of the Moon's rotation ...\" Edinburgh. Of all the\nworks I have seen on the question, this is the most confident, and the\nsorest. {5} A writer on astronomy said of Mr. Jellinger Symons,[18] \"Of\ncourse he convinced no one who knew anything of the subject.\" This\n\"ungenerous slur\" on the speculator's memory appears to have been keenly\nfelt; but its truth is admitted. Those who knew anything of the subject are\n\"the so-called men of science,\" whose three P's were assailed; prestige,\npride, and prejudice: this the author tries to effect for himself with\nthree Q's; quibble, quirk, and quiddity. He explains that the Scribes and\nPharisees would not hear Jesus, and that the lordly bishop of Rome will not\ncast his tiara and keys at the feet of the \"humble presbyter\" who now plays\nthe part of pope in Scotland. I do not know whom he means: but perhaps the\nfriends of the presbyter-pope may consider this an ungenerous slur. The\nbest proof of the astronomer is just such \"as might have been expected from\nthe merest of blockheads\"; but as the giver is of course not a blockhead,\nthis circumstance shows how deeply blinded by prejudice he must be.\n\nOf course the paradoxers do not persuade any persons who know their\nsubjects: and so these Scribes and Pharisees reject the Messiah. We must\nsuppose that the makers of this comparison are Christians: for if they\nthought the Messiah an enthusiast or an impostor, they would be absurd in\ncomparing those who reject what they take for truth with others who once\nrejected what they take for falsehood. And if Christians, they are both\nirreverent and blind to all analogy. The Messiah, with His Divine mission\nproved by miracles which all might see who chose to look, is degraded into\na prototype of James Laurie, ingeniously astronomizing upon ignorant\ngeometry and false logic, and comparing to blockheads those who expose his\nnonsense. Their comparison is as foolish as--supposing {6} them\nChristians--it is profane: but, like errors in general, its other end\npoints to truth. There were Pseudochrists and Antichrists; and a\nConcordance would find the real forerunners of all the paradoxers. But they\nare not so clever as the old false prophets: there are none of whom we\nshould be inclined to say that, if it were possible, they would deceive the\nvery educated. Not an Egyptian among them all can make uproar enough to\ncollect four thousand men that are murderers--of common sense--to lead out\ninto the wilderness. Nothing, says the motto of this work, is so difficult\nto destroy as the errors and false facts propagated by illustrious men\nwhose words have authority. I deny it altogether. There are things much\nmore difficult to destroy: it is much more difficult to destroy the truths\nand real facts supported by such men. And again, it is much more difficult\nto prevent men of no authority from setting up false pretensions; and it is\nmuch more difficult to destroy assertions of fancy speculation. Many an\nerror of thought and learning has fallen before a gradual growth of\nthoughtful and learned opposition. But such things as the quadrature of the\ncircle, etc., are never put down. And why? Because thought can influence\nthought, but thought cannot influence self-conceit: learning can annihilate\nlearning: but learning cannot annihilate ignorance. A sword may cut through\nan iron bar; and the severed ends will not reunite: let it go through the\nair, and the yielding substance is whole again in a moment.\n\n\n\n    Miracles _versus_ Nature: being an application of certain propositions\n    in the theory of chances to the Christian miracles. By\n    Protimalethes.[19] Cambridge, 1847, 8vo.\n\nThe theory, as may be supposed, is carried further than most students of\nthe subject would hold defensible.\n\n{7}\n\n\n\n    An astronomical Lecture. By the Rev. R. Wilson.[20] Greenock, 1847,\n    12mo.\n\nAgainst the moon's rotation on her axis.\n\n\n\n    [Handed about in the streets in 1847: I quote the whole:] Important\n    discovery in astronomy, communicated to the Astronomer Royal, December\n    21st, 1846. That the Sun revolve round the Planets in 25748-2/5 years,\n    in consequence of the combined attraction of the planets and their\n    satellites, and that the Earth revolve round the Moon in 18 years and\n    228 days. D. T. GLAZIER [altered with a pen into GLAZION.] Price one\n    penny.\n\n1847. In the _United Service Magazine_ for September, 1847, Mrs.\nBorron,[21] of Shrewsbury, published some remarks tending to impeach the\nfact that Neptune, the planet found by Galle,[22] really was the planet\nwhich Le Verrier and Adams[23] had a right to claim. This was followed\n(September 14) by two pages, separately circulated, of \"Further\nObservations upon the Planets Neptune and Uranus, with a Theory of\nPerturbations\"; and (October 19, 1848) by three pages of \"A Review of M.\nLeverrier's Exposition.\" Several persons, when the remarkable discovery was\nmade, contended that the planet actually discovered was an intruder; and\nthe future histories of the discovery must contain some account of this\nlittle afterpiece. Tim Linkinwater's theory that there is no place like\nLondon for coincidences, would have been utterly overthrown in favor of\nwhat they used to call the celestial spaces, if there had been a planet\nwhich by chance was put {8} near the place assigned to Neptune at the time\nwhen the discovery was made.\n\n\n\nEARLY IDEAS OF AVIATION.\n\n    Aerial Navigation; containing a description of a proposed flying\n    machine, on a new principle. By Daedalus Britannicus. London, 1847, 8vo.\n\nIn 1842-43 a Mr. Henson[24] had proposed what he called an aeronaut\nsteam-engine, and a Bill was brought in to incorporate an \"Aerial Transit\nCompany.\" The present plan is altogether different, the moving power being\nthe explosion of mixed hydrogen and air. Nothing came of it--not even a\nBill. What the final destiny of the balloon may be no one knows: it may\nreasonably be suspected that difficulties will at last be overcome.\nDarwin,[25] in his \"Botanic Garden\" (1781), has the following prophecy:\n\n \"Soon shall thy arm, unconquered Steam! afar\n  Drag the slow barge, or drive the rapid car;\n  Or, on wide-waving wings expanded, bear\n  The flying chariot through the fields of air.\"\n\nDarwin's contemporaries, no doubt, smiled pity on the poor man. It is worth\nnote that the two true prophecies have been fulfilled in a sense different\nfrom that of the predictions. Darwin was thinking of the suggestion of\nJonathan Hulls,[26] when he spoke of dragging the slow barge: it is only\nvery recently that the steam-tug has been employed on the canals. The car\nwas to be driven, not drawn, and on the common roads. Perhaps, the flying\nchariot will {9} be something of a character which we cannot imagine, even\nwith the two prophecies and their fulfilments to help us.[27]\n\n\n\nTHE SECRET OF THE UNIVERSE DIVULGED.\n\n    A book for the public. New Discovery. The causes of the circulation of\n    the blood; and the true nature of the planetary system. London, 1848,\n    8vo.\n\nLight is the sustainer of motion both in the earth and in the blood. The\nnatural standard, the pulse of a person in health, four beats to one\nrespiration, gives the natural second, which is the measure of the earth's\nprogress in its daily revolution. The Greek fable of the Titans is an\nelaborate exposition of the atomic theory: but any attempt to convince\nlearned classics would only meet their derision; so much does long-fostered\nprejudice stand in the way of truth. The author complains bitterly that men\nof science will not attend to him and others like him: he observes, that\n\"in the time occupied in declining, a man of science might test the\nmerits.\" This is, alas! too true; so well do applicants of this kind know\nhow to stick on. But every rule has its exception: I have heard of one. The\nlate Lord Spencer[28]--the Lord Althorp of the House of Commons--told me\nthat a speculator once got access to him at the Home Office, and was\nproceeding to unfold his way of serving the public. \"I do not understand\nthese things,\" said Lord Althorp, \"but I happen to have ---- (naming an\neminent engineer) upstairs; suppose you talk to him on the subject.\" The\ndiscoverer went up, and in half-an-hour returned, and said, \"I am very much\nobliged to your Lordship for introducing me to Mr. ----; he has convinced\nme {10} that I am quite wrong.\" I supposed, when I heard the story--but it\nwould not have been seemly to say it--that Lord A. exhaled candor and\nsense, which infected those who came within reach: he would have done so,\nif anybody.\n\n\n\nTHE TRISECTION AND QUADRATURE AGAIN.\n\n    A method to trisect a series of angles having relation to each other;\n    also another to trisect any given angle. By James Sabben. 1848 (two\n    quarto pages).\n\n\"The consequence of years of intense thought\": very likely, and very sad.\n\n1848. The following was sent to me in manuscript. I give the whole of it:\n\n\"_Quadrature of the Circle_.--A quadrant is a curvilinear angle traversing\nround and at an equal distance from a given point, called a center, no two\npoints in the curve being at the same angle, but irreptitiously graduating\nfrom 90 to 60. It is therefore a mean angle of 90 and 60, which is 75,\nbecause it is more than 60, and less than 90, approximately from 60 to 90,\nand from 90 to 60, with equal generation in each irreptitious\napproximation, therefore meeting in 75, and which is the mean angle of the\nquadrant.\n\n\"Or suppose a line drawn from a given point at 90, and from the same point\nat 60. Let each of these lines revolve on this point toward each other at\nan equal ratio. They will become one line at 75, and bisect the curve,\nwhich is one-sixth of the entire circle. The result, taking 16 as a\ndiameter, gives an area of 201.072400, and a circumference of 50.2681.\n\n\"The original conception, its natural harmony, and the result, to my own\nmind is a demonstrative truth, which I presume it right to make known,\nthough perhaps at the hazard of unpleasant if not uncourteous remarks.\"\n\nI have added punctuation: the handwriting and spelling {11} are those of an\neducated person; the word _irreptitious_ is indubitable. The whole is a\nnatural curiosity.\n\n\n\n    The quadrature and exact area of the circle demonstrated. By Wm.\n    Peters. 8vo. _n. d._ (circa 1848).[29]\n\n    Suggestions as to the necessity for a revolution in philosophy; and\n    prospectus for the establishment of a new quarterly, to be called the\n    _Physical Philosopher and Heterodox Review_. By Q. E. D. 8vo. 1848.\n\nThese works are by one author, who also published, as appears by\nadvertisement,\n\n\"Newton rescued from the precipitancy of his followers through a century\nand a half,\"[30] and \"Dangers along a coast by correcting (as it is called)\na ship's reckoning by bearings of the land at night fall, or in a fog,\nnearly out of print. Subscriptions are requested for a new edition.\"\n\nThe area of a circle is made four-fifths of the circumscribed square:\nproved on an assumption which it is purposed to explain in a longer\nessay.[31] The author, as Q. E. D., was in controversy with the _Athenaeum_\njournal, and criticised a correspondent, D., who wrote against a certain\nclass of discoverers. He believed the common theories of hydrostatics to be\nwrong, and one of his questions was:\n\n\"Have you ever taken into account anent gravity and gravitation the fact\nthat a five grain cube of cork will of itself half sink in the water,\nwhilst it will take 20 grains of brass, which will sink of itself, to pull\nunder the other half? Fit this if you can, friend D., to your notions of\ngravity and specific gravity, as applied to the construction of a universal\nlaw of gravitation.\"\n\nThis the _Athenaeum_ published--but without some Italics, for which the\neditor was sharply reproved, as a sufficient {12} specimen of the _quod\nerat_ D. _monstrandum_: on which the author remarks--\"D,--Wherefore the e\ncaret? is it D apostrophe? D', D'M, D'Mo, D'Monstrandum; we cannot find the\n_wit_ of it.\" This I conjecture to contain an illusion to the name of the\nsupposed author; but whether De Mocritus, De Mosthenes, or De Moivre was\nintended, I am not willing to decide.\n\n\n\n    The Scriptural Calendar and Chronological Reformer, for the statute\n    year 1849. Including a review of recent publications on the Sabbath\n    question. London, 1849, 12mo.[32]\n\nThis is the almanac of a sect of Christians who keep the Jewish Sabbath,\nhaving a chapel at Mill Yard, Goodman's Fields. They wrote controversial\nworks, and perhaps do so still; but I never chanced to see one.\n\n\n\n    Geometry _versus_ Algebra; or the trisection of an angle geometrically\n    solved. By W. Upton, B.A.[33] Bath (circa 1849). 8vo.\n\nThe author published two tracts under this title, containing different\nalleged proofs: but neither gives any notice of the change. Both contain\nthe same preface, complaining of the British Association for refusing to\nexamine the production. I suppose that the author, finding his first proof\nwrong, invented the second, of which the Association never had the offer;\nand, feeling sure that they would have equally refused to examine the\nsecond, thought it justifiable to {13} present that second as the one which\nthey had refused. Mr. Upton has discovered that the common way of finding\nthe circumference is wrong, would set it right if he had leisure, and, in\nthe mean time, has solved the problem of the duplication of the cube.\n\n_The trisector of an angle, if he demand attention from any mathematician,\nis bound to produce, from his construction, an expression for the sine or\ncosine of the third part of any angle, in terms of the sine or cosine of\nthe angle itself, obtained by help of no higher than the square root._ The\nmathematician knows that such a thing cannot be; but the trisector\nvirtually says it can be, and is bound to produce it, to save time. This is\nthe misfortune of most of the solvers of the celebrated problems, that they\nhave not knowledge enough to present those consequences of their results by\nwhich they can be easily judged. Sometimes they have the knowledge and\nquibble out of the use of it. In many cases a person makes an honest\nbeginning and presents what he is sure is a solution. By conference with\nothers he at last feels uneasy, fears the light, and puts self-love in the\nway of it. Dishonesty sometimes follows. The speculators are, as a class,\nvery apt to imagine that the mathematicians are in fraudulent confederacy\nagainst them: I ought rather to say that each one of them consents to the\nmode in which the rest are treated, and fancies conspiracy against himself.\nThe mania of conspiracy is a very curious subject. I do not mean these\nremarks to apply to the author before me.\n\nOne of Mr. Upton's trisections, if true, would prove the truth of the\nfollowing equation:\n\n  3 cos ([theta] / 3) = 1 + [root](4 - sin^2[theta])\n\nwhich is certainly false.[34]\n\n{14}\n\nIn 1852 I examined a terrific construction, at the request of the late Dr.\nWallich,[35] who was anxious to persuade a poor countryman of his, that\ntrisection of the angle was waste of time. One of the principles was, that\n\"magnitude and direction determine each other.\" The construction was\nequivalent to the assertion that, [theta] being any angle, the cosine of\nits third part is\n\n  sin 3[theta] . cos(5[theta]/2) + sin^2 [theta] sin (5[theta]/2)\n\ndivided by the square root of\n\n  sin^2 3[theta] . cos^2 (5[theta]/2) + sin^4 [theta] + sin 3[theta] . sin\n      5[theta] . sin^2 [theta].\n\nThis is from my rough notes, and I believe it is correct.[36] It is so\nnearly true, unless the angle be very obtuse, that common drawing, applied\nto the construction, will not detect the error. There are many formulae of\nthis kind: and I have several times found a speculator who has discovered\nthe corresponding construction, has seen the approximate success of his\ndrawing--often as great as absolute truth could give in graphical\npractice,--and has then set about his demonstration, in which he always\nsucceeds to his own content.\n\nThere is a trisection of which I have lost both cutting and reference: I\nthink it is in the _United Service Journal_. I could not detect any error\nin it, though certain there must {15} be one. At least I discovered that\ntwo parts of the diagram were incompatible unless a certain point lay in\nline with two others, by which the angle to be trisected--and which was\ntrisected--was bound to be either 0 deg. or 180 deg..\n\nAug. 22, 1866. Mr. Upton sticks to his subject. He has just published \"The\nUptonian Trisection. Respectfully dedicated to the schoolmasters of the\nUnited Kingdom.\" It seems to be a new attempt. He takes no notice of the\nsentence I have put in italics: nor does he mention my notice of him,\nunless he means to include me among those by whom he has been \"ridiculed\nand sneered at\" or \"branded as a brainless heretic.\" I did neither one nor\nthe other: I thought Mr. Upton a paradoxer to whom it was likely to be\nworth while to propound the definite assertion now in italics; and Mr.\nUpton does not find it convenient to take issue on the point. He prefers\ngeneral assertions about algebra. So long as he cannot meet algebra on the\nabove question, he may issue as many \"respectful challenges\" to the\nmathematicians as he can find paper to write: he will meet with no\nattention.\n\n\n\nThere is one trisection which is of more importance than that of the angle.\nIt is easy to get half the paper on which you write for margin; or a\nquarter; but very troublesome to get a third. Show us how, easily and\ncertainly, to fold the paper into three, and you will be a real benefactor\nto society.\n\nEarly in the century there was a Turkish trisector of the angle, Hussein\nEffendi, who published two methods. He was the father of Ameen Bey, who was\nwell known in England thirty years ago as a most amiable and cultivated\ngentleman and an excellent mathematician. He was then a student at\nCambridge; and he died, years ago, in command of the army in Syria. Hussein\nEffendi was instructed in mathematics by Ingliz Selim Effendi, who\ntranslated a work {16} of Bonnycastle[37] into Turkish.[38] This Englishman\nwas Richard Baily, brother of Francis Baily[39] the astronomer, who\nemigrated to Turkey in his youth, and adopted the manners of the Turks, but\nwhether their religion also I never heard, though I should suppose he did.\n\nI now give the letters from the agricultural laborer and his friend,\ndescribed on page 12, Vol. I. They are curiosities; and the history of the\nquadrature can never be well written without some specimens of this kind:\n\n\"Doctor Morgan, Sir. Permit me to address you\n\n\"Brute Creation may perhaps enjoy the faculty of beholding visible things\nwith a more penitrating eye than ourselves. But Spiritual objects are as\nfar out of their reach as though they had no being\n\n\"Nearest therefore to the brute Creation are those men who Suppose\nthemselves to be so far governed by external objects as to believe nothing\nbut what they See and feel And Can accomedate to their Shallow\nunderstanding and Imaginations\n\n\"My Dear Sir Let us all Consult ourselves by the wise proverb.\n\n\"I believe that evry man^s merit & ability aught to be appreciated and\nvalued In proportion to its worth & utility\n\n\"In whatever State or Circumstances they may fortunately or unfortunately\nbe placed\n\n\"And happy it is for evry man to know his worth and place\n\n\"When a Gentleman of your Standing in Society Clad with those honors Can\nnot understand or Solve a problem That is explicitly explained by words and\nLetters and {17} mathematically operated by figuers He had best consult the\nwise proverd\n\n\"Do that which thou Canst understand and Comprehend for thy good.\n\n\"I would recommend that Such Gentleman Change his business\n\n\"And appropriate his time and attention to a Sunday School to Learn what he\nCould and keep the Litle Children form durting their Close\n\n\"With Sincere feelings of Gratitude for your weakness and Inability I am\n\n \"Sir your Superior in Mathematics ----\"\n\n\"1849 June th29.\"\n\n\n\n\"Dor Morgin Sir\n\n\"I wrote and Sent my work to Professor ---- of ---- State of ---- United\nStates\n\n\"I am now in the possession of the facts that he highly approves of my\nwork. And Says he will Insure me Reward in the States\n\n\"I write this that you may understand that I have knowledge of the unfair\nway that I am treated In my own nati County\n\n\"I am told and have reasons to believe that it is the Clergy that treat me\nso unjust.\n\n\"I am not Desirous of heaping Disonors upon my own nation. But if I have to\nLeave this kingdom without my Just dues. The world Shall know how I am and\nhave been treated.\n\n \"I am Sir Desirous of my\n             \"Just dues ----\"\n\n\"1849 July 3.\"\n\n\n\n\"July 7th, 1849.\n\n\"Sir, I have been given to understand that a friend of mine one whom I\nshall never be ashamed to acknowledge as {18} such tho' lowly his origine;\nnay not only not ashamed but proud of doing so for I am one of those who\nesteem and respect a man according to his ability and probity, deeming with\nDr. Watts 'that the mind is the standard of the man,'[40] has laid before\nyou and asked your opinion of his extraordinary performance, viz. the\nquadrature of the circle, he did this with the firmest belief that you\nwould not only treat the matter in a straightforward manner but with the\nconviction that from your known or supposed knowledge of mathematicks would\nhave given an upright and honorable decision upon the subject; but the\nquestion is have you done so? Could I say yes I would with the greatest of\npleasure and have congratulated you upon your decision whatever it might\nhave been but I am sorry to say that I cannot your letter is a paltry\nevasion, you say 'that it is a great pity that you (Mr. ----) should have\nattempted this (the quadrature of the circle) for your mathematical\nknowledge is not sufficient to make you know in what the problem consists,'\nyou don't say in what it does consist _according to your ideas_, oh! no\nnothing of the sort, you enter into no disquisition upon the subject in\norder to show where you think Mr. ---- is wrong and why you have not is\nsimply--_because you cannot_--you know that he has done it and what is if I\nam not wrongly informed _you have been heard to say so_. He has done what\nyou nor any other mathematician as those who call themselves such have\ndone. And what is the reason that you will not candidly acknowledge to him\nas you have to others that he has squared the circle shall I tell you? it\nis because he has performed the feat to obtain the glory of which\nmathematicians have battled from time immemorial that they might encircle\ntheir brows with a wreath of laurels far more glorious than ever conqueror\nwon it is simply this that it is a poor man a {19} humble artisan who has\ngained that victory that you don't like to acknowledge it you don't like to\nbe beaten and worse to acknowledge that you have miscalculated, you have in\nshort too small a soul to acknowledge that he is right.\n\n\"I was asked my opinion and _I_ gave it unhesitatingly in the affirmative\nand I am backed in my opinion not only by Mr. ---- a mathematician and\nwatchmaker residing in the boro of Southwark but by no less an authority\nthan the Professor of mathematics of ---- College ---- ---- United States\nMr. ---- and I presume that he at least is your equal as an authority and\nMr. ---- says that the government of the U.S. will recompense M. D. for the\ndiscovery he has made if so what a reflection upon Old england the boasted\nland of freedom the nursery of arts and sciences that her sons are obliged\nto go to a foreign country to obtain that recompense to which they are\njustly entitled\n\n\"In conclusion I had to contradict an assertion you made to the effect that\n'there is not nor ever was any reward offered by the government of this\ncountry for the discovery of the quadrature of the circle.' I beg to inform\nyou that there _was_ but that it having been deemed an impossibility the\ngovernment has withdrawn it. I do this upon no less an authority than the\nMarquis of Northampton.[41]\n\n \"I am, sir, yours ----\"\n\n\"Dr. Morgan.\"\n\n\n\nTHE MOON'S ROTATION.\n\n    Notes on the Kinematic Effects of Revolution and Rotation, with\n    reference to the Motions of the Moon and of the earth. By Henry\n    Perigal, Jun. Esq. London, 1846-1849, 8vo.\n\n    On the misuse of technical terms. Ambiguity of the terms _Rotation_ and\n    _Revolution_, owing to the double meaning improperly {20} attributed to\n    each of the words. (No date nor place, but by Mr. Perigal,[42] I have\n    no doubt, and containing letters of 1849 and 1850.)\n\n    The moon controversy. Facts _v._ Definitions. By H. P., Jun. London,\n    1856, 8vo. (pp. 4.)\n\nMr. Henry Perigal helped me twenty years ago with the diagrams, direct from\nthe lathe to the wood, for the article \"Trochoidal Curves,\" in the _Penny\nCyclopaedia_: these cuts add very greatly to the value of the article,\nwhich, indeed, could not have been made intelligible without them. He has\nhad many years' experience, as an amateur turner, in combination of double\nand triple circular motions, and has published valuable diagrams in\nprofusion. A person to whom the double circular motion is familiar in the\nlathe naturally looks upon one circle moving upon another as in _simple_\nmotion, if the second circle be fixed to the revolving radius, so that one\nand the same point of the moving circle travels upon the fixed circle. Mr.\nPerigal commenced his attack upon the moon for moving about her axis, in\nthe first of the tracts above, ten years before Mr. Jellinger Symons;[43]\nbut he did not think it necessary to make it a subject for the _Times_\nnewspaper. His familiarity with combined motions enabled him to handle his\narguments much better than Mr. J. Symons could do: in fact, he is the\nclearest assailant of the lot which turned out with Mr. J. Symons. But he\nis as wrong as the rest. The assault is now, I suppose, abandoned, until it\nbecomes epidemic again. This it will do: it is one of those fallacies which\nare very tempting. There was a dispute on the subject in 1748, between\nJames Ferguson[44] and an anonymous opponent; and I think there have been\nothers.\n\n{21}\n\nA poet appears in the field (July 19, 1863) who calls himself Cyclops, and\nwrites four octavo pages. He makes a distinction between _rotation_ and\n_revolution_; and his doctrines and phrases are so like those of Mr.\nPerigal that he is a follower at least. One of his arguments has so often\nbeen used that it is worth while to cite it:\n\n \"Would Mathematicals--forsooth--\n  If true, have failed to prove its truth?\n  Would not they--if they could--submit\n  Some overwhelming proofs of it?\n  But still it totters _proofless_! Hence\n  There's strong presumptive evidence\n  None do--or can--such proof profound\n  Because _the dogma is unsound_.\n  For, were there means of doing so,\n  They would have proved it long ago.\"\n\nThis is only one of the alternatives. Proof requires a person who can give\nand a person who can receive. I feel inspired to add the following:\n\n \"A blind man said, As to the Sun,\n  I'll take my Bible oath there's none;\n  For if there had been one to show\n  They would have shown it long ago.\n  How came he such a goose to be?\n  Did he not know he couldn't see?\n                  Not he!\"\n\nThe absurdity of the verses is in the argument. The writer was not so\nignorant or so dishonest as to affirm that nothing had been offered by the\nother side as proof; accordingly, his syllogism amounts to this: If your\nproposition were true, you could have given proof satisfactory to _me_; but\nthis you have not done, therefore, your proposition is not true.\n\nThe echoes of the moon-controversy reached Benares in 1857, in which year\nwas there published a pamphlet \"Does the Moon Rotate?\" in Sanskrit and\nEnglish. The {22} arguments are much the same as those of the discussion at\nhome.\n\n\n\nON THE NAMES OF RELIGIOUS BODIES.\n\nWe see that there are paradoxers in argument as well as in assertion of\nfact: my plan does not bring me much into contact with these; but another\ninstance may be useful. Sects, whether religious or political, give\nthemselves names which, in meaning, are claimed also by their opponents;\nloyal, liberal, conservative (of good), etc. have been severally\nappropriated by parties. _Whig_ and _Tory_ are unobjectionable names: the\nfirst--which occurs in English ballad as well as in Scotland--is sour\nmilk;[45] the second is a robber. In theology, the Greek Church is\n_Orthodox_, the Roman is _Catholic_, the modern Puritan is _Evangelical_,\netc.\n\nThe word _Christian_ (Vol. I, p. 248[46]) is an instance. When words begin,\nthey carry their meanings. The Jews, who had their Messiah to come, and the\nfollowers of Jesus of Nazareth, who took _Him_ for their Messiah, were both\n_Christians_ (which means _Messianites_): the Jews would never have\ninvented the term to signify _Jesuans_, nor would the disciples have\ninvented such an ambiguous term for themselves; had they done so, the Jews\nwould have disputed it, as they would have done in later times if they had\nhad fair play. The Jews of our day, I see by their newspapers, speak of\nJesus Christ as the _Rabbi Joshua_. But the {23} heathens, who knew little\nor nothing about the Jewish hope, would naturally apply the term\n_Christians_ to the only followers of a _Messiah_ of whom they had heard.\nFor the _Jesuans_ invaded them in a missionary way; while the Jews did not\nattempt, at least openly, to make proselytes.\n\nAll such words as Catholic, etc., are well enough as mere nomenclature; and\nthe world falls for the most part, into any names which parties choose to\ngive themselves. Silly people found inferences on this concession; and, as\nusually happens, they can cite some of their betters. St. Augustine,[47] a\nfreakish arguer, or, to put it in the way of an old writer, _lectorem ne\nmultiloquii taedio fastidiat, Punicis quibusdam argutiis recreare\nsolet_,[48] asks, with triumph, to what chapel a stranger would be\ndirected, if he inquired the way to the _Catholic assembly_. But the best\nexhibition of this kind in our own century is that made by the excellent\nDr. John Milner,[49] in a work (first published in 1801 or 1802) which I\nsuppose still circulates, \"The End of Religious Controversy\": a startling\ntitle which, so far as its truth is concerned, might as well have been \"The\nfloor of the bottomless pit.\" This writer, whom every one of his readers\nwill swear to have been a worthy soul, though many, even of his own sect,\nwill not admire some of his logic, speaks as follows:\n\n\"Letter xxv. _On the true Church being Catholic._ In treating of this third\nmark of the true Church, as expressed in our common creed, I feel my\nspirits sink within me, and I am almost tempted to throw away my pen in\ndespair. For what chance is there of opening the eyes of candid Protestants\nto the other marks of the Church, if they are capable of keeping them shut\nto this? Every time they address the {24} God of Truth, either in solemn\nworship or in private devotion [stretch of rhetoric], they are forced, each\nof them, to repeat: _I believe in_ THE CATHOLIC _Church_, and yet if I ask\nany of them the question: _Are you a_ CATHOLIC? he is sure to answer me,\n_No, I am a_ PROTESTANT! Was there ever a more glaring instance of\ninconsistency and self-condemnation among rational beings!\"\n\n \"John Milner, honest and true,\n  Did what honest people still may do,\n  If they write for the many and not for the few,\n  But what by and bye they must eschew.\"\n\nHe _shortened his clause_; and for a reason. If he had used the whole\nepithet which he knew so well, any one might have given his argument a\nhalf-turn. Had he written, as he ought, \"the _Holy_ Catholic Church\" and\nthen argued as above, some sly Protestant would have parodied him with \"and\nyet if I ask any of them the question: _Are you_ HOLY? he is sure to answer\nme _No, I am a_ SINNER.\" To take the adjective from the Church, and apply\nit to the individual partisan, is recognized slipslop, but not ground of\nargument. If Dr. M. had asked his Protestant whether he belonged to the\nCatholic _Church_, the answer would have been Yes, but not to the Roman\nbranch. When he put his question as he did, he was rightly answered and in\nhis own division. This leaving out words is a common practice, especially\nwhen the omitter is in authority, and cannot be exposed. A year or two ago\na bishop wrote a snubbing letter to a poor parson, who had complained that\nhe was obliged, in burial, to send the worst of sinners to everlasting\nhappiness. The bishop sternly said, \"_hope_[50] is not _assurance_.\" {25}\nCould the clergyman have dared to answer, he would have said, \"No, my Lord!\nbut '_sure and certain_ hope' is as like assurance as a _minikin_ man is\nlike a dwarf.\" Sad to say, a theologian must be illogical: I feel sure that\nif you took the clearest headed writer on logic that ever lived, and made a\nbishop of him, he would be shamed by his own books in a twelvemonth.\n\nMilner's sophism is glaring: but why should Dr. Milner be wiser than St.\nAugustine, one of his teachers? I am tempted to let out the true derivation\nof the word _Catholic, as exclusively applied to the Church of Rome_. All\ncan find it who have access to the _Rituale_ of Bonaventura Piscator[51]\n(lib. i. c. 12, _de nomine Sacrae Ecclesiae_, p. 87 of the Venice {26} folio\nof 1537). I am told that there is a _Rituale_ in the Index Expurgatorius,\nbut I have not thought it worth while to examine whether this be the one: I\nam rather inclined to think, as I have heard elsewhere, that the book was\nheld too dangerous for the faithful to know of it, even by a prohibition:\nit would not surprise me at all if Roman Christians should deny its\nexistence.[52]\n\nIt amuses me to give, at a great distance of time, a small Rowland for a\nsmall Oliver,[53] which I received, _de par l'Eglise_,[54] so far as lay in\nthe Oliver-carrier more than twenty years ago. The following contribution\nof mine to _Notes and Queries_ (3d Ser. vi. p. 175, Aug. 27, 1864) will\nexplain what I say. There had been a complaint that a contributor had used\nthe term _Papist_, which a very excellent dignitary of the Papal system\npronounced an offensive term:\n\n\n\nPAPIST.\n\nThe term _papist_ should be stripped of all except its etymological\nmeaning, and applied to those who give the higher and final authority to\nthe declaration _ex cathedra_[55] of the Pope. See Dr. Wiseman's[56]\narticle, _Catholic Church_, in the _Penny Cyclopaedia_.\n\nWhat is one to do about these names? First, it is clear that offence\nshould, when possible, be avoided: secondly, no one must be required to\ngive a name which favors _any_ assumption made by those to whom it is\ngiven, and not {27} granted by those who give it. Thus the subdivision\nwhich calls itself distinctly _Evangelical_ has no right to expect others\nto concede the title. Now the word _Catholic_, of course, falls under this\nrule; and even _Roman Catholic_ may be refused to those who would restrict\nthe word _Catholic_ to themselves. _Roman Christian_ is unobjectionable,\nsince the Roman Church does not deny the name of Christian to those whom\nshe calls heretics. No one is bound in this matter by Acts of Parliament.\nIn many cases, no doubt, names which have offensive association are used\nmerely by habit, sometimes by hereditary transmission. Boswell records of\nJohnson that he always used the words \"dissenting teacher,\" refusing\n_minister_ and _clergyman_ to all but the recipients of episcopal\nordination.\n\nThis distinctive phrase has been widely adopted: it occurs in the Index of\n3d S. iv. [_Notes and Queries_]. Here we find \"Platts (Rev. John),\nUnitarian teacher, 412;\" the article indexed has \"Unitarian minister.\"\n\nThis, of course is habit: an intentional refusal of the word _minister_\nwould never occur in an index. I remember that, when I first read about Sam\nJohnson's little bit of exclusiveness, I said to myself: \"Teacher? Teacher?\nsurely I remember One who is often called _teacher_, but never _minister_\nor _clergyman_: have not the dissenters got the best of it?\"\n\nWhen I said that the Roman Church concedes the epithet Christians to\nProtestants, I did not mean that all its adherents do the same. There is,\nor was, a Roman newspaper, the _Tablet_, which, seven or eight years ago,\nwas one of the most virulent of the party journals. In it I read, referring\nto some complaint of grievance about mixed marriages, that if _Christians_\nwould marry _Protestants_ they must take the consequences. My memory notes\nthis well; because I recollected, when I saw it, that there was in the\nstable a horse fit to run in the curricle with this one. About seventeen\nyears ago an Oxford M. A., who hated {28} mathematics like a genuine\nOxonian of the last century, was writing on education, and was compelled to\ngive some countenance to the nasty subject. He got out cleverly; for he\ngave as his reason for the permission, that man is an arithmetical,\ngeometrical, and mechanical _animal_, as well as a rational _soul_.\n\nThe _Tablet_ was founded by an old pupil of mine, Mr. Frederic Lucas,[57]\nwho availed himself of his knowledge of me to write some severe\narticles--even abusive, I was told, but I never saw them--against me, for\ncontributing to the _Dublin Review_, and poking my heretic nose into\northodox places. Dr. Wiseman, the editor, came in for his share, and ought\nto have got all. Who ever blamed the pig for intruding himself into the\ncabin when the door was left open? When Mr. Lucas was my pupil, he was of\nthe Society of Friends--in any article but this I should say _Quaker_--and\nwas quiet and gentlemanly, as members of that Church--in any article but\nthis I should, from mere habit, say _sect_--usually are. This is due to his\nmemory; for, by all I heard, when he changed his religion he ceased to be\nLucas couchant, and became Lucas rampant, fanged and langued gules. (I\nlooked into Guillim[58] to see if my terms were right: I could not find\nthem; but to prove I have been there, I notice that he calls a violin a\n_violent_. How comes the word to take this form?) I met with several Roman\nChristians, born and bred, who were very much annoyed at Mr. Lucas and his\ndoings; and said some severe things about new converts needing\nkicking-straps.\n\n{29}\n\nThe mention of Dr. Wiseman reminds me of another word, appropriated by\nChristians to themselves: _fides_;[59] the Roman faith is _fides_, and\nnothing else; and the adherents are _fideles_.[60] Hereby hangs a retort.\nWhen Dr. Wiseman was first in England, he gave a course of lectures in\ndefence of his creed, which were thought very convincing by those who were\nalready convinced. They determined to give him a medal, and there was a\nvery serious discussion about the legend. Dr. Wiseman told me himself that\nhe had answered to his subscribers that he would not have the medal at all\nunless--(naming some Italian authority, whom I forget) approved of the\nlegend. At last _pro fide vindicata_[61] was chosen: this may be read\neither in a Popish or heretical sense. The feminine substantive _fides_\nmeans confidence, trust, (it is made to mean _belief_), but _fidis_, with\nthe same ablative, _fide_, and also feminine, is a _fiddle-string_.[62] If\na Latin writer had had to make a legend signifying \"For the defence of the\nfiddle-string,\" he could not have done it otherwise, in the terseness of a\nlegend, than by writing _pro fide vindicata_. Accordingly, when a Roman\nChristian talks to you of the _faith_, as a thing which is his and not\nyours, you may say _fiddle_. I have searched Bonaventura Piscator in vain\nfor notice of this ambiguity. But the Greeks said fiddle; according to\nSuidas,[63] [Greek: skindapsos][64]--a word meaning a four stringed\ninstrument played with a quill--was an exclamation of contemptuous dissent.\nHow the wits of different races jump!\n\n{30}\n\nI am reminded of a case of _fides vindicata_, which, being in a public\nletter, responding to a public invitation, was not meant to be\nconfidential. Some of the pupils of University College, in which all\nsubdivisions of religion are (1866; _were_, 1867) on a level, have of\ncourse changed their views in after life, and become adherents of various\nhigh churches. On the occasion of a dinner of old students of the College,\nconvened by circular, one of these students, whether then Roman or\nTractarian Christian I do not remember, not content with simply giving\nnegative answer, or none at all, concocted a jorum of theological rebuke,\nand sent it to the Dinner Committee. Heyday! said one of them, this man got\nout of bed backwards! How is that? said the rest. Why, read his name\nbackwards, and you will see. As thus read it was--_No grub_![65]\n\n\n\nTHE WORD CHURCH.\n\nTo return to _Notes and Queries_. The substitution in the (editorial) index\nof \"Unitarian teacher,\" for the contributor's \"Unitarian minister,\" struck\nme very much. I have seldom found such things unmeaning. But as the journal\nhad always been free from editorial sectarianisms,--and very apt to check\nthe contributorial,--I could not be sure in this case. True it was, that\nthe editor and publisher had been changed more than a year before; but this\nwas not of much force. Though one swallow does not make a summer, I have\ngenerally found it show that summer is coming. However, thought I to\nmyself, if this be Little Shibboleth, we shall have Big Shibboleth\nby-and-bye. At last it came. About a twelvemonth afterwards, (3d S. vii. p.\n36) the following was the _editorial_ answer to the question when the\nestablishment was first called the \"Church of England and Ireland\":\n\n{31}\n\n\"That unmeaning clause, 'The United Church of England and Ireland,' which\noccurs on the title-page of _The Book of Common Prayer_, was first used at\nthe commencement of the present century. The authority for this phrase is\nthe fifth article of the Union of 1800: 'That the Churches of England and\nIreland be united into one _Protestant_ (!) episcopal Church, to be called\n\"The United Church of England and Ireland.\"' Of course, churchmen are not\nresponsible for the theology of Acts of Parliament, especially those passed\nduring the dark ages of the Georgian era.\"\n\nThat is to say, the journal gives its adhesion to the party which--under\nthe assumed title of _the_ Church of England--claims for the endowed\ncorporation for the support of religion rights which Parliament cannot\ncontrol, and makes it, in fact, a power above the State. The State has\ngiven an inch: it calls this corporation by the name of the \"United\n_Church_ of England and Ireland,\" as if neither England nor Ireland had any\nother Church. The corporation, accordingly aspires to an ell. But this the\nnation will only give with the aspiration prefixed. To illustrate my\nallusion in a delicate way to polite ears, I will relate what happened in a\nJohnian lecture-room at Cambridge, some fifty years ago, my informant being\npresent. A youth of undue aspirations was giving a proposition, and at last\nsaid, \"Let E F be produced to 'L':\" \"Not quite so far, Mr. ----,\" said the\nlecturer, quietly, to the great amusement of the class, and the utter\nastonishment of the aspirant, who knew no more than a Tractarian the\ntendency of his construction.\n\nThis word _Church_ is made to have a very mystical meaning. The following\ndialogue between Ecclesiastes and Haereticus, which I cannot vouch for, has\noften taken place in spirit, if not in letter: E. The word _Church_\n([Greek: ekklesia])[66] is never used in the New Testament except generally\nor locally for that holy and mystical body to which the sacraments and the\nordinances of Christianity are entrusted. {32} H. Indeed! E. It is beyond a\ndoubt (here he quoted half a dozen texts in support). H. Do you mean that\nany doctrine or ordinance which was solemnly practised by the [Greek:\nekklesia] is binding upon you and me? E. Certainly, unless we should be cut\noff from the congregation of the faithful. H. Have you a couple of hours to\nspare? E. What for? H. If you have, I propose we spend them in crying,\nGreat is Diana of the Ephesians! E. What do you mean? H. You ought to know\nthe solemn service of the [Greek: ekklesia] (Acts xix. 32, 41), at Ephesus;\nwhich any one might take to be true Church, by the more part not knowing\nwherefore they were come together, and which was dismissed, after one of\nthe most sensible sermons ever preached, by the Recorder. E. I see your\nmeaning: it is true, there is that one exception! H. Why, the Recorder's\nsermon itself contains another, the [Greek: ennomos ekklesia],[67]\nlegislative assembly. E. Ah! the New Testament can only be interpreted by\nthe Church! H. I see! the Church interprets itself into existence out of\nthe New Testament, and then interprets the New Testament out of existence\ninto itself!\n\nI look upon all the Churches as fair game which declare of me that _absque\ndubio in aeternum peribo_;[68] not for their presumption towards God, but\nfor their personal insolence towards myself. I find that their sectaries\nstare when I say this. Why! they do not speak of you in _particular_! These\npoor reasoners seem to think that there could be no meaning, as against me,\nunless it should be propounded that \"without doubt he shall perish\neverlastingly, especially A. De Morgan.\" But I hold, with the schoolmen,\nthat \"_Omnis_ homo est animal\" in conjunction with \"Sortes est homo\"\namounts to \"_Sortes_ est animal.\"[69] But they do not mean it _personally_!\nEvery universal proposition is {33} personal to every instance of the\nsubject. If this be not conceded, then I retort, in their own sense and\nmanner, \"Whosoever would serve God, before all things he must not pronounce\nGod's decision upon his neighbor. Which decision, except every one leave to\nGod himself, without doubt he is a bigoted noodle.\"\n\nThe reasoning habit of the educated community, in four cases out of five,\npermits universal propositions to be stated at one time, and denied, _pro\nre nata_,[70] at another. \"Before we proceed to consider any question\ninvolving physical principles, we should set out with _clear ideas_ of the\nnaturally possible and impossible.\" The eminent man who said this, when\nwanting it for his views of mental education (!) never meant it for more\nthan what was in hand, never assumed it in the researches which will give\nhim to posterity! I have heard half-a-dozen defences of his having said\nthis, not one of which affirmed the truth of what was said. A worthy\nclergyman wrote that if A. B. had said a certain thing the point in\nquestion would have been established. It was shown to him that A. B. _had_\nsaid it, to which the reply was a refusal to admit the point because A. B.\nsaid it in a second pamphlet and in answer to objections. And I might give\nfifty such instances with very little search. Always assume more than you\nwant; because you cannot tell how much you may want: put what is over into\nthe didn't-mean-that basket, or the extreme case what-not.\n\n\n\nPROTESTANT AND PAPAL CHRISTENDOM.\n\nSomething near forty years of examination of the theologies on and\noff--more years very much on than quite off--have given me a good title--to\nmyself, I ask no one else for leave--to make the following remarks: A\nconclusion has _premises_, facts or doctrines from proof or authority, and\n_mode of inference_. There may be invention or {34} falsehood of premise,\nwith good logic; and there may be tenable premise, followed by bad logic;\nand there may be both false premise _and_ bad logic. The Roman system has\nsuch a powerful manufactory of premises, that bad logic is little wanted;\nthere is comparatively little of it. The doctrine-forge of the Roman Church\nis one glorious compound of everything that could make Heraclitus[71] sob\nand Democritus[72] snigger. But not the only one. The Protestants, in\ntearing away from the Church of Rome, took with them a fair quantity of the\nresults of the Roman forge, which they could not bring themselves to give\nup. They had more in them of Martin than of Jack. But they would have no\npremises, except from the New Testament; though some eked out with a few\ngeneral Councils. The consequence is that they have been obliged to find\nsuch a logic as would bring the conclusions they require out of the\ncanonical books. And a queer logic it is; nothing but the Roman forge can\nbe compared with the Protestant loom. The picking, the patching, the\npiecing, which goes to the Protestant _termini ad quem_,[73] would be as\nremarkable to the general eye, as the Roman manufacture of _termini a\nquo_,[74] if it were not that the world at large seizes the character of an\nasserted fact better than that of a mode of inference. A grand step towards\nthe deification of a lady, made by alleged revelation 1800 years after her\ndeath, is of glaring evidence: two or three additional shiffle-shuffles\ntowards defence of saying the Athanasian curse in church and unsaying it\nout of church, are hardly noticed. Swift has bungled his satire where he\nmakes Peter a party to finding out what he wants, _totidem syllabis_ and\n_totidem literis_, {35} when he cannot find it _totidem verbis_[75] This is\nProtestant method: the Roman plan is _viam faciam_; the Protestant plan is\n_viam inveniam_.[76] The public at large begins to be conversant with the\nways of _wriggling out_, as shown in the interpretations of the damnatory\nparts of the Athanasian Creed, the phrases of the Burial Service, etc. The\ntime will come when the same public will begin to see the ways of\n_wriggling in_. But one thing at a time: neither Papal Rome nor Protestant\nRome was built--nor will be pulled down--in a day.\n\nThe distinction above drawn between the two great antitheses of Christendom\nmay be illustrated as follows. Two sets of little general dealers lived\nopposite to one another: all sold milk. Each vaunted its own produce: one\nset said that the stuff on the other side the way was only chalk and water;\nthe other said that the opposites sold all sorts of filth, of which calves'\nbrain was the least nasty. Now the fact was that both sets sold milk, and\nfrom the same dairy: but adulterated with different sorts of dirty water:\nand both honestly believed that the mixture was what they were meant to\nsell and ought to sell. The great difference between them, about which the\napprentices fought each other like Trojans, was that the calves' brain men\npoured milk into the water, and the chalk men poured water into the milk.\nThe Greek and Roman sects on one side, the Protestant sects on the other,\nmust all have _churches_: the Greek and Roman sects pour the New Testament\ninto their churches; the Protestant sects pour their churches into the New\nTestament. The Greek and Roman insist upon the New Testament being no more\nthan part and parcel of their churches: the Protestant insist upon their\nchurches being as much part and parcel of the New Testament. All dwell\nvehemently upon the doctrine that there must be milk {36} somewhere; and\neach says--I have it. The doctrine is true: and can be verified by any one\nwho can and will go to the dairy for himself. Him will the several traders\ndeclare to have no milk at all. They will bring their own wares, and\nchallenge a trial: they want nothing but to name the judges. To vary the\nmetaphor, those who have looked at Christianity in open day, know that all\nwho see it through painted windows shut out much of the light of heaven and\ncolor the rest; it matters nothing that the stains are shaped into what are\nmeant for saints and angels.\n\nBut there is another side to the question. To decompose any substance, it\nmust be placed between the poles of the battery. Now theology is but one\npole; philosophy is the other. No one can make out the combinations of our\nday unless he read the writings both of the priest and the philosopher: and\nif any one should hold the first word offensive, I tell him that I mean\n_both_ words to be _significant_. In reading these writings, he will need\nto bring both wires together to find out what it is all about. Time was\nwhen most priests were very explicit about the fate of philosophers, and\nmost philosophers were very candid about their opinion of priests. But\nthough some extremes of the old sorts still remain, there is now, in the\nmiddle, such a fusion of the two pursuits that a plain man is wofully\npuzzled. The theologian writes a philosophy which seems to tell us that the\nNew Testament is a system of psychology; and the philosopher writes a\nChristianity which is utterly unintelligible as to the question whether the\nResurrection be a fact or a transcendental allegory. What between the\ntheologian who assents to the Athanasian denunciation in what seems the\nsense of no denunciation, and the philosopher who parades a Christianity\nwhich looks like no revelation, there is a maze which threatens to have the\nonly possible clue in the theory that everything is something else, and\nnothing is anything at all. But this is a paradox far beyond my handling:\nit is a Budget of itself. {37}\n\n\n\nRELIGION AND PHILOSOPHY.\n\nReligion and Philosophy, the two best gifts of Heaven, set up in opposition\nto each other at the revival of letters; and never did competing tradesmen\nmore grossly misbehave. Bad wishes and bad names flew about like swarms of\nwasps. The Athanasian curses were intended against philosophers; who, had\nthey been a corporation, with state powers to protect them, would have\nformulized a _per contra_. But the tradesmen are beginning to combine: they\nare civil to each other; too civil by half. I speak especially of Great\nBritain. Old theology has run off to ritualism, much lamenting, with no\ncomfort except the discovery that the cloak Paul left at Troas was a\nchasuble. Philosophy, which always had a little sense sewed up in its\ngarments--to pay for its funeral?--has expended a trifle in accommodating\nitself to the new system. But the two are poles of a battery; and a\nquestion arises.\n\n  If Peter Piper picked a peck of pepper,\n  Where is the peck of pepper Peter Piper picked?\n\nIf Religion and Philosophy be the two poles of a battery, whose is the\nbattery Religion and Philosophy have been made the poles of? Is the change\nin the relation of the wires any presumption of a removal of the managers?\nWe know pretty well who handled the instrument: has he resigned or been[77]\nturned out? Has he been put under {38} restriction? A fool may ask more\nquestions than twenty sages can answer: but there is hope; for twenty sages\ncannot ask more questions than one reviewer can answer. I should like to\nsee the opposite sides employed upon the question, What are the _commoda_,\nand what the _pericula_,[78] of the current approximation of Religion and\nPhilosophy?\n\nAll this is very profane and irreverent! It has always been so held by\nthose whose position demands such holding. To describe the Church as it is\npasses for assailing the Church as it ought to be with all who cannot do\nwithout it. In Bedlam[79] a poor creature who fancied he was St. Paul, was\ntold by another patient that he was an impostor; the first maniac lodged a\ncomplaint against the second for calling St. Paul an impostor, which, he\nargued, with much appearance of sanity, ought not to be permitted in a well\nregulated madhouse. Nothing could persuade him that he had missed the\nquestion, which was whether _he_ was St. Paul. The same thing takes place\nin the world _at large_. And especially must be noted the refusal to permit\nto the _profane_ the millionth part of the licence assumed by the _sacred_.\nI give a sound churchman the epitaph of St. John Long; the usual\npronunciation of whose name must be noted--\n\n \"Behold! ye quacks, the vengeance strong\n    On deeds like yours impinging:\n  For here below lies St. John Long[80]\n    Who now must be _long singeing_.\"\n\nHow shameful to pronounce this of the poor man! What, Mr. Orthodox! may I\nnot do in joke to one pretender what {39} you do in earnest--unless you\nquibble--to all the millions of the Greek Church, and a great many others.\nEnough of you and your reasoning! Go and square the circle!\n\nThe few years which end with 1867 have shown, not merely the intermediate\nfusion of Theology and Philosophy of which I have spoken, but much\nconcentration of the two extremes, which looks like a gathering of forces\nfor some very hard fought Armageddon. Extreme theology has been aiming at a\nhigh Church in England, which is to show a new front to all heresy: and\nextreme philosophy is contriving a physical organization which is to\n_think_, and to show that mind is a consequence of matter, or thought a\nrecreation of brain. The physical speculators begin with a possible\nhypothesis, in which they aim at explanation: and so the bold aspirations\nof the author of the _Vestiges_ find standing-ground in the variation of\nspecies by \"natural selection.\" Some relics--so supposed--of extremely\nancient men are brought to help the general cause. Only distant hints are\ngiven that by possibility it may end in the formation of all living\norganisms from a very few, if not from one. The better heads above\nmentioned know that their theory, if true, does not bear upon morals. The\nformation of solar systems from a nebular hypothesis, followed by\norganizations gradually emerging from some curious play of particles, nay,\nthe very evolution of mind and thought from such an apparatus, are all as\nconsistent with a Personal creative power to whom homage and obedience are\ndue, and who has declared himself, as with a blind Nature of Things. A pure\nmaterialist, as to all things visible, may be even a bigotted Christian:\nthis is not frequent, but it is possible. There is a proverb which says, A\npig may fly, but it isn't a likely bird. But when the psychological\nspeculator comes in, he often undertakes to draw inferences from the\nphysical conclusions, by joining on his tremendous apparatus of _a priori_\nknowledge. He deduces that he can _do without_ a God: he can deduce all\nthings {40} without any such necessity. With Occam[81] and Newton he will\nhave no more causes than are necessary to explain phenomena _to him_: and\nif by pure head-work combined with results of physical observation he can\nconstruct his universe, he must be a very _unphilosophical_ man who would\nencumber himself with a useless Creator! There is something tangible about\nmy method, says he; yours is vague. He requires it to be granted that his\nsystem is _positive_ and that yours is _impositive_. So reasoned the stage\ncoachman when the railroads began to depose him--\"If you're upset in a\nstage-coach, why, there you are! but if you're upset on the railroad, where\nare you?\" The answer lies in another question, Which is most positive\nknowledge, God deduced from man and his history, or the postulates of the\nfew who think they can reason _a priori_ on the tacit assumption of\nunlimited command of data?\n\nWe are not yet come to the existence of a school of philosophers who\nexplicitly deny a Creator: but we are on the way, though common sense may\ninterpose. There are always straws which show the direction of the wind. I\nhave before me the printed letter of a medical man--to whose professional\nability I have good testimony--who finds the vital principle in highly\nrarefied oxygen. With the usual logic of such thinkers, he dismisses the\n\"eternal personal identity\" because \"If soul, spirit, mind, which are\nmerely modes of sensation, be the attribute or function of nerve-tissue, it\ncannot possibly have any existence apart from its material organism!\" How\ndoes he know this _impossibility_? If all the mind _we_ know be from\nnerve-tissue, how does it appear that mind in other planets may not be\nanother thing? Nay, when we come to _possibilities_, does not his own\nsystem give a queer one? If highly rarefied oxygen be vital power, more\nhighly rarefied oxygen {41} may be more vital and more powerful. Where is\nthis to stop? Is it _impossible_ that a finite quantity, rarefied _ad\ninfinitum_, may be an Omnipotent? Perhaps the true Genesis, when written,\nwill open with \"In the beginning was an imperial quart of oxygen at 60\ndeg. of Fahrenheit, and the pressure of the atmosphere; and this oxygen\nwas infinitely rarefied; and this oxygen became God.\" For myself, my\naspirations as to this system are Manichaean. The quart of oxygen is the\nOrmuzd, or good principle: another quart, of hydrogen, is the Ahriman, or\nevil principle! My author says that his system explains Freewill and\nImmortality so obviously that it is difficult to read previous speculations\nwith becoming gravity. My deduction explains the conflict of good and evil\nwith such clearness that no one can henceforward read the New Testament\nwith becoming reverence. The surgeon whom I have described is an early bud\nwhich will probably be nipped by the frost and wither on the ground: but\nthere is a good crop coming. Material pneuma is destined to high functions;\nand man is to read by gas-light.\n\n\n\nTHE SUN AN ELECTRIC SPACE.\n\n    The solar system truly solved; demonstrating by the perfect harmony of\n    the planets, founded on the four universal laws, the Sun to be an\n    electric space; and a source of every natural production displayed\n    throughout the solar system. By James Hopkins.[82] London, 1849, 8vo.\n\nThe author says:\n\n\"I am satisfied that I have given the true _laws_ constituting the _Sun_ to\nbe _space_; and I call upon those disposed to maintain the contrary, to\ngive true _laws_ showing him to be a body: until such can be satisfactorily\nestablished, I have an undoubted claim to the credit of my theory,--That\nthe Sun is an _Electric Space_, fed and governed by the {42} planets, which\nhave the property of attracting heat from it; and the means of supplying\nthe necessary _pabulum_ by their degenerated air driven off towards the\ncentral space--the wonderful alembic in which it becomes transmuted to the\nrevivifying necessities of continuous action; and the central space or Sun\nbeing perfectly electric, has the counter property of repulsing the bodies\nthat attract it. How wonderful a conception! How beautiful, how magnificent\nan arrangement!\n\n\"O Centre! O Space! O Electric Space!\"\n\n\n\nJOSEPH ADY.\n\n1849. _Joseph Ady_[83] is entitled to a place in this list of discoverers:\nhis great fault, like that of some others, lay in pushing his method too\nfar. He began by detecting unclaimed dividends, and disclosing them to\ntheir right owners, exacting his fee before he made his communication. He\nthen generalized into trying to get fees from all of the _name_ belonging\nto a dividend; and he gave mysterious hints of danger impending. For\ninstance, he would write to a clergyman that a legal penalty was hanging\nover him; and when the alarmed divine forwarded the sum required for\ndisclosure, he was favored with an extract from some old statute or canon,\nnever repealed, forbidding a clergyman to be a member of a corporation, and\nwas reminded that he had insured his life in the ---- Office, which had a\nroyal charter. He was facetious, was Joseph: he described himself in his\ncirculars as \"personally known to Sir Peter Laurie[84] and all other\naldermen\"; which was nearly true, {43} as he had been before most of them\non charges of false pretence; but I believe he was nearly always within the\nlaw. Sir James Duke, when Lord Mayor, having particularly displeased him by\na decision, his circulars of 1849 contain the following:\n\n\"Should you have cause to complain of any party, Sir J. Duke has contrived\na new law of evidence, viz., write to him, he will consider your letter\nsufficient proof, and make the parties complained of pay without judge or\njury, and will frank you from every expense.\"\n\nI strongly suspect that Joseph Ady believed in himself.\n\nHe sometimes issued a second warning, of a Sibylline character:\n\n\"Should you find cause to complain of anybody, my voluntary referee, the\nRt. Hon. Sir Peter Laurie, Kt., perpetual Deputy Lord Mayor, will see\njustice done you without any charge whatever: he and his toady, -- ----\n----. The accursed of Moses can hang any man: thus, by catching him alone\nand swearing Naboth spake evil against God and the King. Therefore (!) I\nadmit no strangers to a personal conference without a prepayment of 20s.\neach. Had you attended to my former notice you would have received twice as\nmuch: neglect this and you will lose all.\"\n\n\n\nON MODERN ASTROLOGY.\n\n    Zadkiel's Almanac for 1849. Nineteenth number.\n\n    Raphael's Prophetic Almanac for 1849. Twenty-ninth number.\n\n    Reasons for belief in judicial astrology, and remarks on the dangerous\n    character of popish priestcraft. London, 1849, 12mo.\n\n    Astronomy in a nutshell: or the leading problems of the solar system\n    solved by simple proportion only, on the theory of magnetic attraction.\n    By Lieut. Morrison,[85] N. N. London (_s. a._) 12mo.\n\n{44}\n\nLieut. Morrison is Zadkiel Tao Sze, and declares himself in real earnest an\nastrologer. There are a great many books on astrology, but I have not felt\ninterest enough to preserve many of them which have come in my way. If\nanything ever had a fair trial, it was astrology. The idea itself is\nnatural enough. A human being, set down on this earth, without any\ntradition, would probably suspect that the heavenly bodies had something to\ndo with the guidance of affairs. I think that any one who tries will\nascertain that the planets do not prophesy: but if he should find to the\ncontrary, he will of course go on asking. A great many persons class\ntogether belief in astrology and belief in apparitions: the two things\ndiffer in precisely the way in which a science of observation differs from\na science of experiment. Many make the mistake which M. le Marquis made\nwhen he came too late, and hoped M. Cassini[86] would do the eclipse over\nagain for his ladies. The apparition chooses its own time, and comes as\nseldom or as often as it pleases, be it departed spirit, nervous\nderangement, or imposition. Consequently it can only be observed, and not\nexperimented upon. But the heavens, if astrology be true, are prophesying\naway day and night all the year round, and about every body. Experiments\ncan be made, then, except only on rare phenomena, such as eclipses: anybody\nmay choose his time and his question. This is the great difference: and\nexperiments were made, century after century. If astrology had been true,\nit must have lasted in an ever-improving state. If it be true, it is a\ntruth, and a useful truth, which had experience and prejudice both in its\nfavor, and yet lost ground as soon as astronomy, its working tool, began to\nimprove.\n\n\n\n1850. A letter in the handwriting of an educated man, dated from a street\nin which it must be taken that educated persons live, is addressed to the\nSecretary of the {45} Astronomical Society about a matter on which the\nwriter says \"his professional pursuit will enable him to give a\nsatisfactory reply.\" In a question before a court of law it is sworn on one\nside that the moon was shining at a certain hour of a certain night on a\ncertain spot in London; on the other side it is affirmed that she was\nclouded. The Secretary is requested to decide. This is curious, as the\nquestion is not astrological. Persons still send to Greenwich, now and\nthen, to have their fortunes told. In one case, not very many years ago, a\nyoung gentleman begged to know who his wife was to be, and what fee he was\nto remit.\n\nSometimes the astronomer turns conjurer for fun, and his prophesies are\nfulfilled. It is related of Flamsteed[87] that an old woman came to know\nthe whereabouts of a bundle of linen which had strayed. Flamsteed drew a\ncircle, put a square into it, and gravely pointed out a ditch, near her\ncottage, in which he said it would be found. He meant to have given the\nwoman a little good advice when she came back: but she came back in great\ndelight, with the bundle in her hand, found in the very place. The late\nBaron Zach[88] received a letter from Pons,[89] a successful finder of\ncomets, complaining that for a certain period he had found no comets,\nthough he had searched diligently. Zach, a man of much sly humor, told him\nthat no spots had been seen on the sun for about the same time--which was\ntrue,--and assured him that when the spots came back, the comets would come\nwith them. Some time after he got a letter {46} from Pons, who informed him\nwith great satisfaction that he was quite right, that very large spots had\nappeared on the sun, and that he had found a fine comet shortly after. I do\nnot vouch for the first story, but I have the second in Zach's handwriting.\nIt would mend the joke exceedingly if some day a real relation should be\nestablished between comets and solar spots: of late years good reason has\nbeen shown for advancing a connection between these spots and the earth's\nmagnetism.[90] If the two things had been put to Zach, he would probably\nhave chosen the comets. Here is a hint for a paradox: the solar spots are\nthe dead comets, which have parted with their light and heat to feed the\nsun, as was once suggested. I should not wonder if I were too late, and the\nthing had been actually maintained. My list does not contain the twentieth\npart of the possible whole.\n\nThe mention of coincidences suggests an everlasting source of explanations,\napplicable to all that is extraordinary. The great paradox of coincidence\nis that of Leibnitz, known as the _pre-established harmony_, or _law of\ncoincidences_, by which, separately and independently, the body receives\nimpressions, and the mind proceeds as if it had perceived them from\nwithout. Every sensation, and the consequent state of the soul, are\nindependent things coincident in time by the pre-established law. The\nphilosopher could not otherwise _account for_ the connection of mind and\nmatter; and he never goes by so vulgar a rule as _Whatever is, is_; to him\nthat which is not clear as to how, is not at all. Philosophers in general,\nwho tolerate each other's theories much better than Christians do each\nother's failings, seldom revive Leibnitz's fantasy: they seem to act upon\nthe maxim quoted by Father Eustace[91] from the {47} Decretals, _Facinora\nostendi dum puniuntur, flagitia autem abscondi debent_.[92]\n\nThe great _ghost-paradox_, and its theory of _coincidences_, will rise to\nthe surface in the mind of every one. But the use of the word _coincidence_\nis here at variance with its common meaning. When A is constantly\nhappening, and also B, the occurrence of A and B at the same moment is the\nmere coincidence which may be casualty. But the case before us is that A is\nconstantly happening, while B, when it does happen, almost always happens\nwith A, and very rarely without it. That is to say, such is the phenomenon\nasserted: and all who rationally refer it to casualty, affirm that B is\nhappening very often as well as A, but that it is not thought worthy of\nbeing recorded except when A is simultaneous. Of course A is here a death,\nand B the spectral appearance of the person who dies. In talking of this\nsubject it is necessary to put out of the question all who play fast and\nloose with their secret convictions: these had better give us a reason,\nwhen they feel internal pressure for explanation, that there is no\nweathercock at Kilve; this would do for all cases. But persons of real\ninquiry will see that first, experience does not bear out the asserted\nfrequency of the spectre, without the alleged coincidence of death: and\nsecondly, that if the crowd of purely casual spectres were so great that it\nis no wonder that, now and then the person should have died at or near the\nmoment, we ought to expect a much larger proportion of cases in which the\nspectre should come at the moment of the death of one or another of all the\ncluster who are closely connected with the original of the spectre. But\nthis, we know, is almost without example. It remains then, for all, who\nspeculate at all, to look upon the asserted phenomenon, think what they may\nof it, the thing which is to be explained, as a _connection_ in time of the\ndeath, and the {48} simultaneous appearance of the dead. Any person the\nleast used to the theory of probabilities will see that purely casual\ncoincidence, the _wrong spectre_ being comparatively so rare that it may be\nsaid never to occur, is not within the rational field of possibility.\n\nThe purely casual coincidence, from which there is no escape except the\nactual doctrine of special providences, carried down to a very low point of\nspecial intention, requires a junction of the things the like of each of\nwhich is always happening. I will give three instances which have occurred\nto myself within the last few years: I solemnly vouch for the literal truth\nof every part of all three:\n\nIn August 1861, M. Senarmont,[93] of the French Institute, wrote to me to\nthe effect that Fresnel[94] had sent to England, in or shortly after 1824,\na paper for translation and insertion in the _European Review_, which\nshortly afterwards expired. The question was what had become of that paper.\nI examined the _Review_ at the Museum, found no trace of the paper, and\nwrote back to that effect at the Museum, adding that everything now\ndepended on ascertaining the name of the editor, and tracing his papers: of\nthis I thought there was no chance. I posted this letter on my way home, at\na Post Office in the Hampstead Road at the junction with Edward Street, on\nthe opposite side of which is a bookstall. Lounging for a moment over the\nexposed books, _sicut meus est mos_,[95] I saw, within a few minutes of the\nposting of the letter, a little catch-penny book of anecdotes of Macaulay,\nwhich I bought, and ran over for a minute. My eye was soon caught by this\nsentence: \"One of the young fellows immediately wrote to the editor (Mr.\nWalker) {49} of the _European Review_.\" I thus got the clue by which I\nascertained that there was no chance of recovering Fresnel's paper. Of the\nmention of current reviews, not one in a thousand names the editor.\n\nIn the summer of 1865 I made my first acquaintance with the tales of\nNathaniel Hawthorne, and the first I read was about the siege of Boston in\nthe War of Independence. I could not make it out: everybody seemed to have\ngot into somebody else's place. I was beginning the second tale, when a\nparcel arrived: it was a lot of old pamphlets and other rubbish, as he\ncalled it, sent by a friend who had lately sold his books, had not thought\nit worth while to send these things for sale, but thought I might like to\nlook at them and possibly keep some. The first thing I looked at was a\nsheet which, being opened, displayed \"A plan of Boston and its environs,\nshewing the true situation of his Majesty's army and also that of the\nrebels, drawn by an engineer, at Boston Oct. 1775.\" Such detailed plans of\ncurrent sieges being then uncommon, it is explained that \"The principal\npart of this plan was surveyed by Richard Williams, Lieutenant at Boston;\nand sent over by the son of a nobleman to his father in town, by whose\npermission it was published.\" I immediately saw that my confusion arose\nfrom my supposing that the king's troops were besieging the rebels, when it\nwas just the other way.\n\nApril 1, 1853, while engaged in making some notes on a logical point, an\nidea occurred which was perfectly new to me, on the mode of conciliating\nthe notions _omnipresence_ and _indivisibility into parts_. What it was is\nno matter here: suffice it that, since it was published elsewhere (in a\npaper on _Infinity_, _Camb. Phil. Trans._ vol. xi. p. 1) I have not had it\nproduced to me. I had just finished a paragraph on the subject, when a\nparcel came in from a bookseller containing Heywood's[96] _Analysis of\nKant's Critick_, 1844.\n\n{50} On turning over the leaves I found (p. 109) the identical thought\nwhich up to this day, I only know as in my own paper, or in Kant. I feel\nsure I had not seen it before, for it is in Kant's first edition, which was\nnever translated to my knowledge; and it does not appear in the later\neditions. Mr. Heywood gives some account of the first edition.\n\nIn the broadsheet which gave account of the dying scene of Charles II, it\nis said that the Roman Catholic priest was introduced by P. M. A. C. F. The\nchain was this: the Duchess of Portsmouth[97] applied to the Duke of York,\nwho may have consulted his Cordelier confessor, Mansuete, about procuring a\npriest, and the priest was smuggled into the king's room by the Duchess and\nChiffinch.[98] Now the letters are a verbal acrostic of _Pere Mansuete a\nCordelier Friar_, and a syllabic acrostic of _PortsMouth and ChifFinch_.\nThis is a singular coincidence. Macaulay adopted the first interpretation,\npreferring it to the second, which I brought before him as the conjecture\nof a near relative of my own. But Mansuete is not mentioned in his\nnarrative: it may well be doubted whether the writer of a broadside for\nEnglish readers would use _Pere_ instead of _Father_. And the person who\nreally \"reminded\" the Duke of \"the duty he owed to his brother,\" was the\nDuchess and not Mansuete. But my affair is only with the coincidence.\n\nBut there are coincidences which are really connected without the\nconnection being known to those who find in them matter of astonishment.\nPresentiments furnish marked cases: sometimes there is no mystery to those\nwho have the clue. In the _Gentleman's Magazine_ (vol. 80, part 2, p. 33)\nwe read, the subject being presentiment of death, as follows: \"In 1778, to\ncome nearer the recollection of {51} survivors, at the taking of\nPondicherry, Captain John Fletcher, Captain De Morgan, and Lieutenant\nBosanquet, each distinctly foretold his own death on the morning of his\nfate.\" I have no doubt of all three; and I knew it of my grandfather long\nbefore I read the above passage. He saw that the battery he commanded was\nunduly exposed: I think by the sap running through the fort when produced.\nHe represented this to the engineer officers, and to the\ncommander-in-chief; the engineers denied the truth of the statement, the\ncommander believed them, my grandfather quietly observed that he must make\nhis will, and the French fulfilled his prediction. His will bore date the\nday of his death; and I always thought it more remarkable than the\nfulfilment of the prophecy that a soldier should not consider any danger\nshort of one like the above, sufficient reason to make his will. I suppose\nthe other officers were similarly posted. I am told that military men very\noften defer making their wills until just before an action: but to face the\nordinary risks intestate, and to wait until speedy death must be the all\nbut certain consequence of a stupid mistake, is carrying the principle very\nfar. In the matter of coincidences there are, as in other cases, two\nwonderful extremes with every intermediate degree. At one end we have the\nconfident people who can attribute anything to casual coincidence; who\nallow Zadok Imposture and Nathan Coincidence to anoint Solomon Selfconceit\nking. At the other end we have those who see something _very curious_ in\nany coincidence you please, and whose minds yearn for a deep reason. A\nspeculator of this class happened to find that Matthew viii. 28-33 and Luke\nviii. 26-33 contain the same account, that of the demons entering into the\nswine. Very odd! chapters tallying, and verses so nearly: is the\nversification rightly managed? Examination is sure to show that there are\nmonstrous inconsistencies in the mode of division, which being corrected,\nthe verses tally as well as the chapters. And then how comes it? I cannot\ngo on, {52} for I have no gift at torturing a coincidence, but I would lay\ntwopence, if I could make a bet--which I never did in all my life--that\nsome one or more of my readers will try it. Some people say that the study\nof chances tends to awaken a spirit of gambling: I suspect the contrary. At\nany rate, I myself, the writer of a mathematical book and a comparatively\npopular book, have never laid a bet nor played for a stake, however small:\nnot one single time.\n\nIt is useful to record such instances as I have given, with precision and\non the solemn word of the recorder. When such a story as that of Flamsteed\nis told, _a priori_ assures us that it could not have been: the story may\nhave been a _ben trovato_,[99] but not the bundle. It is also useful to\nestablish some of the good jokes which all take for inventions. My friend\nMr. J. Bellingham Inglis,[100] before 1800, saw the tobacconist's carriage\nwith a sample of tobacco in a shield, and the motto _Quid rides_[101] (_N._\n& _Q._, 3d S. i. 245). His father was able to tell him all about it. The\ntobacconist was Jacob Brandon, well known to the elder Mr. Inglis, and the\nperson who started the motto, the instant he was asked for such a thing,\nwas Harry Calender of Lloyd's, a scholar and a wit. My friend Mr. H. Crabb\nRobinson[102] remembers the King's Counsel (Samuel Marryat) who took the\nmotto _Causes produce effects_, when his success enabled him to start a\ncarriage.\n\nThe coincidences of errata are sometimes very remarkable: it may be that\nthe misprint has a sting. The death of Sir W. Hamilton[103] of Edinburgh\nwas known in London on a Thursday, and the editor of the _Athenaeum_ wrote\nto {53} me in the afternoon for a short obituary notice to appear on\nSaturday. I dashed off the few lines which appeared without a moment to\nthink: and those of my readers who might perhaps think me capable of\ncontriving errata with meaning will, I am sure, allow the hurry, the\noccasion, and my own peculiar relation to the departed, as sufficient\nreasons for believing in my entire innocence. Of course I could not see a\nproof: and two errata occurred. The words \"addition to Stewart\"[104]\nrequire \"_for_ addition to _read_ edition of.\" This represents what had\nbeen insisted on by the Edinburgh publisher, who, frightened by the edition\nof Reid,[105] had stipulated for a simple reprint without notes. Again\n\"principles of logic and mathematics\" required \"_for_ mathematics _read_\nmetaphysics.\" No four words could be put together which would have so good\na title to be Hamilton's motto.\n\n\n\nApril 1850, found in the letter-box, three loose leaves, well printed and\nover punctuated, being\n\n    Chapter VI. Brethren, lo I come, holding forth the word of life, for so\n    I am commanded.... Chapter VII. Hear my prayer, O generations! and walk\n    by the way, to drink the waters of the river.... Chapter VIII. Hearken\n    o earth, earth, earth, and the kings of the earth, and their armies....\n\nA very large collection might be made of such apostolic writings. They go\non well enough in a misty--meant for mystical--imitation of St. Paul or the\nprophets, until at last some prodigious want of keeping shows the education\nof the writer. For example, after half a page which might {54} pass for\nIrving's[106] preaching--though a person to whom it was presented as such\nwould say that most likely the head and tail would make something more like\nhead and tail of it--we are astounded by a declaration from the _Holy\nSpirit_, speaking of himself, that he is \"not ashamed of the Gospel of\nChrist.\" It would be long before we should find in _educated_ rhapsody--of\nwhich there are specimens enough--such a thing as a person of the Trinity\ntaking merit for moral courage enough to stand where St. Peter fell. The\nfollowing declaration comes next--\"I will judge between cattle and cattle,\nthat use their tongues.\"\n\n\n\nTHE FIGURE OF THE EARTH.\n\n    The figure of the earth. By J. L. Murphy,[107] of Birmingham. (London\n    and Birmingham, 4 pages, 12mo.) (1850?)\n\nMr. Murphy invites attention and objection to some assertions, as that the\nearth is prolate, not oblate. \"If the philosopher's conclusion be right,\nthen the pole is the center of a valley (!) thirteen miles deep.\" Hence it\nwould be very warm. It is answer enough to ask--Who knows that it is not?\n\n\n\n    *** A paragraph in the MS. appears to have been inserted in this place\n    by mistake. It will be found in the Appendix at the end of this\n    volume.--S. E. De M.\n\n\n\nPERPETUAL MOTION.\n\n1851. The following letter was written by one of a class of persons whom,\nafter much experience of them, I {55} do _not_ pronounce insane. But in\nthis case the second sentence gives a suspicion of actual delusion of the\nsenses; the third looks like that eye for the main chance which passes for\nsanity on the Stock Exchange and elsewhere:\n\n15th Sept. 1851.\n\n\"Gentlemen,--I pray you take steps to make known that yesterday I completed\nmy invention which will give motion to every country on the Earth;--to move\nMachinery!--the long sought in vain 'Perpetual Motion'!!--I was supported\nat the time by the Queen and H.R.H. Prince Albert. If, Gentlemen, you can\nadvise me how to proceed to claim the reward, if any is offered by the\nGovernment, or how to secure the PATENT for the machine, or in any way\nassist me by advice in this great work, I shall most graciously acknowledge\nyour consideration.\n\nThese are my convictions that my SEVERAL discoveries will be realized: and\nthis great one can be at once acted upon: although at this moment it only\nexists in my mind, from my knowledge of certain fixed principles in\nnature:--the Machine I have not made, as I only completed the discovery\nYESTERDAY, Sunday!\n\n          I have, etc. ---- ----\"\n\n  To the Directors of the\n  London University, Gower Street.\n\n\n\nON SPIRITUALISM.\n\n    The Divine Drama of History and Civilisation. By the Rev. James Smith,\n    M.A.[108] London, 1854, 8vo.\n\nI have several books on that great paradox of our day, _Spiritualism_, but\nI shall exclude all but three. The bibliography of this subject is now very\nlarge. The question is one both of evidence and speculation;--Are the facts\n{56} true? Are they caused by spirits? These I shall not enter upon: I\nshall merely recommend this work as that of a spiritualist who does not\nenter on the subject, which he takes for granted, but applies his derived\nviews to the history of mankind with learning and thought. Mr. Smith was a\nman of a very peculiar turn of thinking. He was, when alive, the editor, or\n_an_ editor, of the _Family Herald_: I say when alive, to speak according\nto knowledge; for, if his own views be true, he may have a hand in it\nstill. The answers to correspondents, in his time, were piquant and\noriginal above any I ever saw. I think a very readable book might be made\nout of them, resembling \"Guesses at Truth:\" the turn given to an inquiry\nabout morals, religion, or socials, is often of the highest degree of\n_unexpectedness_; the poor querist would find himself right in a most\nunpalatable way.\n\nAnswers to correspondents, in newspapers, are very often the fag ends of\nliterature. I shall never forget the following. A person was invited to\nname a rule without exception, if he could: he answered \"A man _must_ be\npresent when he is shaved.\" A lady--what right have ladies to decide\nquestions about shaving?--said this was not properly a rule; and the oracle\nwas consulted. The editor agreed with the lady; he said that \"a man _must_\nbe present when he is shaved\" is not a _rule_, but a _fact_.\n\n\n\n[Among my anonymous communicants is one who states that I have done\ninjustice to the Rev. James Smith in \"referring to him as a spiritualist,\"\nand placing his \"Divine Drama\" among paradoxes: \"it is no paradox, nor do\n_spiritualistic_ views mar or weaken the execution of the design.\" Quite\ntrue: for the design is to produce and enforce \"spiritualistic views\"; and\nleather does not mar nor weaken a shoemaker's plan. I knew Mr. Smith well,\nand have often talked to him on the subject: but more testimony from me is\nunnecessary; his book will speak for itself. {57} His peculiar style will\njustify a little more quotation than is just necessary to prove the point.\nLooking at the \"battle of opinion\" now in progress, we see that Mr. Smith\nwas a prescient:\n\n(P. 588.) \"From the general review of parties in England, it is evident\nthat no country in the world is better prepared for the great Battle of\nOpinion. Where else can the battle be fought but where the armies are\narrayed? And here they all are, Greek, Roman, Anglican, Scotch, Lutheran,\nCalvinist, Established and Territorial, with Baronial Bishops, and\nNonestablished of every grade--churches with living prophets and apostles,\nand churches with dead prophets and apostles, and apostolical churches\nwithout apostles, and philosophies without either prophets or apostles, and\nonly wanting one more, 'the Christian Church,' like Aaron's rod, to swallow\nup and digest them all, and then bud and flourish. As if to prepare our\nminds for this desirable and inevitable consummation, different parties\nhave been favored with a revival of that very spirit of revelation by which\nthe Church itself was originally founded. There is a complete series of\nspiritual revelations in England and the United States, besides mesmeric\nphenomena that bear a resemblance to revelation, and thus gradually open\nthe mind of the philosophical and infidel classes, as well as the professed\nbelievers of that old revelation which they never witnessed in living\naction, to a better understanding of that Law of Nature (for it is a Law of\nNature) in which all revelation originates and by which its spiritual\ncommunications are regulated.\"\n\nMr. Smith proceeds to say that there are _only_ thirty-five incorporated\nchurches in England, all formed from the New Testament except five, to each\nof which five he concedes a revelation of its own. The five are the\nQuakers, the Swedenborgians, the Southcottians, the Irvingites, and the\nMormonites. Of Joanna Southcott he speaks as follows: {58}\n\n(P. 592.) \"Joanna Southcott[109] is not very gallantly treated by the\ngentlemen of the Press, who, we believe, without knowing anything about\nher, merely pick up their idea of her character from the rabble. We once\nentertained the same rabble idea of her; but having read her works--for we\nreally have read them--we now regard her with great respect. However, there\nis a great abundance of chaff and straw to her grain; but the grain is\ngood, and as we do not eat either the chaff or straw if we can avoid it,\nnor even the raw grain, but thrash it and winnow it, and grind it and bake\nit, we find it, after undergoing this process, not only very palatable, but\na special dainty of its kind. But the husk is an insurmountable obstacle to\nthose learned and educated gentlemen who judge of books entirely by the\nstyle and the grammar, or those who eat grain as it grows, like the cattle.\nSuch men would reject all prological revelation; for there never was and\nprobably never will be a revelation by voice and vision communicated in\nclassical manner. It would be an invasion of the rights and prerogatives of\nHumanity, and as contrary to the Divine and Established order of mundane\ngovernment, as a field of quartern loaves or hot French rolls.\"\n\n\n\nMr. Smith's book is spiritualism from beginning to end; and my anonymous\ngainsayer, honest of course, is either ignorant of the work he thinks he\nhas read, or has a most remarkable development of the organ of\nimperception.]\n\n\n\nA CONDENSED HISTORY OF MATHEMATICS.\n\nI cut the following from a Sunday paper in 1849:\n\n\"X. Y.--The Chaldeans began the mathematics, in which the Egyptians\nexcelled. Then crossing the sea, by means {59} of Thales,[110] the\nMilesian, they came into Greece, where they were improved very much by\nPythagoras,[111] Anaxagoras,[112] and Anopides[113] of Chios. These were\nfollowed by Briso,[114] Antipho, [two circle-squarers; where is Euclid?]\nand Hippocrates,[115] but the excellence of the algebraic art was begun by\nGeber,[116] an Arabian astronomer, and was carried on by Cardanus,[117]\nTartaglia,[118] Clavius,[119], Stevinus,[120] Ghetaldus,[121]\nHerig_e_nius,[122] Fran. Van Schooten [meaning Francis Van Schooten[123]],\nFlorida de Beau_m_e,[124] etc.\"\n\nBryso was a mistaken man. Antipho had the disadvantage of being in advance\nof his age. He had the notion of which the modern geometry has made so\nmuch, that of {60} a circle being the polygon of an infinitely great number\nof sides. He could make no use of it, but the notion itself made him a\nsophist in the eyes of Aristotle, Eutocius,[125] etc. Geber, an Arab\nastronomer, and a reputed conjurer in Europe, seems to have given his name\nto unintelligible language in the word _gibberish_. At one time _algebra_\nwas traced to him; but very absurdly, though I have heard it suggested that\n_algebra_ and _gibberish_ must have had one inventor.\n\nAny person who meddles with the circle may find himself the crane who was\nnetted among the geese: as Antipho for one, and Olivier de Serres[126] for\nanother. This last gentleman ascertained, by weighing, that the area of the\ncircle is very nearly that of the square on the side of the inscribed\nequilateral triangle: which it is, as near as 3.162 ... to 3.141.... He did\nnot pretend to more than approximation; but Montucla and others\nmisunderstood him, and, still worse, misunderstood their own\nmisunderstanding, and made him say the circle was exactly double of the\nequilateral triangle. He was let out of limbo by Lacroix, in a note to his\nedition of Montucla's _History of Quadrature_.\n\n\n\nST. VITUS, PATRON OF CYCLOMETERS.\n\n    Quadratura del cerchio, trisezione dell' angulo, et duplicazione del\n    cubo, problemi geometricamente risolute e dimostrate dal Reverendo\n    Arciprete di San Vito D. Domenico Anghera,[127] Malta, 1854, 8vo.\n\n    {61}\n\n    Equazioni geometriche, estratte dalla lettera del Rev. Arciprete ... al\n    Professore Pullicino[128] sulla quadratura del cerchio. Milan, 1855 or\n    1856, 8vo.\n\n    Il Mediterraneo gazetta di Malta, 26 Decembre 1855, No. 909: also 911,\n    912, 913, 914, 936, 939.\n\n    The Malta Times, Tuesday, 9th June 1857.\n\n    Misura esatta del cerchio, dal Rev. D. Anghera. Malta, 1857, 12mo.\n\n    Quadrature of the circle ... by the Rev. D. Anghera, Archpriest of St.\n    Vito. Malta, 1858, 12mo.\n\nI have looked for St. Vitus in catalogues of saints, but never found his\nlegend, though he figures as a day-mark in the oldest almanacs. He must be\nproperly accredited, since he was an archpriest. And I pronounce and\nordain, by right accruing from the trouble I have taken in this subject,\nthat he, St. Vitus, who leads his votaries a never-ending and unmeaning\ndance, shall henceforth be held and taken to be the patron saint of the\ncircle-squarer. His day is the 15th of June, which is also that of St.\nModestus,[129] with whom the said circle-squarer often has nothing to do.\nAnd he must not put himself under the first saint with a slantendicular\nreference to the other, as is much to be feared was done by the Cardinal\nwho came to govern England with a title containing St. Pudentiana,[130] who\nshares a day with _St. Dunstan_. The Archpriest of St. Vitus will have it\nthat the square inscribed in a semicircle is half of the semicircle, or the\ncircumference 3-1/5 diameters. He is active and able, with {62} nothing\nwrong about him except his paradoxes. In the second tract named he has\ngiven the testimonials of crowned heads and ministers, etc. as follows.\nLouis-Napoleon gives thanks. The minister at Turin refers it to the Academy\nof Sciences, and hopes so much labor will be judged _degna di pregio_.[131]\nThe Vice-Chancellor of Oxford--a blunt Englishman--begs to say that the\nUniversity has never proposed the problem, as some affirm. The Prince\nRegent of Baden has received the work with lively interest. The Academy of\nVienna is not in a position to enter into the question. The Academy of\nTurin offers the most _distinct_ thanks. The Academy della Crusca attends\nonly to literature, but gives thanks. The Queen of Spain has received the\nwork with the highest appreciation. The University of Salamanca gives\ninfinite thanks, and feels true satisfaction in having the book. Lord\nPalmerston gives thanks, by the hand of \"William San.\" The Viceroy of\nEgypt, not being yet up in Italian, will spend his first moments of leisure\nin studying the book, when it shall have been translated into French: in\nthe mean time he congratulates the author upon his victory over a problem\nso long held insoluble. All this is seriously published as a rate in aid of\ndemonstration. If these royal compliments cannot make the circumference of\na circle about 2 per cent. larger than geometry will have it --which is all\nthat is wanted--no wonder that thrones are shaky.\n\nI am informed that the legend of St. Vitus is given by Ribadeneira[132] in\nhis lives of Saints, and that Baronius,[133] in {63} his _Martyrologium\nRomanum_, refers to several authors who have written concerning him. There\nis an account in Mrs. Jameson's[134] _History of Sacred and Legendary Art_\n(ed. of 1863, p. 544). But it seems that St. Vitus is the patron saint of\n_all_ dances; so that I was not so far wrong in making him the protector of\nthe cyclometers. Why he is represented with a cock is a disputed point,\nwhich is now made clear: next after _gallus gallinaceus_[135] himself,\nthere is no crower like the circle-squarer.\n\n\n\nCELEBRATED APPROXIMATIONS OF [pi].\n\nThe following is an extract from the _English Cyclopaedia_, Art. TABLES:\n\n\"1853. William Shanks,[136] _Contributions to Mathematics, comprising\nchiefly the Rectification of the Circle to 607 Places of Tables_, London,\n1853. (QUADRATURE OF THE CIRCLE.) Here is a _table_, because it tabulates\nthe results of the subordinate steps of this enormous calculation as far as\n527 decimals: the remainder being added as results only during the\nprinting. For instance, one step is the calculation of the reciprocal of\n601.5^{601}; and the result is given. The number of pages required to\ndescribe these results is 87. Mr. Shanks has also thrown off, as chips or\nsplinters, the values of the base of Napier's logarithms, and of its\nlogarithms of 2, 3, 5, 10, to 137 decimals; and the value of the modulus\n.4342 ... to 136 decimals: with the 13th, 25th, 37th ... up to the 721st\npowers of 2. These tremendous stretches of calculation--at least we so call\nthem in our day--are useful in several respects; they prove more than {64}\nthe capacity of this or that computer for labor and accuracy; they show\nthat there is in the community an increase of skill and courage. We say in\nthe community: we fully believe that the unequalled turnip which every now\nand then appears in the newspapers is a sufficient presumption that the\naverage turnip is growing bigger, and the whole crop heavier. All who know\nthe history of the quadrature are aware that the several increases of\nnumbers of decimals to which [pi] has been carried have been indications of\na general increase in the power to calculate, and in courage to face the\nlabor. Here is a comparison of two different times. In the day of\nCocker,[137] the pupil was directed to perform a common subtraction with a\nvoice-accompaniment of this kind: '7 from 4 I cannot, but add 10, 7 from 14\nremains 7, set down 7 and carry 1; 8 and 1 which I carry is 9, 9 from 2 I\ncannot, etc.' We have before us the announcement of the following _table_,\nundated, as open to inspection at the Crystal Palace, Sydenham, in two\ndiagrams of 7 ft. 2 in, by 6 ft. 6 in.: 'The figure 9 involved into the\n912th power, and antecedent powers or involutions, containing upwards of\n73,000 figures. Also, the proofs of the above, containing upwards of\n146,000 figures. By Samuel Fancourt, of Mincing Lane, London, and completed\nby him in the year 1837, at the age of sixteen. N.B. The whole operation\nperformed by simple arithmetic.' The young operator calculated by\nsuccessive squaring the 2d, 4th, 8th, etc., powers up to the 512th, with\nproof by division. But 511 multiplications by 9, in the short (or 10-1)\nway, would have been much easier. The 2d, 32d, 64th, 128th, 256th, and\n512th powers are given at the back of the announcement. The powers of 2\nhave been calculated for many purposes. In Vol. II of his _Magia\nUniversalis Naturae et Artis_, Herbipoli, 1658, 4to, the Jesuit Gaspar\nSchott[138] having discovered, on some grounds of theological {65} magic,\nthat the degrees of grace of the Virgin Mary were in number the 256th power\nof 2, calculated that number. Whether or no his number correctly\nrepresented the result he announced, he certainly calculated it rightly, as\nwe find by comparison with Mr. Shanks.\"\n\n\n\nThere is a point about Mr. Shanks's 608 figures of the value of [pi] which\nattracts attention, perhaps without deserving it. It might be expected\nthat, in so many figures, the nine digits and the cipher would occur each\nabout the same number of times; that is, each about 61 times. But the fact\nstands thus: 3 occurs 68 times; 9 and 2 occur 67 times each; 4 occurs 64\ntimes; 1 and 6 occur 62 times each; 0 occurs 60 times; 8 occurs 58 times; 5\noccurs 56 times; and 7 occurs only 44 times. Now, if all the digits were\nequally likely, and 608 drawings were made, it is 45 to 1 against the\nnumber of sevens being as distant from the probable average (say 61) as 44\non one side or 78 on the other. There must be some reason why the number 7\nis thus deprived of its fair share in the structure. Here is a field of\nspeculation in which two branches of inquirers might unite. There is but\none number which is treated with an unfairness which is incredible as an\naccident; and that number is the mystic number _seven_! If the cyclometers\nand the apocalyptics would lay their heads together until they come to a\nunanimous verdict on this phenomenon, and would publish nothing until they\nare of one mind, they would earn the gratitude of their race.--I was wrong:\nit is the Pyramid-speculator who should have been appealed to. A\ncorrespondent of my friend Prof. Piazzi Smyth[139] notices that 3 is the\nnumber of most frequency, and that 3-1/7 is the nearest approximation to it\nin simple digits. Professor Smyth himself, whose word on Egypt is paradox\nof a very high order, backed by a great quantity of useful labor, the\nresults which will be made available by those who do not receive {66} the\nparadoxes, is inclined to see confirmation for some of his theory in these\nphenomena.\n\n\n\nCURIOUS CALCULATIONS.\n\nThese paradoxes of calculation sometimes appear as illustrations of the\nvalue of a new method. In 1863, Mr. G. Suffield,[140] M.A., and Mr. J. R.\nLunn,[141] M.A., of Clare College and of St. John's College, Cambridge,\npublished the whole quotient of 10000 ... divided by 7699, throughout the\nwhole of one of the recurring periods, having 7698 digits. This was done in\nillustration of Mr. Suffield's method of _Synthetic division_.\n\nAnother instance of computation carried to paradoxical length, in order to\nillustrate a method, is the solution of x^3 - 2x = 5, the example given of\nNewton's method, on which all improvements have been tested. In 1831,\nFourier's[142] posthumous work on equations showed 33 figures of solution,\ngot with enormous labor. Thinking this a good opportunity to illustrate the\nsuperiority of the method of W. G. Horner,[143] not yet known in France,\nand not much known in {67} England, I proposed to one of my classes, in\n1841, to beat Fourier on this point, as a Christmas exercise. I received\nseveral answers, agreeing with each other, to 50 places of decimals. In\n1848, I repeated the proposal, requesting that 50 places might be exceeded:\nI obtained answers of 75, 65, 63, 58, 57, and 52 places. But one answer, by\nMr. W. Harris Johnston,[144] of Dundalk, and of the Excise Office, went to\n101 decimal places. To test the accuracy of this, I requested Mr. Johnston\nto undertake another equation, connected with the former one in a way which\nI did not explain. His solution verified the former one, but he was unable\nto see the connection, even when his result was obtained. My reader may be\nas much at a loss: the two solutions are:\n\n  2.0945514815423265...\n  9.0544851845767340...\n\nThe results are published in the _Mathematician_, Vol. III, p. 290. In\n1851, another pupil of mine, Mr. J. Power Hicks,[145] carried the result to\n152 decimal places, without knowing what Mr. Johnston had done. The result\nis in the _English Cyclopaedia_, article INVOLUTION AND EVOLUTION.\n\nI remark that when I write the initial of a Christian name, the most usual\nname of that initial is understood. I never saw the name of W. G. Horner\nwritten at length, until I applied to a relative of his, who told me that\nhe was, as I supposed, Wm. _George_, but that he was named after a relative\nof that _surname_.\n\nThe square root of 2, to 110 decimal places, was given {68} me in 1852 by\nmy pupil, Mr. William Henry Colvill, now (1867) Civil Surgeon at Baghdad.\nIt was\n\n  1.4142135623730950488016887242096980785696\n    7187537694807317667973799073247846210703\n    885038753432764157273501384623\n\nMr. James Steel[146] of Birkenhead verified this by actual multiplication,\nand produced\n\n  2 - 2580413 / 10^{117}\n\nas the square.\n\n\n\n    Calcolo decidozzinale del Barone Silvio Ferrari. Turin, 1854, 4to.\n\nThis is a serious proposal to alter our numeral system and to count by\ntwelves. Thus 10 would be twelve, 11 thirteen, etc., two new symbols being\ninvented for ten and eleven. The names of numbers must of course be\nchanged. There are persons who think such changes practicable. I thought\nthis proposal absurd when I first saw it, and I think so still:[147] but\nthe one I shall presently describe beats it so completely in that point,\nthat I have not a smile left for this one.\n\n\n\nON COMETS.\n\n    The successful and therefore probably true theory of Comets. London,\n    1854. (4pp. duodecimo.)\n\nThe author is the late Mr. Peter Legh,[148] of Norbury Booths Hall,\nKnutsford, who published for eight or ten {69} years the _Ombrological\nAlmanac_, a work of asserted discovery in meteorology. The theory of comets\nis that the joint attraction of the new moon and several planets in the\ndirection of the sun, draws off the gases from the earth, and forms these\ncometic meteors. But how these meteors come to describe orbits round the\nsun, and to become capable of having their returns predicted, is not\nexplained.\n\n\n\nA NEW PHASE OF MORMONISM.\n\n    The Mormon, New York, Saturday, Oct. 27, 1855.\n\nA newspaper headed by a grand picture of starred and striped banners,\nbeehive, and eagle surmounting it. A scroll on each side: on the left,\n\"Mormon creed. Mind your own business. Brigham Young;\"[149] on the right,\n\"Given by inspiration of God. Joseph Smith.\"[150] A leading article on the\ndiscoveries of Prof. Orson Pratt[151] says, \"Mormonism has long taken the\nlead in religion: it will soon be in the van both in science and politics.\"\nAt the beginning of the paper is Professor Pratt's \"Law of Planetary\nRotation.\" The cube roots of the densities of the planets are as the square\nroots of their periods of rotation. The squares of the cube roots of the\nmasses divided by the squares of the diameters are as the periods of\nrotation. Arithmetical verification attempted, and the whole very modestly\nstated {70} and commented on. Dated G. S. L. City, Utah Ter., Aug. 1, 1855.\nIf the creed, as above, be correctly given, no wonder the Mormonites are in\nsuch bad odor.\n\n\n\nMATHEMATICAL ILLUSTRATIONS OF DOCTRINE.\n\n    The two estates; or both worlds mathematically considered. London,\n    1855, small (pp. 16).\n\nThe author has published mathematical works with his name. The present\ntract is intended to illustrate mathematically a point which may be guessed\nfrom the title. But the symbols do very little in the way of illustration:\nthus, x being the _present value_ of the future estate (eternal happiness),\nand a of all that this world can give, the author impresses it on the\nmathematician that, x being infinitely greater than a, x + a = x, so that a\nneed not be considered. This will not act much more powerfully on a\nmathematician by virtue of the symbols than if those same symbols had been\ndispensed with: even though, as the author adds, \"It was this method of\nneglecting infinitely small quantities that Sir Isaac Newton was indebted\nto for his greatest discoveries.\"\n\nThere has been a moderate quantity of well-meant attempt to enforce,\nsometimes motive, sometimes doctrine, by arguments drawn from mathematics,\nthe proponents being persons unskilled in that science for the most part.\nThe ground is very dangerous: for the illustration often turns the other\nway with greater power, in a manner which requires only a little more\nknowledge to see. I have, in my life, heard from the pulpit or read, at\nleast a dozen times, that all sin is infinitely great, proved as follows.\nThe greater the being, the greater the sin of any offence against him:\ntherefore the offence committed against an infinite being is infinitely\ngreat. Now the mathematician, of which the proposers of this argument are\nnot aware, is perfectly familiar with quantities which increase together,\nand never cease increasing, but so that one of them remains finite when\n{71} the other becomes infinite. In fact, the argument is a perfect _non\nsequitur_.[152] Those who propose it have in their minds, though in a\ncloudy and indefinite form, the idea of the increase of guilt being\n_proportionate_ to the increase of greatness in the being offended. But\nthis it would never do to state: for by such statement not only would the\nargument lose all that it has of the picturesque, but the asserted premise\nwould have no strong air of exact truth. How could any one undertake to\nappeal to conscience to declare that an offence against a being 4-7/10\ntimes as great as another is exactly, no more and no less, 4-7/10 times as\ngreat an offence against the other?\n\nThe infinite character of the offence against an infinite being is laid\ndown in Dryden's _Religio Laici_,[153] and is, no doubt, an old argument:\n\n \"For, granting we have sinned, and that th' offence\n  Of man is made against Omnipotence,\n  Some price that bears proportion must be paid,\n  And infinite with infinite be weighed.\n  See then the Deist lost; remorse for vice\n  Not paid; or, paid, inadequate in price.\"\n\nDryden, in the words \"bears proportion\" is in verse more accurate than most\nof the recent repeaters in prose. And this is not the only case of the kind\nin his argumentative poetry.\n\nMy old friend, the late Dr. Olinthus Gregory,[154] who was a sound and\nlearned mathematician, adopted this dangerous kind of illustration in his\n_Letters on the Christian Religion_. {72} He argued, by parallel, from what\nhe supposed to be the necessarily mysterious nature of the _impossible_\nquantity of algebra to the necessarily mysterious nature of certain\ndoctrines of his system of Christianity. But all the difficulty and mystery\nof the impossible quantity is now cleared away by the advance of\nalgebraical thought: and yet Dr. Gregory's book continues to be sold, and\nno doubt the illustration is still accepted as appropriate.\n\nThe mode of argument used by the author of the tract above named has a\nstriking defect. He talks of reducing this world and the next to \"present\nvalue,\" as an actuary does with successive lives or next presentations.\nDoes value make interest? and if not, why? And if it do, then the present\nvalue of an eternity is _not_ infinitely great. Who is ignorant that a\nperpetual annuity at five per cent is worth only twenty years' purchase?\nThis point ought to be discussed by a person who treats heaven as a\ndeferred perpetual annuity. I do not ask him to do so, and would rather he\ndid not; but if he _will_ do it, he must either deal with the question of\ndiscount, or be asked the reason why.\n\nWhen a very young man, I was frequently exhorted to one or another view of\nreligion by pastors and others who thought that a mathematical argument\nwould be irresistible. And I heard the following more than once, and have\nsince seen it in print, I forget where. Since eternal happiness belonged to\nthe particular views in question, a benefit infinitely great, then, even if\nthe probability of their arguments were small, or even infinitely small,\nyet the product of the chance and benefit, according to the usual rule,\nmight give a result which no one ought in prudence to pass over. They did\nnot see that this applied to all systems as well as their own. I take this\nargument to be the most perverse of all the perversions I have heard or\nread on the subject: there is some high authority for it, whom I forget.\n\nThe moral of all this is, that such things as the preceding should be kept\nout of the way of those who are not {73} mathematicians, because they do\nnot understand the argument; and of those who are, because they do.\n\n[The high authority referred to above is Pascal, an early cultivator of\nmathematical probability, and obviously too much enamoured of his new\npursuit. But he conceives himself bound to wager on one side or the other.\nTo the argument (_Pensees_, ch. 7)[155] that \"le juste est de ne point\nparier,\" he answers, \"Oui: mais il faut parier: vous etes embarque; et ne\nparier point que Dieu est, c'est parier qu'il n'est pas.\"[156] Leaving\nPascal's argument to make its way with a person who, _being a sceptic_, is\nyet positive that the issue is salvation or perdition, if a God there\nbe,--for the case as put by Pascal requires this,--I shall merely observe\nthat a person who elects to believe in God, as the best chance of gain, is\nnot one who, according to Pascal's creed, or any other worth naming, will\nreally secure that gain. I wonder whether Pascal's curious imagination ever\npresented to him in sleep his convert, in the future state, shaken out of a\nred-hot dice-box upon a red-hot hazard-table, as perhaps he might have\nbeen, if Dante had been the later of the two. The original idea is due to\nthe elder Arnobius,[157] who, as cited by Bayle,[158] speaks thus:\n\n\"Sed et ipse [Christus] quae pollicetur, non probat. Ita est. Nulla enim, ut\ndixi, futurorum potest existere comprobatio. Cum ergo haec sit conditio\nfuturorum, ut teneri et comprehendi nullius possint anticipationis attactu;\nnonne {74} purior ratio est, ex duobus incertis, et in ambigua expectatione\npendentibus, id potius credere, quod aliquas spes ferat, quam omnino quod\nnullas? In illo enim periculi nihil est, si quod dicitur imminere, cassum\nfiat et vacuum: in hoc damnum est maximum, id est salutis amissio, si cum\ntempus advenerit aperiatur non fuisse mendacium.\"[159]\n\nReally Arnobius seems to have got as much out of the notion, in the third\ncentury, as if he had been fourteen centuries later, with the arithmetic of\nchances to help him.]\n\n\n\nNOVUM ORGANUM MORALIUM.\n\n    The Sentinel, vol. ix. no. 27. London, Saturday, May 26, 1855.\n\nThis is the first London number of an Irish paper, Protestant in politics.\nIt opens with \"Suggestions on the subject of a _Novum Organum Moralium_,\"\nwhich is the application of algebra and the differential calculus to\nmorals, socials, and politics. There is also a leading article on the\nsubject, and some applications in notes to other articles. A separate\npublication was afterwards made, with the addition of a long Preface; the\nauthor being a clergyman who I presume must have been the editor of the\n_Sentinel_.\n\n    Suggestions as to the employment of a _Novum Organum Moralium_. Or,\n    thoughts on the nature of the Differential Calculus, and on the\n    application of its principles to metaphysics, with a view to the\n    attainment of demonstration and certainty in moral, {75} political and\n    ecclesiastical affairs. By Tresham Dames Gregg,[160] Chaplain of St.\n    Mary's, within the church of St. Nicholas intra muros, Dublin. London,\n    1859, 8vo. (pp. xl + 32).\n\nI have a personal interest in this system, as will appear from the\nfollowing extract from the newspaper:\n\n    \"We were subsequently referred to De Morgan's _Formal Logic_ and\n    Boole's _Laws of Thought_[161] both very elaborate works, and greatly\n    in the direction taken by ourselves. That the writers amazingly surpass\n    us in learning we most willingly admit, but we venture to pronounce of\n    both their learned treatises, that they deal with the subject in a mode\n    that is scholastic to an excess.... That their works have been for a\n    considerable space of time before the world and effected nothing, would\n    argue that they have overlooked the vital nature of the theme.... On\n    the whole, the writings of De Morgan and Boole go to the full\n    justification of our principle without in any wise so trenching upon\n    our ground as to render us open to reproach in claiming our Calculus as\n    a great discovery.... But we renounce any paltry jealousy as to a\n    matter so vast. If De Morgan and Boole have had a priority in the case,\n    to them we cheerfully shall resign the glory and honor. If such be the\n    truth, they have neither done justice to the discovery, nor to\n    themselves [quite true]. They have, under the circumstances, acted like\n    'the foolish man, who roasteth not that which he taketh {76} in\n    hunting.... It will be sufficient for us, however, to be the Columbus\n    of these great Americi, and popularize what they found, _if_ they found\n    it. We, as from the mountain top, will then become _their_ trumpeters,\n    and cry glory to De Morgan and glory to Boole, under Him who is the\n    source of all glory, the only good and wise, to Whom be glory for ever!\n    _If_ they be our predecessors in this matter, they have, under Him,\n    taken moral questions out of the category of probabilities, and\n    rendered them perfectly certain. In that case, let their books be read\n    by those who may doubt the principles this day laid before the world as\n    a great discovery, by our newspaper. Our cry shall be [Greek:\n    eurekasi]![162] Let us hope that they will join us, and henceforth keep\n    their light [_sic_] from under their bushel.\"\n\nFor myself, and for my old friend Mr. Boole, who I am sure would join me, I\ndisclaim both priority, simultaneity, and posteriority, and request that\nnothing may be trumpeted from the mountain top except our abjuration of all\ncommunity of thought or operation with this _Novum Organum_.\n\nTo such community we can make no more claim than Americus could make to\nbeing the forerunner of Columbus who popularized his discoveries. We do not\nwish for any [Greek: eurekasi] and not even for [Greek: heurekasi]. For\nself and Boole, I point out what would have convinced either of us that\nthis house is divided against itself.\n\n[Alpha] being an apostolic element, [delta] the doctrinal element, and\n[Chi] the body of the faithful, the church is [Alpha] [delta] [Chi], we are\ntold. Also, that if [Alpha] become negative, or the Apostolicity become\nDiabolicity [my words]; or if [delta] become negative, and doctrine become\nheresy; or if [Chi] become negative, that is, if the faithful become\nunfaithful; the church becomes negative, \"the very opposite to what it\nought to be.\" For self and Boole, I admit this. But--which is not\nnoticed--if [Alpha] and [delta] should _both_ become negative, diabolical\norigin {77} and heretical doctrine, then the church, [Alpha] [delta] [Chi],\nis still positive, what it ought to be, unless [Chi] be also negative, or\nthe people unfaithful to it, in which case it is a bad church. Now, self\nand Boole--though I admit I have not asked my partner--are of opinion that\na diabolical church with false doctrine does harm when the people are\nfaithful, and can do good only when the people are unfaithful. We may be\nwrong, but this is what we _do_ think. Accordingly, we have caught nothing,\nand can therefore roast nothing of our own: I content myself with roasting\na joint of Mr. Gregg's larder.\n\nThese mathematical vagaries have uses which will justify a large amount of\nquotation: and in a score of years this may perhaps be the only attainable\nrecord. I therefore proceed.\n\nAfter observing that by this calculus juries (heaven help them! say I) can\ncalculate damages \"almost to a nicety,\" and further that it is made\nabundantly evident that c e x is \"the general expression for an\nindividual,\" it is noted that the number of the Beast is not given in the\nRevelation in words at length, but as [Greek: chxw'].[163] On this the\nfollowing remark is made:\n\n\"Can it be possible that we have in this case a specimen given to us of the\narithmetic of heaven, and an expression revealed, which indicates by its\nfunction of addibility, the name of the church in question, and of each\nmember of it; and by its function of multiplicability the doctrine, the\nmission, and the members of the great Synagogue of Apostacy? We merely\npropound these questions;--we do not pretend to solve them.\"\n\nAfter a translation in blank verse--a very pretty one--of the 18th Psalm,\nthe author proceeds as follows, to render it into differential calculus:\n\n{78}\n\n\"And the whole tells us just this, that David did what he could. He\naugmented those elements of his constitution which were (_exceptis\nexcipiendis_)[164] subject to himself, and the Almighty then augmented his\npersonal qualities, and his vocational _status_. Otherwise, to throw the\nmatter into the expression of our notation, the variable e was augmented,\nand c x rose proportionally. The law of the variation, according to our\ntheory, would be thus expressed. The resultant was David the king c e x [c\n= r?] (who had been David the shepherd boy), and from the conditions of the\ntheorem we have\n\n  du/de = ce(dx/de) + ex(dc/de)x + cx\n\nwhich, in the terms of ordinary language, just means, the increase of\nDavid's educational excellence or qualities--his piety, his prayerfulness,\nhis humility, obedience, etc.--was so great, that when multiplied by his\noriginal talent and position, it produced a product so great as to be equal\nin its amount to royalty, honor, wealth, and power, etc.: in short, to all\nthe attributes of majesty.\"[165]\n\nThe \"solution of the family problem\" is of high interest. It is to\ndetermine the effect on the family in general from a change [of conduct] in\none of them. The person chosen is one of the maid-servants.\n\n\"Let c e x be the father; c_1e_1x_1 the mother, etc. The family then\nconsists of the maid's master, her mistress, her young master, her young\nmistress, and fellow servant. Now the master's calling (or c) is to\nexercise his share of control over this servant, and mind the rest of his\nbusiness: call this remainder a, and let his calling generally, or all his\naffairs, be to his maid-servant as m : y, i.e., y = (mz/c); ... {79} and\nthis expression will represent his relation to the servant. Consequently,\n\n  c e x = (a + mz/c)e x; otherwise (a + mz/c)e x\n\nis the expression for the father when viewed as the girl's master.\"\n\nI have no objection to repeat so far; but I will not give the formula for\nthe maid's relation to her young master; for I am not quite sure that all\nyoung masters are to be trusted with it. Suffice it that the son will be\naffected directly as his influence over her, and inversely as his\nvocational power: if then he should have some influence and no vocational\npower, the effect on him would be infinite. This is dismal to think of.\nFurther, the formula brings out that if one servant improve, the other must\ndeteriorate, and _vice versa_. This is not the experience of most families:\nand the author remarks as follows:\n\n\"That is, we should venture to say, a very beautiful result, and we may say\nit yielded us no little astonishment. What our calculation might lead to we\nnever dreamt of; that it should educe a conclusion so recondite that our\nunassisted power never could have attained to, and which, if we could have\nconjectured it, would have been at best the most distant probability, that\nconclusion being itself, as it would appear, the quintessence of truth,\nafforded us a measure of satisfaction that was not slight.\"\n\nThat the writings of Mr. Boole and myself \"go to the full justification of\"\nthis \"principle,\" is only true in the sense in which the Scotch use, or did\nuse, the word _justification_.\n\n\n\nA TRIBUTE TO BOOLE.\n\n[The last number of this Budget had stood in type for months, waiting until\nthere should be a little cessation of correspondence more connected with\nthe things of the day. {80} I had quite forgotten what it was to contain;\nand little thought, when I read the proof, that my allusions to my friend\nMr. Boole, then in life and health, would not be printed till many weeks\nafter his death. Had I remembered what my last number contained, I should\nhave added my expression of regret and admiration to the numerous obituary\ntestimonials, which this great loss to science has called forth.\n\nThe system of logic alluded to in the last number of this series is but one\nof many proofs of genius and patience combined. I might legitimately have\nentered it among my _paradoxes_, or things counter to general opinion: but\nit is a paradox which, like that of Copernicus, excited admiration from its\nfirst appearance. That the symbolic processes of algebra, invented as tools\nof numerical calculation, should be competent to express every act of\nthought, and to furnish the grammar and dictionary of an all-containing\nsystem of logic, would not have been believed until it was proved. When\nHobbes,[166] in the time of the Commonwealth, published his _Computation or\nLogique_, he had a remote glimpse of some of the points which are placed in\nthe light of day by Mr. Boole. The unity of the forms of thought in all the\napplications of reason, however remotely separated, will one day be matter\nof notoriety and common wonder: and Boole's name will be remembered in\nconnection with one of the most important steps towards the attainment of\nthis knowledge.]\n\n\n\nDECIMALS RUN RIOT.\n\n    The Decimal System as a whole. By Dover Statter.[167] London and\n    Liverpool, 1856, 8vo.\n\n{81}\n\nThe proposition is to make everything decimal. The day, now 24 hours, is to\nbe made 10 hours. The year is to have ten months, Unusber, Duober, etc.\nFortunately there are ten commandments, so there will be neither addition\nto, nor deduction from, the moral law. But the twelve apostles! Even\nrejecting Judas, there is a whole apostle of difficulty. These points the\nauthor does not touch.\n\n\n\nON PHONETIC SPELLING.\n\n    The first book of Phonetic Reading. London, Fred. Pitman,[168] Phonetic\n    Depot, 20, Paternoster Row, 1856, 12mo.\n\n    The Phonetic Journal. Devoted to the propagation of phonetic reading,\n    phonetic longhand, phonetic shorthand, and phonetic printing. No. 46.\n    Saturday, 15 November 1856. Vol. 15.\n\nI write the titles of a couple out of several tracts which I have by me.\nBut the number of publications issued by the promoters of this spirited\nattempt is very large indeed.[169] The attempt itself has had no success\nwith the mass of the public. This I do not regret. Had the world found that\nthe change was useful, I should have gone contentedly with the stream; but\nnot without regretting our old language. I admit the difficulties which our\nunpronounceable spelling puts in the way of learning to read: and I have no\ndoubt that, as affirmed, it is easier to teach children phonetically, and\nafterwards to introduce them to our common system, than to proceed in the\nusual way. But by the usual way I mean proceeding by letters from the very\nbeginning. If, which I am sure is a better plan, children be taught at the\ncommencement very much by _complete words_, as if they were learning\nChinese, and be gradually accustomed to {82} resolve the known words into\nletters, a fraction, perhaps a considerable one, of the advantage of the\nphonetic system is destroyed. It must be remembered that a phonetic system\ncan only be an approximation. The differences of pronunciation existing\namong educated persons are so great, that, on the phonetic system,\ndifferent persons ought to spell differently.\n\nBut the phonetic party have produced something which will immortalize their\nplan: I mean their _shorthand_, which has had a fraction of the success it\ndeserves. All who know anything of shorthand must see that nothing but a\nphonetic system can be worthy of the name: and the system promulgated is\nskilfully done. Were I a young man I should apply myself to it\nsystematically. I believe this is the only system in which books were ever\npublished. I wish some one would contribute to a public journal a brief\naccount of the dates and circumstances of the phonetic movement, not\nforgetting a list of the books published in shorthand.\n\nA child beginning to read by himself may owe terrible dreams and waking\nimages of horror to our spelling, as I did when six years old. In one of\nthe common poetry-books there is an admonition against confining little\nbirds in cages, and the child is asked what if a great giant, amazingly\nstrong, were to take you away, shut you up,\n\n  And feed you with vic-tu-als you ne-ver could bear.\n\nThe book was hyphened for the beginner's use; and I had not the least idea\nthat _vic-tu-als_ were _vittles_: by the sound of the word I judged they\nmust be of iron; and it entered into my soul.\n\nThe worst of the phonetic shorthand book is that they nowhere, so far as I\nhave seen, give _all_ the symbols, in every stage of advancement, together,\nin one or following pages. It is symbols and talk, more symbols and more\ntalk, etc. A universal view of the signs ought to begin the works. {83}\n\n\n\nA HANDFUL OF LITTLE PARADOXERS.\n\n    Ombrological Almanac. Seventeenth year. An essay on Anemology and\n    Ombrology. By Peter Legh,[170] Esq. London, 1856, 12mo.\n\nMr. Legh, already mentioned, was an intelligent country gentleman, and a\nlegitimate speculator. But the clue was not reserved for him.\n\n    The proof that the three angles of a triangle are equal to two right\n    angles looked for in the inflation of the circle. By Gen. Perronet\n    Thompson. London, 1856, 8vo. (pp. 4.)\n\nAnother attempt, the third, at this old difficulty, which cannot be put\ninto few words of explanation.[171]\n\n    Comets considered as volcanoes, and the cause of their velocity and\n    other phenomena thereby explained. London (_circa_ 1856), 8vo.\n\nThe title explains the book better than the book explains the title.\n\n\n\n1856. A stranger applied to me to know what the ideas of a friend of his\nwere worth upon the magnitude of the earth. The matter being one involving\npoints of antiquity, I mentioned various persons whose speculations he\nseemed to have ignored; among others, Thales. The reply was, \"I am\ninstructed by the author to inform you that he is perfectly acquainted with\nthe works of Thales, Euclid, Archimedes, ...\" I had some thought of asking\nwhether he had used the Elzevir edition of Thales,[172] which is known to\nbe very incomplete, or that of Professor Niemand with the lections,\nNirgend, 1824, 2 vols. folio; just to see whether the {84} last would not\nhave been the very edition he had read. But I refrained, in mercy.\n\n\n\n    The moon is the image of the Earth, and is not a solid body. By T^{he}\n    Longitude.[173] (Private Circulation.) In five parts. London, 1856,\n    1857, 1857; Calcutta, 1858, 1858, 8vo.\n\nThe earth is \"brought to a focus\"; it describes a \"looped orbit round the\nsun.\" The eclipse of the sun is thus explained: \"At the time of eclipses,\nthe image is more or less so directly before or behind the earth that, in\nthe case of new moon, bright rays of the sun fall and bear upon the spot\nwhere the figure of the earth is brought to a focus, that is, bear upon the\nimage of the earth, when a darkness beyond is produced reaching to the\nearth, and the sun becomes more or less eclipsed.\" How the earth is\n\"brought to a focus\" we do not find stated. Writers of this kind always\nhave the argument that some things which have been ridiculed at first have\nbeen finally established. Those who put into the lottery had the same kind\nof argument; but were always answered by being reminded how many blanks\nthere were to one prize. I am loath to pronounce against anything: but it\ndoes force itself upon me that the author of these tracts has drawn a\nblank.\n\n\n\nLUNAR MOTION AGAIN.\n\n    _Times_, April 6 or 7, 1856. The moon has no rotary motion.\n\nA letter from Mr. Jellinger Symons,[174] inspector of schools, which\ncommenced a controversy of many letters and pamphlets. This dispute comes\non at intervals, and will continue to do so. It sometimes arises from\ninability to understand the character of simple rotation, geometrically;\nsometimes from not understanding the mechanical doctrine of rotation.\n\n{85}\n\n\n\n    Lunar Motion. The whole argument stated, and illustrated by diagrams;\n    with letters from the Astronomer Royal. By Jellinger C. Symons. London,\n    1856, 8vo.\n\nThe Astronomer Royal endeavored to disentangle Mr. J. C. Symons, but\nfailed. Mr. Airy[175] can correct the error of a ship's compasses, because\nhe can put her head which way he pleases: but this he cannot do with a\nspeculator.\n\nMr. Symons, in this tract, insinuated that the rotation of the moon is one\nof the silver shrines of the craftsmen. To see a thing so clearly as to be\nsatisfied that all who say they do not see it are telling wilful falsehood,\nis the nature of man. Many of all sects find much comfort in it, when they\nthink of the others; many unbelievers solace themselves with it against\nbelievers; priests of old time founded the right of persecution upon it,\nand of our time, in some cases, the right of slander: many of the\nparadoxers make it an argument against students of science. But I must say\nfor men of science, for the whole body, that they are fully persuaded of\nthe honesty of the paradoxers. The simple truth is, that all those I have\nmentioned, believers, unbelievers, priests, paradoxers, are not so sure\nthey are right in their points of difference that they can safely allow\nthemselves to be persuaded of the honesty of opponents. Those who know\ndemonstration are differently situated. I suspect a train might be laid for\nthe formation of a better habit in this way. We know that Suvaroff[176]\ntaught his Russians at Ismail not to fear the Turks by accustoming them to\ncharge bundles of faggots dressed in turbans, etc.\n\n  At which your wise men sneered in phrases witty,\n  He made no answer--but he took the city!\n\nWould it not be a good thing to exercise boys, in pairs, in the following\ndialogue:--Sir, you are quite wrong!--Sir, {86} I am sure you honestly\nthink so! This was suggested by what used to take place at Cambridge in my\nday. By statute, every B.A. was obliged to perform a certain number of\ndisputations, and the _father_ of the college had to affirm that it had\nbeen done. Some were performed in earnest: the rest were huddled over as\nfollows. Two candidates occupied the places of the respondent and the\nopponent: _Recte statuit Newtonus_, said the respondent: _Recte non statuit\nNewtonus_,[177] said the opponent. This was repeated the requisite number\nof times, and counted for as many _acts_ and _opponencies_. The parties\nthen changed places, and each unsaid what he had said on the other side of\nthe house: I remember thinking that it was capital drill for the House of\nCommons, if any of us should ever get there. The process was repeated with\nevery pair of candidates.\n\nThe real disputations were very severe exercises. I was badgered for two\nhours with arguments given and answered in Latin,--or what we called\nLatin--against Newton's first section, Lagrange's[178] derived functions,\nand Locke[179] on innate principles. And though I _took off_ everything,\nand was pronounced by the moderator to have disputed _magno honore_,[180] I\nnever had such a strain of thought in my life. For the inferior opponents\nwere made as sharp as their betters by their tutors, who kept lists of\nqueer objections, drawn from all quarters. The opponents used to meet the\nday before to compare their arguments, that the same might not come twice\nover. But, after I left Cambridge, it became the fashion to invite the\nrespondent to be present, who therefore learnt all that was to be brought\nagainst him. This made the whole thing a farce: and the disputations were\nabolished.\n\n{87}\n\n\n\n    The Doctrine of the Moon's Rotation, considered in a letter to the\n    Astronomical Censor of the _Athenaeum_. By Jones L. MacElshender.[181]\n    Edinburgh, 1856, 8vo.\n\nThis is an appeal to those cultivated persons who will read it \"to overrule\nthe _dicta_ of judges who would sacrifice truth and justice to professional\nrule, or personal pique, pride, or prejudice\"; meaning, the great mass of\nthose who have studied the subject. But how? Suppose the \"cultivated\npersons\" were to side with the author, would those who have conclusions to\ndraw and applications to make consent to be wrong because the \"general body\nof intelligent men,\" who make no special study of the subject, are against\nthem? They would do no such thing: they would request the general body of\nintelligent men to find their own astronomy, and welcome. But the truth is,\nthat this intelligent body knows better: and no persons know better that\nthey know better than the speculators themselves.\n\nBut suppose the general body were to combine, in opposition to those who\nhave studied. Of course all my list must be admitted to their trial; and\nthen arises the question whether both sides are to be heard. If so, the\ngeneral body of the intelligent must hear all the established side have to\nsay: that is, they must become just as much of students as the inculpated\northodox themselves. And will they not then get into _professional rule_,\npique, pride, and prejudice, as the others did? But if, which I suspect,\nthey are intended to judge as they are, they will be in a rare difficulty.\nAll the paradoxers are of like pretensions: they cannot, as a class, be\nright, for each one contradicts a great many of the rest. There will be the\npuzzle which silenced the crew of the cutter in Marryat's novel of the Dog\nFiend.[182] \"A tog is a tog,\" said Jansen.--\"Yes,\" replied another, \"we all\nknow a dog is a dog; but the question is--Is _this_ dog {88} a dog?\" And\nthis question would arise upon every dog of them all.\n\n\n\nZETETIC ASTRONOMY.\n\n    Zetetic Astronomy: Earth not a globe. 1857 (Broadsheet).\n\nThough only a traveling lecturer's advertisement, there are so many\narguments and quotations that it is a little pamphlet. The lecturer gained\ngreat praise from provincial newspapers for his ingenuity in proving that\nthe earth is a flat, surrounded by ice. Some of the journals rather incline\nto the view: but the _Leicester Advertiser_ thinks that the statements\n\"would seem very seriously to invalidate some of the most important\nconclusions of modern astronomy,\" while the _Norfolk Herald_ is clear that\n\"there must be a great error on one side or the other.\" This broadsheet is\nprinted at Aylesbury in 1857, and the lecturer calls himself _Parallax_:\nbut at Trowbridge, in 1849, he was S. Goulden.[183] In this last\nadvertisement is the following announcement: \"A paper on the above subjects\nwas read before the Council and Members of the Royal Astronomical Society,\nSomerset House, Strand, London (Sir John F. W. Herschel,[184] President),\nFriday, Dec. 8, 1848.\" No account of such a paper appears in the _Notice_\nfor that month: I suspect that the above is Mr. S. Goulden's way of\nrepresenting the following occurrence: Dec. 8, 1848, the Secretary of the\nAstronomical Society (De Morgan by name) said, at the close of the\nproceedings,--\"Now, gentlemen, if you will promise not to tell the Council,\nI will read something for your amusement\": and he then read a few of the\narguments which had been transmitted by the lecturer. The fact is worth\nnoting that from 1849 to 1857, arguments on the roundness or flatness of\nthe earth did itinerate. I have {89} no doubt they did much good: for very\nfew persons have any distinct idea of the evidence for the rotundity of the\nearth. The _Blackburn Standard_ and _Preston Guardian_ (Dec. 12 and 16,\n1849) unite in stating that the lecturer ran away from his second lecture\nat Burnley, having been rather too hard pressed at the end of his first\nlecture to explain why the large hull of a ship disappeared before the\nsails. The persons present and waiting for the second lecture assuaged\ntheir disappointment by concluding that the lecturer had slipped off the\nicy edge of his flat disk, and that he would not be seen again till he\npeeped up on the opposite side.\n\nBut, strange as it may appear, the opposer of the earth's roundness has\nmore of a case--or less of a want of case--than the arithmetical squarer of\nthe circle. The evidence that the earth is round is but cumulative and\ncircumstantial: scores of phenomena ask, separately and independently, what\nother explanation can be imagined except the sphericity of the earth. The\nevidence for the earth's figure is tremendously powerful of its kind; but\nthe proof that the circumference is 3.14159265... times the diameter is of\na higher kind, being absolute mathematical demonstration.\n\nThe Zetetic system still lives in lectures and books; as it ought to do,\nfor there is no way of teaching a truth comparable to opposition. The last\nI heard of it was in lectures at Plymouth, in October, 1864. Since this\ntime a prospectus has been issued of a work entitled \"The Earth not a\nGlobe\"; but whether it has been published I do not know. The contents are\nas follows:\n\n\n\n\"The Earth a Plane--How circumnavigated.--How time is lost or gained.--Why\na ship's hull disappears (when outward bound) before the mast head.--Why\nthe Polar Star sets when we proceed Southward, etc.--Why a pendulum\nvibrates with less velocity at the Equator than {90} at the Pole.--The\nallowance for rotundity _supposed_ to be made by surveyors, not made in\npractice.--Measurement of Arcs of the Meridian unsatisfactory.--Degrees of\nLongitude North and South of the Equator considered.--Eclipses and Earth's\nform considered.--The Earth no motion on axis or in orbit.--How the Sun\nmoves above the Earth's surface concentric with the North Pole.--Cause of\nDay and Night, Winter and Summer; the long alternation of light and\ndarkness at the Pole.--Cause of the Sun rising and setting.--Distance of\nthe Sun from London, 4,028 miles--How measured.--_Challenge to\nMathematicians._--Cause of Tides.--Moon self-luminous, NOT a\nreflector.--Cause of Solar and Lunar eclipses.--Stars _not worlds_; their\ndistance.--Earth, the _only material_ world; its true position in the\nuniverse; its condition and ultimate destruction by fire (2 Peter iii.),\netc.\"\n\nI wish there were geoplatylogical lectures in every town; in England\n(_platylogical_, in composition, need not mean _babbling_). The late Mr.\nHenry Archer[185] would, if alive, be very much obliged to me for recording\nhis vehement denial of the roundness of the earth: he was excited if he\nheard any one call it a globe. I cannot produce his proof from the\nPyramids, and from some caves in Arabia. He had other curious notions, of\ncourse: I should no more believe that a flat earth was a man's only\nparadox, than I should that Dutens,[186] the editor of Leibnitz, was\neccentric only in supplying a tooth which he had lost by one which he found\nin an Italian tomb, and fully believed that it had once belonged to Scipio\nAfricanus, whose family vault was discovered, it is supposed, in 1780. Mr.\nArcher is of note as {91} the suggester of the perforated border of the\npostage-stamps, and, I think, of the way of doing it; for this he got\n4000l. reward. He was a civil engineer.\n\n(_August 28, 1865._) The _Zetetic Astronomy_ has come into my hands. When,\nin 1851, I went to see the Great Exhibition, I heard an organ played by a\nperformer who seemed very desirous to exhibit one particular stop. \"What do\nyou think of that stop?\" I was asked.--\"That depends on the name of it,\"\nsaid I.--\"Oh! what can the name have to do with the sound? 'that which we\ncall a rose,' etc.\"--\"The name has everything to do with it: if it be a\nflute-stop, I think it very harsh; but if it be a railway-whistle-stop, I\nthink it very sweet.\" So as to this book: if it be childish, it is clever;\nif it be mannish, it is unusually foolish. The flat earth, floating\ntremulously on the sea; the sun moving always over the flat, giving day\nwhen near enough, and night when too far off; the self-luminous moon, with\na semi-transparent invisible moon, created to give her an eclipse now and\nthen; the new law of perspective, by which the vanishing of the hull before\nthe masts, usually thought to prove the earth globular, really proves it\nflat;--all these and other things are well fitted to form exercises for a\nperson who is learning the elements of astronomy. The manner in which the\nsun dips into the sea, especially in tropical climates, upsets the whole.\nMungo Park,[187] I think, gives an African hypothesis which explains\nphenomena better than this. The sun dips into the western ocean, and the\npeople there cut him in pieces, fry him in a pan, and then join him\ntogether again, take him round the underway, and set him up in the east. I\nhope this book will be read, and that many will be puzzled by it: for there\nare many whose notions of astronomy deserve no better fate. There is no\nsubject on which there is so little {92} accurate conception as that of the\nmotions of the heavenly bodies. The author, though confident in the\nextreme, neither impeaches the honesty of those whose opinions he assails,\nnor allots them any future inconvenience: in these points he is worthy to\nlive on a globe, and to revolve in twenty-four hours.\n\n\n\n(_October, 1866._) A follower appears, in a work dedicated to the preceding\nauthor: it is _Theoretical Astronomy examined and exposed by Common Sense_.\nThe author has 128 well-stuffed octavo pages. I hope he will not be the\nlast. He prints the newspaper accounts of his work: the _Church Times_\nsays--not seeing how the satire might be retorted--\"We never began to\ndespair of Scripture until we discovered that 'Common Sense' had taken up\nthe cudgels in its defence.\" This paper considers our author as the type of\na _Protestant_. The author himself, who gives a summary of his arguments in\nverse, has one couplet which is worth quoting:\n\n \"How is't that sailors, bound to sea, with _a 'globe'_ would never start,\n  But in its place will always take _Mercator's_[188] LEVEL _chart_!\"\n\nTo which I answer:\n\n  Why, really Mr. Common Sense, you've never got so far\n  As to think Mercator's planisphere shows countries as they are;\n  It won't do to measure distances; it points out how to steer,\n  But this distortion's not for you; another is, I fear.\n  The earth must be a cylinder, if seaman's charts be true,\n  Or else the boundaries, right and left, are one as well as two;\n  They contradict the notion that we dwell upon a plain,\n  For straight away, without a turn, will bring you home again.\n  There are various plane projections; and each one has its use:\n  I wish a milder word would rhyme--but really you're a goose!\n\nThe great wish of persons who expose themselves as above, is to be argued\nwith, and to be treated as reputable {93} and refutable opponents. \"Common\nSense\" reminds us that no amount of \"blatant ridicule\" will turn right into\nwrong. He is perfectly correct: but then no amount of bad argument will\nturn wrong into right. These two things balance; and we are just where we\nwere: but you should answer our arguments, for whom, I ask? Would reason\nconvince this kind of reasoner? The issue is a short and a clear one. If\nthese parties be what I contend they are, then ridicule is made for them:\nif not, for what or for whom? If they be right, they are only passing\nthrough the appointed trial of all good things. Appeal is made to the\nfuture: and my Budget is intended to show samples of the long line of\nheroes who have fallen without victory, each of whom had his day of\nconfidence and his prophecy of success. Let the future decide: they say\nroundly that the earth is flat; I say flatly that it is round.\n\nThe paradoxers all want reason, and not ridicule: they are all accessible,\nand would yield to conviction. Well then, let them reason with one another!\nThey divide into squads, each with a subject, and as many different\nopinions as persons in each squad. If they be really what they say they\nare, the true man of each set can put down all the rest, and can come\ncrowned with glory and girdled with scalps, to the attack on the orthodox\nmisbelievers. But they know, to a man, that the rest are not fit to be\nreasoned with: they pay the regulars the compliment of believing that the\nonly chance lies with them. They think in their hearts, each one for\nhimself, that ridicule is of fit appliance to the rest.\n\n\n\n    Miranda. A book divided into three parts, entitled Souls, Numbers,\n    Stars, on the Neo-Christian Religion ... Vol. i. London, 1858, 1859,\n    1860. 8vo.\n\nThe name of the author is Filopanti.[189] He announces himself as the 49th\nand last Emanuel: his immediate {94} predecessors were Emanuel Washington,\nEmanuel Newton, and Emanuel Galileo. He is to collect nations into one\nfamily. He knows the transmigrations of the whole human race. Thus\nDescartes became William III of England: Roger Bacon became Boccaccio. But\nCharles IX,[190] in retribution for the massacre of St. Bartholomew, was\nhanged in London under the name of Barthelemy for the murder of Collard:\nand many of the Protestants whom he killed as King of France were shouting\nat his death before the Old Bailey.\n\n\n\nTHE SABBATH--THE GREAT PYRAMID\n\n    A Letter to the members of the Anglo-Biblical Institute, dated Sept. 7,\n    1858, and signed 'Herman Heinfetter.'[191] (Broadsheet.)\n\nThis gentleman is well known to the readers of the _Athenaeum_, in which,\nfor nearly twenty years, he has inserted, as advertisements, long arguments\nin favor of Christians keeping the Jewish Sabbath, beginning on Friday\nEvening. The present letter maintains that, by the force of the definite\narticle, the _days_ of creation may not be consecutive, but may have any\ntime--millions of years--between them. This ingenious way of reconciling\nthe author of Genesis and the indications of geology is worthy to be added\nto the list, already pretty numerous. Mr. Heinfetter has taken such pains\nto make himself a public agitator, that {95} I do not feel it to be any\ninvasion of private life if I state that I have heard he is a large\ncorn-dealer. No doubt he is a member of the congregation whose almanac has\nalready been described.\n\n\n\n    The great Pyramid. Why was it built? And who built it? By John Taylor,\n    1859,[192] 12mo.\n\nThis work is very learned, and may be referred to for the history of\nprevious speculations. It professes to connect the dimensions of the\nPyramid with a system of metrology which is supposed to have left strong\ntraces in the systems of modern times; showing the Egyptians to have had\ngood approximate knowledge of the dimensions of the earth, and of the\nquadrature of the circle. These are points on which coincidence is hard to\ndistinguish from intention. Sir John Herschel[193] noticed this work, and\ngave several coincidences, in the _Athenaeum_, Nos. 1696 and 1697, April 28\nand May 5, 1860: and there are some remarks by Mr. Taylor in No. 1701, June\n2, 1860.\n\nMr. Taylor's most recent publication is--\n\n    The battle of the Standards: the ancient, of four thousand years,\n    against the modern, of the last fifty years--the less perfect of the\n    two. London, 1864, 12mo.\n\nThis is intended as an appendix to the work on the Pyramid. Mr. Taylor\ndistinctly attributes the original system to revelation, of which he says\nthe Great Pyramid is the record. We are advancing, he remarks, towards the\nend of the Christian dispensation, and he adds that it is satisfactory to\nsee that we retain the standards which were given by unwritten revelation\n700 years before Moses. This is lighting the candle at both ends; for\nmyself, I shall not undertake to deny or affirm either what is said about\nthe dark past or what is hinted about the dark future.\n\n{96}\n\nMy old friend Mr. Taylor is well known as the author of the argument which\nhas convinced many, even most, that Sir Philip Francis[194] was Junius:\npamphlet, 1813; supplement, 1817; second edition \"The Identity of Junius\nwith a distinguished living character established,\" London, 1818, 8vo. He\ntold me that Sir Philip Francis, in a short conversation with him, made\nonly this remark, \"You may depend upon it you are quite mistaken:\" the\nphrase appears to me remarkable; it has an air of criticism on the book,\nfree from all personal denial. He also mentioned that a hearer told him\nthat Sir Philip said, speaking of writers on the question,--\"Those fellows,\nfor half-a-crown, would prove that Jesus Christ was Junius.\"\n\nMr. Taylor implies, I think, that he is the first who started the\nsuggestion that Sir Philip Francis was Junius, which I have no means either\nof confirming or refuting. If it be so [and I now know that Mr. Taylor\nhimself never heard of any predecessor], the circumstance is very\nremarkable: it is seldom indeed that the first proposer of any solution of\na great and vexed question is the person who so nearly establishes his\npoint in general opinion as Mr. Taylor has done.\n\nAs to the Junius question in general, there is a little bit of the\nphilosophy of horse-racing which may be usefully applied. A man who is so\nconfident of his horse that he places him far above any other, may\nnevertheless, and does, refuse to give odds against all in the field: for\nmany small adverse chances united make a big chance for one or other of the\nopponents. I suspect Mr. Taylor has made it at least 20 to 1 for Francis\nagainst any one competitor who has been named: but what the odds may be\nagainst the {97} whole field is more difficult to settle. What if the real\nJunius should be some person not yet named?\n\nMr. Jopling, _Leisure Hour_, May 23, 1863, relies on the porphyry coffer of\nthe Great Pyramid, in which he finds \"the most ancient and accurate\nstandard of measure in existence.\"\n\nI am shocked at being obliged to place a thoughtful and learned writer, and\nan old friend, before such a successor as he here meets with. But\nchronological arrangement defies all other arrangement.\n\n(I had hoped that the preceding account would have met Mr. Taylor's eye in\nprint: but he died during the last summer. For a man of a very thoughtful\nand quiet temperament, he had a curious turn for vexed questions. But he\nreflected very long and very patiently before he published: and all his\nworks are valuable for their accurate learning, whichever side the reader\nmay take.)\n\n\n\nMRS. ELIZABETH COTTLE.\n\n1859. _The Cottle Church._--For more than twenty years printed papers have\nbeen sent about in the name of Elizabeth Cottle.[195] It is not so\nremarkable that such papers should be concocted as that they should\ncirculate for such a length of time without attracting public attention.\nEighty years ago Mrs. Cottle might have rivalled Lieut. Brothers or Joanna\nSouthcott.[196] Long hence, when the now current volumes of our journals\nare well-ransacked works of reference, those who look into them will be\nglad to see this {98} feature of our time: I therefore make a few extracts,\nfaithfully copied as to type. The Italic is from the New Testament; the\nRoman is the requisite interpretation:\n\n\"Robert Cottle '_was numbered_ (5196) _with the transgressors_' at the back\nof the Church in Norwood Cemetery, May 12, 1858--Isa. liii. 12. The Rev.\nJ. G. Collinson, Minister of St. James's Church, Chapham, the then district\nchurch, before All Saints was built, read the funeral service _over the\nSepulchre wherein never before man was laid_.\n\n\"_Hewn on the stone_, 'at the mouth of the Sepulchre,' is his name,--Robert\nCottle, born at Bristol, June 2, 1774; died at Kirkstall Lodge, Clapham\nPark, May 6, 1858. _And that day_ (May 12, 1858) _was the preparation_ (day\nand year for 'the PREPARED place for you'--Cottleites---by the widowed\nmother of the Father's house, at Kirkstall Lodge--John xiv. 2, 3). _And the\nSabbath_ (Christmas Day, Dec. 25, 1859) _drew on_ (for the resurrection of\nthe Christian body on 'the third [Protestant Sun]-day'--1 Cor. xv. 35).\n_Why seek ye the living_ (God of the New Jerusalem--Heb. xii. 22; Rev. iii.\n12) _among the dead_ (men): _he_ (the God of Jesus) _is not here_ (in the\ngrave), _but is risen_ (in the person of the Holy Ghost, from the supper of\n'the dead in the second death' of Paganism). _Remember how he spake unto\nyou_ (in the church of the Rev. George Clayton,[197] April 14, 1839). _I\nwill not drink henceforth_ (at this last Cottle supper) _of the fruit of\nthis_ (Trinity) _vine, until that day_ (Christmas Day, 1859), _when I_\n(Elizabeth Cottle) _drink it new with you_ (Cottleites) _in my Father's\nkingdom_--John xv. _If this_ (Trinitarian) _cup may not pass away from me_\n(Elizabeth Cottle, April 14, 1839), _except I drink it_ ('new with you\nCottleites, in my Father's Kingdom'), _thy will be done_--Matt. xxvi. 29,\n42, 64. 'Our Father which art (God) in Heaven,' _hallowed be thy name, thy_\n(Cottle) _kingdom_ {99} _come, thy will be done in earth, as it is_ (done)\n_in_ (the new) _Heaven_ (and new earth of the new name of Cottle--Rev. xxi.\n1; iii. 12).\n\n\"... Queen Elizabeth, from A.D. 1558 to 1566. _And this_ WORD _yet once\nmore_ (by a second Elizabeth--the WORD of his oath) _signifieth_ (at John\nScott's baptism of the Holy Ghost) _the removing of those things_ (those\nGods and those doctrines) _that are made_ (according to the Creeds and\nCommandments of men) _that those things_ (in the moral law of God) _which\ncannot be shaken_ (as a rule of faith and practice) _may remain, wherefore\nwe receiving_ (from Elizabeth) _a kingdom_ (of God,) _which cannot be\nmoved_ (by Satan) _let us have grace_ (in his Grace of Canterbury) _whereby\nwe may serve God acceptably_ (with the acceptable sacrifice of Elizabeth's\nbody and blood of the communion of the Holy Ghost) _with reverence_ (for\ntruth) _and godly fear_ (of the unpardonable sin of blasphemy against the\nHoly Ghost) _for our God_ (the Holy Ghost) _is a consuming fire_ (to the\nnation that will not serve him in the Cottle Church). We cannot defend\nourselves against the Almighty, and if He is our defence, no nation can\ninvade us.\n\n\"In verse 4 the Church of St. Peter is _in prison between four quaternions\nof soldiers_--the Holy Alliance of 1815. Rev. vii. i. Elizabeth, _the Angel\nof the Lord_ Jesus _appears_ to the Jewish and Christian body with _the\nvision_ of prophecy to the Rev. Geo. Clayton and his clerical brethren,\nApril 8th, 1839. _Rhoda_ was the name of her maid at Putney Terrace who\nused _to open the door to her Peter_, the Rev. Robert Ashton,[198] the\nPastor of 'the little flock' 'of 120 names together, assembled in an upper\n(school) room' at Putney Chapel, to which little flock she gave the\nrevelation (Acts. i. 13, 15) _of Jesus the same_ King of the Jews\n_yesterday_ at the prayer meeting, Dec. 31, 1841, _and to-day_, {100} Jan.\n1, 1842, _and for ever_. See book of Life, page 24. Matt. xviii. 19, xxi.\n13-16. In verse 6 the Italian body of St. Peter _is sleeping_ 'in the\nsecond death' _between the two_ Imperial _soldiers_ of France and Austria.\nThe Emperor of France from Jan. 1, to July 11, 1859, causes the Italian\n_chains of St. Peter to fall off from his_ Imperial _hands_.\n\n\"_I say unto thee_, Robert Ashton, _thou art Peter_, a stone, _and upon\nthis rock_, of truth, _will I_ Elizabeth, the angel of Jesus, _build my_\nCottle _Church, and the gates of hell_, the doors of St. Peter, at Rome,\nshall not prevail against it--Matt. xvi. 18. Rev. iii. 7-12.\"\n\nThis will be enough for the purpose. When any one who pleases can circulate\nnew revelations of this kind, uninterrupted and unattended to, new\nrevelations will cease to be a good investment of excentricity. I take it\nfor granted that the gentlemen whose names are mentioned have nothing to do\nwith the circulars or their doctrines. Any lady who may happen to be\nintrusted with a revelation may nominate her own pastor, or any other\nclergyman, one of her apostles; and it is difficult to say to what court\nthe nominees can appeal to get the commission abrogated.\n\n_March 16, 1865._ During the last two years the circulars have continued.\nIt is hinted that funds are low: and two gentlemen who are represented as\ngone \"to Bethlehem asylum in despair\" say that Mrs. Cottle \"will spend all\nthat she hath, while Her Majesty's Ministers are flourishing on the wages\nof sin.\" The following is perhaps one of the most remarkable passages in\nthe whole:\n\n\"_Extol and magnify Him_ (Jehovah, the Everlasting God, see the Magnificat\nand Luke i. 45, 46--68--73--79), _that rideth_ (by rail and steam over land\nand sea, from his holy habitation at Kirkstall Lodge, Psa. lxxvii. 19, 20),\n_upon the_ (Cottle) _heavens, as it were_ (Sept. 9, 1864, see pages 21,\n170), _upon an_ (exercising, Psa. cxxxi. 1), _horse_-(chair, bought of Mr.\nJohn Ward, Leicester-square).\" {101}\n\nI have pretty good evidence that there is a clergyman who thinks Mrs.\nCottle a very sensible woman.\n\n[_The Cottle Church._ Had I chanced to light upon it at the time of\nwriting, I should certainly have given the following. A printed letter to\nthe _Western Times_, by Mr. Robert Cottle, was accompanied by a manuscript\nletter from Mrs. Cottle, apparently a circular. The date was Nov^{r}. 1853,\nand the subject was the procedure against Mr. Maurice[199] at King's\nCollege for doubting that God would punish human sins by an existence of\ntorture lasting through years numbered by millions of millions of millions\nof millions (repeat the word _millions_ without end,) etc. The memory of\nMr. Cottle has, I think, a right to the quotation: he seems to have been no\nparticipator in the notions of his wife:\n\n\"The clergy of the Established Church, taken at the round number of 20,000,\nmay, in their first estate, be likened to 20,000 gold blanks, destined to\nbecome sovereigns, in succession,--they are placed between the matrix of\nthe Mint, when, by the pressure of the screw, they receive the impress that\nfits them to become part of the current coin of the realm. In a way\nsomewhat analogous this great body of the clergy have each passed through\nthe crucibles of Oxford and Cambridge,--have been assayed by the Bishop's\nchaplain, touching the health of their souls, and the validity of their\ncall by the Divine Spirit, and then the gentle pressure of a prelate's hand\nupon their heads; and the words--'Receive the Holy Ghost,' have, in a brief\nspace of time, wrought a {102} change in them, much akin to the miracle of\ntransubstantiation--the priests are completed, and they become the current\necclesiastical coin of our country. The whole body of clergy, here spoken\nof, have undergone the preliminary induction of baptism and confirmation;\nand all have been duly ordained, _professing_ to hold one faith, and to\nbelieve in the selfsame doctrines! In short, to be as identical as the\n20,000 sovereigns, if compared one with the other. But mind is not\nmalleable and ductile, like gold; and all the preparations of tests,\ncreeds, and catechisms will not insure uniformity of belief. No stamp of\northodoxy will produce the same impress on the minds of different men.\nVariety is manifest, and patent, upon everything mental and material. The\nAlmighty has not created, nor man fashioned, two things alike! How futile,\nthen, is the attempt to shape and mould man's apprehension of divine truth\nby one fallible standard of man's invention! If proof of this be required,\nan appeal might be made to history and the experience of eighteen hundred\nyears.\"\n\nThis is an argument of force against the reasonableness of expecting tens\nof thousands of educated readers of the New Testament to find the doctrine\nabove described in it. The lady's argument against the doctrine itself is\nvery striking. Speaking of an outcry on this matter among the Dissenters\nagainst one of their body, who was the son of \"the White Stone (Rev. ii.\n17), or the Roman cement-maker,\" she says--\n\n\"If the doctrine for which they so wickedly fight were true, what would\nbecome of the black gentlemen for whose redemption I have been sacrificed\nfrom April 8 1839.\"\n\nThere are certainly very curious points about this revelation. There have\nbeen many surmises about the final restoration of the infernal spirits,\nfrom the earliest ages of Christianity until our own day: a collection of\nthem would be worth making. On reading this in proof, I see a possibility\nthat by \"black gentlemen\" may be meant the clergy: {103} I suppose my first\ninterpretation must have been suggested by context: I leave the point to\nthe reader's sagacity.]\n\n\n\nJAMES SMITH, ARCH-PARADOXER.\n\n    The Problem of squaring the circle solved; or, the circumference and\n    area of the circle discovered. By James Smith.[200] London, 1859, 8vo.\n\n    On the relations of a square inscribed in a circle. Read at the British\n    Association, Sept. 1859, published in the Liverpool Courier, Oct. 8,\n    1859, and reprinted in broadsheet.\n\n    The question: Are there any commensurable relations between a circle\n    and other Geometrical figures? Answered by a member of the British\n    Association ... London, 1860, 8vo.--[This has been translated into\n    French by M. Armand Grange, Bordeaux, 1863, 8vo.]\n\n    The Quadrature of the Circle. Correspondence between an eminent\n    mathematician and James Smith, Esq. (Member of the Mersey Docks and\n    Harbour Board), London, 1861, 8vo. (pp. 200).\n\n    Letter to the ... British Association ... by James Smith, Esq.\n    Liverpool, 1861, 8vo.\n\n    Letter to the ... British Association ... by James Smith, Esq.\n    Liverpool, 1862, 8vo.--[These letters the author promised to continue.]\n\n    A Nut to crack for the readers of Professor De Morgan's 'Budget of\n    Paradoxes.' By James Smith, Esq. Liverpool, 1863, 8vo.\n\n    Paper read at the Liverpool Literary and Philosophical Society,\n    reported in the Liverpool Daily Courier, Jan. 26, 1864. Reprinted as a\n    pamphlet.\n\n    The Quadrature of the circle, or the true ratio between the diameter\n    and circumference geometrically and mathematically demonstrated. By\n    James Smith, Esq. Liverpool, 1865, 8vo.\n\n    {104}\n\n    [On the relations between the dimensions and distances of the Sun,\n    Moon, and Earth; a paper read before the Literary and Philosophical\n    Society of Liverpool, Jan. 25, 1864. By James Smith, Esq.\n\n    The British Association in Jeopardy, and Dr. Whewell, the Master of\n    Trinity, in the stocks without hope of escape. Printed for the authors\n    (J. S. confessed, and also hidden under _Nauticus_). (No date, 1865).\n\n    The British Association in Jeopardy, and Professor De Morgan in the\n    Pillory without hope of escape. London, 1866, 8vo.]\n\nWhen my work appeared in numbers, I had not anything like an adequate idea\nof Mr. James Smith's superiority to the rest of the world in the points in\nwhich he is superior. He is beyond a doubt the ablest head at unreasoning,\nand the greatest hand at writing it, of all who have tried in our day to\nattach their names to an error. Common cyclometers sink into puny orthodoxy\nby his side.\n\nThe behavior of this singular character induces me to pay him the\ncompliment which Achilles paid Hector, to drag him round the walls again\nand again. He was treated with unusual notice and in the most gentle\nmanner. The unnamed mathematician, E. M. bestowed a volume of mild\ncorrespondence upon him; Rowan Hamilton[201] quietly proved him wrong in a\nway accessible to an ordinary schoolboy; Whewell,[202] as we shall see,\ngave him the means of seeing himself wrong, even more easily than by\nHamilton's method. Nothing would do; it was small kick and silly fling at\nall; and he exposed his conceit by alleging that he, James Smith, had\nplaced Whewell in the stocks. He will therefore be universally pronounced a\nproper object of the severest literary punishment: but the opinion of all\nwho can put two propositions together will be that of the many strokes I\nhave given, the hardest and most telling are my republications of his own\nattempts to reason.\n\nHe will come out of my hands in the position he ought {105} to hold, the\nSupreme Pontiff of cyclometers, the vicegerent of St. Vitus upon earth, the\nMamamouchi of burlesque on inference. I begin with a review of him which\nappeared in the _Athenaeum_ of May 11, 1861. Mr. Smith says I wrote it: this\nI neither affirm nor deny; to do either would be a sin against the\neditorial system elsewhere described. Many persons tell me they know me by\nmy style; let them form a guess: I can only say that many have declared as\nabove while fastening on me something which I had never seen nor heard of.\n\n\n\n    The Quadrature of the Circle: Correspondence between an Eminent\n    Mathematician and James Smith, Esq. (Edinburgh, Oliver & Boyd; London,\n    Simpkin, Marshall & Co.)\n\n\"A few weeks ago we were in perpetual motion. We did not then suppose that\nanything would tempt us on a circle-squaring expedition: but the\ncircumstances of the book above named have a peculiarity which induces us\nto give it a few words.\n\n\"Mr. James Smith, a gentleman residing near Liverpool, was some years ago\nseized with the _morbus cyclometricus_.[203] The symptoms soon took a\ndefined form: his circumference shrank into exactly 3-1/8 times his\ndiameter, instead of close to 3-16/113, which the mathematician knows to be\nso near to truth that the error is hardly at the rate of a foot in 2,000\nmiles. This shrinking of the circumference remained until it became\nabsolutely necessary that it should be examined by the British Association.\nThis body, which as Mr. James Smith found to his sorrow, has some interest\nin 'jealously guarding the mysteries of their profession,' refused at first\nto entertain the question. On this Mr. Smith changed his 'tactics' and the\nname of his paper, and smuggled in the subject under the form of 'The\nRelations of a Circle inscribed in a Square'! The paper was thus forced\nupon the Association, for Mr. Smith informs us that he {106} 'gave the\nSection to understand that he was not the man that would permit even the\nBritish Association to trifle with him.' In other words, the Association\nbore with and were bored with the paper, as the shortest way out of the\nmatter. Mr. Smith also circulated a pamphlet. Some kind-hearted man, who\ndid not know the disorder as well as we do, and who appears in Mr. Smith's\nhandsome octavo as E. M.--the initials of 'eminent mathematician'--wrote to\nhim and offered to show him in a page that he was all wrong. Mr. Smith\nthereupon opened a correspondence, which is the bulk of the volume. When\nthe correspondence was far advanced, Mr. Smith announced his intention to\npublish. His benevolent instructor--we mean in intention--protested against\nthe publication, saying 'I do not wish to be gibbeted to the world as\nhaving been foolish enough to enter upon what I feel now to have been a\nridiculous enterprise.'\n\n\"For this Mr. Smith cared nothing: he persisted in the publication, and the\nbook is before us. Mr. Smith has had so much grace as to conceal his kind\nadviser's name under E. M., that is to say, he has divided the wrong among\nall who may be suspected of having attempted so hopeless a task as that of\nputting a little sense into his head. He has violated the decencies of\nprivate life. Against the will of the kind-hearted man who undertook his\ncase, he has published letters which were intended for no other purpose\nthan to clear his poor head of a hopeless delusion. He deserves the\nseverest castigation; and he will get it: his abuse of confidence will\nstick by him all his days. Not that he has done his benefactor--in\nintention, again--any harm. The patience with which E. M. put the blunders\ninto intelligible form, and the perseverance with which he tried to find a\ncranny-hole for common reasoning to get in at, are more than respectable:\nthey are admirable. It is, we can assure E. M., a good thing that the\nnature of the circle-squarer should be so completely exposed as in this\nvolume. The benefit which he intended Mr. James Smith may be {107}\nconferred upon others. And we should very much like to know his name, and\nif agreeable to him, to publish it. As to Mr. James Smith, we can only say\nthis: he is not mad. Madmen reason rightly upon wrong premises: Mr. Smith\nreasons wrongly upon no premises at all.\n\n\"E. M. very soon found out that, to all appearance, Mr. Smith got a circle\nof 3-1/8 times the diameter by making it the supposition to set out with\nthat there was such a circle; and then finding certain consequences which,\nso it happened, were not inconsistent with the supposition on which they\nwere made. Error is sometimes self-consistent. However, E. M., to be quite\nsure of his ground, wrote a short letter, stating what he took to be Mr.\nSmith's hypothesis, containing the following: 'On AC as diameter, describe\nthe circle D, which by hypothesis shall be equal to three and one-eighth\ntimes the length of AC.... I beg, before proceeding further, to ask whether\nI have rightly stated your argument.' To which Mr. Smith replied: 'You have\nstated my argument with perfect accuracy.' Still E. M. went on, and we\ncould not help, after the above, taking these letters as the initials of\nEverlasting Mercy. At last, however, when Mr. Smith flatly denied that the\narea of the circle lies between those of the inscribed and circumscribed\npolygons, E. M. was fairly beaten, and gave up the task. Mr. Smith was left\nto write his preface, to talk about the certain victory of truth--which,\noddly enough, is the consolation of all hopelessly mistaken men; to compare\nhimself with Galileo; and to expose to the world the perverse behavior of\nthe Astronomer Royal, on whom he wanted to fasten a conversation, and who\nreplied, 'It would be a waste of time, Sir, to listen to anything you could\nhave to say on such a subject.'\n\n\"Having thus disposed of Mr. James Smith, we proceed to a few remarks on\nthe subject: it is one which a journal would never originate, but which is\nrendered necessary from time to time by the attempts of the autopseustic to\nbecome {108} heteropseustic. To the mathematician we have nothing to say:\nthe question is, what kind of assurance can be given to the world at large\nthat the wicked mathematicians are not acting in concert to keep down their\nsuperior, Mr. James Smith, the current Galileo of the quadrature of the\ncircle.\n\n\"Let us first observe that this question does not stand alone:\nindependently of the millions of similar problems which exist in higher\nmathematics, the finding of the diagonal of a square has just the same\ndifficulty, namely, the entrance of a pair of lines of which one cannot be\ndefinitely expressed by means of the other. We will show the reader who is\nup to the multiplication-table how he may go on, on, on, ever nearer, never\nthere, in finding the diagonal of a square from the side.\n\n\"Write down the following rows of figures, and more, if you like, in the\nway described:\n\n  1   2   5   12   29   70   169   408     985\n  1   3   7   17   41   99   239   577   1393\n\nAfter the second, each number is made up of double the last increased by\nthe last but one: thus, 5 is 1 more than twice 2, 12 is 2 more than twice\n5, 239 is 41 more than twice 99. Now, take out two adjacent numbers from\nthe upper line, and the one below the first from the lower: as\n\n  70   169\n  99.\n\nMultiply together 99 and 169, giving 16,731. If, then, you will say that 70\ndiagonals are exactly equal to 99 sides, you are in error about the\ndiagonal, but an error the amount of which is not so great as the 16,731st\npart of the diagonal. Similarly, to say that five diagonals make exactly\nseven sides does not involve an error of the 84th part of the diagonal.\n\n\"Now, why has not the question of _crossing the square_ been as celebrated\nas that of _squaring the circle_? Merely because Euclid demonstrated the\nimpossibility of the first {109} question, while that of the second was not\ndemonstrated, completely, until the last century.\n\n\"The mathematicians have many methods, totally different from each other,\nof arriving at one and the same result, their celebrated approximation to\nthe circumference of the circle. An intrepid calculator has, in our own\ntime, carried his approximation to what they call 607 decimal places: this\nhas been done by Mr. Shanks,[204] of Houghton-le-Spring, and Dr.\nRutherford[205] has verified 441 of these places. But though 607 looks\nlarge, the general public will form but a hazy notion of the extent of\naccuracy acquired. We have seen, in Charles Knight's[206] _English\nCyclopaedia_, an account of the matter which may illustrate the\nunimaginable, though rationally conceivable, extent of accuracy obtained.\n\n\"Say that the blood-globule of one of our animalcules is a millionth of an\ninch in diameter. Fashion in thought a globe like our own, but so much\nlarger that our globe is but a blood-globule in one of its animalcules:\nnever mind the microscope which shows the creature being rather a bulky\ninstrument. Call this the first globe _above_ us. Let the first globe above\nus be but a blood-globule, as to size, in the animalcule of a still larger\nglobe, which call the second globe above us. Go on in this way to the\ntwentieth globe above us. Now go down just as far on the other side. Let\nthe blood-globule with which we started be a globe peopled with animals\nlike ours, but rather smaller: {110} and call this the first globe below\nus. Take a blood-globule out of this globe, people it, and call it the\nsecond globe below us: and so on to the twentieth globe below us. This is a\nfine stretch of progression both ways. Now give the giant of the twentieth\nglobe _above_ us the 607 decimal places, and, when he has measured the\ndiameter of his globe with accuracy worthy of his size, let him calculate\nthe circumference of his equator from the 607 places. Bring the little\nphilosopher from the twentieth globe _below_ us with his very best\nmicroscope, and set him to see the small error which the giant must make.\nHe will not succeed, unless his microscopes be much better for his size\nthan ours are for ours.\n\n\"Now it must be remembered by any one who would laugh at the closeness of\nthe approximation, that the mathematician generally goes _nearer_; in fact\nhis theorems have usually no error at all. The very person who is\nbewildered by the preceding description may easily forget that if there\nwere _no error at all_, the Lilliputian of the millionth globe below us\ncould not find a flaw in the Brobdingnagian of the millionth globe above.\nThe three angles of a triangle, of perfect accuracy of form, are\n_absolutely_ equal to two right angles; no stretch of progression will\ndetect _any_ error.\n\n\"Now think of Mr. Lacomme's mathematical adviser (_ante_, Vol. I, p. 46)\nmaking a difficulty of advising a stonemason about the quantity of pavement\nin a circular floor!\n\n\"We will now, for our non-calculating reader, put the matter in another\nway. We see that a circle-squarer can advance, with the utmost confidence,\nthe assertion that when the diameter is 1,000, the circumference is\naccurately 3,125: the mathematician declaring that it is a trifle more than\n3,141-1/2. If the squarer be right, the mathematician has erred by about a\n200th part of the whole: or has not kept his accounts right by about 10s.\nin every 100l. Of course, if he set out with such an error he will\naccumulate blunder upon blunder. Now, if there be a process in which {111}\nclose knowledge of the circle is requisite, it is in the prediction of the\nmoon's place--say, as to the time of passing the meridian at Greenwich--on\na given day. We cannot give the least idea of the complication of details:\nbut common sense will tell us that if a mathematician cannot find his way\nround the circle without a relative error four times as big as a\nstockbroker's commission, he must needs be dreadfully out in his attempt to\npredict the time of passage of the moon. Now, what is the fact? His error\nis less than a second of time, and the moon takes 27 days odd to revolve.\nThat is to say, setting out with 10s. in 100l. of error in his\ncircumference, he gets within the fifth part of a farthing in 100l. in\npredicting the moon's transit. Now we cannot think that the respect in\nwhich mathematical science is held is great enough--though we find it not\nsmall--to make this go down. That respect is founded upon a notion that\nright ends are got by right means: it will hardly be credited that the\ntruth can be got to farthings out of data which are wrong by shillings.\nEven the celebrated Hamilton[207] of Edinburgh, who held that in\nmathematics there was no way of going wrong, was fully impressed with the\nbelief that this was because error was avoided from the beginning. He never\nwent so far as to say that a mathematician who begins wrong must end right\nsomehow.\n\n\"There is always a difficulty about the mode in which the thinking man of\ncommon life is to deal with subjects he has not studied to a professional\nextent. He must form opinions on matters theological, political, legal,\nmedical, and social. If he can make up his mind to choose a guide, there\nis, of course, no perplexity: but on all the subjects mentioned the\ndirection-posts point different ways. Now why should he not form his\nopinion upon an abstract mathematical question? Why not conclude that, as\nto the circle, it is possible Mr. James Smith may be the man, just {112} as\nAdam Smith[208] was the man of things then to come, or Luther, or Galileo?\nIt is true that there is an unanimity among mathematicians which prevails\nin no other class: but this makes the chance of their all being wrong only\ndifferent in degree. And more than this, is it not generally thought among\nus that priests and physicians were never so much wrong as when there was\nmost appearance of unanimity among them? To the preceding questions we see\nno answer except this, that the individual inquirer may as rationally\ndecide a mathematical question for himself as a theological or a medical\nquestion, so soon as he can put himself into a position in mathematics,\nlevel with that in which he stands in theology or medicine. The every-day\nthought and reading of common life have a certain resemblance to the\nthought and reading demanded by the learned faculties. The research, the\nbalance of evidence, the estimation of probabilities, which are used in a\nquestion of medicine, are closely akin in character, however different the\nmatter of application, to those which serve a merchant to draw his\nconclusions about the markets. But the mathematicians have methods of their\nown, to which nothing in common life bears close analogy, as to the nature\nof the results or the character of the conclusions. The logic of\nmathematics is certainly that of common life: but the data are of a\ndifferent species; they do not admit of doubt. An expert arithmetician,\nsuch as is Mr. J. Smith, may fancy that calculation, merely as such, is\nmathematics: but the value of his book, and in this point of view it is not\nsmall, is the full manner in which it shows that a practised arithmetician,\nventuring into the field of mathematical demonstration, may show himself\nutterly destitute of all that distinguishes the reasoning geometrical\ninvestigator from the calculator.\n\n{113}\n\n\"And further, it should be remembered that in mathematics the power of\nverifying results far exceeds that which is found in anything else: and\nalso the variety of distinct methods by which they can be attained. It\nfollows from all this that a person who desires to be as near the truth as\nhe can will not judge the results of mathematical demonstration to be open\nto his criticism, in the same degree as results of other kinds. Should he\nfeel compelled to decide, there is no harm done: his circle may be 3-1/8\ntimes its diameter, if it please him. But we must warn him that, in order\nto get this circle, he must, as Mr. James Smith has done, _make it at\nhome_: the laws of space and thought beg leave respectfully to decline the\norder.\"\n\n\n\nI will insert now at length, from the _Athenaeum_ of June 8, 1861, the easy\nrefutation given by my deceased friend, with the remarks which precede.\n\n\"Mr. James Smith, of whose performance in the way of squaring the circle we\nspoke some weeks ago in terms short of entire acquiescence, has advertised\nhimself in our columns, as our readers will have seen. He has also\nforwarded his letter to the Liverpool _Albion_, with an additional\nstatement, which he did not make in _our_ journal. He denies that he has\nviolated the decencies of private life, since his correspondent revised the\nproofs of his own letters, and his 'protest had respect only to making his\nname public.' This statement Mr. James Smith precedes by saying that we\nhave treated as true what we well knew to be false: and he follows by\nsaying that we have not read his work, or we should have known the above\nfacts to be true. Mr. Smith's pretext is as follows. His correspondent\nE. M. says, 'My letters were not intended for publication, and I protest\nagainst their being published,' and he subjoins 'Therefore I must desire\nthat my name may not be used.' The obvious meaning is that E. M. protested\nagainst the publication altogether, but, judging that Mr. Smith was {114}\ndetermined to publish, desired that his name should not be used. That he\nafterwards corrected the proofs merely means that he thought it wiser to\nlet them pass under his own eyes than to leave them entirely to Mr. Smith.\n\n\"We have received from Sir W. Rowan Hamilton[209] a proof that the\ncircumference is more than 3-1/8 diameters, requiring nothing but a\nknowledge of four books of Euclid. We give it in brief as an exercise for\nour juvenile readers to fill up. It reminds us of the old days when real\ngeometers used to think it worth while seriously to demolish pretenders.\nMr. Smith's fame is now assured: Sir W. R. Hamilton's brief and easy\nexposure will procure him notice in connection with this celebrated\nproblem.\n\n\"It is to be shown that the perimeter of a regular polygon of 20 sides is\ngreater than 3-1/8 diameters of the circle, and still more, of course, is\nthe circumference of the circle greater than 3-1/8 diameters.\n\n\"1. It follows from the 4th Book of Euclid, that the rectangle under the\nside of a regular decagon inscribed in a circle, and that side increased by\nthe radius, is equal to the square of the radius. But the product 791 (791\n+ 1280) is less than 1280 x 1280; if then the radius be 1280 the side of\nthe decagon is greater than 791.\n\n\"2. When a diameter bisects a chord, the square of the chord is equal to\nthe rectangle under the doubles of the segments of the diameter. But the\nproduct 125 (4 x 1280 - 125) is less than 791 x 791. If then the bisected\nchord be a side of the decagon, and if the radius be still 1280, the double\nof the lesser segment exceeds 125.\n\n\"3. The rectangle under this doubled segment and the radius is equal to the\nsquare of the side of an inscribed regular polygon of 20 sides. But the\nproduct 125 x 1280 is equal to 400 x 400; therefore, the side of the\nlast-mentioned polygon is greater than 400, if the radius be still 1280. In\nother words, if the radius be represented by the new {115} member 16, and\ntherefore the diameter by 32, this side is greater than 5, and the\nperimeter exceeds 100. So that, finally, if the diameter be 8, the\nperimeter of the inscribed regular polygon of 20 sides, and still more the\ncircumference of the circle, is greater than 25: that is, the circumference\nis more than 3-1/8 diameters.\"\n\nThe last work in the list was thus noticed in the _Athenaeum_, May 27, 1865.\n\n\"Mr. James Smith appears to be tired of waiting for his place in the Budget\nof Paradoxes, and accordingly publishes a long letter to Professor De\nMorgan, with various prefaces and postscripts. The letter opens by a hint\nthat the Budget appears at very long intervals, and 'apparently without any\nsufficient reason for it.' As Mr. Smith hints that he should like to see\nMr. De Morgan, whom he calls an 'elephant of mathematics,' 'pumping his\nbrains' 'behind the scenes'--an odd thing for an elephant to do, and an odd\nplace to do it in--to get an answer, we think he may mean to hint that the\nBudget is delayed until the pump has worked successfully. Mr. Smith is\ninformed that we have had the whole manuscript of the Budget, excepting\nonly a final summing-up, in our hands since October, 1863. [This does not\nrefer to the Supplement.] There has been no delay: we knew from the\nbeginning that a series of historical articles would be frequently\ninterrupted by the things of the day. Mr. James Smith lets out that he has\nnever been able to get a private line from Mr. De Morgan in answer to his\ncommunications: we should have guessed it. He says, 'The Professor is an\nold bird and not to be easily caught, and by no efforts of mine have I been\nable, up to the present moment, either to induce or twit him into a\ndiscussion....' Mr. Smith curtails the proverb: old birds are not to be\ncaught with _chaff_, nor with _twit_, which seems to be Mr. Smith's word\nfor his own chaff, and, so long as the first letter is sounded, a very\nproper word. Why does he not try a little grain of sense? Mr. Smith\nevidently {116} thinks that, in his character as an elephant, the Professor\nhas not pumped up brain enough to furnish forth a bird. In serious earnest,\nMr. Smith needs no answer. In one thing he excites our curiosity: what is\nmeant by demonstrating 'geometrically _and_ mathematically?'\"\n\nI now proceed to my original treatment of the case.\n\n\n\nMr. James Smith will, I have no doubt, be the most uneclipsed\ncircle-squarer of our day. He will not owe this distinction to his being an\ninfluential and respected member of the commercial world of Liverpool, even\nthough the power of publishing which his means give him should induce him\nto issue a whole library upon one paradox. Neither will he owe it to the\npains taken with him by a mathematician who corresponded with him until the\njoint letters filled an octavo volume. Neither will he owe it to the notice\ntaken of him by Sir William Hamilton, of Dublin, who refuted him in a\nmanner intelligible to an ordinary student of Euclid, which refutation he\ncalls a remarkable paradox easily explainable, but without explaining it.\nWhat he will owe it to I proceed to show.\n\nUntil the publication of the _Nut to Crack_ Mr. James Smith stood among\ncircle-squarers in general. I might have treated him with ridicule, as I\nhave done others: and he says that he does not doubt he shall come in for\nhis share at the tail end of my Budget. But I can make a better job of him\nthan so, as Locke would have phrased it: he is such a very striking example\nof something I have said on the use of logic that I prefer to make an\nexample of his writings. On one point indeed he well deserves the\n_scutica_,[210] if not the _horribile flagellum_.[211] He tells me that he\nwill bring his solution to me in such a form as shall compel me to admit it\nas _un fait accompli_ [_une faute accomplie?_][212] {117} or leave myself\nopen to the humiliating charge of mathematical ignorance and folly. He has\nalso honored me with some private letters. In the first of these he gives\nme a \"piece of information,\" after which he cannot imagine that I, \"as an\nhonest mathematician,\" can possibly have the slightest hesitation in\nadmitting his solution. There is a tolerable reservoir of modest assurance\nin a man who writes to a perfect stranger with what he takes for an\nargument, and gives an oblique threat of imputation of dishonesty in case\nthe argument be not admitted without hesitation; not to speak of the minor\ncharges of ignorance and folly. All this is blind self-confidence, without\nmixture of malicious meaning; and I rather like it: it makes me understand\nhow Sam Johnson came to say of his old friend Mrs. Cobb,[213]--\"I love Moll\nCobb for her impudence.\" I have now done with my friend's _suaviter in\nmodo_,[214] and proceed to his _fortiter in re_[215]: I shall show that he\n_has_ convicted himself of ignorance and folly, with an honesty and candor\nworthy of a better value of [pi].\n\nMr. Smith's method of proving that every circle is 3-1/8 diameters is to\nassume that it is so,--\"if you dislike the term datum, then, by hypothesis,\nlet 8 circumferences be exactly equal to 25 diameters,\"--and then to show\nthat every other supposition is thereby made absurd. The right to this\nassumption is enforced in the \"Nut\" by the following analogy:\n\n\"I think you (!) will not dare (!) to dispute my right to this hypothesis,\nwhen I can prove by means of it that every other value of [pi] will lead to\nthe grossest absurdities; unless indeed, you are prepared to dispute the\nright of Euclid to adopt a false line hypothetically for the purpose {118}\nof a '_reductio ad absurdum_'[216] demonstration, in pure geometry.\"\n\n\n\nEuclid assumes what he wants to _disprove_, and shows that his _assumption_\nleads to absurdity, and so _upsets itself_. Mr. Smith assumes what he wants\nto _prove_, and shows that _his_ assumption makes _other propositions_ lead\nto absurdity. This is enough for all who can reason. Mr. James Smith cannot\nbe argued with; he has the whip-hand of all the thinkers in the world.\nMontucla would have said of Mr. Smith what he said of the gentleman who\nsquared his circle by giving 50 and 49 the same square root, _Il a perdu le\ndroit d'etre frappe de l'evidence_.[217]\n\nIt is Mr. Smith's habit, when he finds a conclusion agreeing with its own\nassumption, to regard that agreement as proof of the assumption. The\nfollowing is the \"piece of information\" which will settle me, if I be\nhonest. Assuming [pi] to be 3-1/8, he finds out by working instance after\ninstance that the mean proportional between one-fifth of the area and\none-fifth of eight is the radius. That is,\n\n  if [pi] = 25/8, sqrt(([pi]r^2)/5 . 8/5) = r.\n\nThis \"remarkable general principle\" may fail to establish Mr. Smith's\nquadrature, even in an honest mind, if that mind should happen to know\nthat, a and b being any two numbers whatever, we need only assume--\n\n  [pi] = a^2/b, to get at sqrt(([pi]r^2)/a . b/a) = r.\n\nWe naturally ask what sort of glimmer can Mr. Smith have of the subject\nwhich he professes to treat? On this point he has given satisfactory\ninformation. I had mentioned the old problem of finding two mean\nproportionals, {119} as a preliminary to the duplication of the cube. On\nthis mention Mr. Smith writes as follows. I put a few words in capitals;\nand I write rq[218] for the sign of the square root, which embarrasses\nsmall type:\n\n\"This establishes the following _infallible_ rule, for finding two mean\nproportionals OF EQUAL VALUE, and is more than a preliminary, to the famous\nold problem of 'Squaring the circle.' Let any finite number, say 20, and\nits fourth part = (1/4)(20) = 5, be given numbers. Then rq(20 x 5) = rq 100 =\n10, is their mean proportional. Let this be a given mean proportional TO\nFIND ANOTHER MEAN PROPORTIONAL OF EQUAL VALUE. Then\n\n  20 x [pi]/4 = 20 x 3.125/4 = 20 x .78125 = 15.625\n\nwill be the first number; as\n\n  25 : 16 :: rq 20 : rq 8.192: and (rq 8.192)^2 x [pi]/4 = 8.192 x .78125 =\n      6.4\n\nwill be the second number; therefore rq(15.625 x 6.4) = rq 100 = 10, is the\nrequired mean proportional.... Now, my good Sir, however competent you may\nbe to prove every man a fool [not _every_ man, Mr. Smith! only _some_; pray\nlearn logical quantification] who now thinks, or in times gone by has\nthought, the 'Squaring of the Circle' _a possibility_; I doubt, and, on the\nevidence afforded by your Budget, I cannot help doubting, whether you were\never before competent to find two mean proportionals _by my unique\nmethod_.\"--(_Nut_, pp. 47, 48.) [That I never was, I solemnly declare!]\n\nAll readers can be made to see the following exposure. When 5 and 20 are\ngiven, x is a mean proportional when in 5, x, 20, 5 is to x as x to 20. And\nx must be 10. But x and y are two mean proportionals when in 5, x, y, 20, x\n{120} is a mean proportional between 5 and y, and y is a mean proportional\nbetween x and 20. And these means are x = 5 [cuberoot]4, y = 5\n[cuberoot]16. But Mr. Smith finds _one_ mean, finds it _again_ in a\nroundabout way, and produces 10 and 10 as the two (equal!) means, in\nsolution of the \"famous old problem.\" This is enough: if more were wanted,\nthere is more where this came from. Let it not be forgotten that Mr. Smith\nhas found a translator abroad, two, perhaps three, followers at home,\nand--most surprising of all--a real mathematician to try to set him right.\nAnd this mathematician did not discover the character of the subsoil of the\nland he was trying to cultivate until a goodly octavo volume of letters had\npassed and repassed. I have noticed, in more quarters than one, an apparent\nwant of perception of the _full_ amount of Mr. Smith's ignorance: persons\nwho have not been in contact with the non-geometrical circle-squarers have\na kind of doubt as to whether anybody can carry things so far. But I am an\n\"old bird\" as Mr. Smith himself calls me; a Simorg, an \"all-knowing Bird of\nAges\" in matters of cyclometry.\n\nThe curious phenomena of thought here exhibited illustrate, as above said,\na remark I have long ago made on the effect of proper study of logic. Most\npersons reason well enough on matter to which they are accustomed, and in\nterms with which they are familiar. But in unaccustomed matter, and with\nuse of strange terms, few except those who are practised in the\nabstractions of pure logic can be tolerably sure to keep their feet. And\none of the reasons is easily stated: terms which are not quite familiar\npartake of the vagueness of the X and Y on which the student of logic\nlearns to see the formal force of a proposition independently of its\nmaterial elements.\n\nI make the following quotation from my fourth paper on logic in the\n_Cambridge Transactions_:\n\n\"The uncultivated reason proceeds by a process almost entirely material.\nThough the necessary law of thought {121} must determine the conclusion of\nthe ploughboy as much as that of Aristotle himself, the ploughboy's\nconclusion will only be tolerably sure when the matter of it is such as\ncomes within his usual cognizance. He knows that geese being all birds does\nnot make all birds geese, but mainly because there are ducks, chickens,\npartridges, etc. A beginner in geometry, when asked what follows from\n'Every A is B,' answers 'Every B is A.' That is, the necessary laws of\nthought, except in minds which have examined their tools, are not very sure\nto work correct conclusions except upon familiar matter.... As the\ncultivation of the individual increases, the laws of thought which are of\nmost usual application are applied to familiar matter with tolerable\nsafety. But difficulty and risk of error make a new appearance with a new\nsubject; and this, in most cases, until new subjects are familiar things,\nunusual matter common, untried nomenclature habitual; that is, until it is\na habit to be occupied upon a novelty. It is observed that many persons\nreason well in some things and badly in others; and this is attributed to\nthe consequence of employing the mind too much upon one or another subject.\nBut those who know the truth of the preceding remarks will not have far to\nseek for what is often, perhaps most often, the true reason.... I maintain\nthat logic tends to make the power of reason over the unusual and\nunfamiliar more nearly equal to the power over the usual and familiar than\nit would otherwise be. The second is increased; but the first is almost\ncreated.\"\n\nMr. James Smith, by bringing ignorance, folly, dishonesty into contact with\nmy name, in the way of conditional insinuation, has done me a good turn: he\nhas given me right to a freedom of personal remark which I might have\ndeclined to take in the case of a person who is useful and respected in\nmatters which he understands.\n\nTit for tat is logic all the world over. By the way, what has become of the\nrest of the maxim: we never hear it {122} now. When I was a boy, in some\nparts of the country at least, it ran thus:\n\n \"Tit for tat;\n  Butter for fat:\n  If you kill my dog,\n  I'll kill your cat.\"\n\nHe is a glaring instance of the truth of the observations quoted above. I\nwill answer for it that, at the Mersey Dock Board, he never dreams of\nproving that the balance at the banker's is larger than that in the book by\nassuming that the larger sum is there, and then proving that the other\nsupposition--the smaller balance--is upon that assumption, an absurdity. He\nnever says to another director, How can you dare to refuse me a right to\nassume the larger balance, when you yourself, the other day,\nsaid,--Suppose, for argument's sake, we had 80,000l. at the banker's,\nthough you knew the book only showed 30,000l.? This is the way in which he\nhas supported his geometrical paradox by Euclid's example: and this is not\nthe way he reasons at the board; I know it by the character of him as a man\nof business which has reached my ears from several quarters. But in\ngeometry and rational arithmetic he is a smatterer, though expert at\ncomputation; at the board he is a trained man of business. The language of\ngeometry is so new to him that he does not know what is meant by \"two mean\nproportionals:\" but all the phrases of commerce are rooted in his mind. He\nis most unerasably booked in the history of the squaring of the circle, as\nthe speculator who took a right to assume a proposition for the destruction\nof other propositions, on the express ground that Euclid assumes a\nproposition to show that it destroys itself: which is as if the curate\nshould demand permission to throttle the squire because St. Patrick drove\nthe vermin to suicide to save themselves from slaughter. He is conspicuous\nas a speculator who, more visibly than almost any other known to history,\nreasoned in a circle by way of reasoning on a circle. But {123} what I have\nchiefly to do with is the force of instance which he has lent to my\nassertion that men who have not had real training in pure logic are unsafe\nreasoners in matter which is not familiar. It is hard to get first-rate\nexamples of this, because there are few who find the way to the printer\nuntil practice and reflection have given security against the grossest\nslips. I cannot but think that his case will lead many to take what I have\nsaid into consideration, among those who are competent to think of the\ngreat mental disciplines. To this end I should desire him to continue his\nefforts, to amplify and develop his great principle, that of proving a\nproposition by assuming it and taking as confirmation every consequence\nthat does not contradict the assumption.\n\nSince my Budget commenced, Mr. Smith has written me notes: the portion\nwhich I have preserved--I suppose several have been mislaid--makes a\nhundred and seven pages of note-paper, closely written. To all this I have\nnot answered one word: but I think I cannot have read fewer than forty\npages. In the last letter the writer informs me that he will not write at\ngreater length until I have given him an answer, according to the \"rules of\ngood society.\" Did I not know that for every inch I wrote back he would\nreturn an ell? Surely in vain the net is spread in the eyes of anything\nthat hath a wing. There were several good excuses for not writing to Mr. J.\nSmith: I will mention five. First, I distinctly announced at the beginning\nof this Budget that I would not communicate with squarers of the circle.\nSecondly, any answer I might choose to give might with perfect propriety be\nreserved for this article; had the imputation of incivility been made after\nthe first note, I should immediately have replied to this effect: but I\npresumed it was quite understood. Thirdly, Mr. Smith, by his publication of\nE. M.'s letters against the wish of the writer, had put himself out of the\npale of correspondence. Fourthly, he had also gone beyond the rules of good\nsociety in sending {124} letter after letter to a person who had shown by\nhis silence an intention to avoid correspondence. Fifthly, these same rules\nof good society are contrived to be flexible or frangible in extreme cases:\notherwise there would be no living under them; and good society would be\nbad. Father Aldrovand has laid down the necessary distinction--\"I tell\nthee, thou foolish Fleming, the text speaketh but of promises made unto\nChristians, and there is in the rubric a special exemption of such as are\nmade to Welchmen.\" There is also a rubric to the rules of good society; and\nsquarers of the circle are among those whom there is special permission not\nto answer: they are the wild Welchmen of geometry, who are always\nassailing, but never taking, the Garde Douloureuse[219] of the circle. \"At\nthis commentary,\" proceeds the story, \"the Fleming grinned so broadly as to\nshow his whole case of broad strong white teeth.\" I know not whether the\nWelchman would have done the like, but I hope Mr. James Smith will: and I\nhope he has as good a case to show as Wilkin Flammock. For I wish him long\nlife and long health, and should be very glad to see so much energy\nemployed in a productive way. I hope he wishes me the same: if not, I will\ngive him what all his judicious friends will think a good reason for doing\nso. His pamphlets and letters are all tied up together, and will form a\ncurious lot when death or cessation of power to forage among book-shelves\nshall bring my little library to the hammer. And this time may not be far\noff: for I was X years old in A.D. X^2; not 4 in A.D. 16, nor 5 in A.D. 25,\nbut still in one case under that law. And now I have made my own age a\nproblem of quadrature, and Mr. J. Smith may solve it. But I protest against\nhis method of assuming a result, and making itself prove itself: he might\nin this way, as sure as eggs is eggs (a corruption of X is X), make me\n1,864 years old, which is a great deal too much.\n\n{125}\n\n_April 5, 1864._--Mr. Smith continues to write me long letters, to which he\nhints that I am to answer. In his last, of 31 closely written sides of\nnote-paper, he informs me, with reference to my obstinate silence, that\nthough I think myself and am thought by others to be a mathematical\nGoliath, I have resolved to play the mathematical snail, and keep within my\nshell. A mathematical _snail_! This cannot be the thing so called which\nregulates the striking of a clock; for it would mean that I am to make Mr.\nSmith sound the true time of day, which I would by no means undertake upon\na clock that gains 19 seconds odd in every hour by false quadrature. But he\nventures to tell me that pebbles from the sling of simple truth and common\nsense will ultimately crack my shell, and put me _hors de combat_.[220] The\nconfusion of images is amusing: Goliath turning himself into a snail to\navoid [pi] = 3-1/8, and James Smith, Esq., of the Mersey Dock Board: and\nput _hors de combat_--which should have been _cache_[221]--by pebbles from\na sling. If Goliath had crept into a snail-shell, David would have cracked\nthe Philistine with his foot. There is something like modesty in the\nimplication that the crack-shell pebble has not yet taken effect; it might\nhave been thought that the slinger would by this time have been singing--\n\n \"And thrice [and one-eighth] I routed all my foes,\n  And thrice [and one-eighth] I slew the slain.\"\n\nBut he promises to give the public his nut-cracker if I do not, before the\nBudget is concluded, \"unravel\" the paradox, which is the\nmathematico-geometrical nut he has given me to crack. Mr. Smith is a crack\nman: he will crack his own nut; he will crack my shell; in the mean time he\ncracks himself up. Heaven send he do not crack himself into lateral\ncontiguity with himself.\n\nOn June 27 I received a letter, in the handwriting of Mr. James Smith,\nsigned Nauticus. I have ascertained {126} that one of the letters to the\n_Athenaeum_ signed Nauticus is in the same handwriting. I make a few\nextracts:\n\n\"... The important question at issue has been treated by a brace of\nmathematical birds with too much levity. It may be said, however, that\nsarcasm and ridicule sometimes succeed, where reason fails.... Such a\ncourse is not well suited to a discussion.... For this reason I shall for\nthe future [this implies there has been a past, so that Nauticus is not\nbefore me for the first time] endeavor to confine myself to dry reasoning\nfrom incontrovertible premises.\n\n... It appears to me that so far as his theory is concerned he comes off\nunscathed. You might have found \"a hole in Smith's circle\" (have you seen a\npamphlet bearing this title? [I never heard of it until now]), but after\nall it is quite possible the hole may have been left by design, for the\npurpose of entrapping the unwary.\"\n\n[On the publication of the above, the author of the pamphlet obligingly\nforwarded a copy to me of _A Hole in Smith's Circle_--by a Cantab: Longman\nand Co., 1859, (pp. 15). \"It is pity to lose any fun we can get out of the\naffair,\" says my almamaternal brother: to which I add that in such a case\nwarning without joke is worse than none at all, as giving a false idea of\nthe nature of the danger. The Cantab takes some absurdities on which I have\nnot dwelt: but there are enough to afford a Cantab from every college his\nown separate hunting ground.]\n\nDoes this hint that his mode of proof, namely, assuming the thing to be\nproved, was a design to entrap the unwary? if so, it bangs Banagher. Was\nhis confounding two mean proportionals with one mean proportional found\ntwice over a trick of the same intent? if so, it beats cockfighting. That\nNauticus is Mr. Smith appears from other internal evidence. In 1819, Mr.\nJ. C. Hobhouse[222] was sent to Newgate for a {127} libel on the House of\nCommons which was only intended for a libel on Lord Erskine.[223] The\nex-Chancellor had taken Mr. Hobhouse to be thinking of him in a certain\nsentence; this Mr. Hobhouse denied, adding, \"There is but one man in the\ncountry who is always thinking of Lord Erskine.\" I say that there is but\none man of our day who would couple me and Mr. James Smith as a \"brace of\nmathematical birds.\"\n\nMr. Smith's \"theory\" is unscathed by me. Not a doubt about it: but how does\nhe himself come off? I should never think of refuting a theory proved by\nassumption of itself. I left Mr. Smith's [pi] untouched: or, if I put in my\nthumb and pulled out a plum, it was to give a notion of the cook, not of\nthe dish. The \"important question at issue\" was not the circle: it was,\nwholly and solely, whether the abbreviation of _James_ might be spelled\n_Jimm_.[224] This is personal to the verge of scurrility: but in literary\ncontroversy the challenger names the weapons, and Mr. Smith begins with\ncharge of ignorance, folly, and dishonesty, by conditional implication. So\nthat the question is, not the personality of a word, but its applicability\nto the person designated: it is enough if, as the Latin grammar has it,\n_Verbum personale concordat cum nominativo_.[225]\n\nI may plead precedent for taking a liberty with the orthography of _Jem_.\nAn instructor of youth was scandalized at the abrupt and irregular--but\nvery effective--opening of Wordsworth's little piece:\n\n{128}\n\n         \"A simple child\n  That lightly draws its breath,\n  And feels its life in every limb,\n  What should it know of death?\"\n\nSo he mended the matter by instructing his pupils to read the first line\nthus:\n\n \"A simple child, dear brother ----.\"\n\nThe brother, we infer from sound, was to be James, and the blank must\ntherefore be filled up with _Jimb_.\n\nI will notice one point of the letter, to make a little more distinction\nbetween the two birds. Nauticus lays down--quite correctly--that the sine\nof an angle is less than its circular measure. He then takes 3.1416 for\n180 deg., and finds that 36' is .010472. But this is exactly what he finds\nfor the sine of 36' in tables: he concludes that either 3.1416 or the\ntables must be wrong. He does not know that sines, as well as [pi], are\ninterminable decimals, of which the tables, to save printing, only take in\na finite number. He is a six-figure man: let us go thrice again to make up\nnine, and we have as follows:\n\n  Circular measure of 36'         .010471975...\n  Sine of 36'                     .010471784...\n  Excess of measure over sine     .000000191...\n\nMr. Smith invites me to say which is wrong, the quadrature, or the tables:\nI leave him to guess. He says his assertions \"arise naturally and\nnecessarily out of the arguments of a circle-squarer:\" he might just as\nwell lay down that all the pigs went to market because it is recorded that\n\"_This_ pig went to market.\" I must say for circle-squarers that very few\nbring their pigs to so poor a market. I answer the above argument because\nit is, of all which Mr. James Smith has produced, the only one which rises\nto the level of a schoolboy: to meet him halfway I descend to that level.\n\nMr. Smith asks me to solve a problem in the _Athenaeum_: {129} and I will do\nit, because the question will illustrate what is _below_ schoolboy level.\n\n\"Let x represent the circular measure of an angle of 15 deg., and y half\nthe sine of an angle of 30 deg. = area of the square on the radius of a\ncircle of diameter unity = .25. If x - y = xy, firstly, what is the\narithmetical value of xy? secondly, what is the angle of which xy\nrepresents the circular measure?\"\n\nIf x represent 15 deg. and y be 1/4, xy represents 3 deg. 45', whether\nx - y be xy or no. But, y being 1/4, x - y is _not_ xy unless x be 1/3,\nthat is, unless 12x or [pi] be 4, which Mr. Smith would not admit. How\ncould a person who had just received such a lesson as I had given\nimmediately pray for further exposure, furnishing the stuff so liberally\nas this? Is it possible that Mr. Smith, because he signs himself\nNauticus, means to deny his own very regular, legible, and peculiar\nhand? It is enough to make the other members of the Liverpool Dock Board\ncry, Mersey on the man!\n\nMr. Smith says that for the future he will give up what he calls sarcasm,\nand confine himself, \"as far as possible,\" to what he calls dry reasoning\nfrom incontrovertible premises. If I have fairly taught him that _his_\nsarcasm will not succeed, I hope he will find that his wit's end is his\nlogic's beginning.\n\nI now reply to a question I have been asked again and again since my last\nBudget appeared: Why do you take so much trouble to expose such a reasoner\nas Mr. Smith? I answer as a deceased friend of mine used to answer on like\noccasions--A man's capacity is no measure of his power to do mischief. Mr.\nSmith has untiring energy, which does something; self-evident honesty of\nconviction, which does more; and a long purse, which does most of all. He\nhas made at least ten publications, full of figures which few readers can\ncriticize. A great many people are staggered to this extent, that they\nimagine there must be {130} the indefinite _something_ in the mysterious\n_all this_. They are brought to the point of suspicion that the\nmathematicians ought not to treat \"all this\" with such undisguised\ncontempt, at least. Now I have no fear for [pi]: but I do think it possible\nthat general opinion might in time demand that the crowd of\ncircle-squarers, etc. should be admitted to the honors of opposition; and\nthis would be a time-tax of five per cent., one man with another, upon\nthose who are better employed. Mr. James Smith may be made useful, in hands\nwhich understand how to do it, towards preventing such opinion from\ngrowing. A speculator who expressly assumes what he wants to prove, and\nargues that all which contradicts it is absurd, _because_ it cannot stand\nside by side with his assumption, is a case which can be exposed to all.\nAnd the best person to expose it is one who has lived in the past as well\nas the present, who takes misthinking from points of view which none but a\nstudent of history can occupy, and who has something of a turn for the\nbusiness.\n\nWhether I have any motive but public good must be referred to those who can\ndecide whether a missionary chooses his pursuit solely to convert the\nheathen. I shall certainly be thought to have a little of the spirit of\nCol. Quagg, who delighted in strapping the Grace-walking Brethren. I must\nquote this myself: if I do not, some one else will, and then where am I?\nThe Colonel's principle is described as follows:\n\n\"I licks ye because I kin, and because I like, and because ye'se critters\nthat licks is good for. Skins ye have on, and skins I'll have off; hard or\nsoft, wet or dry, spring or fall. Walk in grace if ye like till pumpkins is\npeaches; but licked ye must be till your toe-nails drop off and your noses\nbleed blue ink. And--licked--they--were--accordingly.\"\n\nI am reminded of this by the excessive confidence with which Mr. James\nSmith predicted that he would treat me as Zephaniah Stockdolloger (Sam\nSlick calls it _slockdollager_) treated Goliah Quagg. He has announced his\n{131} intention of bringing me, with a contrite heart, and clean\nshaved,--4159265... razored down to 25,--to a camp-meeting of\ncircle-squarers. But there is this difference: Zephaniah only wanted to\npass the Colonel's smithy in peace; Mr. James Smith sought a fight with me.\nAs soon as this Budget began to appear, he oiled his own strap, and\nattempted to treat me as the terrible Colonel would have treated the\ninoffensive brother.\n\nHe is at liberty to try again.\n\n\n\nTHE MOON HOAX.\n\n    The Moon-hoax; or the discovery that the moon has a vast population of\n    human beings. By Richard Adams Locke.[226] New York, 1859, 8vo.\n\nThis is a reprint of the hoax already mentioned. I suppose R. A. Locke is\nthe name assumed by M. Nicollet.[227] The publisher informs us that when\nthe hoax first appeared day by day in a morning paper, the circulation\nincreased fivefold, and the paper obtained a permanent footing. Besides\nthis, an edition of 60,000 was sold off in less than one month.\n\nThe discovery was also published under the name of A. R. Grant.[228]\nSohncke's[229] _Bibliotheca Mathematica_ confounds this Grant with Prof. R.\nGrant[230] of Glasgow, the author of the _History of Physical Astronomy_,\nwho is accordingly made to guarantee the discoveries in the moon. I hope\nAdams Locke will not merge in J. C. Adams,[231] the co-discoverer of\nNeptune. Sohncke gives the titles of {132} three French translations of the\nMoon hoax at Paris, of one at Bordeaux, and of Italian translations at\nParma, Palermo, and Milan.\n\nA Correspondent, who is evidently fully master of details, which he has\ngiven at length, informs me that the Moon hoax appeared first in the _New\nYork Sun_, of which R. A. Locke was editor. It so much resembled a story\nthen recently published by Edgar A. Poe, in a Southern paper, \"Adventures\nof Hans Pfaal,\" that some New York journals published the two side by side.\nMr. Locke, when he left the _New York Sun_, started another paper, and\ndiscovered the manuscript of Mungo Park;[232] but this did not deceive. The\n_Sun_, however, continued its career, and had a great success in an account\nof a balloon voyage from England to America, in seventy-five hours, by Mr.\nMonck Mason,[233] Mr. Harrison Ainsworth,[234] and others. I have no doubt\nthat M. Nicollet was the author of the Moon hoax,[235] written in a way\nwhich marks the practised observatory astronomer beyond all doubt, and by\nevidence seen in the most minute details. Nicollet had an eye to Europe. I\nsuspect that he took Poe's story, and made it a basis for his own. Mr.\nLocke, it would seem, when he attempted a fabrication for himself, did not\nsucceed.\n\n\n\n    The Earth we inhabit, its past, present, and future. By Capt.\n    Drayson.[236] London, 1859, 8vo.\n\nThe earth is growing; absolutely growing larger: its diameter increases\nthree-quarters of an inch per mile every year. The foundations of our\nbuildings will give way in {133} time: the telegraph cables break, and no\ncause ever assigned except ships' anchors, and such things. The book is for\nthose whose common sense is unwarped, who can judge evidence as well as the\nablest philosopher. The prospect is not a bad one, for population increases\nso fast that a larger earth will be wanted in time, unless emigration to\nthe Moon can be managed, a proposal of which it much surprises me that\nBishop Wilkins has a monopoly.\n\n\n\nIMPALEMENT BY REQUEST.\n\n_Athenaeum_, August, 19, 1865. _Notice to Correspondents._\n\n\"R. W.--If you will consult the opening chapter of the Budget of Paradoxes,\nyou will see that the author presents only works in his own library at a\ngiven date; and this for a purpose explained. For ourselves we have\ncarefully avoided allowing any writers to present themselves in our columns\non the ground that the Budget has passed them over. We gather that Mr. De\nMorgan contemplates additions at a future time, perhaps in a separate and\naugmented work; if so, those who complain that others of no greater claims\nthan themselves have been ridiculed may find themselves where they wish to\nbe. We have done what we can for you by forwarding your letter to Mr. De\nMorgan.\"\n\nThe author of \"An Essay on the Constitution of the Earth,\" published in\n1844, demanded of the _Athenaeum_, as an _act of fairness_, that a letter\nfrom him should be published, proving that he had as much right to be\n\"impaled\" as Capt. Drayson. He holds, on speculative grounds, what the\nother claims to have proved by measurement, namely, that the earth is\ngrowing; and he believes that in time--a good long time, not _our_\ntime--the earth and other planets may grow into suns, with systems of their\nown.\n\nThis gentleman sent me a copy of his work, after the commencement of my\nBudget; but I have no recollection of having received it, and I cannot find\nit on the (nursery? {134} quarantine?) shelves on which I keep my\nunestablished discoveries. Had I known of this work in time, (see the\nIntroduction) I should of course, have impaled it (heraldically) with the\nother work; but the two are very different. Capt. Drayson professes to\nprove his point by results of observation; and I think he does not succeed.\nThe author before me only speculates; and a speculator can get any\nconclusion into his premises, if he will only build or hire them of shape\nand size to suit. It reminds me of a statement I heard years ago, that a\nscore of persons, or near it, were to dine inside the skull of one of the\naboriginal animals, dear little creatures! Whereat I wondered vastly,\nnothing doubting; facts being stubborn and not easy drove, as Mrs. Gamp\nsaid. But I soon learned that the skull was not a real one, but\nartificially constructed by the methods--methods which have had striking\nverifications, too--which enable zoologists to go the whole hog by help of\na toe or a bit of tail. This took off the edge of the wonder: a hundred\npeople can dine inside an inference, if you draw it large enough. The\nmethod might happen to fail for once: for instance, the toe-bone might have\nbeen abnormalized by therian or saurian malady; and the possibility of such\nfailure, even when of small probability, is of great alleviation. The\nauthor before me is, apparently, the sole fabricator of his own premises.\nWith vital force in the earth and continual creation on the part of the\noriginal Creator, he expands our bit of a residence as desired. But, as the\nNewtoness of Cookery observed, First catch your hare. When this is done,\nwhen you _have_ a growing earth, you shall dress it with all manner of\nproximate causes, and serve it up with a growing Moon for sauce, a growing\nSun, if it please you, at the other end, and growing planets for\nside-dishes. Hoping this amount of impalement will be satisfactory, I go on\nto something else. {135}\n\n\n\nTHE HAILESEAN SYSTEM OF ASTRONOMY.\n\n    _The Hailesean System of Astronomy._ By John Davey Hailes[237] (two\n    pages duodecimo, 1860).\n\nHe offers to _take_ 100,000l. to 1,000l. that he shows the sun to be less\nthan seven millions of miles from the earth. The earth in the center,\nrevolving eastward, the sun revolving westward, so that they \"meet at half\nthe circle distance in the 24 hours.\" The diameter of the circle being\n9839458303, the circumference is 30911569920.\n\nThe following written challenge was forwarded to the Council of the\nAstronomical Society: it will show the \"general reader\"--and help him\ntowards earning his name--what sort of things come every now and then to\nour scientific bodies. I have added punctuation:\n\n                  _Challenge._\n                  1,000 to 30,000.\n \"Leverrier's[238] name stand placed first. Do the worthy Frenchman\n     justice.\n  By awarding him the medal in a trice.\n  Give Adams[239] an extra--of which neck and neck the race.\n  Now I challenge to meet them and the F.R.S.'s all,\n  For good will and _one_ thousand pounds to their _thirty_ thousand\n      withall,\n  That I produce a system, which shall measure the time,\n  When the Sun was vertical to Gibeon, afterward to Syene.\n  To meet any time in London--name your own period,\n  To be decided by a majority of twelve persons--a President, _odd_.\n  That mean, if the twelve equally divide, the President decide,\n  I should prefer the Bishop of London, over the meeting to preside.\n                                JOHN DAVY HAILES.\"\n  Feb. 17, 1847.\"\n\nMr. Hailes still issues his flying sheets. The last I have met with\n(October 7, 1863) informs us that the latitude of {136} England is slowly\nincreasing, which is the true cause of the alteration in the variation of\nthe magnet.\n\n[Mr. Hailes continues his researches. Witness his new Hailesean system of\nAstronomy, displaying Joshua's miracle-time, origin of time from science,\nwith Bible and Egyptian history. Rewards offered for astronomical problems.\nWith magnetism, etc. etc. Astronomical challenge to all the world.\nPublished at Cambridge, in 1865. The author agrees with Newton in one\nmarked point. _Errores quam minimi non sunt contemnendi_,[240] says Isaac:\nmeaning in figures, not in orthography. Mr. Hailes enters into the spirit,\nboth positive and negative, of this dictum, by giving the distance of\n_Sidius_ from the center of the earth at 163,162,008 miles 10 feet 8 inches\n17-28ths of an inch. Of course, he is aware that the center of _figure_ of\nthe earth is 17.1998 inches from the center of _gravity_. Which of the two\nis he speaking of?]\n\n\n\n    The Divine Mystery of Life. London [1861], 18mo. (pp.32).\n\nThe author has added one class to zoology, which is printed in capitals, as\nderived from _zoe_, life, not from _zoon_, animal. That class is of\n_Incorporealia_, order I., _Infinitum_, of one genus without plurality,\n_Deus_: order II., _Finita_, angels good and evil. The rest is all about a\ntriune system, with a diagram. The author is not aware that [Greek: zoon]\nis not _animal_, but _living being_. Aristotle had classed gods under\n[Greek: zoa], and has been called to account for it by moderns who have\ntaken the word to mean _animal_.\n\n\n\nA CHANCE FOR INVENTORS.\n\n    Explication du Zodiaque de Denderah, des Pyramides, et de Genese. Par\n    le Capitaine au longcours Justin Roblin.[241] Caen, 1861. 8vo.\n\n{137}\n\nCapt. Roblin, having discovered the sites of gold and diamond mines by help\nof the zodiac of Denderah, offered half to the shareholders of a company\nwhich he proposed to form. One of our journals, by help of the zodiac of\nEsne, offered, at five francs a head, to tell the shareholders the exact\namount of gold and diamonds which each would get, and to make up the amount\npredicted to those who got less. There are moods of the market in England\nin which this company could have been formed: so we must not laugh at our\nneighbors.\n\n\n\nJOHANNES VON GUMPACH.\n\n    A million's worth of property, and five hundred lives annually lost at\n    sea by the Theory of Gravitation. A letter on the true figure of the\n    earth, addressed to the Astronomer Royal, by Johannes von Gumpach.[242]\n    London, 1861, 8vo. (pp. 54).\n\n    The true figure and dimensions of the earth, in a letter addressed to\n    the Astronomer Royal. By Joh. von Gumpach. 2nd ed. entirely recast.\n    London, 1862, 8vo. (pp. 266).\n\n    Two issues of a letter published with two different title-pages, one\n    addressed to the Secretary of the Royal Society, the other to the\n    Secretary of the Royal Astronomical Society. It would seem that the\n    same letter is also issued with two other titles, addressed to the\n    British Association and the Royal Geographical Society. By Joh. von\n    Gumpach. London, 1862, 8vo.\n\n    Baby-Worlds. An essay on the nascent members of our solar household. By\n    Joh. von Gumpach. London, 1863, 8vo.\n\nThe earth, it appears, instead of being flattened, is elongated at the\npoles: by ignorance of which the loss above mentioned occurs yearly. There\nis, or is to be, a substitute for attraction and an \"application hitherto\nneglected, of a {138} recognized law of optics to the astronomical theory,\nshowing the true orbits of the heavenly bodies to be perfectly circular,\nand their orbital motions to be perfectly uniform.\" all irregularities\nbeing, I suppose, optical delusions. Mr. Von Gumpach is a learned man; what\nelse, time must show.\n\n\n\nSLANDER PARADOXES.\n\n    Perpetuum Mobile: or Search for self-motive Power. By Henry\n    Dircks.[243] London, 1861, 8vo.\n\nA useful collection on the history of the attempts at perpetual motion,\nthat is, at obtaining the consequences of power without any power to\nproduce them. September 7, 1863, a correspondent of the _Times_ gave an\nanecdote of George Stephenson,[244] which he obtained from Robert\nStephenson.[245] A perpetual motionist wanted to explain his method; to\nwhich George replied--\"Sir! I shall believe it when I see you take yourself\nup by the waistband, and carry yourself about the room.\" Never was the\nproblem better stated.\n\nThere is a paradox of which I ought to give a specimen, I mean the\n_slander-paradox_; the case of a person who takes it into his head, upon\nevidence furnished entirely by the workings of his own thoughts, that some\nother person has committed a foul act of which the world at large would no\nmore suppose him guilty than they would suppose that the earth is a flat\nbordered by ice. If I were to determine on giving cases in which the\nself-deluded person imagines {139} a conspiracy against _himself_, there\nwould be no end of choices. Many of the grosser cases are found at last to\nbe accompanied by mental disorder, and it is difficult to avoid referring\nthe whole class to something different from simple misuse of the reasoning\npower. The first instance is one which puts in a strong light the state of\nthings in which we live, brought about by our glorious freedom of thought,\nspeech, and writing. The Government treated it with neglect, the press with\nsilent contempt, and I will answer for it many of my readers now hear of it\nfor the first time, when it comes to be enrolled among circle-squarers and\nearth-stoppers, where, as the old philosopher said, it will not gravitate,\nbeing _in proprio loco_.[246]\n\n1862. On new year's day, 1862, when the nation was in the full tide of\nsympathy with the Queen, and regret for its own loss, a paper called the\n_Free Press_ published a number devoted to the consideration of the causes\nof the death of the Prince Consort. It is so rambling and inconsecutive\nthat it takes more than one reading to understand it. It is against the\n_Times_ newspaper. First, the following insinuation:\n\n\"To the legal mind, the part of [the part taken by] the _Times_ will\npresent a _prima facie_ case of the gravest nature, in the evident\nfore-knowledge of the event, and the preparation to turn it to account when\nit should have occurred. The article printed on Saturday must have been\nwritten on Friday. That article could not have appeared had the Prince been\nintended to live.\"\n\nNext, it is affirmed that the _Times_ intended to convey the idea that the\nPrince had been poisoned.\n\n\"Up to this point we are merely dealing with words which the _Times_\npublishes, and these can leave not a shadow of doubt that there is an\nintention to promulgate the idea that Prince Albert had been poisoned.\"\n\nThe article then goes on with a strange olio of {140} insinuations to the\neffect that the Prince was the obstacle to Russian intrigue, and that if he\nshould have been poisoned,--which the writer strongly hints may have been\nthe case,--some Minister under the influence of Russia must have done it.\nEnough for this record. _Un sot trouve toujours un plus sot qui\nl'admire_:[247] who can he be in this case?\n\n\n\nTHE NEPTUNE CONTROVERSY.\n\n1846. At the end of this year arose the celebrated controversy relative to\nthe discovery of Neptune. Those who know it are well aware that Mr.\nAdams's[248] now undoubted right to rank with Le Verrier[249] was made sure\nat the very outset by the manner in which Mr. Airy,[250] the Astronomer\nRoyal, came forward to state what had taken place between himself and Mr.\nAdams. Those who know all the story about Mr. Airy being arrested in his\nprogress by the neglect of Mr. Adams to answer a letter, with all the\nimputations which might have been thrown upon himself for laxity in the\nmatter, know also that Mr. Airy's conduct exhibited moral courage, honest\nfeeling, and willingness to sacrifice himself, if need were, to the\nattainment of the ends of private justice, and the establishment of a\nnational claim. A writer in a magazine, in a long and elaborate article,\nargued the supposition--put in every way except downright assertion, after\nthe fashion of such things--that Mr. Airy had communicated Mr. Adams's\nresults to M. Le Verrier, with intention that they should be used. His\npresumption as to motive is that, had Mr. Adams been recognized, \"then the\ndiscovery must have been indisputably an _Englishman's_, and that\nEnglishman not the Astronomer Royal.\" Mr. Adams's conclusions were\n\"retouched in France, and sent {141} over the year after.\" The proof given\nis that it cannot be \"imagined\" otherwise.\n\n\"Can it then be imagined that the Astronomer Royal received such results\nfrom Mr. Adams, supported as they were by Professor Challis's[251] valuable\ntestimony as to their probable accuracy, and did not bring the French\nastronomer acquainted with them, especially as he was aware that his friend\nwas engaged in matters bearing directly upon these results?\"\n\nThe whole argument the author styles \"evidence which I consider it\ndifficult to refute.\" He ends by calling upon certain persons, of whom I am\none, to \"see ample justice done.\" This is the duty of every one, according\nto his opportunities. So when the reputed author--the article being\nanonymous--was, in 1849, proposed as a Fellow of the Astronomical Society,\nI joined--if I remember right, I originated--an opposition to his election,\nuntil either the authorship should be denied, or a proper retraction made.\nThe friends of the author neither denied the first, nor produced the\nsecond: and they judged it prudent to withdraw the proposal. Had I heard of\nany subsequent repentance, I would have taken some other instance, instead\nof this: should I yet hear of such a thing, I will take care to notice it\nin the continuation of this list, which I confidently expect, life and\nhealth permitting, to be able to make in a few years. This much may be\nsaid, that the author, in a lecture on the subject, given in 1849, and\npublished with his name, did _not_ repeat the charge.\n\n[The libel was published in the _Mechanics' Magazine_,[252] (vol. for 1846,\npp. 604-615): and the editor supported it as follows, (vol. for 1847, p.\n476). In answer to Mr. Sheepshanks's charitable hope that he had been\nhoaxed, {142} he says: \"Mr. Sheepshanks cannot certainly have read the\narticle referred to.... Severe and inculpatory it is--unjust some may deem\nit (though we ourselves are out of the number.)... A 'hoax' forsooth! May\nwe be often the dupes of such hoaxes!\" He then goes on to describe the\narticle as directed against the Astronomer Royal's alleged neglect to give\nMr. Adams that \"encouragement and protection\" which was his due, and _does\nnot hint one word_ about the article containing the charge of having\nsecretly and fraudulently transmitted news of Mr. Adams's researches to\nFrance, that an Englishman might not have the honor of the discovery. Mr.\nSheepshanks having called this a \"deliberate calumny,\" without a particle\nof proof or probability to support it, the editor says \"what the reverend\ngentleman means by this, we are at a loss to understand.\" He then proceeds\n_not_ to remember. I repeat here, what I have said elsewhere, that the\nmanagement of the journal has changed hands; but from 1846 to 1856, it had\nthe collar of S.S. (scientific slander). The prayer for more such things\nwas answered (See p. 349).]\n\n\n\nJAMES IVORY.[253]\n\nI have said that those who are possessed with the idea of conspiracy\nagainst themselves are apt to imagine both conspirators and their bad\nmotives and actions. A person who should take up the idea of combination\nagainst himself without feeling ill-will and originating accusations would\nbe indeed a paradox. But such a paradox has existed. It is very well known,\nboth in and beyond the scientific world, that the late James Ivory was\nsubject to the {143} impression of which I am speaking; and the diaries and\nother sources of anecdote of our day will certainly, sooner or later, make\nit a part of his biography. The consequence will be that to his memory will\nbe attached the unfavorable impression which the usual conduct of such\npersons creates; unless it should happen that some one who knows the real\nstate of the case puts the two sides of it properly together. Ivory was of\nthat note in the scientific world which may be guessed from Laplace's\ndescription of him as the first geometer in Britain and one of the first in\nEurope. Being in possession of accurate knowledge of his peculiarity in\nmore cases than one; and in one case under his own hand: and having been\nable to make full inquiry about him, especially from my friend the late\nThomas Galloway[254]--who came after him at Sandhurst--one of the few\npersons with whom he was intimate:--I have decided, after full\ndeliberation, to forestall the future biographies.\n\nThat Ivory was haunted by the fear of which I have spoken, to the fullest\nextent, came to my own public and official knowledge, as Secretary of the\nAstronomical Society. It was the duty of Mr. Epps,[255] the Assistant\nSecretary, at the time when Francis Baily[256] first announced his\ndiscovery of the Flamsteed Papers, to report to me that Mr. Ivory had\ncalled at the Society's apartments to inquire into the contents of those\npapers, and to express his hope that Mr. Baily was not attacking living\npersons under the names of Newton and Flamsteed.[257] Mr. Galloway, to whom\nI communicated this, immediately went to Mr. Ivory, and succeeded, after\nsome explanation, in setting him right. This is but one of many instances\nin which a man of thoroughly sound judgment in every other respect seemed\nto be under a complete chain of delusions about the conduct of {144} others\nto himself. But the paradox is this:--I never could learn that Ivory,\npassing his life under the impression that secret and unprovoked enemies\nwere at work upon his character, ever originated a charge, imputed a bad\nmotive, or allowed himself an uncourteous expression. Some letters of his,\nnow in my possession, referring to a private matter, are, except in the\nmain impression on which they proceed, unobjectionable in every point: they\nmight have been written by a cautious friend, whose object was, if\npossible, to prevent a difference from becoming a duel without compromising\nhis principal's rights or character. Knowing that in some quarters the\nknowledge of Ivory's peculiarity is more or less connected with a notion\nthat the usual consequences followed, I think the preceding statement due\nto his memory.\n\n\n\nTHREE CLASSES OF JOURNALS.\n\nIn such a record as the present, which mixes up the grossest speculative\nabsurdities with every degree of what is better, an instance of another\nkind may find an appropriate place. The faults of journalism, when merely\nexposed by other journalism pass by and are no more regarded. A distinct\naccount of an undeniable meanness, recorded in a work of amusement and\nreference both, may have its use: such a thing may act as a warning. An\neditor who is going to indulge his private grudge may be prevented from\ncounting upon oblivion as a matter of certainty.\n\nThere are three kinds of journals, with reference to the mode of entrance\nof contributors. First, as a thing which has been, but which now hardly\nexists, there is the journal in which the editor receives a fixed sum to\n_find the matter_. In such a journal, every article which the editor can\nget a friend to give him is so much in his own pocket, which has a great\ntendency to lower the character of the articles; but I am not concerned\nwith this point. Secondly, there is the journal which is supported by\nvoluntary contributions of {145} matter, the editor selecting. Thirdly,\nthere is the journal in which the contributor is paid by the proprietors in\na manner with which the literary editor has nothing to do.\n\nThe third class is the safe class, as its editors know: and, as a usual\nrule, they refuse unpaid contributions of the editorial cast. It is said\nthat when Canning[258] declined a cheque forwarded for an article in the\n_Quarterly_, John Murray[259] sent it back with a blunt threat that if he\ndid not take his money he could never be admitted again. The great\npublisher told him that if men like himself in position worked for nothing,\nall the men like himself in talent who could not afford it would not work\nfor the _Quarterly_. If the above did not happen between Canning and\nMurray, it _must have happened_ between some other two. Now journals of the\nsecond class--and of the first, if such there be--have a fault to which\nthey alone are very liable, to say nothing of the editorial function (see\nthe paper at the beginning, p. 11 et seq.), being very much cramped, a sort\nof gratitude towards effective contributors leads the journal to help their\npersonal likes and dislikes, and to sympathize with them. Moreover, this\nsort of journal is more accessible than others to articles conveying\npersonal imputation: and when these provoke discussion, the journal is apt\nto take the part of the assailant to whom it lent itself in the first\ninstance.\n\n\n\nTHE MECHANICS' MAGAZINE.\n\nAmong the journals which went all lengths with contributors whom they\nvalued, was the _Mechanics' Magazine_[260] in the period 1846-56. I cannot\nsay that matters have not mended in the last ten years: and I draw some\n{146} presumption that they have mended from my not having heard, since\n1856, of anything resembling former proceedings. And on actual inquiry,\nmade since the last sentence was written, I find that the property has\nchanged hands, the editor is no longer the same, and the management is of a\ndifferent stamp. This journal is chiefly supported by voluntary articles:\nand it is the journal in which, as above noted, the ridiculous charge\nagainst the Astronomer Royal was made in 1849. The following instance of\nattempt at revenge is so amusing that I select it as the instance of the\ndefect which I intend to illustrate; for its puerility brings out in better\nrelief the points which are not so easily seen in more adult attempts.\n\nThe _Mechanics' Magazine_, which by its connection with engineering, etc.,\nhad always taken somewhat of a mathematical character, began, a little\nbefore 1846, to have more to do with abstract science. Observing this, I\nbegan to send short communications, which were always thankfully received,\ninserted, and well spoken of. Any one who looks for my name in that journal\nin 1846-49, will see nothing but the most respectful and even laudatory\nmention. In May 1849 occurred the affair at the Astronomical Society, and\nmy share in forcing the withdrawal of the name of the alleged contributor\nto the journal. In February 1850 occurred the opportunity of payment. The\n_Companion to the Almanac_[261] had to be noticed, in which, as then usual,\nwas an article signed with my name. I shall give the review of this article\nentire, as a sample of a certain style, as well as an illustration of my\npoint. The reader will observe that my name is not mentioned. This would\nnot have done; the readers of the Magazine would have stared to see a name\nof not infrequent occurrence in previous years all of a sudden fallen from\nthe heaven of respect into the pit of contempt, like Lucifer, son of the\nmorning. But before {147} giving the review, I shall observe that Mr.\nAdams, in whose _favor_ the attack on the Astronomer Royal was made, did\nnot appreciate the favor; and of course did not come forward to shield his\nchampion. This gave deadly offence, as appear from the following passage,\n(February 16, 1850):\n\n\"It was our intention to enter into a comparison of the contents of our\nNautical Almanack with those of its rival, the _Connaissance des Temps_;\nbut we shall defer it for the present. The Nautical Almanack for 1851 will\ncontain Mr. Adams's paper 'On the Perturbation of Uranus'; and when it\ncomes, in due course, before the public, we are quite sure that that\ngentleman will expect that we shall again enter upon the subject with\npeculiar delight. Whilst we have a thorough loathing for mean, cowardly,\ncrawlers--we have an especial pleasure in maintaining the claims of men who\nare truly grateful as well as highly talented: Mr. Adams, therefore, will\nfind that he cannot be disappointed--and the occasion will afford us an\nopportunity for making the comparison to which we have adverted.\"\n\nThis passage illustrates what I have said on the editorial function (Vol.\nI, p. 15). What precedes and follows has some criticism on the Government,\nthe Astronomer Royal, etc., but reserved in allusion, oblique in sarcasm,\nand not fiercely uncourteous. The coarseness of the passage I have quoted\nshows editorial insertion, which is also shown by its blunder. The inserter\nis waiting for the Almanac of 1851 that he may review Mr. Adams's paper,\nwhich is to be contained in it. His own contributor, only two sentences\nbefore the insertion, had said, \"The Nautical Almanac, we believe, is\npublished three or four years in advance.\" In fact, the Almanac for\n1851--with Mr. Adams's paper at the end--was published at the end of 1847\nor very beginning of 1848; it had therefore been more than two years before\nthe public when the passage quoted was written. And probably every person\nin the country who was fit to review Mr. Adams's {148} paper--and most of\nthose who were fit to read it--knew that it had been widely circulated, in\nrevise, at the end of 1846: my copy has written on it, \"2d revise, December\n27, 1846, at noon,\" in the handwriting of the Superintendent of the\nAlmanac; and I know that there was an extensive issue of these revises,\nbrought out by the Le-Verrier-and-Adams discussion. I now give the review\nof myself, (February 23, 1850):\n\n\"_The British Almanack and Companion._\n\n\"The Companion to this Almanack, for some years after its first\npublication, annually contained scientific articles by Sir J. Lubbock[262]\nand others of a high order and great interest; we have now, however, closed\nthe publication as a scientific one in remembrance of what it was, and not\nin consequence of what it is. Its list of contributors on science, has\ngrown 'small by degrees and beautifully less,' until it has dwindled down\nto one--'a last rose of summer left withering alone.' The one contributor\nhas contributed one paper 'On Ancient and Modern Usage in Reckoning.'\n\n\"The learned critic's _chef d'oeuvre_, is considered, by competent judges,\nto be an Essay on _Old Almanacks_ printed a few years ago in this annual,\nand supposed to be written with the view of surpassing a profound memoir on\nthe same subject by James O. Halliwell,[263] Esq., F.R. and A.S.S., but the\ntremendous effort which the learned writer then made to excel many titled\ncompetitors for honors in the antique line appears to have had a sad effect\nupon his mental powers--at any rate, his efforts have since yearly become\nduller and duller; happily, at last, we should suppose, 'the ancient {149}\nand modern usage in reckoning' indicates the lowest point to which the _vis\ninertia_ of the learned writer's peculiar genius can force him.\n\n\"We will give a few extracts from the article.\n\n\"The learned author says, 'Those who are accustomed to settle the meaning\nof ancient phrases by self-examination will find some _strange_ conclusions\narrived at by us.' The writer never wrote a more correct sentence--it\nadmits of no kind of dispute.\n\n\"'Language and counting,' says the learned author, 'both came before the\nlogical discussion of either. It is not allowable to argue that something\nis or was, because it ought to be or ought to have been. That two negatives\nmake an affirmative, ought to be; if _no_ man have done _nothing_, the man\nwho has done nothing does not exist, and _every_ man has done _something_.\nBut in Greek, and in uneducated English, it is unquestionable that 'no man\nhas done nothing' is only an emphatic way of saying that no man has done\n_anything_; and it would be absurd to reason that it could not have been\nso, because it should not.'--p. 5.\n\n\"'But there _is_ another difference between old and new times, yet more\nremarkable, for we have _nothing_ of it now: whereas in things indivisible\nwe count with our fathers, and should say in buying an acre of land, that\nthe result has no parts, and that the purchaser, till he owns all the\nground, owns none, the change of possession being instantaneous. This\nsecond difference lies in the habit of considering nothing, nought, zero,\ncipher, or whatever it may be called, to be at the beginning of the scale\nof numbers. Count four days from Monday: we should now say Tuesday,\nWednesday, Thursday, Friday; formerly, it would have been Monday, Tuesday,\nWednesday, Thursday. Had we asked, what at that rate is the first day from\nMonday, all would have stared at a phrase they had never heard. Those who\nwere capable of extending language would have said, Why it must be Monday\nitself: the rest would have said, there can {150} be no first day from\nMonday, for the day after is Tuesday, which must be the second day: Monday,\none; Tuesday, two,'--p. 10.\n\n\"We assure our readers that the whole article is equally lucid, and its\nlogic alike formal.\n\n\"There are some exceedingly valuable footnotes; we give one of the most\ninteresting, taken from the learned Mr. Halliwell's profound book on\nNursery Rhymes[264]--a celebrated production, for which it is supposed the\nauthor was made F.R.S.\n\n \"'_One's nine_,\n  Two's some,\n  Three's a many,\n  Four's a penny,\n  Five's a little hundred.'\n\n'The last line refers to five score, the so-called hundred being more\nusually six score. The first line, looked at etymologically, is _one is not\none_, and the change of thought by which _nine_, the decimal of _one_, aims\nto be associated with the decimal of _plurality_ is curious:'--Very.\n\n\"This valuable and profound essay will very probably be transferred to the\nnext edition of the learned Mr. Halliwell's rare work, of kindred worth,\nentitled 'RARA MATHEMATICA,' it will then be deservedly handed down to\nposterity as a covering for cheap trunks--a most appropriate archive for\nsuch a treasure.\"\n\n\n\nIn December, 1846, the _Mechanics' Magazine_ published a libel on Airy in\nthe matter of the discovery of Neptune. In May, 1849, one * * * was to have\nbeen brought forward for election at the Astronomical Society, and was\nopposed by me and others, on the ground that he was the probable author of\nthis libel, and that he would not, perhaps could {151} not, deny it. [N.B.\nI no more doubt that he was the author then I doubt that I am the author of\nthis sentence.][265]\n\nAccordingly, * * * was withdrawn, and a discussion took place, for which\nsee the _Athenaeum_, No. 1126, May 26, 1849, p. 544. The _Mechanics'\nMagazine_ was very sore, but up to this day has never ventured beyond an\nattack on Airy, private whisperings against Adams--(see _ante_, p.\n147),--and the above against myself. In due time, I doubt not my name will\nappear as one of the _ames damnees_[266] of the _Mechanics' Magazine_.[267]\n\n\n\nT. S. DAVIES ON EUCLID.\n\nFirst, as to Mr. Halliwell. The late Thomas Stephens Davies,[268] excellent\nin geometry, and most learned in its history, was also a good hand at\nenmity, though not implacable. He and Mr. Halliwell, who had long before\nbeen very much one, were, at this date, very much two. I do not think T. S.\nDavies wrote this article; and I think that by giving my reasons I shall do\nservice to his memory. It must have been written at the beginning of\nFebruary; and within three days of that time T. S. Davies was making over\nto me, by his own free act, to be kept until claimed by the relatives, what\nall who knew even his writings knew that he considered as the most precious\ndeposit he had ever had in his keeping--Horner's[269] papers. His letter\nannouncing the transmission is dated February 2, 1850. This is a strong\npoint; but there is another quite as strong. Euclid and {152} his writings\nwere matters on which T. S. Davies knew neither fear nor favor: he could\nnot have written lightly about a man who stood high with him as a judge of\nEuclid. Now in this very letter of Feb. 2, there is a sentence which I\nhighly value, because, as aforesaid, it is on a point on which he would\nnever have yielded anything, to which he had paid life-long attention, and\non which he had the bias of having long stood alone. In fact, knowing--and\nwhat I shall quote confirms me,--that in the matter of Euclid his hand was\nagainst every man, I expected, when I sent him a copy of my 22-column\narticle, \"Eucleides\" in Smith's _Dictionary_,[270] to have received back a\ncriticism, that would have blown me out of the water: and I thought it not\nunlikely that a man so well up in the subject might have made me feel\ndemolished on some points. Instead of this, I got the following: \"Although\non one or two minor points I do not quite accord with your views, yet as a\nwhole and without regard to any minor points, I think you are the first who\nhas succeeded in a delineation of Euclid as a geometer.\" All this duly\nconsidered, it is utterly incredible that T. S. Davies should have written\nthe review in question. And yet Mr. Halliwell is treated just as T. S.\nDavies would have treated him, as to tone and spirit. The inference in my\nmind is that we have here a marked instance of the joining of hatreds which\ntakes place in journals supported by voluntary contributions of matter.\nShould anything ever have revived this article--and no one ever knows what\nmight have been fished up from the forgotten mass of journals--the\ntreatment of Mr. Halliwell would certainly have thrown a suspicion on T. S.\nDavies, a large and regular contributor to the Magazine. It is good service\nto his memory to point out what makes it incredible that he should have\nwritten so unworthy an article.\n\nThe fault is this. There are four extracts: the first {153} three are\nperfectly well printed. The printing of the _Mechanics' Magazine_ was very\ngood. I was always exceedingly satisfied with the manner in which my\narticles appeared, without my seeing proof. Most likely these extracts were\nprinted from my printed paper; if not the extractor was a good copier. I\nknow this by a test which has often served me. I use the subjunctive--\"if\nno man _have_ done nothing,\" an ordinary transcriber, narrating a quotation\nalmost always lets his own habit write _has_. The fourth extract has three\nalterations, all tending to make me ridiculous. _None_ is altered, in two\nplaces, into _nine_, _denial_ into _decimal_, and _comes_ into _aims_; so\nthat \"none, the denial of one, comes to be associated with the denial of\nplurality,\" reads as \"nine, the decimal of one, aims to be associated with\nthe decimal of plurality.\" This is intentional; had it been a compositor's\nreading of bad handwriting, these would not have been the only mistakes; to\nsay nothing of the corrector of the press. And both the compositor and\nreader would have guessed, from the first line being translated into \"one\nis not one,\" that it must have been \"one's none,\" not \"one's nine.\" But it\nwas not intended that the gem should be recovered from the unfathomed cave,\nand set in a Budget of Paradoxes.\n\nWe have had plenty of slander-paradox. I now give a halfpennyworth of bread\nto all this sack, an instance of the paradox of benevolence, in which an\nindividual runs counter to all the ideas of his time, and sees his way into\nthe next century. At Amiens, at the end of the last century, an institution\nwas endowed by a M. de Morgan, to whom I hope I am of kin, but I cannot\ntrace it; the name is common at Amiens. It was the first of the kind I ever\nheard of. It is a Salle d'Asyle for children, who are taught and washed and\ntaken care of during the hours in which their parents must be at work. The\nfounder was a large wholesale grocer and colonial importer, who was made a\nBaron by Napoleon I for his commercial success and his charities. {154}\n\n\n\nJAS. SMITH AGAIN.\n\n1862. Mr. Smith replies to me, still signing himself Nauticus: I give an\nextract:\n\n\"By hypothesis [what, again!] let 14 deg. 24' be the chord of an arc of\n15 deg. [but I wont, says 14 deg. 24'], and consequently equal to a side\nof a regular polygon of 24 sides inscribed in the circle. Then 4 times\n14 deg. 24' = 57 deg. 36' = the radius of the circle ...\"\n\nThat is, four times the chord of an arc is the chord of four times the arc:\nand the sum of four sides of a certain pentagon is equal to the fifth. This\nis the capital of the column, the crown of the arch, the apex of the\npyramid, the watershed of the elevation. Oh! J. S.! J. S.! groans\nGeometry--_Summum J. S. summa injuria_![271] The other J. S., Joseph\nScaliger,[272] as already mentioned, had his own way of denying that a\nstraight line is always the shortest distance between two points. A\nparallel might be instituted, but not in half a column. And J. S. the\n_second_ has been so tightly handled that he may now be dismissed, with an\ninscription for his circular shield, obtained by changing _Lexica contexat_\ninto _Circus quadrandus_ in an epigram of J. S. the _first_:\n\n \"Si quem dura manet sententia judicis, olim\n  Damnatum aerumnis suppliciisque caput,\n  Hunc neque fabrili lassent ergastula massa,\n  Nec rigidas vexent fossa metalla manus.\n  Circus quadrandus: nam--caetera quid moror?--omnes\n  Poenarum facies hic labor unus habet.\"[273]\n\n{155}\n\nI had written as far as _damnatum_ when in came the letter of Nauticus as a\nprinted slip, with a request that I would consider the slip as a 'revised\ncopy.' Not a word of alteration in the part I have quoted! And in the\nevening came a letter desiring that I would alter a gross error; but not\nthe one above: this is revising without revision! If there were cyclometers\nenough of this stamp, they would, as cultivation progresses--and really,\nwith John Stuart Mill in for Westminster, it seems on the move, even\nthough, as I learn while correcting the proof, Gladstone be out from\nOxford; for Oxford is no worse than in 1829, while Westminster is far above\nwhat she ever has been: election time excuses even such a parenthesis as\nthis--be engaged to amuse those who can afford it with paralogism at their\nmeals, after the manner of the other jokers who wore the caps and bells.\nThe rich would then order their dinners with _panem et Circenses_,--up with\nthe victuals and the circle-games--as the poor did in the days of old.\n\nMr. Smith is determined that half a column shall not do. Not a day without\nsomething from him: letter, printed proof, pamphlet. In what is the last at\nthis moment of writing he tells me that part of the title of a work of his\nwill be \"Professor De Morgan in the pillory without hope of escape.\" And\nwhere will he be himself? This I detected by an effort of reasoning which I\nnever could have made except by following in his steps. In all matters\nconnected with [pi] the letters l and g are closely related: this appears\nin the well-known formula for the time of oscillation [pi] [sqrt](l : g).\nHence g may be written for l, but only once: do it twice, and you require\nthe time to be [pi] [sqrt](l^2 : g^2). This may be reinforced by observing\nthat if as a datum, or if you dislike that word, by hypothesis, the first l\nbe a g, it is absurd that it should be an l. Write g for the first l, and\nwe have _un fait accompli_. I shall be in pillory; and overhead, in a\ncloud, will sit Mr. James Smith on one stick laid across two others, under\na nimbus of 3-1/8 diameters to {156} the circumference--in [pi]-glory. Oh\nfor a drawing of this scene! Mr. De Morgan presents his compliments to Mr.\nJames Smith, and requests the honor of an exchange of photographs.\n\n_July 26._--Another printed letter.--Mr. James Smith begs for a distinct\nanswer to the following plain question: \"Have I not in this communication\nbrought under your notice _truths_ that were never before dreamed of in\nyour geometrical and mathematical philosophy?\" To which, he having taken\nthe precaution to print the word _truths_ in italics, I can conscientiously\nanswer, Yes, you have. And now I shall take no more notice of these\n_truths_, until I receive something which surpasses all that has yet been\ndone.\n\n\n\nA FEW SMALL PARADOXERS.\n\n    The Circle secerned from the Square; and its area gauged in terms of a\n    triangle common to both. By Wm. Houlston,[274] Esq. London and Jersey,\n    1862, 4to.\n\nMr. Houlston squares at about four poetical quotations in a page, and\nbrings out [pi] = 3.14213.... His frontispiece is a variegated diagram,\nhaving parts designated Inigo and Outigo. All which relieves the subject,\nbut does not remove the error.\n\n\n\n    Considerations respecting the figure of the Earth.... By C. F.\n    Bakewell.[275] London, 1862, 8vo.\n\nNewton and others think that in a revolving sphere the {157} loose surface\nmatter will tend to the equator: Mr. Bakewell thinks it will tend to the\npoles.\n\n\n\n    On eccentric and centric force: a new theory of projection. By H. F. A.\n    Pratt, M.D.[276] London, 1862, 8vo.\n\nDr. Pratt not only upsets Newton, but cuts away the very ground he stands\non: for he destroys the first law of motion, and will not have the natural\ntendency of matter in motion to be rectilinear. This, as we have seen, was\nJohn Walsh's[277] notion. In a more recent work \"On Orbital Motion,\"\nLondon, 1863, 8vo., Dr. Pratt insists on another of Walsh's notions,\nnamely, that the precession of the equinoxes is caused by the motion of the\nsolar system round a distant central sun. In this last work the author\nrefers to a few notes, which completely destroy the theory of gravitation\nin terms \"perfectly intelligible as well to the unlearned as to the\nlearned\": to me they are quite unintelligible, which rather tends to\nconfirm a notion I have long had, that I am neither one thing nor the\nother. There is an ambiguity of phrase which delights a writer on logic,\nalways on the look-out for specimens of _homonymia_ or _aequivocatio_. The\nauthor, as a physician, is accustomed to \"appeal from mere formulae\":\naccordingly, he sets at nought the whole of the mathematics, which he does\nnot understand. This equivocation between the formula of the physician and\nthat of the mathematician is as good, though not so perceptible to the\nworld at large, as that made by Mr. Briggs's friend in _Punch's_ picture,\nwhich I cut out to paste into my Logic. Mr. Briggs wrote for a couple of\n_bruisers_, meaning to prepare oats for his horses: his friend sent him the\nWhitechapel Chicken and the Bayswater Slasher, with the gloves, all ready.\n\n{158}\n\n\n\n    On matter and ether, and the secret laws of physical change. By T. R.\n    Birks, M.A.[278] Cambridge, 1862, 8vo.\n\nBold efforts are made at molecular theories, and the one before me is ably\naimed. When the Newton of this subject shall be seated in his place, books\nlike the present will be sharply looked into, to see what amount of\nanticipation they have made.\n\n\n\nDR. THORN AND MR. BIDEN.\n\n    The history of the 'thorn tree and bush' from the earliest to the\n    present time: in which is clearly and plainly shown the descent of her\n    most gracious Majesty and her Anglo-Saxon people from the half tribe of\n    Ephraim, and possibly from the half tribe of Manasseh; and consequently\n    her right and title to possess, at the present moment, for herself and\n    for them, a share or shares of the desolate cities and places in the\n    land of their forefathers! By Theta, M.D.[279] (Private circulation.)\n    London, 1862, 8vo.\n\nThis is much about _Thorn_, and its connected words, Thor, Thoth, Theta,\netc. It is a very mysterious vagary. The author of it is the person whom I\nhave described elsewhere as having for his device the round man in the\nthree-cornered hole, the writer of the little heap of satirical anonymous\nletters about the Beast and 666. By accident I discovered the writer: so\nthat if there be any more thorns to crackle under the pot, they need not be\nanonymous.\n\nNor will they be anonymous. Since I wrote the above, I have received\n_onymous_ letters, as _ominous_ as the rest. The writer, William Thorn,\nM.D., is obliged to reveal {159} himself, since it is his object to prove\nthat he himself is one 666. By using W for double Vau (or 12) he cooks the\nnumber out of his own name. But he says it is the number not of a beast but\nof a man, and adds, \"Thereby hangs a tale!\" which sounds like\ncontradiction. He informs me that he will talk the matter over with me: but\nI shall certainly have nothing to say to a gentleman of his number; it is\nbest to keep on the safe side.\n\nIn one letter I am informed that not a line should I have had, but for my\n\"sneer at 666,\" which, therefore, I am well pleased to have given. I am\nalso told that my name means the \"'garden of death,' that place in which\nthe tree of knowledge was plucked, and so you are like your name 'dead' to\nthe fact that you are an Israelite, like those in Ezekiel 37 ch.\" Some\nhints are given that I shall not fare well in the next world, which any one\nwho reads the chapter in Ezekiel will see is quite against his comparison.\nThe reader must not imagine that my prognosticator means _Morgan_ to be a\ncorruption of _Mortjardin_; he proves his point by Hebrew: but any\nphilologist would tell him the true derivation of the name, and how\n_Glamorgan_ came to get it. It will be of much comfort to those young men\nwho have not got through to know that the tree of knowledge itself was once\nin the same case. And so good bye to 666 for the present, and the\nassumption that the enigma is to be solved by the united numeral forces of\nthe letters of a word.\n\nIt is worthy of note that, as soon as my Budget commenced, two guardian\nspirits started up, fellow men as to the flesh, both totally unknown to me:\nthey have stuck to me from first to last. James Smith, Esq., finally\nNauticus, watches over my character in this world, and would fain preserve\nme from ignorance, folly, and dishonesty, by inclosing me in a magic circle\nof 3-1/8 diameters in circumference. The round man in the three-cornered\nhole, finally William Thorn, M.D., takes charge of my future destiny, {160}\nand tries to bring me to the truth by unfolding a score of meanings--all\nright--of 666. He hints that I, and my wife, are servants of Satan: at\nleast he desires us both to remember that we cannot serve God and Satan;\nand he can hardly mean that we are serving the first, and that he would\nhave us serve the second. As becomes an interpreter of the Apocalypse, he\nuses seven different seals; but not more than one to one letter. If his\nseals be all signet-rings, he must be what Aristophanes calls a\nsphragidonychargocometical fellow. But--and many thanks to him for the\nsame--though an M.D., he has not sent me a single vial. And so much for my\ntree of secular knowledge and my tree of spiritual life: I dismiss them\nwith thanks from myself and thanks from my reader. The dual of the\nPythagorean system was Isis and Diana; of the Jewish law, Moses and Aaron;\nand of the City of London, Gog and Magog; of the Paradoxiad, James Smith,\nEsq., and William Thorn, M.D.\n\n_September, 1866._ Mr. James Biden[280] has favored me with some of his\npublications. He is a rival of Dr. Thorn; a prophet by name-right and\ncrest-right. He is of royal descent through the De Biduns. He is the\n_watchman_ of Ezekiel: God has told him so. He is the author of _The True\nChurch_, a phrase which seems to have a book-meaning and a mission-meaning.\nHe shall speak for himself:\n\n\"A crest of the Bidens has significance. It is a lion rampant between\nwings--wings in Scripture denote the flight of time. Thus the beasts or\nliving creatures of the Revelations have each six wings, intimating a\ncondition of mankind up to and towards the close of six thousand years of\nBible teaching. The two wings of the crest would thus intimate power\ntowards the expiration of 2000 years, as time is marked in the history of\nGreat Britain.\n\n{161}\n\n\"In a recent publication, _The Pestilence, Why Inflicted_, are given many\nreasons why the writer thinks himself to be the appointed watchman foretold\nby Ezekiel, chapters iii. and xxxiii. Among the reasons are many prophecies\nfulfilled in him. Of these it is now needful to note two as bearing\nespecially on the subject of the reign of Darius.\n\n\"1.--In Daniel it is said, 'Darius the Median took the kingdom, being about\nthreescore and two years old.'--Daniel v. 31.\n\n\"When 'Belshazzar' the king of the Chaldeans is found wanting, Darius takes\nthe kingdom. It is not given him by the popular voice; he asserts his\nright, and this is not denied. He takes it when about sixty-two years of\nage. The language of Daniel is prophetic, and Darius has in another an\nantitype. The writer was born July 18th, 1803; and the claim was asserted\nat the close of 1865, when he was about sixty-two years of age.\n\n\"The claims which have been asserted demand a settled faith, and which\ncould only be reached through a long course of divine teaching.\"\n\nWhen I was a little boy at school, one of my school-fellows took it into\nhis head to set up a lottery of marbles: the thing took, and he made a\nstony profit. Soon, one after another, every boy had his lottery, and it\nwas, \"I won't put into yours unless you put into mine.\" This knocked up the\nscheme. It will be the same with the prophets. Dr. Thorn, Mr. Biden, Mrs.\nCottle,[281] etc. will grow imitators, until we are all pointed out in the\nBible: but A will not admit B's claim unless B admits his. For myself, as\nelsewhere shown, I am the first Beast in the Revelations.\n\nEvery contraband prophet gets a few followers: it is a great point to make\nthese sequacious people into Buridan's asses, which they will become when\nprophets are so numerous that there is no choosing.\n\n{162}\n\n\n\nSIR G. C. LEWIS.\n\n    An historical survey of the Astronomy of the Ancients. By the Rt. Hon.\n    Sir G. C. Lewis.[282] 8vo. 1862.\n\nThere are few men of our day whom I admire more than the late Sir G. Lewis:\nhe was honest, earnest, sagacious, learned, and industrious. He probably\nsacrificed his life to his conjunction of literature and politics: and he\nstood high as a minister of state in addition to his character as a man of\nletters. The work above named is of great value, and will be read for its\nintrinsic merit, consulted for its crowd of valuable references, quoted for\nits aid to one side of many a discussion, and opposed for its force against\nthe other. Its author was also a wit and a satirist. I know of three\nclassical satires of our day which are inimitable imitations: Mr.\nMalden's[283] _Pragmatized Legends_, Mr. Mansel's[284] _Phrontisterion_,\nand Sir G. Cornewall Lewis's _Inscriptio Antiqua_. In this last,\nHEYDIDDLEDIDDLETHECATANDTHEFIDDLE etc. is treated as an Oscan inscription,\nand rendered into Latin by approved methods. As few readers have seen it, I\ngive the result:\n\n    \"Hejus dedit libenter, dedit libenter. Deus propitius [est], deus\n    [donatori] libenter favet. Deus in viarum {163} junctura ovorum dape\n    [colitur], deus mundi. Deus in litatione voluit, benigno animo, haedum,\n    taurum intra fines [loci sacri] portandos. Deus, bis lustratus, beat\n    fossam sacrae libationis.\"[285]\n\nHow then comes the history of astronomy among the paradoxes? Simply because\nthe author, so admirably when writing about what he knew, did not know what\nhe did not know, and blundered like a circle-squarer. And why should the\nfaults of so good a writer be recorded in such a list as the present? For\nthree reasons: First, and foremost, because if the exposure be not made by\nsome one, the errors will gradually ooze out, and the work will get the\ncharacter of inaccurate. Nothing hurts a book of which few can fathom the\ndepths so much as a plain blunder or two on the surface. Secondly, because\nthe reviews either passed over these errors or treated them too gently,\nrather implying their existence than exposing them. Thirdly, because they\nstrongly illustrate the melancholy truth, that no one knows enough to write\nabout what he does not know. The distinctness of the errors is a merit; it\nproceeds from the clear-headedness of the author. The suppression in the\njournals may be due partly to admiration of the talent and energy which\nlived two difficult lives at once, partly to respect for high position in\npublic affairs, partly to some of the critics being themselves men of\nlearning only, unable to detect the errors. But we know that action and\nreaction are equal and contrary. If our generation take no notice of\ndefects, and allow them to go down undetected among merits, the next\ngeneration will discover them, will perhaps believe us incapable of\ndetecting them, at least will pronounce our judgment good for nothing, and\nwill form an {164} opinion in which the merits will be underrated: so it\nhas been, is, and will be. The best thing that can be done for the memory\nof the author is to remove the unsound part that the remainder may thrive.\nThe errors do not affect the work; they occur in passages which might very\nwell have been omitted: and I consider that, in making them conspicuous, I\nam but cutting away a deleterious fungus from a noble tree.\n\n(P. 154). The periodic times of the five planets were stated by\nEudoxus,[286] as we learn from Simplicius;[287] the following is his\nstatement, to which the true times are subjoined, for the sake of\ncomparison:\n\n            STATEMENT OF EUDOXUS        TRUE TIME\n  Mercury          1 year             --    87d. 23h.\n  Venus            1   \"              --   224d. 16h.\n  Mars             2   \"              1y.  321d. 23h.\n  Jupiter         12   \"             11y.  315d. 14h.\n  Saturn          30   \"             29y.  174d.  1h.\n\nUpon this determination two remarks may be made. First, the error with\nrespect to Mercury and Venus is considerable; with respect to Mercury, it\nis, in round numbers, 365 instead of 88 days, more than four times too\nmuch. Aristotle remarks that Eudoxus distinguishes Mercury and Venus from\nthe other three planets by giving them one sphere each, with the poles in\ncommon. The proximity of Mercury to the sun would render its course\ndifficult to observe and to measure, but the cause of the large error with\nrespect to Venus (130 days) is not apparent.\n\n{165}\n\nSir G. Lewis takes Eudoxus as making the planets move round the sun; he has\naccordingly compared the _geocentric_ periods of Eudoxus with our\n_heliocentric_ periods. What greater blunder can be made by a writer on\nancient astronomy than giving Eudoxus the Copernican system? If Mercury\nwere a black spot in the middle of the sun it would of course move round\nthe earth in a year, or appear to do so: let it swing a little on one side\nand the other of the sun, and the average period is still a year, with\nslight departures both ways. The same for Venus, with larger departures.\nSay that a person not much accustomed to the distinction might for once\nwrite down the mistake; how are we to explain its remaining in the mind in\na permanent form, and being made a ground for such speculation as that of\nthe difficulty of observing Mercury leading to a period four times what it\nought to be, corrected in proof and published by an industrious and\nthoughtful person? Only in one way: the writer was quite out of his depth.\nThis one case is conclusive; be it said with all respect for the real\nstaple of the work and of the author. He knew well the difference of the\nsystems, but not the effect of the difference: he is another instance of\nwhat I have had to illustrate by help of a very different person, that it\nis difficult to reason well upon matter which is not familiar.\n\n\n\n(P. 254). Copernicus, in fact, supposed the axis of the earth to be always\nturned towards the Sun.^{(169)} [(169). See Delambre, _Hist. Astr. Mod._,\nVol. I, p. 96]. It was reserved to Kepler to propound the hypothesis of the\nconstant parallelism of the earth's axis to itself.\n\n\n\nIf there be one thing more prominent than another in the work of Copernicus\nhimself, in the popular explanations of it, and in the page of\nDelambre[288] cited, it is that the _parallelism of the earth's axis_ is a\nglaring part of the {166} theory of Copernicus. What Kepler[289] did was to\nthrow away, as unnecessary, the method by which Copernicus, _per fas et\nnefas_,[290] secured it. Copernicus, thinking of the earth's orbital\nrevolution as those would think who were accustomed to the _solid\norbs_--and much as the stoppers of the moon's rotation do now: why do they\nnot strengthen themselves with Copernicus?--thought that the earth's axis\nwould always incline the same end towards the sun, unless measures were\ntaken to prevent it. He _did_ take measures: he invented a _compensating_\nconical motion of the axis to preserve the parallelism; and, which is one\nof the most remarkable points of his system, he obtained the precession of\nthe equinoxes by giving the necessary trifle more than compensation. What\nstares us in the face at the beginning of the paragraph to which the author\nrefers?\n\n\"C'est donc pour arriver a ce parallelisme, ou pour le conserver, que\nCopernic a cru devoir recourir a ce mouvement egal et oppose qui detruit\nl'effet qu'il attribue si gratuitement au premier, de deranger le\nparallelisme.\"[291]\n\nParallelism at any price, is the motto of Copernicus: you need not pay so\ndear, is the remark of Kepler.\n\nThe opinions given by Sir G. Lewis about the effects of modern astronomy,\nwhich he does not understand and singularly undervalues, will now be seen\nto be of no authority. He fancies that--to give an instance--for the\ndetermination of a ship's place, the invention of chronometers has been far\nmore important than any improvement in astronomical theory (p. 254). Not to\nspeak of latitude,--though the omission is not without importance,--he\nought to have known that longitude is found by the difference between what\no'clock it is at Greenwich and at the ship's place, at {167} one absolute\nmoment of time. Now if a chronometer were quite perfect--which no\nchronometer is, be it said--and would truly tell Greenwich mean time all\nover the world, it ought to have been clear that just as good a watch is\nwanted for the time at _the place of observation_, before the longitude of\nthat place with respect to Greenwich can be found. There is no such watch,\nexcept the starry heaven itself: and that watch can only be read by\nastronomical observation, aided by the best knowledge of the heavenly\nmotions.\n\nI think I have done Sir G. Lewis's very excellent book more good than all\nthe reviewers put together.\n\nI will give an old instance in which literature got into confusion about\nastronomy. Theophrastus,[292] who is either the culprit or his historian,\nattributes to Meton,[293] the contriver of the lunar calendar of nineteen\nyears, which lasts to this day, that his solstices were determined for him\nby a certain Phaeinus of Elis on Mount Lycabettus. Nobody else mentions\nthis astronomer: though it is pretty certain that Meton himself made more\nthan one appointment with him for the purpose of observing solstices; and\nwe may be sure that if either were behind his time, it was Meton. For\n_Phaeinus Helius_ is the shining sun himself; and in the astronomical poet\nAratus[294] we read about the nineteen years of the shining sun:\n\n  [Greek: Enneakaideka kukla phaeinou eelioio].[295]\n\nSome man of letters must have turned Apollo into Phaeinus of Elis; and\nthere he is in the histories of astronomy to {168} this day. Salmasius[296]\nwill have Aratus to have meant him, and proposes to read [Greek: eleioio]:\nhe did not observe that Phaeinus is a very common adjective of Aratus, and\nthat, if his conjecture were right, this Phaeinus would be the only\nnon-mythical man in the poems of Aratus.\n\n[When I read Sir George Lewis's book, the points which I have criticized\nstruck me as not to be wondered at, but I did not remember why at the time.\nA Chancellor of the Exchequer and a writer on ancient astronomy are birds\nof such different trees that the second did not recall the first. In 1855 I\nwas one of a deputation of about twenty persons who waited on Sir G. Lewis,\nas Chancellor of the Exchequer, on the subject of a decimal coinage. The\ndeputation was one of much force: Mr. Airy, with myself and others,\nrepresented mathematics; William Brown,[297] whose dealings with the United\nStates were reckoned by yearly millions, counted duodecimally in England\nand decimally in America, was the best, but not the only, representative of\ncommerce. There were bullionists, accountants, retailers, etc. Sir G. L.\nwalked into the room, took his seat, and without waiting one moment, began\nto read the deputation a smart lecture on the evils of a decimal coinage;\nit would require alteration of all the tables, it would impede calculation,\netc. etc. Of those arguments against it which weighed with many of better\nknowledge than his, he obviously knew nothing. The members of the\ndeputation began to make their statements, and met with curious denials. He\ninterrupted me with \"Surely there is no doubt that the calculations of our\nbooks of arithmetic are easier {169} than those in the French books.\" He\nwas not aware that the _universally admitted_ superiority of decimal\n_calculation_ made many of those who prefer our system for the market and\nthe counter cast a longing and lingering look towards decimals. My answer\nand the smiles which he saw around, made him give a queer puzzled look,\nwhich seemed to say, \"I may be out of my depth here!\" His manner changed,\nand he listened. I saw both the slap-dash mode in which he dealt with\nsubjects on which he had not thought, and the temperament which admitted\nsuspicion when the means of knowledge came in his way. Having seen his two\nphases, I wonder neither at his more than usual exhibition of shallowness\nwhen shallow, nor at the intensity of the contrast when he had greater\ndepth.]\n\n\n\nDECIMAL COINAGE.\n\nAmong the paradoxers are the political paradoxers who care not how far they\ngo in debate, their only object being to carry the House with them for the\ncurrent evening. What I have said of editors I repeat of them. The\npreservation of a very marked instance, the association of political\nrecklessness with cyclometrical and Apocalyptic absurdity, may have a\ntendency to warn, not indeed any hardened public-man and sinner, but some\nyoung minds which have yearnings towards politics, and are in formation of\nhabits.\n\nIn the debate on decimal coinage of July 12, 1855, Mr. Lowe,[298] then\nmember for Kidderminster, an effective speaker and a smart man, exhibited\nhimself in a speech on which I wrote a comment for the Decimal Association.\nI have seldom seen a more wretched attempt to distort the points of a\npublic question than the whole of this speech. Looking at the intelligence\nshown by the speaker on other occasions, {170} it is clear that if charity,\ninstead of believing all things, believed only all things but one, he might\ntremble for his political character; for the honesty of his intention on\nthis occasion might be the incredible exception. I give a few paragraphs\nwith comments:\n\n\"In commenting on the humorous, but still argumentative speech of Mr. Lowe,\nthe member for Kidderminster, we may observe, in general, that it consists\nof points which have been several times set forth, and several times\nanswered. Mr. Lowe has seen these answers, but does not allude to them, far\nless attempt to meet them. There are, no doubt, individuals, who show in\ntheir public speaking the outward and visible signs of a greater degree of\nacuteness than they can summon to guide their private thinking. If Mr. Lowe\nbe not one of these, if the power of his mind in the closet be at all\ncomparable to the power of his tongue in the House, it may be suspected\nthat his reserve with respect to what has been put forward by the very\nparties against whom he was contending, arises from one or both of two\nthings--a high opinion of the arguments which he ignored--a low opinion of\nthe generality of the persons whom he addressed. [Both, I doubt not].\n\n\"Did they calculate in florins  In the name of common sense,\n?\"                              how can it be objected to a\n                                system that people do not use\n                                it before it is introduced?\n                                Let the decimal system be\n                                completed, and calculation\n                                shall be made in florins; that\n                                is, florins shall take their\n                                proper place. If florins were\n                                introduced _now_, there must\n                                be a column for the odd\n                                shilling.\n\"He was glad that some hon.     If the hon. gentleman make\ngentleman had derived benefit   this assertion of himself, it\nfrom the issue of florins. His  is not for us to gainsay it.\nonly experience of their        It only proves that he is one\nconvenience was, that when he   of that class of {171} men who\nought to have received          are described in the old song,\nhalf-a-crown, he had generally  of which one couplet runs\nreceived a florin, and when he  thus:\nought to have paid a florin,\nhe had generally paid               I sold my cow to buy me a\nhalf-a-crown.\" (Hear, hear,     calf;\nand laughter.)                  I never make a bargain but I\n                                lose half,\n                                With a etc. etc. etc.\n\nBut he cannot mean that Englishmen in general are so easily managed. And as\nto Jonathan, who is but John lengthened out a little, he would see creation\nwhittled into chips before he would even split what may henceforth be\ncalled the Kidderminster difference. The House, not unmoved--for it\nlaughed--with sly humor decided that the introduction of the florin had\nbeen \"eminently successful and satisfactory.\"\n\nThe truth is that Mr. Lowe here attacks nothing except the coexistence of\nthe florin and half-crown. We are endeavoring to abolish the half-crown.\nLet Mr. Lowe join us; and he will, if we succeed, be relieved from the\npressure on his pocket which must arise from having the turn of the market\nalways against him.\n\n\"From a florin they get to 2    Note the sophism of expressing\n2-5ths of a penny, but who      our coin in terms of the\never bought anything, who ever  penny, which we abandon,\nreckoned or wished to reckon    instead of the florin, which\nin such a coin as that?\"        we retain. Remember that this\n(Hear, hear.)                   2 2-5ths is the hundredth part\n                                of the pound, which is called,\n                                as yet, a _cent_. Nobody buys\n                                anything at a cent, because\n                                the cent is not yet\n                                introduced. Nobody reckons in\n                                cents for the same reason.\n                                Everybody wishes to reckon in\n                                cents, who wishes to combine\n                                the advantage of decimal\n                                reckoning with the\n                                preservation of the pound as\n                                {172} the highest unit of\n                                account; amongst others, a\n                                majority of the House of\n                                Commons, the Bank of England,\n                                the majority of London\n                                bankers, the Chambers of\n                                Commerce in various places,\n                                etc. etc. etc.\n\"Such a coin could never come   Does 2-1/2d. never pass from\ninto general circulation        hand to hand? And is 2-1/2d.\nbecause it represents nothing   so precisely the modulus of\nwhich corresponds with any of   popular wants, that an\nthe wants of the people.\"       alteration of 4 per cent.\n                                would make it useless? Of all\n                                the values which 2-1/2d.\n                                measures, from three pounds of\n                                potatoes down to certain\n                                arguments used in the House of\n                                Commons, there is not one for\n                                which a cent would not do just\n                                as well. Mr. Lowe has fallen\n                                into the misconception of the\n                                person who admired the\n                                dispensation of Providence by\n                                which large rivers are made to\n                                run through cities so great\n                                and towns so many. If the cent\n                                were to be introduced\n                                to-morrow, straightway the\n                                buns and cakes, the soda-water\n                                bottles, the short omnibus\n                                fares, the bunches of\n                                radishes, etc. etc. etc.,\n                                would adapt themselves to the\n                                coin.\n\"If the proposed system were    The confusion of ideas here\nadopted, they would all be      exhibited is most instructive.\ncompelled to live in decimals   The speaker is under the\nfor ever; if a man dined at a   impression that _we_ are\npublic house he would have to   introducing fractions: the\npay for his dinner in decimal   truth is, that we only want to\nfractions. (Hear, hear.) He     abandon the _more difficult_\nobjected to that, for he        fractions which we _have got_,\nthought that a man ought to be  and to introduce _easier\nable to pay for his dinner in   fractions_. Does he deny this?\nintegers.\" (Hear, hear, and a   Let us trace his denial to its\nlaugh.)                         legitimate consequences. A man\n                                ought to pay for his dinner in\n                                integers.\n\n{173}\n\nNow, if Mr. Lowe insists on it that our integer is the pound, he is bound\nto admit that the present integer is the pound, of which a shilling, etc.,\nare fractions. The next time he has a chop and a pint of stout in the city,\nthe waiter should say--\"A pound, sir, to you,\" and should add, \"Please to\nremember the waiter in integers.\" Mr. Lowe fancies that when he pays one\nand sixpence, he pays in integers, and so he does, if his integer be a\npenny or a sixpence. Let him bring his mind to contemplate a mil as the\ninteger, the lowest integer, and the seven cents five mils which he would\npay under the new system would be payment in integers also. But, as it\nhappens with some others, he looks _up_ the present system, with\nCocker,[299] and Walkingame,[300] and always looks _down_ the proposed\nsystem. The word _decimal_ is obstinately associated with _fractions_, for\nwhich there is no need. Hence it becomes so much of a bugbear, that, to\nparody the lines of Pope, which probably suggested one of Mr. Lowe's\nphrases--\n\n \"Dinner he finds too painful an endeavor,\n  Condemned to pay in decimals for ever.\"\n\n\"The present system, however,   A pleasant sum even for an\nhad not yet been changed into   accomplished mathematician.\ndecimal system. That change     What does divided by the\nmight appear very easy to       decimal of a pound mean?\naccomplished mathematicians     Perhaps it means _reduced_ to\nand men of science, but it was  the decimal of a pound! Mr.\none which it would be very      Lowe supposes, as many others\ndifficult to carry out. (Hear,  do, that, after the change,\nhear). What would have to be    all calculations will be\ndone? Every sum would have to   _proposed in old money_, and\nbe reduced into a vulgar        then _converted into new_. He\nfraction of a pound, and then   cannot hit the {174} idea that\ndivided by the decimal of a     the new coins will take the\npound--a pleasant sum for an    place of the old. This lack of\nold applewoman to work out!\"    apprehension will presently\n(Hear, hear, and laughter.)     appear further.\n\"It would not be an agreeable   Let the members be assured\ntask, even for some members of  that nine half-pence will be,\nthat House, to reduce 4-1/2d.,  for every practical purpose,\nor nine half-pence, to mils.\"   18 mils. But now to the fact\n(Hear, hear.)                   asserted. Davies Gilbert[301]\n                                used to maintain that during\n                                the long period he sat in the\n                                House, he never knew more than\n                                three men in it, at one time,\n                                who had a tolerable notion of\n                                fractions. [I heard him give\n                                the names of three at the time\n                                when he spoke: they were\n                                Warburton,[302] Pollock,[303]\n                                and Hume.[304] He himself was\n                                then out of Parliament.]\n                                Joseph Hume affirmed that he\n                                had never met with more than\n                                ten members who were\n                                arithmeticians. But both these\n                                gentlemen had a high standard.\n                                Mr. Lowe has given a much more\n                                damaging opinion. He evidently\n                                means that the general run of\n                                members could not do his\n                                question. It is done as\n                                follows: Since farthings gain\n                                on mils, at the rate of a\n                                whole mil in 24 farthings (24\n                                farthings being 25 mils), it\n                                is clear that 18 farthings\n                                being three-quarters of 24\n                                farthings, will gain\n                                three-quarters of a mil; that\n                                is, 18 farthings are eighteen\n                                {175} mils and three-quarters\n                                of a mil. Any number of\n                                farthings is as many mils and\n                                as many twenty-fourths of a\n                                mil. To a certain extent, we\n                                feel able to protest against\n                                the manner in which\n                                Kidderminster has treated the\n                                other constituencies. We do\n                                not hold it impossible to give\n                                the Members of the House in\n                                general a sufficient knowledge\n                                of the meaning and\n                                consequences of the _decimal_\n                                succession of units, tens,\n                                hundreds, thousands, etc.; and\n                                we believe that there are in\n                                the House itself competent\n                                men, in number enough to teach\n                                all the rest. All that is\n                                wanted is the power of\n                                starting from the known to\n                                arrive at the unknown. Now\n                                there is one kind of decimals\n                                with which every member is\n                                acquainted--the _Chiltern\n                                Hundreds_. If public opinion\n                                would enable the competent\n                                minority to start from this in\n                                their teaching, not as a\n                                basis, but as an alternative,\n                                in three weeks the\n                                fundamentals would be\n                                acquired, and members in\n                                general would be as fit to\n                                turn 4-1/2d. into mils, as any\n                                boys on the lower forms of a\n                                commercial school.\n\n                                For a long period of years,\n                                allusion to the general\n                                ignorance of arithmetic, has\n                                been a standing mode of\n                                argument, and has always been\n                                well received: whenever one\n                                member describes others as\n                                _knownothings_, those others\n                                cry _Hear_ to the country in a\n                                transport of delight. In the\n                                meanwhile the country is\n                                gradually arriving at the\n                                conclusion that a true joke is\n                                no joke.\n\"The main objection was, if     Fine words, wrongly used. The\nthey went below 6d., that the   new coins are commensurable\nnew scale of coins would not    with, and in a finite ratio\nbe commensurate in any finite   to, the old ones. The farthing\nratio with anything in this     is to the mil as 25 to 24. The\nnew currency of mils.\"          speaker has something here in\n                                the bud, which we shall\n                                presently meet with in the\n                                flower; and fallacies are more\n                                easily nipped in flower than\n                                in bud. {176}\n\"No less than five of our       This dreadful change of value\npresent coins must be called    consists in sixpence farthing\nin, or else--which would be     going to the half-shilling\nworse--new values must be       instead of sixpence. Whether\ngiven to them.\"                 the new farthings be called\n                                mils or not is of no\n                                consequence.\n\"If a poor man put a penny in   Mr. Lowe, who cannot pass a\nhis pocket, it would come out   half-crown for more than a\na coin of different value,      florin, or get in a florin at\nwhich he would not understand.  less than half-a-crown, has\nSuppose he owed another man a   such a high faith in the\npenny, how was he to pay him ?  sterner stuff of his fellow\nWas he to pay him in mils?      countrymen, that he believes\nFour mils would be too little,  any two of them would go to\nand five mils would be too      fisty cuffs for the 25th part\nmuch. The hon. gentlemen said   of a farthing. He reasons\nthere would be only a mil       thus: He has often heard in\nbetween them. That was exactly  the streets, \"I'd fight you\nit. He believed there would be  for the fiftieth part of a\na 'mill' between them.\" (Much   farden:\" and having (that is,\nlaughter.)                      for a Member) a notion both of\n                                fractions and logic, he infers\n                                that those who would fight for\n                                the 50th of a farthing would,\n                                _a fortiori_, fight for a\n                                25th. His mistake arises from\n                                his not knowing that when a\n                                person offers to fight another\n                                for 1/200d., he really means\n                                to fight for love; and that\n                                the stake is merely a matter\n                                of form, a feigned issue, a\n                                _pro forma_ report of\n                                progress. Do the Members of\n                                the House think they have all\n                                the forms to themselves?\n\"What would be the present      We should hardly believe all\nexpression for four-pence?      this to be uttered in earnest,\nWhy, 0.166 (a laugh); for       if we had not known {177} that\nthreepence? .0125; for a        several persons who have not\npenny? .004166, and so on _ad   Mr. Lowe's humor, nevertheless\ninfinitum_ (a laugh); for a     have his impressions on this\nhalf-penny? .002083 _ad         point. It must therefore be\ninfinitum_. (A laugh). What     answered; but how is this to\nwould be the present            be done seriously?\nexpression for a farthing?\nWhy, .0010416 _ad infinitum_.   _Dialogue between a member of\n(A laugh). And this was the     Parliament and an orange-boy,\nsystem which was to cause such  three days after the\na saving in figures, and these  introduction of the complete\nwere the quantities into which  decimal system. The member,\nthe poor would have to reduce   going down to the House, wants\nthe current coin of the realm.  oranges to sustain his voice\n(Cheers). With every respect    in a two hours' speech on\nfor decimal fractions, of       moving that 100000l. be placed\nwhich he boasted no profound    at the disposal of Her\nknowledge, he doubted whether   Majesty, to supply the poor\nthe poor were equal to mental   with ready-reckoners._\narithmetic of this kind,\n(hear, hear) and he hoped the   _Boy._ Fine oranges! two a\nadoption of the system would    penny! two a penny! {178}\nbe deferred until there were\nsome proof that they would be   _Member._ Here boy, two! Now,\nable to understand it; for,     how am I to pay you?\nafter all, this was the\nquestion of the poor, and the   _Boy._ Give you change, your\nwhole weight of the change      honor.\nwould fall upon them. Let the\nrich by all means have          _Member._ Ah! but how? Where's\npermission to perplex           your ready-reckoner?\nthemselves by any division of\na pound they pleased; but do    _Boy._ I sells a better sort\nnot let them, by any            nor them. Mine's real Cheyny.\nexperiment like this, impose\ndifficulties upon the poor and  _Member._ But you see a\ncompel men to carry             farthing is now .0014166666\nready-reckoners in their        _ad infinitum_, and if we\npocket to give them all these   multiply this by 4----\nfractional quantities.\" (Hear,\nhear.)                          _Boy._ Hold hard, Guv'ner; I\n                                sees what you're arter. Now\n                                what'll you stand if I puts\n                                you up to it? which Bill Smith\n                                he put me up in two minutes,\n                                cause he goes to the Ragged\n                                School.\n\n                                _Member._ You don't mean that\n                                you do without a book!\n\n                                _Boy._ Book be blowed. Come\n                                now, old un, here's summut for\n                                both on us. I got a florin,\n                                you gives me a half-a-crown\n                                for it, and I larns you the\n                                new money, gives you your\n                                oranges, and calls you a brick\n                                into the bargain.\n\n                                _Member_ (_to himself_). Never\n                                had such a chance of getting\n                                off half-a-crown for value\n                                since that ---- fellow Bowring\n                                carried his crochet.\n                                (_Aloud._) Well, boy, it's a\n                                bargain. Now!\n\n                                _Boy._ Why, look 'e here, my\n                                trump, its a farden more to\n                                the tizzy--that's what it is.\n\n                                _Member_. What's that?\n\n                                _Boy._ Why, you knows a\n                                sixpence when you sees it.\n                                (_Aside_). Blest if I think he\n                                does! Well, its six browns and\n                                a farden now. A lady buys two\n                                oranges, and forks {179} out a\n                                sixpence; well in coorse, I\n                                hands over fippence farden\n                                astead of fippence. I always\n                                gives a farden more change,\n                                and takes according.\n\n                                _Member_ (_in utter surprise,\n                                lets his oranges tumble into\n                                the gutter_). Never mind! They\n                                won't be wanted now. (_Walks\n                                off one way. Boy makes a pass\n                                of naso-digital mesmerism, and\n                                walks off the other way_).\n\nTo the poor, who keep no books, the whole secret is \"Sixpence farthing to\nthe half shilling, twelve pence halfpenny to the shilling.\" The _new\ntwopence halfpenny_, or cent, will be at once five to the shilling.\n\nIn conclusion, we remark that three very common misconceptions run through\nthe hon. Member's argument; and, combined in different proportions, give\nvariety to his patterns.\n\nFirst, he will have it that we design to bring the uneducated into contact\nwith _decimal fractions_. If it be so, it will only be as M. Jourdain was\nbrought into contact with prose. In fact, _Quoi! quand je dis, Nicole,\napportez-moi mes pantoufles, c'est de la prose?_[305] may be rendered:\n\"What! do you mean that _ten to the florin is a cent a piece_ must be\ncalled decimal reckoning?\" If we had to comfort a poor man, horror-struck\nby the threat of _decimals_, we should tell him what manner of fractions\nhad been inflicted upon him hitherto; nothing less awful than\n_quarto-duodecimo-vicesimals_, we should assure him.\n\nSecondly, he assumes that the penny, such as it now is, will remain, as a\ncoin of estimation, after it has ceased to be a coin of exchange; and that\nthe mass of the people will continue to think of prices in old pence, and\nto calculate them in new ones, or else in new mils. No answer is required\nto this, beyond the mere statement of the nature of the assumption and\ndenial.\n\n{180}\n\nThirdly, he attributes to the uneducated community a want of perception and\nof operative power which really does not belong to them. The evidence\noffered to the Committee of the House shows that no fear is entertained on\nthis point by those who come most in contact with farthing purchasers. And\nthis would seem to be a rule,--that is, fear of the intelligence of the\nlower orders in the minds of those who are not in daily communication with\nthem, no fear at all in the minds of those who are.\n\nA remarkable instance of this distinction happened five-and-twenty years\nago. The Admiralty requested the Astronomical Society to report on the\nalterations which should be made in the _Nautical Almanac_, the seaman's\nguide-book over the ocean. The greatest alteration proposed was the\ndescription of celestial phenomena in _mean_ (or clock time), instead of\n_apparent_ (or sundial) time, till then always employed. This change would\nrequire that in a great many operations the seaman should let alone what he\nformerly altered by addition or subtraction, and alter by addition or\nsubtraction what he formerly let alone; provided always that what he\nformerly altered by addition he should, when he altered at all, alter by\nsubtraction, and _vice versa_. This was a tolerably difficult change for\nuneducated skippers, working by rules they had only learned by rote. The\nAstronomical Society appointed a Committee of forty, of whom nine were\nnaval officers or merchant seamen [I was on this Committee]. Some men of\nscience were much afraid of the change. They could not trust an ignorant\nskipper or mate to make those alterations in their routine, on the\ncorrectness of which the ship might depend. Had the Committee consisted of\nmen of science only, the change might never have been ventured on. But the\nnaval men laughed, and said there was nothing to fear; and on their\nauthority the alteration was made. The upshot was, that, after the new\nalmanacs appeared, not a word of complaint was ever heard on the matter.\nHad the House of Commons had to {181} decide this question, with Mr. Lowe\nto quote the description given by Basil Hall[306] (who, by the way, was one\nof the Committee) of an observation on which the safety of the ship\ndepended, worked out by the light of a lantern in a gale of wind off a lee\nshore, this simple and useful change might at this moment have been in the\nhands of its tenth Government Commission.\n\n\n\n[_Aug. 14, 1866._ The Committee was appointed in the spring of 1830: it\nconsisted of forty members. Death, of course, has been busy; there are now\nleft Lord Shaftesbury,[307] Mr. Babbage,[308] Sir John Herschel,[309] Sir\nThomas Maclear[310] (Astronomer Royal at the Cape of Good Hope), Dr.\nRobinson[311] (of Armagh), Sir James South,[312] Lord Wrottesley,[313] and\nmyself].\n\n{182}\n\n\n\nTHE TONAL SYSTEM.\n\n    Project of a new system of arithmetic, weight, measure, and coins,\n    proposed to be called the tonal system, with sixteen to the base. By\n    J. W. Mystrom.[314] Philadelphia, 1862, 8vo.\n\nThat is to say, sixteen is to take the place of ten, and to be written 10.\nThe whole language is to be changed; every man of us is to be\nsixteen-stringed Jack and every woman sixteen-stringed Jill. Our old _one_,\n_two_, _three_, up to sixteen, are to be (_Noll_ going for nothing, which\nwill please those who dislike the memory of _Old Noll_) replaced by An, De,\nTi, Go, Su, By, Ra, Me, Ni, Ko, Hu, Vy, La, Po, Fy, Ton; and then Ton-an,\nTon-de, etc. for 17, 18, etc. The number which in the system has the symbol\n\n  28(13)5(11)7(14)0(15)\n\n(using our present compounds instead of new types) is to be pronounced\n\n  Detam-memill-lasan-suton-hubong-ramill-posanfy.\n\nThe year is to have sixteen months, and here they are:\n\n  Anuary, Debrian, Timander, Gostus,\n  Suvenary, Bylian, Ratamber, Mesudius,\n  Nictoary, Kolumbian, Husamber, Vyctorius,\n  Lamboary, Polian, Fylander, Tonborius.\n\nSurely An-month, De-month, etc. would do as well. Probably the wants of\npoetry were considered. But what are we to do with our old poets? For\nexample--\n\n \"It was a night of lovely June,\n  High rose in cloudless blue the moon.\"\n\nLet us translate--\n\n \"It was a night of lovely Nictoary,\n  High rose in cloudless blue the (what, in the name of all that is\n      absurd?).\"\n\nAnd again, _Fylander_ thrown into our December! What is {183} to become of\nthose lines of Praed, which I remember coming out when I was at\nCambridge,--\n\n \"Oh! now's the time of all the year for flowers and fun, the Maydays;\n  To trim your whiskers, curl your hair, and sinivate the ladies.\"\n\nIf I were asked which I preferred, this system or that of Baron\nFerrari[315] already mentioned, proceeding by _twelves_, I should reply,\nwith Candide, when he had the option given of running the gauntlet or being\nshot: Les volontes sont libres, et je ne veux ni l'un ni l'autre.[316] We\ncan imagine a speculator providing such a system for Utopia as it would be\nin the mind of a Laputan: but to explain how an engineer who has surveyed\nmankind from Philadelphia to Rostof on the Don should for a moment\nentertain the idea of such a system being actually adopted, would beat a\njury of solar-system-makers, though they were shut up from the beginning of\nAnuary to the end of Tonborius. When I see such a scheme as this imagined\nto be practicable, I admire the wisdom of Providence in providing the\nquadrature of the circle, etc., to open a harmless sphere of action to the\npossessors of the kind of ingenuity which it displays. Those who cultivate\nmathematics have a right to speak strongly on such efforts of arithmetic as\nthis: for, to my knowledge, persons who have no knowledge are frequently\ndisposed to imagine that their makers are true brothers of the craft, a\nlittle more intelligible than the rest.\n\n\n\nSOME SMALL PARADOXERS.\n\n    Vis inertiae victa,[317] or Fallacies affecting science. By James\n    Reddie.[318] London, 1862, 8vo.\n\n{184}\n\nAn attack on the Newtonian mechanics; revolution by gravitation\ndemonstrably impossible; much to be said for the earth being the immovable\ncenter. A good analysis of contents at the beginning, a thing seldom found.\nThe author has followed up his attack in a paper submitted to the British\nAssociation, but which it appears the Association declined to consider. It\nis entitled--\n\n\n\n    _Victoria Toto Coelo_; or, Modern Astronomy recast. London, 1863, 8vo.\n\nAt the end is a criticism of Sir G. Lewis's _History of Ancient Astronomy_.\n\n\n\n    On the definition and nature of the Science of Political Economy. By H.\n    Dunning Macleod,[319] Esq. Cambridge, 1862, 8vo.\n\nA paper read--but, according to the report, not understood--at the British\nAssociation. There is a notion that political economy is entirely\nmathematical; and its negative quantity is strongly recommended for study:\nit contains \"the whole of the Funds, Credit, 32 parts out of 33 of the\nvalue of Land....\" The mathematics are described as consisting of--first,\nnumber, or Arithmetic; secondly, the theory of dependent quantities,\nsubdivided into dependence by cause and effect, and dependence by\nsimultaneous variations; thirdly, \"independent quantities or unconnected\nevents, which is the theory of probabilities.\" I am not ashamed, having the\nBritish Association as a co-non-intelligent, to say I do not understand\nthis: there is a paradox in it, and the author should give further\nexplanation, especially of his negative quantity. Mr. Macleod has gained\n{185} praise from great names for his political economy; but this, I\nsuspect, must have been for other parts of his system.\n\n\n\n    On the principles and practice of just Intonation, with a view to the\n    abolition of temperament.... By General Perronet Thompson.[320] Sixth\n    Edition. London, 1862, 8vo.\n\nHere is General Thompson again, with another paradox: but always master of\nthe subject, always well up in what his predecessors have done, and always\naiming at a useful end. He desires to abolish temperament by additional\nkeys, and has constructed an enharmonic organ with forty sounds in the\noctave. If this can be introduced, I, for one, shall delight to hear it:\nbut there are very great difficulties in the way, greater than stood even\nin the way of the repeal of the bread-tax.\n\nIn a paper on the beats of organ-pipes and on temperament published some\nyears ago, I said that equal temperament appeared to me insipid, and not so\nagreeable as the effect of the instrument when in progress towards being\nwhat is called out of tune, before it becomes offensively wrong. There is\nthroughout that period unequal temperament, determined by accident. General\nThompson, taking me one way, says I have launched a declaration which is\nlikely to make an epoch in musical practice; a public musical critic,\ntaking me another way, quizzes me for preferring music _out of tune_. I do\nnot think I deserve either one remark or the other. My opponent critic, I\nsuspect, takes _equally tempered_ and _in tune_ to be phrases of one\nmeaning. But by equal temperament is meant equal distribution among all the\nkeys of the error which an instrument _must_ have, which, with twelve\nsounds only in the octave, professes to be fit for all the keys. I am\nreminded of the equal temperament which was once applied to the postmen's\njackets. The coats were all made for the average man: the {186} consequence\nwas that all the tall men had their tails too short; all the short men had\nthem too long. Some one innocently asked why the tall men did not change\ncoats with the short ones.\n\n\n\n    A diagram illustrating a discovery in the relation of circles to\n    right-lined geometrical figures. London, 1863, 12mo.\n\nThe circle is divided into equal sectors, which are joined head and tail:\nbut a property is supposed which is not true.\n\n\n\n    An attempt to assign the square roots of negative powers; or what is\n    [sqrt] -1? By F.H. Laing.[321] London, 1863, 8vo.\n\nIf I understand the author, -a and +a are the square roots of -a^2, as\nproved by multiplying them together. The author seems quite unaware of what\nhas been done in the last fifty years.\n\n\n\nBYRNE'S DUAL ARITHMETIC.\n\n    Dual Arithmetic. A new art. By Oliver Byrne.[322] London, 1863, 8vo.\n\nThe plan is to throw numbers into the form a(1.1)^{b} (1.01)^{c}\n(1.001)^{d}... and to operate with this form. This is an ingenious and\nelaborate speculation; and I have no doubt the author has practised his\nmethod until he could surprise any one else by his use of it. But I doubt\nif he will persuade others to use it. As asked of Wilkins's universal\nlanguage, Where is the second man to come from?\n\nAn effective predecessor in the same line of invention {187} was the late\nMr. Thomas Weddle,[323] in his \"New, simple, and general method of solving\nnumeric equations of all orders,\" 4to, 1842. The Royal Society, to which\nthis paper was offered, declined to print it: they ought to have printed an\norganized method, which, without subsidiary tables, showed them, in six\nquarto pages, the solution (x=8.367975431) of the equation\n\n  1379.664 x^{622} + 2686034 x 10^{432} x^{152} - 17290224 x 10^{518}\n      x^{60} + 2524156 x 10^{574} = 0.\n\nThe method proceeds by successive factors of the form, a being the first\napproximation, a x 1.b x 1.0c x 1.00d.... In my copy I find a few\ncorrections made by me at the time in Mr. Weddle's announcement. \"It was\nread before that learned body [the R. S.] and they were pleased [but] to\ntransmit their thanks to the author. The en[dis]couragement which he\nreceived induces [obliges] him to lay the result of his enquiries in this\nimportant branch of mathematics before the public [, at his own expense; he\nbeing an usher in a school at Newcastle].\" Which is most satirical, Mr.\nWeddle or myself? The Society, in the account which it gave of this paper,\ndescribed it as a \"new and remarkably simple method\" possessing \"several\nimportant advantages.\" Mr. Rutherford's[324] extended value of [pi] was\nread at the very next meeting, and was printed in the _Transactions_; and\nvery properly: Mr. Weddle's paper was excluded, and very very improperly.\n\n\n\nHORNER'S METHOD.\n\nI think it may be admited that the indisposition to look at and encourage\nimprovements of calculation which once {188} marked the Royal Society is no\nlonger in existence. But not without severe lessons. They had the luck to\naccept Horner's[325] now celebrated paper, containing the method which is\nfar on the way to become universal: but they refused the paper in which\nHorner developed his views of this and other subjects: it was printed by\nT. S. Davies[326] after Horner's death. I make myself responsible for the\nstatement that the Society could not reject this paper, yet felt unwilling\nto print it, and suggested that it should be withdrawn; which was done.\n\nBut the severest lesson was the loss of _Barrett's Method_,[327] now the\nuniversal instrument of the actuary in his highest calculations. It was\npresented to the Royal Society, and refused admission into the\n_Transactions_: Francis Baily[328] printed it. The Society is now better\ninformed: \"_live and learn_,\" meaning \"_must live, so better learn_,\" ought\nto be the especial motto of a corporation, and is generally acted on, more\nor less.\n\nHorner's method begins to be introduced at Cambridge: it was published in\n1820. I remember that when I first went to Cambridge (in 1823) I heard my\ntutor say, in conversation, there is no doubt that the true method of\nsolving equations is the one which was published a few years ago in the\n_Philosophical Transactions_. I wondered it was not taught, but presumed\nthat it belonged to the higher mathematics. This Horner himself had in his\nhead: and in a sense it is true; for all lower branches belong to the\nhigher: but he would have stared to have been told that he, Horner, {189}\nwas without a European predecessor, and in the distinctive part of his\ndiscovery was heir-at-law to the nameless\nBrahmin--Tartar--Antenoachian--what you please--who concocted the\nextraction of the square root.\n\nIt was somewhat more than twenty years after I had thus heard a Cambridge\ntutor show sense of the true place of Horner's method, that a pupil of mine\nwho had passed on to Cambridge was desired by his college tutor to solve a\ncertain cubic equation--one of an integer root of two figures. In a minute\nthe work and answer were presented, by Horner's method. \"How!\" said the\ntutor, \"this can't be, you know.\" \"There is the answer, Sir!\" said my\npupil, greatly amused, for my pupils learnt, not only Horner's method, but\nthe estimation it held at Cambridge. \"Yes!\" said the tutor, \"there is the\nanswer certainly; but it _stands to reason_ that a cubic equation cannot be\nsolved in this space.\" He then sat down, went through a process about ten\ntimes as long, and then said with triumph: \"There! that is the way to solve\na cubic equation!\"\n\nI think the tutor in this case was never matched, except by the country\norganist. A master of the instrument went into the organ-loft during\nservice, and asked the organist to let him _play the congregation out_;\nconsent was given. The stranger, when the time came, began a voluntary\nwhich made the people open their ears, and wonder who had got into the\nloft: they kept their places to enjoy the treat. When the organist saw\nthis, he pushed the interloper off the stool, with \"You'll never play 'em\nout this side Christmas.\" He then began his own drone, and the congregation\nbegan to move quietly away. \"There,\" said he, \"that's the way to play 'em\nout!\"\n\nI have not scrupled to bear hard on my own university, on the Royal\nSociety, and on other respectable existences: being very much the friend of\nall. I will now clear the Royal Society from a very small and obscure\nslander, simply because I know how. This dissertation began with {190} the\nwork of Mr. Oliver Byrne, the dual arithmetician, etc. This writer\npublished, in 1849, a method of calculating logarithms.[329] First, a long\nlist of instances in which, as he alleges, foreign discoverers have been\npillaged by Englishmen, or turned into Englishmen: for example,\nO'Neill,[330] so called by Mr. Byrne, the rectifier of the semi-cubical\nparabola claimed by the Saxons under the name of _Neal_: the grandfather of\nthis mathematician was conspicuous enough as _Neal_; he was archbishop of\nYork. This list, says the writer, might be continued without end; but he\nhas mercy, and finishes with his own case, as follows:--\"About twenty years\nago, I discovered this method of directly calculating logarithms. I could\ngenerally find the logarithm of any number in a minute or two without the\nuse of books or tables. The importance of the discovery subjected me to all\nsorts of prying. Some asserted that I committed a table of logarithms to\nmemory; others attributed it to a peculiar mental property; and when\nSocieties and individuals failed to extract my secret, they never failed to\ntraduce the inventor and the invention. Among the learned Societies, the\nRoyal Society of London played a very base part. When I have more space and\ntime at my disposal, I will revert to this subject again.\"\n\nSuch a trumpery story as this remains unnoticed at the time; but when all\nare gone, a stray copy from a stall falls into hands which, not knowing\nwhat to make of it, make history of it. It is a very curious distortion.\nThe reader may take it on my authority, that the Royal Society played no\npart, good or bad, nor had the option of playing a part. {191} But I myself\n_pars magna fui_:[331] and when the author has \"space and time\" at his\ndisposal, he must not take all of them; I shall want a little of both.\n\n\n\nARE ATOMS WORLDS?\n\n    The mystery of being; or are ultimate atoms inhabited worlds? By\n    Nicholas Odgers.[332] Redruth and London, 1863, 8vo.\n\nThis book, as a paradox, beats quadrature, duplication, trisection,\nphilosopher's stone, perpetual motion, magic, astrology, mesmerism,\nclairvoyance, spiritualism, homoeopathy, hydropathy, kinesipathy, Essays\nand Reviews, and Bishop Colenso,[333] all put together. Of all the\nsuppositions I have given as actually argued, this is the one which is\nhardest to deny, and hardest to admit. Reserving the question--as beyond\nhuman discussion--whether our particles of carbon, etc. are _clusters_ of\nworlds, the author produces his reasons for thinking that they are at least\nsingle worlds. Of course--though not mentioned--the possibility is to be\nadded of the same thing being true of the particles which make up our\nparticles, and so down, for ever: and, on the other hand, of our planets\nand stars as being particles in some larger universe, and so up, for ever.\n\n \"Great fleas have little fleas upon their backs to bite 'em,\n  And little fleas have lesser fleas, and so _ad infinitum._\n  And the great fleas themselves, in turn, have greater fleas to go on;\n  While these again have greater still, and greater still, and so on.\"[334]\n\nI have often had the notion that all the nebulae we see, including our own,\nwhich we call the Milky Way, may be particles of snuff in the box of a\ngiant of a proportionately {192} larger universe. Of course the minim of\ntime--a million of years or whatever the geologists make it[335]--which our\nlittle affair has lasted, is but a very small fraction of a second to the\ngreat creature in whose nose we shall all be in a few tens of thousands of\nmillions of millions of millions of years.\n\nAll this is quite possible, and the probabilities for and against are quite\nout of reach. Perhaps also all the worlds, both above and below us, are\nfac-similes of our own. If so, away goes free will for good and all;\nunless, indeed, we underpin our system with the hypothesis that all the\nfac-simile bodies of different sizes are actuated by a common soul. These\nacute supplementary notions of mine go far to get rid of the difficulty\nwhich some have found in the common theory that the soul inhabits the body:\nit has been stated that there is, somewhere or another, a world of souls\nwhich communicate with their bodies by wondrous filaments of a nature\nneither mental nor material, but of a _tertium quid_ fit to be a\ngo-between; as it were a corporispiritual copper encased in a\nspiritucorporeal gutta-percha. My theory is that every soul is everywhere\n_in posse_, as the schoolmen said, but not anywhere _in actu_, except where\nit finds one of its bodies. These _a priori_ difficulties being thus\nremoved, the system of particle-worlds is reduced to a dry question of\nfact, and remitted to the decision of the microscope. And a grand field may\nthus be opened, as optical science progresses! For the worlds are not\nfac-similes of ours in time: there is not a moment of _our_ past, and not a\nmoment of _our_ future, but is the _present_ of one or more of the\nparticles. A will write the death of Caesar, and B the building of the\nPyramids, by actual observation of the processes with a power of a thousand\nmillions; C will discover the commencement of the Millennium, and D the\n{193} termination of Ersch and Gruber's Lexicon,[336] as mere physical\nphenomena. Against this glorious future there is a sad omen: the initials\nof the forerunner of this discovery are--NO!\n\n\n\nTHE SUPERNATURAL.\n\n    The History of the Supernatural in all ages and nations, and in all\n    Churches, Christian and Pagan: demonstrating a universal faith. By Wm.\n    Howitt.[337] London, 2 vols. 8vo. 1863.\n\nMr. Howitt is a preacher of spiritualism. He cements an enormous collection\nof alleged facts with a vivid outpouring of exhortation, and an unsparing\nflow of sarcasm against the scorners of all classes. He and the Rev. J.\nSmith[338] (_ante_, 1854) are the most thoroughgoing universalists of all\nthe writers I know on spiritualism. If either can insert the small end of\nthe wedge, he will not let you off one fraction of the conclusion that all\ncountries, in all ages, have been the theaters of one vast spiritual\ndisplay. And I suspect that this consequence cannot be avoided, if any part\nof the system be of truly spiritual origin. Mr. Howitt treats the\nphilosophers either as ignorant babies, or as conscious spirit-fearers: and\nseems much inclined to accuse the world at large of dreading, lest by the\nactual presence of the other world their Christianity should imbibe a\nspiritual element which would unfit it for the purposes of their lives.\n\n{194}\n\n\n\nFROM MATTER TO SPIRIT.\n\n    From Matter to Spirit. By C. D. With a preface by A. B.[339] London,\n    1863, 8vo.\n\nThis is a work on Spiritual Manifestations. The author upholds the facts\nfor spiritual phenomena: the prefator suspends his opinion as to the cause,\nthough he upholds the facts. The work begins systematically with the lower\nclass of phenomena, proceeds to the higher class, and offers a theory,\nsuggested by the facts, of the connection of the present and future life. I\nagree in the main with A. B.; but can, of course, make none but horrescent\nreference to his treatment of the smaller philosophers. This is always the\nway with your paradoxers: they behave towards orthodoxy as the thresher\nfish behaves towards the whale. But if true, as is said, that the drubbing\nclears the great fish of parasites which he could not otherwise get rid of,\nhe ought to bear no malice. This preface retorts a little of that contempt\nwhich the \"philosophical world\" has bestowed with heaped measure upon those\nwho have believed their senses, and have drawn natural, even if hasty,\ninferences. There is philosophercraft as well as priestcraft, both from one\nsource, both of one spirit. In English cities and towns, the minister of\nreligion has been tamed: so many weapons are bared against him when he\nobtrudes his office in a dictatory manner, that, as a rule, there is no\nmore quiet and modest member of society than the urban clergyman.\nDomination over religious belief is reserved for the exclusive use of those\nwho admit the right: the rare exception to this mode of behavior is laughed\nat as a bigot, or shunned as a nuisance. But the overbearing minister of\nnature, who snaps you with _unphilosophical_ as the clergyman once\nfrightened you with _infidel_, is still a recognized member of society,\nwants taming, and will get it. He wears the priest's cast-off {195}\nclothes, dyed to escape detection: the better sort of philosophers would\ngladly set him to square the circle.\n\nThe book just named appeared about the same time as this Budget began in\nthe _Athenaeum_. It was commonly attributed, the book to my wife, the\npreface to myself. Some time after, our names were actually announced by\nthe publisher, who ought to know. It will be held to confirm this statement\nthat I announce our having in our possession some twenty reviews of\ndifferent lengths, and of all characters: who ever collects a number of\nreviews of a book, except the author?\n\nA great many of these reviews settle the matter _a priori_. If there had\nbeen spirits in the matter, they would have done this, and they would not\nhave done that. Jean Meslier[340] said there could be no God over all, for,\n_if_ there had been one, He would have established a universal religion. If\nJ. M. _knew_ that, J. M. was right: but if J. M. did not know that, then\nJ. M. was on the \"high priori road,\" and may be left to his course. The\nsame to all who know what spirits would do and would not do.\n\nA. B. very distinctly said that he knew some of the asserted facts,\nbelieved others on testimony, but did not pretend to know whether they were\ncaused by spirits, or had some unknown and unimagined origin. This he said\nas clearly as I could have said it myself. But a great many persons cannot\nunderstand such a frame of mind: their own apparatus is a kind of\nspirit-level, and their conclusion on any subject is the little bubble,\nwhich is always at one end or the other. Many of the reviewers declare that\nA. B. is a secret believer in the spirit-hypothesis: and one of them wishes\nthat he had \"endorsed his opinion more boldly.\" According to this reviewer,\nany one who writes \"I boldly {196} say I am unable to choose,\" contradicts\nhimself. In truth, a person who does say it has a good deal of courage, for\neach side believes that he secretly favors the other; and both look upon\nhim as a coward. In spite of all this, A. B. boldly repeats that he feels\nassured of many of the facts of _spiritualism_, and that he cannot pretend\nto affirm or deny anything about their cause.\n\nThe great bulk of the illogical part of the educated community--whether\nmajority or minority I know not; perhaps six of one and half-a-dozen of the\nother--have not power to make a distinction, cannot be made to take a\ndistinction, and of course, never attempt to shake a distinction. With them\nall such things are evasions, subterfuges, come-offs, loopholes, etc. They\nwould hang a man for horse-stealing under a statute against sheep-stealing;\nand would laugh at you if you quibbled about the distinction between a\nhorse and a sheep. I divide the illogical--I mean people who have not that\namount of natural use of sound inference which is really not uncommon--into\nthree classes:--First class, three varieties: the Niddy, the Noddy, and the\nNoodle. Second class, three varieties: the Niddy-Noddy, the Niddy-Noodle,\nand the Noddy-Noodle. Third class, undivided: the Niddy-Noddy-Noodle. No\nperson has a right to be angry with me for more than one of these\nsubdivisions.\n\nThe want of distinction was illustrated to me, when a boy, about 1820, by\nthe report of a trial which I shall never forget: boys read newspapers more\nkeenly than men. Every now and then a bench of country magistrates rather\nastonishes the town populations, accustomed to rub their brains[341]\nagainst one another. Such a story as the following would, {197} in our day,\nbring down grave remarks from above: but I write of the olden (or\nEldon[342]) time, when nothing but conviction in a court of record would\ndisplace a magistrate. In that day the third-class amalgamator of distinct\nthings was often on the bench of quarter-sessions.\n\nAn attorney was charged with having been out at night poaching. A clear\n_alibi_ was established; and perjury had certainly been committed. The\nwhole gave reason to suspect that some ill-willers thought the bench\ndisliked the attorney so much that any conviction was certain on any\nevidence. The bench did dislike the attorney: but not to the extent of\nthinking he could snare any partridges in the fields while he was asleep in\nbed, except the dream-partridges which are not always protected by the\ndream-laws. So the chairman said, \"Mr. ----, you are discharged; but you\nshould consider this one of the most fortunate days of your life.\" The\nattorney indignantly remonstrated, but the magistrate was right; for he\nsaid, \"Mr. ----, you have frequently been employed to defend poachers: have\nyou been careful to impress upon them the enormity of their practices?\" It\nappeared in a wrangling conversation that the magistrates saw little moral\ndifference between poaching and being a poacher's professional defender\nwithout lecturing him on his wickedness: but they admitted with reluctance,\nthat there was a legal distinction; and the brain of N^3 could no further\ngo. This is nearly fifty years ago; and Westernism was not quite extinct.\nIf the present lords of the hills and the valleys want to shine, let them\npublish a true history of their own order. I am just old enough to remember\nsome of the last of the squires and parsons who protested against teaching\nthe poor to read and write. They now write books for the working classes,\ngive them lectures, and the like. There is now no class, as a class, more\nhighly educated, broadly educated, and deeply educated, {198} than those\nwho were, in old times, best described as partridge-popping squireens. I\nhave myself, when a boy, heard Old Booby speaking with pride of Young Booby\nas having too high a spirit to be confined to books: and I suspected that\nhis dislike to teaching the poor arose in fact from a feeling that they\nwould, if taught a little, pass his heir.\n\nA. B. recommended the spirit-theory as an hypothesis on which to ground\ninquiry; that is, as the means of suggestion for the direction of inquiry.\nEvery person who knows anything of the progress of physics understands what\nis meant; but not the reviewers I speak of. Many of them consider A. B. as\n_adopting_ the spirit-hypothesis. The whole book was written, as both the\nauthors point out, to suggest inquiry to those who are curious; C. D.\nfirmly believing, A. B. as above. Neither C. D. nor A. B. make any other\npretence. Both dwell upon the absence of authentications and the\nsuppression of names as utterly preventive of anything like proof. And\nA. B. says that his reader \"will give him credit, if not himself a goose,\nfor seeing that the tender of an anonymous cheque would be of equal effect,\nwhether drawn on the Bank of England or on Aldgate Pump.\" By this test a\nnumber of the reviewers are found to be geese: for they take the authors as\noffering proof, and insist, against the authors, on the very point on which\nthe authors had themselves insisted beforehand.\n\nLeaving aside imperceptions of this kind, I proceed to notice a clerical\nand medical review. I have lived much in the middle ages, especially since\nthe invention of printing; and from thence I have brought away a high\nrespect for and grateful recollection of--the priest in everything but\ntheology, and the physician in everything but medicine. The professional\nharness was unfavorable to all progress, except on a beaten road; the\nprofessional blinkers prevented all but the beaten road from being seen:\nthe professional reins were pulled at the slightest attempt to quicken\npace, even on the permitted path; and the {199} professional whip was\nheavily laid on at the slightest attempt to diverge. But when the\nintelligent man of either class turned his attention out of his ordinary\nwork, he had, in most cases, the freshness and vigor of a boy at play, and\nlike the boy, he felt his freedom all the more from the contrast of\nschool-restraint.\n\nIn the case of medicine, and physics generally, the learned were, in some\nessential points, more rational than many of their present impugners. They\npass for having put _a priori_ obstacles in the way of progress: they might\nrather be reproved for too much belief in progress obtained by _a priori_\nmeans. They would have shouted with laughter at a dunce who--in a review I\nread, but without making a note--declared that he would not believe his\nsenses except when what they showed him was capable of explanation upon\nsome known principle. I have seen such stuff as this attributed to the\nschoolmen; but only by those who knew nothing about them. The following,\nwhich I wrote some years ago, will give a notion of a distinction worth\nremembering. It is addressed to the authorities of the College of\nPhysicians.\n\n\"The ignominy of the word _empiric_ dates from the ages in which scholastic\nphilosophy deduced physical consequences _a priori_;--the ages in which,\nbecause a lion is strong, rubbing with lion's fat would have been held an\ninfallible tonic. In those happy days, if a physician had given decoction\nof a certain bark, only because in numberless instances that decoction had\nbeen found to strengthen the patient, he would have been a miserable\nempiric. Not that the colleges would have passed over his returns because\nthey were empirical: they knew better. They were as skilful in finding\ncauses for facts, as facts for causes. The president and the elects of that\nday would have walked out into the forest with a rope, and would have\npulled heartily at the tree which yielded the bark: nor would they ever\nhave left it until they had pulled out a legitimate {200} reason. If the\ntree had resisted all their efforts, they would have said, 'Ah! no wonder\nnow; the bark of a strong tree makes a strong man.' But if they had managed\nto serve the tree as you would like to serve homoeopathy, then it would\nhave been 'We might have guessed it; all the _virtus roborativa_ has\nsettled in the bark.' They admitted, as we know from Moliere, the _virtus\ndormitiva_[343] of opium, for no other reason than that opium _facit\ndormire_.[344] Had the medicine not been previously _known_, they would,\nstrange as it may seem to modern pharmacopoeists, have accorded a _virtus\ndormitiva_ to the new _facit dormire_. On this point they have been\nmisapprehended. They were prone to infer _facit_ from a _virtus_ imagined\n_a priori_; and they were ready in supplying _facit_ in favor of an\northodox _virtus_. They might have gone so far, for example, under\npre-notional impressions, as the alliterative allopath, who, when\nmaintenance of truth was busy opposing the progress of science called\n_vaccination_, declared that some of its patients coughed like cows, and\nbellowed like bulls; but they never refused to find _virtus_ when _facit_\ncame upon them, no matter whence. They would rather have accepted Tenterden\nsteeple than have rejected the Goodwin Sands. They would have laughed their\nmodern imitators to scorn: but as they are not here, we do it for them.\n\n\"The man of our day--the _a priori_ philosopher--tries the question whether\nopium can cause sleep by finding out in the recesses of his own noddle\nwhether the drug can have a dormitive power: Well! but did not the\nschoolman do the same? He did; but mark the distinction. The schoolman had\nrecourse to first principles, when there was no opium to try it by: our man\nsettles the point in the same way _with a lump of opium before him_. The\nschoolman shifted his principles with his facts: the man of our\ndrawing-rooms will fight facts with his principles, just as an old {201}\nphysician would have done in actual practice, with the rod of his _Church_\nat his back.\n\n\"The story about Galileo--which seems to have been either a joke made\nagainst him, or by him--illustrates this. _Nature abhors a vacuum_ was the\nexplanation of the water rising in a pump: but they found that the water\nwould not rise more than 32 feet. They asked for explanation: what does the\nsatirist make the schoolmen say? That the stoppage is _not_ a fact, because\nnature abhors a vacuum? No! but that the principle should be that nature\nabhors a vacuum as far as 32 feet. And this is what would have been done.\n\n\"There are still among us both priests and physicians who would have\nbelonged, had they lived three or four centuries ago, to the glorious band\nof whom I have spoken, the majority of the intelligent, working well for\nmankind out of the professional pursuit. But we have a great many who have\nhelped to abase their classes. Go where we may, we find specimens of the\nlower orders of the ministry of religion and the ministry of health showing\nthemselves smaller than the small of other pursuits. And how is this?\nFirst, because each profession is entered upon a mere working smack of its\nknowledge, without any depth of education, general or professional. Not\nthat this is the whole explanation, nor in itself objectionable: the great\nmass of the world must be tended, soul and body, by those who are neither\nHookers[345] nor Harveys[346]: let such persons not venture _ultra\ncrepidam_, and they are useful and respectable. But, secondly, there is a\nvast upheaving of thought from the depths of commonplace learning. I am a\nclergyman! Sir! I am a medical man! Sir! and forthwith the nature of things\nis picked to pieces, and there is a race, with the last the winner, between\nPhilosophy mounted on Folly's donkey, and Folly mounted on Philosophy's\ndonkey. How fortunate {202} it is for Law that her battles are fought by\npoliticians in the Houses of Parliament. Not that it is better done: but\nthen _politics_ bears the blame.\"\n\nI now come to the medical review. After a quantity of remark which has been\nalready disposed of, the writer shows Greek learning, a field in which the\nold physician would have had a little knowledge. A. B., for the joke's\nsake, had left untranslated, as being too deep, a remarkably easy sentence\nof Aristotle, to the effect that what has happened was possible, for if\nimpossible it would not have happened. The reviewer, in \"simple\nastonishment,\"--it was simple--at the pretended incapacity--I was told by\nA. B. that the joke was intended to draw out a reviewer--translates:--He\nsays that this sentence is A. B.'s summing up of the evidence of\nSpiritualism. Now, being a sort of _alter ego_[347] of A. B., I do declare\nthat he is not such a fool as to rest the evidence of Spiritualism--the\n_spirit explanation_--upon the occurrence of certain facts proving the\npossibility of those very facts. In truth, A. B. refuses to receive\nspiritualism, while he receives the facts: this is the gist of his whole\npreface, which simply admits spiritualism among the qualified candidates,\nand does not know what others there may be.\n\nThe reviewer speaks of Aristotle as \"that clear thinker and concise\nwriter.\" I strongly suspect that his knowledge of Aristotle was limited to\nthe single sentence which he had translated or got translated. Aristotle is\nconcise in _phrase_, not in book, and is powerful and profound in thought:\nbut no one who knows that his writing, all we have of him, is the very\nopposite of clear, will pretend to decide that he thought clearly. As his\nwriting, so probably was his thought; and his books are, if not anything\nbut clear, at least anything good but clear. Nobody thinks them clear\nexcept a person who always clears difficulties: which I have no doubt was\nthe reviewer's habit; that is, if he ever took the field {203} at all. The\ngentleman who read Euclid, all except the As and Bs and the pictures of\nscratches and scrawls, is the type of a numerous class.\n\nThe reviewer finds that the word _amosgepotically_, used by A. B., is\nutterly mysterious and incomprehensible. He hopes his translation of the\nbit of Greek will shield him from imputation of ignorance: and thinks the\nword may be referred to the \"obscure dialect\" out of which sprung\n_aneroid_, _kalos geusis sauce_, and _Anaxyridian trousers_. To lump the\nfirst two phrases with the third smacks of ignorance in a Greek critic; for\n[Greek: anaxuridia], _breeches_, would have turned up in the lexicon; and\n_kalos geusis_, though absurd, is not obscure. And [Greek: amosgepos],\n_somehow or other_, is as easily found as [Greek: anaxuridia]. The word\n_aneroid_, I admit, has puzzled better scholars than the critic: but never\none who knows the unscholarlike way in which words ending in [Greek: eides]\nhave been rendered. The _aneroid barometer_ does _not_ use a column of air\nin the same way as the old instrument. Now [Greek: aeroeides]--properly\n_like_ the atmosphere--is by scientific non-scholarship rendered having to\ndo with the atmosphere; and [Greek: anaeroeides]--say _anaeroid_--denies\nhaving to do with the atmosphere; a nice thing to say of an instrument\nwhich is to measure the weight of the atmosphere. One more absurdity, and\nwe have _aneroid_, and there you are. The critic ends with a declaration\nthat nothing in the book shakes his faith in a _Quarterly_ reviewer who\nsaid that suspension of opinion, until further evidence arrives, is\njustifiable: a strange summing up for an article which insists upon utter\nrejection being unavoidable.[348] The expressed aim of both A. B. and C. D.\nwas to excite inquiry, and get further evidence: until this is done,\nneither asks for a verdict.\n\nOh where! and oh where! is old Medicine's learning gone! There _was_ some\nin the days of yore, when Popery {204} was on! And it's oh! for some Greek,\njust to find a word upon! The reviewer who, lexicon in hand, can neither\nmake out _anaxyridical_, _amosgepotical_, _kalos geusis_, nor distinguish\nthem from _aneroid_, cannot be trusted when he says he has translated a\nsentence of Aristotle. He may have done it; but, as he says of\nspiritualism, we must suspend our opinion until further evidence shall\narrive.\n\nWe now come to the theological review. I have before alluded to the faults\nof logic which are Protestant necessities: but I never said that Protestant\nargument had _nothing but_ paralogism. The writer before me attains this\ncompleteness: from beginning to end he is of that confusion and perversion\nwhich, as applied to interpretation of the New Testament, is so common as\nto pass unnoticed by sermon-hearers; but which, when applied out of church,\nis exposed with laughter in all subjects except theology. I shall take one\ninstance, putting some words in italics.\n\n_A. B._                         _Theological Critic._\n\nMy state of mind, which refers  ... he proceeds to argue that\nthe whole _either_ to unseen    he himself is outside its\nintelligence, _or something     sacred pale because he refers\nwhich man has never had any     all these strange phenomena to\nconception of_, proves me to    _unseen spiritual\nbe out of the pale of the       intelligence_.\nRoyal Society.\n\nThe possibility of a _yet unimagined_ cause is insisted on in several\nplaces. On this ground it is argued by A. B. that spiritualists are\n\"incautious\" for giving in at once to the spirit doctrine. But, it is said,\nthey may be justified by the philosophers, who make the flint _axes_, as\nthey call them, to be the works of men, because no one can see _what else\nthey can be_. This kind of adoption, _condemned_ as a conclusion, is\n_approved_ as a provisional theory, suggestive of direction of inquiry:\nexperience having shown that {205} inquiry directed by a _wrong_ theory has\nled to more good than inquiry without any theory at all. All this A. B. has\nfully set forth, in several pages. On it the reviewer remarks that \"with\ninfinite satisfaction he tries to justify his view of the case by urging\nthat there is no other way of accounting for it; after the fashion of the\nphilosophers of our own day, who conclude that certain flints found in the\ndrift are the work of men, because the geologist does not see what else\nthey can be.\" After this twist of meaning, the reviewer proceeds to say,\nand A. B. would certainly join him, \"There is no need to combat any such\nmode of reasoning as this, because it would apply with equal force and\njustice to any theory whatever, however fantastic, profane, or silly.\" And\nso, having shown how the reviewer has hung himself, I leave him\nfunipendulous.\n\nOne instance more, and I have done. A reviewer, not theological, speaking\nof the common argument that things which are derided are not _therefore_ to\nbe rejected, writes as follows:--\"It might as well be said that they who\nlaughed at Jenner[349] and vaccination were, in a certain but very\nunsatisfactory way, witnesses to the possible excellence of the system of\nSt. John Long.\"[350] Of course it _might_: and of course it _is_ said by\nall people of common sense. In introducing the word \"possible,\" the\nreviewer has hit the point: I suspect that this word was introduced during\nrevision, to put the sentence into fighting order; hurry preventing it\nbeing seen that the sentence was thus made to fight on the wrong side.\nJenner, who was laughed at, was right; therefore, it is not\nimpossible--that is, it is _possible_--that a derided system may be right.\nMark the three gradations: _in medio tutissimus ibis_.[351]\n\n{206}\n\n_Reviewer._--If a system be derided, it is no ground of suspense that\nderided systems have turned out true: if it were, you would suspend your\nopinion about St. John Long on account of Jenner.--_Ans._ You ought to do\nso, as to _possibility_; and _before examination_; not with the notion that\nJ. proves St. J. _probable_; only _possible_.\n\n_Common Sense._--The past emergence of truths out of derided systems proves\nthat there is a practical certainty of like occurrence to come. But,\ninasmuch as a hundred speculative fooleries are started for one truth, the\nmind is permitted to approach the examination of any one given novelty with\na bias against it of a hundred to one: and this permission is given because\nso it will be, leave or no leave. Every one has licence not to jump over\nthe moon.\n\n_Paradoxer._--Great men have been derided, and I am derided: which proves\nthat my system ought to be adopted. This is a summary of all the degrees in\nwhich paradoxers contend for the former derision of truths now established,\ngiving their systems _probability_. I annex a paragraph which D [e &c.]\ninserted in the _Athenaeum_ of October 23, 1847.\n\n\"_Discoverers and Discoveries._\n\n\"Aristotle once sent his servant to the cellar to fetch wine:--and the\nfellow brought him back small beer. The Stagirite (who knew the difference)\ncalled him a blockhead. 'Sir,' said the man, 'all I can say is, that I\nfound it in the cellar.' The philosopher muttered to himself that an\naffirmative conclusion could not be proved in the second figure,--and Mrs.\nAristotle, who was by, was not less effective in her remark, that small\nbeer was not wine because it was in the same cellar. Both were right\nenough: and our philosophers might take a lesson from either--for they\ninsinuate an affirmative conclusion in the second figure. Great discoverers\nhave been little valued by established {207} schools,--and they are little\nvalued. The results of true science are strange at first,--and so are\ntheir's. Many great men have opposed existing notions,--and so do they. All\ngreat men were obscure at first,--and they are obscure. Thinking men\ndoubt,--and they doubt. Their small beer, I grant, has come out of the same\ncellar as the wine; but this is not enough. If they had let it stand awhile\nin the old wine-casks, it might have imbibed a little of the flavor.\"\n\n\n\nThere are better reviews than I have noticed; which, though entirely\ndissenting, are unassailable on their own principles. What I have given\nrepresents five-sixths of the whole. But it must be confessed that the\nfraction of fairness and moderation and suspended opinion which the\ndoctrine of _Spirit Manifestations_ has met with--even in the lower\nreviews--is strikingly large compared to what would have been the case\nfifty years ago. It is to be hoped that our popular and periodical\nliteratures are giving us one thinker created for twenty geese\ndouble-feathered: if this hope be realized, we shall do! Seeing all that I\nsee, I am not prepared to go the length of a friend of mine who, after\nreading a good specimen of the lower reviewing, exclaimed--Oh! if all the\nfools in the world could be rolled up into one fool, what a reviewer he\nwould make!\n\n\n\n    Calendrier Universel et Perpetuel; par le Commandeur P. J. Arson.[352]\n    Publie par ses Enfans (Oeuvre posthume). Nice, 1863, 4to.\n\nI shall not give any account of this curious calendar, with all its changes\nand symbols. But there is one proposal, which, could we alter the general\nnotions of time--a thing of very dubious possibility--would be convenient.\nThe week is made to wax and wane, culminating on the Sunday, {208} which\ncomes in the middle. Thursday, Friday, Saturday, are ascending or waxing\ndays; Monday, Tuesday, Wednesday, are descending or waning days. Our six\ndays, lumped together after the great distinguishing day, Sunday, are too\nmany to be distinctly thought of together: a division of three preceding\nand three following the day of most note would be much more easily used.\nBut all this comes too late. It may be, nevertheless, that some individuals\nmay be able to adjust their affairs with advantage by referring Thursday,\nFriday, Saturday, to the following Sunday, and Monday, Tuesday, Wednesday,\nto the preceding Sunday. But M. Arson's proposal to alter the names of the\ndays is no more necessary than it is practicable.\n\n\n\nCYCLOMETRY.\n\nI am not to enter anything I do not possess. The reader therefore will not\nlearn from me the feats of many a man-at-arms in these subjects. He must be\ncontent, unless he will bestir himself for himself, not to know how Mr.\nPatrick Cody trisects the angle at Mullinavat, or Professor Recalcati\nsquares the circle at Milan. But this last is to be done by subscription,\nat five francs a head: a banker is named who guarantees restitution if the\nsolution be not perfectly rigorous; the banker himself, I suppose, is the\njudge. I have heard of a man of business who settled the circle in this\nway: if it can be reduced to a debtor and creditor account, it can\ncertainly be done; if not, it is not worth doing. Montucla will give the\naccounts of the lawsuits which wagers on the problem have produced in\nFrance.\n\nNeither will I enter at length upon the success of the new squarer who\nadvertises (Nov. 1863) in a country paper that, having read that the\ncircular ratio was undetermined, \"I thought it very strange that so many\ngreat scholars in all ages should have failed in finding the true ratio,\nand have been determined to try myself.... I am about to secure the {209}\nbenefit of the discovery, so until then the public cannot know my new and\ntrue ratio.\" I have been informed that this trial makes the diameter to the\ncircumference as 64 to 201, giving [pi] = 3.140625 exactly. The result was\nobtained by the discoverer in three weeks after he first heard of the\nexistence of the difficulty. This quadrator has since published a little\nslip, and entered it at Stationers' Hall. He says he has done it by actual\nmeasurement; and I hear from a private source that he uses a disk of 12\ninches diameter, which he rolls upon a straight rail. Mr. James Smith did\nthe same at one time; as did also his partisan at Bordeaux. We have, then,\nboth 3.125 and 3.140625, by actual measurement. The second result is more\nthan the first by about one part in 200. The second rolling is a very\ncreditable one; it is about as much below the mark as Archimedes was above\nit. Its performer is a joiner, who evidently knows well what he is about\nwhen he measures; he is not wrong by 1 in 3,000.\n\nThe reader will smile at the quiet self-sufficiency with which \"I have been\ndetermined to try myself\" follows the information that \"so many great\nscholars in all ages\" have failed. It is an admirable spirit, when\naccompanied by common sense and uncommon self-knowledge. When I was an\nundergraduate there was a little attendant in the library who gave me the\nfollowing,--\"As to cleaning this library, Sir, if I have spoken to the\nMaster once about it, I have spoken fifty times: but it is of no use; he\nwill not employ _littery_ men; and so I am obliged to look after it\nmyself.\"\n\nI do not think I have mentioned the bright form of quadrature in which a\nsquare is made equal to a circle by making each side equal to a quarter of\nthe circumference. The last squarer of this kind whom I have seen figures\nin the last number of the _Athenaeum_ for 1855: he says the thing is no\nlonger a _problem_, but an _axiom_. He does not know that the area of the\ncircle is greater than that of any other figure of the same circuit. This\nany one might see without {210} mathematics. How is it possible that the\nfigure of greatest area should have any one length in its circuit unlike in\nform to any other part of the same length?\n\nThe feeling which tempts persons to this problem is that which, in romance,\nmade it impossible for a knight to pass a castle which belonged to a giant\nor an enchanter. I once gave a lecture on the subject: a gentleman who was\nintroduced to it by what I said remarked, loud enough to be heard by all\naround, \"Only prove to me that it is impossible, and I will set about it\nthis very evening.\"\n\nThis rinderpest of geometry cannot be cured, when once it has seated itself\nin the system: all that can be done is to apply what the learned call\nprophylactics to those who are yet sound. When once the virus gets into the\nbrain, the victim goes round the flame like a moth; first one way and then\nthe other, beginning where he ended, and ending where he begun: thus\nverifying the old line\n\n \"In girum imus nocte, ecce! et consumimur igni.\"[353]\n\nEvery mathematician knows that scores of methods, differing altogether from\neach other in process, all end in this mysterious 3.14159..., which insists\non calling itself the circumference to a unit of diameter. A reader who is\ncompetent to follow processes of arithmetic may be easily satisfied that\nsuch methods do actually exist. I will give a sketch, carried out to a few\nfigures, of three: the first two I never met with in my reading; the third\nis the old method of Vieta.[354] [I find that both the first and second\nmethods are contained in a theorem of Euler.]\n\nWhat Mr. James Smith says of these methods is worth noting. He says I have\ngiven three \"_fancy_ proofs\" of the value of [pi]: he evidently takes me to\nbe offering demonstration. He proceeds thus:--\n\n\"His first proof is traceable to the diameter of a circle {211} of radius\n1. His second, to the side of any inscribed equilateral triangle to a\ncircle of radius 1. His third, to a radius of a circle of diameter 1. Now,\nit may be frankly admitted that we can arrive at the same result by many\nother modes of arithmetical calculation, all of which may be shown to have\nsome sort of relation to a circle; but, after all, these results are mere\nexhibitions of the properties of numbers, and have no more to do with the\nratio of diameter to circumference in a circle than the price of sugar with\nthe mean height of spring tides. (_Corr._ Oct. 21, 1865).\"\n\nI quote this because it is one of the few cases--other than absolute\nassumption of the conclusion--in which Mr. Smith's conclusions would be\ntrue if his premise were true. Had I given what follows as _proof_, it\nwould have been properly remarked, that I had only exhibited properties of\nnumbers. But I took care to tell my reader that I was only going to show\nhim _methods_ which end in 3.14159.... The proofs that these methods\nestablish the value of [pi] are for those who will read and can understand.\n\n  200000000      31415       3799\n   66666667                  2817\n   26666667                  1363\n   11428571                   661\n    5079365                   321\n    2308802                   156\n    1065601                    76\n     497281                    37\n     234014                    18\n     110849                     9\n      52785                     5\n      25245                     2\n      12118                     1\n       5834\n   --------     --------  -------\n  314153799      31415       9265\n\n{212}\n\n1. Take any diameter, double it, take 1-3d of that double, 2-5ths of the\nlast, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so\non. The sum of all is the circumference of that diameter. The preceding is\nthe process when the diameter is a hundred millions: the errors arising\nfrom rejection of fractions being lessened by proceeding on a thousand\nmillions, and striking off one figure. Here 200 etc. is double of the\ndiameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.;\n114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.\n\n2. To the square root of 3 add its half. Take _half_ the third part of\nthis; half 2-5ths of the last; half 3-7ths of the last; and so on. The sum\nis the circumference to a unit of diameter.\n\n    Square root of 3....  1.73205081\n                           .86602540\n                        ------------\n                          2.59807621\n                           .43301270\n                           .08660254\n                             1855768\n                              412393\n                               93726\n                               21629\n                                5047\n                                1188\n                                 281\n                                  67\n                                  16\n                                   4\n                                   1\n                        ------------\n                          3.14159265\n\n3. Take the square root of 1/2; the square root of half of one more than\nthis; the square root of half of one more {213} than the last; and so on,\nuntil we come as near to unity as the number of figures chosen will permit.\nMultiply all the results together, and divide 2 by the product: the\nquotient is an approximation to the circumference when the diameter is\nunity. Taking aim at four figures, that is, working to five figures to\nsecure accuracy in the fourth, we have .70712 for the square root of 1/2;\n.92390 for the square root of half one more than .70712; and so on, through\n.98080, .99520, .99880, .99970, .99992, .99998. The product of the eight\nresults is .63667; divide 2 by this, and the quotient is 3.1413..., of\nwhich four figures are correct. Had the product been .636363... instead of\n.63667..., the famous result of Archimedes, 22-7ths, would have been\naccurately true. It is singular that no cyclometer maintains that\nArchimedes hit it exactly.\n\nA literary journal could hardly admit as much as the preceding, if it stood\nalone. But in my present undertaking it passes as the halfpennyworth of\nbread to many gallons of sack. Many more methods might be given, all ending\nin the same result, let that result mean what it may.\n\nNow since dozens of methods, to which dozens more might be added at\npleasure, concur in giving one and the same result; and since these methods\nare declared by all who have shown knowledge of mathematics to be\n_demonstrated_: it is not asking too much of a person who has just a little\nknowledge of the first elements that he should learn more, and put his hand\nupon the error, before he intrudes his assertion of the existence of error\nupon those who have given more time and attention to it than himself, and\nwho are in possession, over and above many demonstrations, of many\nconsequences verifying each other, of which he can know nothing. This is\nall that is required. Let any one square the circle, and persuade his\nfriends, if he and they please: let him print, and let all read who choose.\nBut let him abstain from intruding himself upon those who have been\nsatisfied by existing demonstration, until he is prepared {214} to lay his\nfinger on the point in which existing demonstration is wrong. Let him also\nsay what this mysterious 3.14159... really is, which comes in at every door\nand window, and down every chimney, calling itself the circumference to a\nunit of diameter. This most impudent and successful impostor holds false\ntitle-deeds in his hands, and invites examination: surely those who can\nfind out the rightful owner are equally able to detect the forgery. All the\nquadrators are agreed that, be the right what it may, 3.14159... is wrong.\nIt would be well if they would put their heads together, and say what this\nwrong result really means. The mathematicians of all ages have tried all\nmanner of processes, with one object in view, and by methods which are\nadmitted to yield demonstration in countless cases. They have all arrived\nat one result. A large number of opponents unite in declaring this result\nwrong, and all agree in two points: first, in differing among themselves;\nsecondly, in declining to point out what that curious result really is\nwhich the mathematical methods all agree in giving.\n\nMost of the quadrators are not aware that it has been fully demonstrated\nthat no two numbers whatsoever can represent the ratio of the diameter to\nthe circumference with perfect accuracy. When therefore we are told that\neither 8 to 25 or 64 to 201 is the true ratio, we know that it is no such\nthing, without the necessity of examination. The point that is left open,\nas not fully demonstrated to be impossible, is the _geometrical_\nquadrature, the determination of the circumference by the straight line and\ncircle, used as in Euclid. The general run of circle-squarers, hearing that\nthe quadrature is not pronounced to be _demonstratively_ impossible,\nimagine that the _arithmetical_ quadrature is open to their ingenuity.\nBefore attempting the arithmetical problem, they ought to acquire knowledge\nenough to read Lambert's[355] demonstration (last given in Brewster's[356]\ntranslation {215} of Legendre's[357] Geometry) and, if they can, to refute\nit. [It will be given in an Appendix.] Probably some have begun this way,\nand have caught a Tartar who has refused to let them go: I have never heard\nof any one who, in producing his own demonstration, has laid his finger on\nthe faulty part of Lambert's investigation. This is the answer to those who\nthink that the mathematicians treat the arithmetical squarers too lightly,\nand that as some person may succeed at last, all attempts should be\nexamined. Those who have so thought, not knowing that there is\ndemonstration on the point, will probably admit that a person who\ncontradicts a theorem of which the demonstration has been acknowledged for\na century by all who have alluded to it as read by themselves, may\nreasonably be required to point out the error before he demands attention\nto his own result.\n\n_Apopempsis of the Tutelaries._--Again and again I am told that I spend too\nmuch time and trouble upon my two tutelaries: but when I come to my\nsumming-up I shall make it appear that I have a purpose. Some say I am too\nhard upon them: but this is quite a mistake. Both of them beat little\nOliver himself in the art and science of asking for more; but without\nOliver's excuse, for I had given good allowance. Both began with me, not I\nwith them: and both knew what they had to expect when they applied for a\nsecond helping.\n\nOn July 31, the Monday after the publication of my remarks on my 666\ncorrespondent, I found _three_ notes in separate envelopes, addressed to me\nat \"7A, University College.\" When I saw the three new digits I was taken\nrhythmopoetic, as follows--\n\n  Here's the Doctor again with his figs, and by Heavens!\n  He was always at sixes, and now he's at sevens.\n\nTo understand this fully the reader must know that the greater part of\nApocalyptic interpretation has long been condensed, in my mind, into the\nTurkish street-cry--In the {216} name of the Prophet! figs! I make a few\nextracts. The reader will observe that Dr. Thorn grumbles at his _private_\nletters being _publicly_ ridiculed. A man was summoned for a glutolactic\nassault; he complained of the publication of his proceeding: I kicked etc.\n_in confidence_, he said.\n\n\"After reading your last, which tries in every way to hold me up to public\nridicule for daring to write you privately ['that you would be d----d,'\nomitted by accident] one would say, Why have anything to do with such a\ntesty person? [Wrong word; no testy person can manage cool and consecutive\nridicule. Quaere, what is this word? Is it anything but a corruption of the\nobsolete word _tetchy_ of the same meaning? Some think _touchy_ is our\nmodern form of _tetchy_, which I greatly doubt]. My answer is, the poor man\nis lamentably ignorant; he is not only so, but 'out of the way' [quite\ntrue; my readers know me by this time for an out-of-the-way person. What\nother could tackle my squad of paradoxers? What other would undertake the\njob?] Can he be brought back and form one of those who in Ezekiel 37 ch.\nhave the Spirit breathed into them and live.... Have I any other feeling\ntowards you except that of peace and goodwill? [Not to your distinct\nknowledge; but in all those who send people to 'the other place' for\ncontempt of their interpretations, there is a lurking wish which is father\nto the thought; 'you _will_ be d----d' and 'you _be_ d--d' are Siamese\ntwins]. Of course your sneer at 666 brought plain words; but when men\nmeddle with what they do not understand (not having the double _Vahu_) they\nmust be dealt with faithfully by those who do.... [They must; which\njustifies the Budget of Paradoxes: but no occasion to send them anywhere;\nno preachee and floggee too, as the negro said]. Many will find the text\nProv. i. 26 fully realized. [All this contains distinct assumption of a\nright 'of course' to declare accursed those who do not respect the writer's\nvagary].... If I could but get the [Hebrew: A], the Ox-head, which in Old\nHebrew was just the Latin Digamma, F, out {217} of your name, and could\nthen Thau you with the Thau of Ezekiel ix, 4, the [chi], then you would\nbear the number of a man! But this is too hard for me, although not so for\nthe Lord! Jer. xxxii. 17.... And now a word: is ridicule the right thing in\nso solemn a matter as the discussion of Holy Writ? [Is food for ridicule\nthe right thing? Did I discuss Holy Writ? I did not: I concussed profane\nscribble. Even the Doctor did not _discuss_; he only enunciated and\ndenunciated out of the mass of inferences which a mystical head has found\npremises for in the Bible].\"\n\n  M    40\n  O    70\n  R   100\n  G     6\n  N    50\n      ----\n      266\n  [Hebrew: t]=[chi] 400\n\n[That ill opinions are near relations of ill wishes, will be detected by\nthose who are on the look out. The following was taken down in a Scotch\nChurch by Mr. Cobden,[358] who handed it to a Roman friend of mine, for his\ndelectation (in 1855): \"Lord, we thank thee that thou hast brought the Pope\ninto trouble; and we pray that thou wouldst be mercifully pleased to\nincrease the same.\"]\n\nHere is a martyr who quarrels with his crown; a missionary who reviles his\npersecutor: send him to New Zealand, and he would disagree with the Maoris\nwho ate him. Man of unilateral reciprocity! have you, who write to a\nstranger with hints that that stranger and his wife are children of\nperdition, the bad taste to complain of a facer in return? As James\nSmith[359]--the Attorney-wit, not the Dock-cyclometer--said, or nearly\nsaid,\n\n   \"A pretty thing, forsooth!\n  Is he to burn, all scalding hot,\n  Me and my wife, and am I not\n    To job him out a tooth?\"\n\n{218}\n\nThose who think parody vulgar will be pleased to substitute for the above a\nquotation from Butler[360]:--\n\n \"There's nothing so absurd or vain\n  Or barbarous or inhumane,\n  But if it lay the least pretence\n  To piety and godliness,\n  Or tender-hearted conscience,\n  And zeal for gospel truths profess,--\n  Does sacred instantly commence,\n  And all that dare but question it are straight\n  Pronounced th' uncircumcised and reprobate,\n  As malefactors that escape and fly\n  Into a sanctuary for defence,\n  Must not be brought to justice thence,\n  Although their crimes be ne'er so great and high.\n  And he that dares presume to do't\n  Is sentenced and delivered up\n  To Satan that engaged him to't.\"\n\n\n\nTHE NUMBER OF THE BEAST.\n\nOf all the drolleries of controversy none is more amusing than the manner\nin which those who provoke a combat expect to lay down the laws of\nretaliation. You must not strike this way! you must not parry that way! If\nyou don't take care, we shall never meddle with you again! We were not\n_prepared_ for such as this! Why did we have anything to do with such a\ntesty person? M. Jourdain must needs show Nicole, his servant-maid, how\ngood a thing it was to be sure of fighting without being killed, by care\nand tierce.[361] \"Et cela n'est il pas beau d'etre assure de son fait quand\non se bat contre quelqu'un? La, pousse moi un peu, pour voir. NICOLE. Eh\nbien! quoi? M. JOURDAIN. Tout beau. Hola! {219} Ho! doucement. Diantre soit\nla coquine! NICOLE. Vous me dites de pousser. M. JOURDAIN. Oui; mais tu me\npousses en tierce, avant que de pousser en quarte, et tu n'as pas la\npatience que je pare.\"\n\nHis colleague, my secular tutelary, who also made an anachronistic onset,\nwith his repartees and his retorts, before there was anything to fire at,\ntakes what I give by way of subsequent provocation with a good humor which\nwould make a convert of me if he could afford .01659265 ... of a grain of\nlogic. He instantly sent me his photograph for the asking, and another\nletter in proof. The Thor-hammerer does nothing but grumble, except when he\ntells a good story, which he says he had from Dr. Abernethy.[362] A Mr.\nJames Dunlop was popping at the Papists with a 666-rifled gun, when Dr.\nChalmers[363] quietly said, \"Why, Dunlop, you bear it yourself,\" and handed\nhim a paper on which the numerals in\n\n  I A C O B V S         D V N L O P V S\n  1  100    5         500 5  50     5\n\nwere added up. This is almost as good as the _Filii Dei Vicarius_, the\nnumerical letters of which also make 666. No more of these crazy--I first\nwrote _puerile_, but why should young cricketers be libelled?--attempts to\nextract religious use from numerical vagaries, and to make God over all a\nproposer of _salvation conundrums_: and no more of the trumpery hints about\nfuture destiny which is too great a compliment to call blasphemous. If the\nDoctor will cipher upon the letter in [Greek: en hoi metroi metreite\nmetrethesetai humin][364] with _double Vahu_ cubic measure, he will perhaps\nlearn to leave off trying to frighten me into gathering grapes from thorns.\n\nMystical hermeneutics may be put to good use by out-of-the-way people. They\nmay be made to call the attention {220} of the many to a distinction well\nknown among the learned. The books of the New Testament have been for 1,500\nyears divided into two classes: the _acknowledged_ ([Greek:\nhomologoumena]), which it has always been paradox not to receive; and the\n_controverted_ ([Greek: antilegomena]), about which there has always been\nthat difference of opinion which no scholar overlooks, however he may\ndecide for himself after balance of evidence. Eusebius,[365] who first (l.\n3, c. 25) recorded the distinction--which was much insisted on by the early\nProtestants--states the books which are questioned as doubtful, but which\nyet are approved and acknowledged by _many_--or _the many_, it is not easy\nto say which he means--to be the Epistles of James and Jude, the second of\nPeter and the second and third of John. In other places he speaks\ndoubtingly of the Epistle to the Hebrews. The Apocalypse he does not even\nadmit into this class, for he proceeds as follows--I use the second edition\nof the English folio translation (1709), to avert suspicion of bias from\nmyself:--\n\n\"Among the _spurious_ [[Greek: nothoi]] let there be ranked both the work\nentitled the _Acts of Paul_, and the book called _Pastor_, and the\n_Revelation of Peter_: and moreover, that which is called the _Epistle of\nBarnabas_, and that named the _Doctrines of the Apostles_: and moreover, as\nI said, the _Revelation of John_ (if you think good), which some, as I have\nsaid, do reject, but others allow of, and admit among those books which are\nreceived as unquestionable and undoubted.\"\n\nEusebius, though he will not admit the Apocalypse even into the\n_controverted_ list, but gives permission to call it _spurious_, yet\nqualifies his permission in a manner which almost annihilates the\ndistinctive force of [Greek: nothos], and gives the book a claim to rank\n(if you think good, again) in the controverted list. And this is the\nimpression received by {221} the mind of Lardner, who gives Eusebius fully\nand fairly, but when he sums up, considers his author as admitting the\nApocalypse into the second list. A stick may easily be found to beat the\nfather of ecclesiastical history. There are whole faggots in writers as\nopposite as Baronius and Gibbon, who are perhaps his two most celebrated\nsons. But we can hardly imagine him totally misrepresenting the state of\nopinion of those for whom and among whom he wrote. The usual plan, that of\nmaking an author take the views of his readers, is more easy in his case\nthan in that of any other writer: for, as the riddle says, he is\nYou-see-by-us; and to this reading of his name he has often been subjected.\nDr. Nathaniel Lardner,[366] who, though heterodox in doctrine, tries hard\nto be orthodox as to the Canon, is \"sometimes apt to think\" that the list\nshould be collected and divided as in Eusebius. He would have no one of the\ncontroverted books to be allowed, by itself, to establish any doctrine.\nEven without going so far, a due use of early opinion and long continued\ndiscussion would perhaps prevent rational people from being induced by\nthose who have the _double Vahu_ to place the Apocalypse _above_ the\nGospels, which all the Bivahuites do in effect, and some are said to have\ndone in express words. But my especial purpose is to point out that an easy\nway of getting rid of 665 out of 666 of the mystics is to require them to\nestablish the Apocalypse before they begin. See if they even know so much\nas that there is a crowd of testimonies for and against, running through\nthe first four centuries, which makes this book the most difficult of the\nwhole Canon. Try this method, and you will escape beautiful, as the French\nsay. Dean Alford,[367] in Vol. IV, p. 8, of his New Testament, gives an\nelaborate handling of this question. He concludes by saying that he cannot\n{222} venture to refuse his consent to the tradition that the Apostle is\nthe author. This modified adherence, or non-nonadherence, pretty well\nrepresents the feeling of orthodox Protestants, when learning and common\nsense come together.\n\nI have often, in former days, had the attempt made to place the Apocalypse\non my neck as containing prophecies yet unfulfilled. The preceding method\nprevents success; and so does the following. It may almost be taken for\ngranted that theological system-fighters do not read the New Testament:\nthey hunt it for detached texts; they listen to it in church in that state\nof quiescent nonentity which is called reverent attention: but they never\nread it. When it is brought forward, you must pretend to find it necessary\nto turn to the book itself: you must read \"The revelation ... to show unto\nhis servants _things which must shortly come to pass_.... Blessed is he\nthat readeth ... _for the time is at hand_.\" You must then ask your mystic\nwhether things deferred for 1800 years were shortly to come to pass, etc.?\nYou must tell him that the Greek [Greek: en tachei], rendered \"shortly,\" is\nas strong a phrase as the language has to signify _soon_. The interpreter\nwill probably look as if he had never read this opening: the chances are\nthat he takes up the book to see whether you have been committing a fraud.\nHe will then give you some exquisite evasion: I have heard it pleaded that\nthe above was a _mere preamble_. This word _mere_ is all-sufficient: it\nturns anything into nothing. Perhaps he will say that the argument is that\nof the Papists: if so, tell him that there is no Christian sect but bears\ntrue witness against some one or more absurdities in other sects.\n\nAn anonyme suggests that [Greek: en tachei] may not be \"soon,\" it may be\n\"quickly, without reference to time when:\" he continues thus, \"May not time\nbe 'at hand' when it is ready to come, no matter how long delayed?\" I now\nunderstand what *** and *** meant when they borrowed my books and promised\nto return them quickly, it was \"without {223} reference to time when.\" As\nto time at _hand_--provided you make a long _arm_--I admire the quirk, but\ncannot receive it: the word is [Greek: engus], which is a word of\n_closeness_ in time, in place, in reckoning, in kindred, etc.\n\nAnother gentleman is not surprised that Apocalyptic reading leads to a\ndoubt of the \"canonicity\" of the book: it ought not to rest on church\ntestimony, but on visible miracle. He offers me, or any reader of the\n_Athenaeum_, the \"sight of a miracle to that effect, and within forty-eight\nhours' journey (fare paid).\" I seldom travel, and my first thought was\nwhether my carpet-bag would be found without a regular hunt: but, on\nreading further, I found that it was only a concordance that would be\nwanted. Forty hours' collection and numerical calculation of Greek nouns\nwould make it--should I happen to agree with the writer--many hundred\nmillions to one that Revelation xiii is superhuman. There is but one verse\n(the fifth) which the writer does not see verified. I looked at this verse,\nand was much startled. The Budget began in October 1863: should it last\nuntil March 1867--it is now August 1866--it is clear that I am the first\nBeast, and my paradoxers are the saints whom I persecute.\n\n[The Budget _did_ terminate in March 1867: I hope the gentleman will be\nsatisfied with the resulting interpretation.]\n\nThe same opponent is surprised that I should suppose a thing which \"comes\nto pass\" must be completed, and cannot contain what is to happen 1800 years\nafter. All who have any knowledge of English idiom know that a thing\n_comes_ to pass when it happens, and _came_ to pass afterwards. But as the\noriginal is Greek, we must look at the Greek: it is [Greek: dei genesthai]\nfor \"must come to pass,\" and we know that [Greek: egeneto] is what is\nusually translated \"came to pass.\" No word of more finished completion\nexists in Greek.\n\nAnd now for a last round of biter-bit with the Thor-hammerer, of whom, as\nin the other case, I shall take no {224} more notice until he can contrive\nto surpass himself, which I doubt his being able to do. He informs me that\nby changing A into [Hebrew: t] in my name he can make a 666 of _me_;\nadding, \"This is too hard for me, although not so for the Lord!\" Sheer\nnonsense! He could just as easily have directed to \"Prof. De Morg[Hebrew:\nt]n\" as have assigned me apartment 7A in University College. It would have\nbeen seen for whom it was intended: and if not, it would still have reached\nme, for my colleagues have for many a year handed all out-of-the-way things\nover to me. There is no 7A: but 7 is the Museum of Materia Medica. I took\nthe only hint which the address gave: I inquired for hellebore, but they\ntold me it was not now recognized, that the old notion of its value was\nquite obsolete, and that they had nothing which was considered a specific\nin senary or septenary cases. The great platitude is the reference of such\na difficulty as writing [Hebrew: t] for A to the Almighty! Not childish,\nbut fatuous: real childishness is delightful. I knew an infant to whom,\nbefore he could speak plain, his parents had attempted to give notions of\nthe Divine attributes: a wise plan, many think. His father had dandled him\nup-side-down, ending with, There now! Papa could not dance on his head! The\nmannikin made a solemn face, and said, _But Dod tood_! I think the Doctor\nhas rather mistaken the way of becoming as a little child, intended in\nMatt. xviii. 3: let us hope the will may be taken for the deed.\n\nTwo poets have given images of transition from infancy to manhood:\nDryden,--for the Hind is Dryden himself on all fours! and Wordsworth, in\nhis own character of broad-nailed, featherless biped:\n\n \"The priest continues what the nurse began,\n  And thus the child imposes on the man.\"\n   \"The child's the father of the man,\n    And I could wish my days to be\n    Bound each to each by natural piety.\"\n\n{225}\n\nIn Wordsworth's aspiration it is meant that sense and piety should grow\ntogether: in Dryden's description a combination of Mysticism And Bigotry\n(can this be the _double Vahu_?), personified as \"the priest,\"--who always\ncatches it on this score, though the same spirit is found in all\nassociations,--succeeds the boguey-teaching of the nurse. Never was the\ncontrast of smile and scowl, of light and darkness, better seen than in the\ntwo pictures. But an acrostic distinction may be drawn. When mysticism\npredominates over bigotry, we have the grotesque picturesque, and the\nnatural order of words gives us _Mab_, an appropriate suggestion. But when\nbigotry has the upper hand, we see _Bam_, which is just as appropriate; for\nbigotry nearly always deals with facts and logic so as to require the\napplication of at least one of the minor words by which dishonesty is\nsignified. I think that M is the Doctor's initial, and that Queen Mab\ntickles him in his sleep with the sharp end of a 6.\n\n(_Monday, August 21._) Three weeks having elapsed without notice from me of\nthe Doctor, I receive a reminder of his existence, in which I find that as\nI am the Daniel who judges the Magi of Babylon, it is to be pointed out\nthat Daniel \"bore a certain number, that of a man (beloved), Daniel, ch.\n10. v. 11, and which you certainly do not.\" Then, \"by Greek power,\"\nBelteshazzar is made = 666. Here is another awkward imitation of the way of\na baby child. When you have sported with the tiny creature until it runs\naway offended, by the time you have got into conversation again you will\nfind the game is to be renewed: a little head peeps out from a hiding-place\nwith \"I don't love you.\" The proper rejoinder is, \"Very well! then I'll\nhave pussy.\" But in the case before me there is a rule of three sums to do;\nas baby : Pussy Dr. :: 666 : the answer required. I will work it out, if I\ncan.\n\nThe squaring of the circle and the discovery of the Beast are the two\ngoals--and goals also--of many unbalanced intellects, and of a few\ninstances of the better kind. {226} I might have said more of 666, but I am\nnot deep in its bibliography. A work has come into my hands which contains\na large number of noted cases: to some of my readers it will be a treat to\nsee the collection; and the sight will perhaps be of some use to those who\nhave read controversy on the few celebrated cases which are of general\nnotoriety. It is written by a learned decipherer, a man who really knew the\nhistory of the subject, the Rev. David Thom,[368] of Bold Street Chapel,\nLiverpool, who died, I am told, a few years ago.\n\nAnybody who reads his book will be inclined to parody a criticism which was\nonce made on Paley's[369] Evidences--\"Well! if there be anything in\nChristianity, this man is no fool.\" And, if he should chance to remember\nit, he will be strongly reminded of a sentence in my opening chapter,--\"The\nmanner in which a paradoxer will show himself, as to sense or nonsense,\nwill not depend upon what he maintains, but upon whether he has or has not\nmade a sufficient knowledge of what has been done by others, _especially as\nto the mode of doing it_, a preliminary to inventing knowledge for\nhimself.\" And this is reinforced by the fact that Mr. Thom, though a\nscholar, was not conspicuous for learning, except in this his great\npursuit. He was a paradoxer on other points. He reconciled Calvinism and\neternal reprobation with Universalism and final salvation; showing these\ntwo doctrines to be all one.\n\nThis gentleman must not be confounded with the Rev. John Hamilton Thom[370]\n(no relation), at or near the same {227} time and until recently, of\nRenshaw Street Chapel, Liverpool who was one of the minority in the\nLiverpool controversy when, nearly thirty years ago, _three_ heretical\nUnitarian schooners exchanged shotted sermons with _thirteen_ Orthodox\nships of the line, and put up their challengers' dander--an American\ncorruption of _d--d anger_--to such an extent, by quiet and respectful\nargument, that those opponents actually addressed a printed intercession to\nthe Almighty for the Unitarian triad, as for \"Jews, Turks, Infidels, and\nHeretics.\" So much for the distinction, which both gentlemen would thank me\nfor making very clear: I take it quite for granted that a guesser at 666\nwould feel horrified at being taken for a Unitarian, and that a Unitarian\nwould feel queerified at being taken for a guesser at 666. Mr. David Thom's\nbook is _The Number and Names of the Apocalyptic Beasts_, Part I, 1848,\n8vo.: I think the second part was never published. I give the Greek and\nLatin solutions, omitting the Hebrew: as usual, all the Greek letters are\nnumeral, but only M D C L X V I of the Latin. I do not give either the\ndecipherers or their reasons: I have not room for this; nor would I, if I\ncould, bias my reader for one rather than another.\n\nD. F. Julianus Caesar Atheus (or Aug.[371]); Diocles Augustus; Ludovicus;\nSilvester Secundus; Linus Secundus; {228} Vicarius Filii Dei; Doctor et Rex\nLatinus; Paulo V. Vice-Deo; Vicarius Generalis Dei in Terris; Ipse\nCatholicae Ecclesiae Visibile Caput; Dux Cleri; Una, Vera, Catholica,\nInfallibilis Ecclesia; Auctoritas politica ecclesiasticaque Papalis (Latina\nwill also do); Lutherus Ductor Gregis; Calvinus tristis fidei interpres;\nDic Lux ; Ludvvic; Will. Laud; [Greek: Lateinos];[372] [Greek: he latine\nbasileia]; [Greek: ekklesia italika]; [Greek: euanthas]; [Greek: teitan];\n[Greek: arnoume]; [Greek: lampetis]; [Greek: ho niketes]; [Greek: kakos\nhodegos]; [Greek: alethes blaberos]; [Greek: palai baskanos]; [Greek: amnos\nadikos]; [Greek: antemos]; [Greek: genserikos]; [Greek: euinas]; [Greek:\nBenediktos]; [Greek: Bonibazios g. papa x. e. e. e. a.], meaning Boniface\nIII. Pope 68th, bishop of bishops the first! [Greek: oulpios]; [Greek: dios\neimi he heras]; [Greek: he missa he papike]; [Greek: loutherana]; [Greek:\nsaxoneios]; [Greek: Bezza antitheos] (Beza); [Greek: he alazoneia biou];\n[Greek: Maometis]; [Greek: Maometes b.]; [Greek: theos eimi epi gaies];\n[Greek: iapetos]; [Greek: papeiskos]; [Greek: dioklasianos]; [Greek:\ncheina]; [Greek: braski]; [Greek: Ion Paune]; [Greek: koupoks]; (cowpox,\n[Greek: s] being the _vau_; certainly the {229} vaccinated have the mark of\nthe Beast); [Greek: Bonneparte]; [Greek: N. Boneparte]; [Greek: euporia];\n[Greek: paradosis]; [Greek: to megatherion].\n\nAll sects fasten this number on their opponents. It is found in _Martin\nLauter_, affirmed to be the true way of writing the name, by carrying\nnumbers through the Roman Alphabet. Some Jews, according to Mr. Thorn,\nfound it in [Hebrew: JSHW NTSRJ] _Jesus of Nazareth_. I find on inquiry\nthat this satire was actually put forth by some medieval rabbis, but that\nit is not idiomatic: it represents quite fairly \"Jesus Nazarene,\" but the\nHebrew wants an article quite as much as the English wants \"the.\"\n\nMr. David Thom's own solution hits hard at all sides: he finds a 666 for\nboth beasts; [Greek: he phren] (the mind) for the first, and [Greek:\nekklesiai sarkikai] (fleshly churches) for the second. A solution which\nembodies all mental philosophy in one beast and all dogmatic theology in\nthe other, is very tempting: for in these are the two great supports of\nAntichrist. It will not, however, mislead me, who have known the true\nexplanation a long time. The three sixes indicate that any two of the three\nsubdivisions, Roman, Greek, and Protestant, are, in corruption of\nChristianity, six of one and half a dozen of the other: the distinctions of\nunits, tens, hundreds, are nothing but the old way (1 Samuel xviii. 7, and\nConcordance at _ten_, _hundred_, _thousand_) of symbolizing differences of\nnumber in the subdivisions.\n\nIt may be good to know that, even in speculations on 666, there are\ndifferent degrees of unreason. All the diviners, when they get a colleague\nor an opponent, at once proceed to reckon him up: but some do it in play\nand some in earnest. Mr. David Thom found a young gentleman of the name St.\nClaire busy at the Beast number: he forthwith added the letters in [Greek:\nst klaire] and found 666: this was good fun. But my spiritual tutelary,\nwhen he found that he could not make a beast of me, except by changing\n[Hebrew: A] into [Hebrew: T], solemnly referred the difficulty to the\nAlmighty: this was poor earnest. {230}\n\nI am glad I did not notice, in time to insert it in the _Athenaeum_, a very\nremarkable paradoxer brought forward by Mr. Thom, his friend Mr.\nWapshare[373]: it is a little too strong for the general public. In the\n_Athenaeum_ they would have seen and read it: but this book will be avoided\nby the weaker brethren. It is as follows:\n\n\"God, the Elohim, was six days in creating all things, and having made MAN\nhe entered into his rest. He is no more seen as a Creator, as Elohim, but\nas Jehovah, the _Lord_ of the Sabbath, and the Spirit of life in MAN, which\nSpirit worketh _sin in the flesh_; for the Spirit of Love, in all flesh, is\nLust, or the spirit of a beast, So Rom. vii. And which Spirit is\n_crucified_ in the flesh. He then, as Jehovah--as the power of the Law,\n_in_ and _over_ all flesh, John viii. 44--increases that which he has made\nas the Elohim, and his power shall last for 6 days, or 6 periods of time,\ncomputed at a millennium of years; and at the end of which six days, he who\nis the Spirit of all flesh shall manifest himself as the Holy Spirit of\nAlmighty Love, and of all truth; and so shall the Church have her Sabbath\nof Rest--all contention being at an end. This is, as well as I may now\nexpress it, my solution of the mystery in Hebrew, and in Greek, and also in\nLatin, IHS. For he that was lifted up _is_ King of the Jews, and is the\nLord of all Life, working in us, both to will and to do; as is manifest in\nthe Jews--they slaying him that his blood might be _good_ for the healing\nof the nations, of all people and tongues. As the Father of all _natural_\nflesh, he is the Spirit of Lust, as in all _beasts_; as the Father, or King\nof the Jews, he is the Devil, as he himself witnesseth in John viii.,\nalready referred to. As lifted up, he is transformed into the Spirit of\nLove, a light to the Gentiles, and the glory of his people Israel.... For\nthere is but ONE God, ONE Lord, ONE Spirit, ONE body, etc. and he who was\nSatan, the Spirit of life in that body, is, in {231} Christ crucified, seen\nin the Spirit that is in all, and through all and over all, God blessed for\never.\"\n\nAll this seems well meant, and Mr. Thom prints it as convinced of its\npiety, and \"pronounces no opinion.\" Mystics of all sorts! see what you may\ncome to, or what may come to you! I have inserted the above for your good.\n\nThere is nothing in this world so steady as some of the paradoxers. They\nare like the spiders who go on spinning after they have web enough to catch\nall the flies in the neighborhood, if the flies would but come. They are\nlike the wild bees who go on making honey which they never can eat, proving\n_sic vos non vobis_ to be a physical necessity of their own contriving. But\nnobody robs their hives: no, unlike the bees, they go about offering their\nware to any who will take it as a gift. I had just written the last\nsentence (Oct. 30, 1866, 8.45 A.M.) when in comes the second note received\nthis morning from Dr. Thorn: at 1.30 P.M. came in a third. These arise out\nof the above account of the Rev. D. Thom, published Oct. 27: three notes\nhad arrived before.\n\nFor curiosity I give one day's allowance, supposing these to be all: more\nmay arrive before night.\n\n29th Oct. 1866.\n\n\"Dear Sir,--\n\nIn re [swastika].[374]\n\n\"So that 'Zaphnath Paaneah' may be after all the revealer of the 'Northern\nTau' [Greek: Phaneroo]--To make manifest, shew, or explain; and this may\nsatisfy the House of Joseph in Amos 5^c. While Belteshazzar = 666 may be\nalso satisfactory to the House of David, and so we may have Zech. 10^c.\n6^v. in operation when Ezekiel 37^c. 16^v. has been realised;--but there,\nwhat is the use of writing, it is all Coptic {232} to a man who has not\n[swastika], The Thau of the North, the double Vahu [Hebrew: W\\qamats\\W].\nLook at Jeremiah 3^c. 8^v. and then to Psalm 83 for 'hidden ones' [Hebrew:\nTS\\sheva\\PW\\dagesh\\N\\segol\\Y Y\\sheva\\HW\\qamats\\H]--The Zephoni Jehovah, and\nsay whether they have any connection with the Zephon _Thau_. The Hammer of\nThor of Jeremiah 23^c. 29^v. as I gave you in No. 3 of my present edition.\n\nYours truly\n\nLE CHEVALIER AU CIN.\"\n\n_By Greek Power._\n\n  C =  20\n  H =   8\n  E =   5\n  V =   6\n  A =   1\n  L =  30\n  I =  10\n  E =   5\n  R = 100\n\n  A =   1\n  U = 400\n\n  C =  20\n  I =  10\n  N =  50\n     ----\n      666\n\nThere will be thousands of Morgans who will be among the wise and prudent\nof Hosea 14^c. 9^v. when the Seventh Angel sounds, let me number _that One_\nby Greek, Rev. 17^c. 1^v: {233}\n\n    S = 200\n    E  =   5\n  x V  =   6\n    E  =   5\n    N  =  50\n    T  = 300\n    H  =   8\n\n    A =   1\n    N  =  50\n  x G  =   6\n    E  =   5\n    L  =  30\n       ----\n        666\n\n    V and G = 12 ought to be equal to one Gammadion or ^3[swastika]3 x 4 =\n    12, what say you?\n\nLondon, October 29, 1866.\n\n\"Dear Sir,--\n\nIn re [swastika] versus [maltese cross].\n\nHowever pretentious the X or [maltese cross] may be, and it is peculiarly\nso just now in this land; after all it is only made of two Roman V's--and\nso is only = [ one inverted](10)--and therefore is not the perfect number\n12 of Revel^n, but is the mark of the goddess _Decima_!\n\nYours truly\n\nWM. THORN.\"\n\nHad the _one_ who sent forth a pastoral (Romish) the other day, remained\namongst the faithful expectants, see how he would have numbered, whereas he\nsold himself for the privilege of signing\n\n[maltese cross] HENRY E. MANNING.[375]\n\n{234}\n\n_By English Key._\n\n  H =   8\n  E =   5\n  N =  40\n  R =  80\n  Y = 140\n\n  E =   5\n  D =   4\n  W = 120\n  A =   1\n  R =  80\n  D =   4\n\n  M =  30\n  A =   1\n  N =  40\n  N =  40\n  I =   9\n  N =  40\n  G =   7\n  [swastika] = 12\n      ----\n       666\n\n    Can you now understand the difference between [swastika] and [maltese\n    cross] or X? Look to my challenge.\n\nCutting from newspaper:--\n\nITALY.\n\nRome (_via_ Marseilles), October\n\nMr. Gladstone has paid a visit to the Pope.\n\n_By Greek Power._\n\n  G =   6\n  L =  30\n  A =   1\n  D =   4\n  S = 200\n  T = 300\n  O =  70\n  N =  50\n  E =   5\n     ----\n      666\n\nAnd what then [swastika]?\n\n{235}\n\nIn other letters _John Stuart Mill_ is 666 if the _a_ be left out;\n_Chasuble_ is perfect. _John Brighte_[376] is a _fait accompli_; and I am\nasked whether intellect can account for the final e. Very easily: this\nBeast is not the M. P., but another person who spells his name differently.\nBut if John Sturt Mill and John Brighte choose so to write themselves, they\nmay.\n\nA curious collection; a mystical phantasmagoria! There are those who will\ntry to find meaning: there are those who will try to find purpose.\n\n \"And some they said--What are you at?\n  And some--What are you arter?\"\n\nMy account of Mr. Thom and his 666 appeared on October 27: and on the 29th\nI received from the editor a copy of Mr. Thom's sermons published in 1863\n(he died Feb. 27, 1862) with best wishes for my health and happiness. The\neditor does not name himself in the book; but he signed his name in my\ncopy: and may my circumference never be more than 3-1/8 of my diameter if\nthe signature, name and writing both, were not that of my [circle square]\ning friend Mr. James Smith! And so I have come in contact with him on 666\nas well as on [pi]! I should have nothing left to live for, had I not\nhappened to hear that he has a perpetual motion on hand. I returned thanks\nand kind regards: and Miss Miggs's words--\"Here's forgivenesses of\ninjuries! here's amicablenesses!\"--rang in my ears. But I was made slightly\nuncomfortable: how could the war go on after this armistice? Could I ever\nmake it understood that the truce only extended to the double Vahu and\nthings thereunto relating? It was once held by seafaring men that there was\nno peace with Spaniards beyond the line: I was determined that there must\nbe no concord with J. S. inside the circle; that this must be a special\nexception, like Father Huddleston {236} and old Grouse in the gun-room. I\nwas not long in anxiety; twenty-four hours after the book of sermons there\ncame a copy of the threatened exposure--_The British Association in\nJeopardy, and Professor De Morgan in the Pillory without hope of escape_.\nBy James Smith, Esq. London and Liverpool, 8vo., 1866 (pp. 94). This\nexposure consists of reprints from the _Athenaeum_ and _Correspondent_: of\nthings new there is but one. In a short preface Mr. J. S. particularly\nrecommends to \"_read to the end_.\" At the end is an appendix of two pages,\nin type as large as the work; a very prominent peroration. It is an article\nfrom the _Athenaeum_, left out of its place. In the last sentence Mr. J.\nSmith, who had asked whether his character as an honest Geometer and\nMathematician was not at stake, is warned against the _fallacia plurium\ninterrogationum_.[377] He is told that there is not a more honest\nwhat's-his-name in the world: but that as to the counter which he calls his\ncharacter as a mathematician, he is assured that it has been staked years\nago, and lost. And thus truth has the last word. There is no occasion to\nsay much about reprints. One of them is a letter [that given above] of\nAugust 25, 1865, written by Mr. J. S. to the _Correspondent_. It is one of\nhis quadratures; and the joke is that I am made to be the writer: it\nappears as what Mr. J. S. hopes I shall have the sense to write in the\n_Athenaeum_ and forestall him. When I saw myself thus quoted--yes! quoted!\ndouble commas, first person--I felt as I suppose did Wm. Wilberforce[378]\nwhen he set eyes on the affectionate benediction of the potato which\nwaggish comrades had imposed on a raw Irish reporter as part of his speech.\nI felt as Martin[379] of {237} Galway--kind friend of the poor dumb\ncreatures!--when he was told that the newspapers had put him in Italics. \"I\nappeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics?\nDo I ever speak in Italics?\" I appeal to editor and readers, whether I ever\nsquared the circle until a week or two ago, when I gave my charitable mode\nof reconciling the discrepant cyclometers.\n\nThe absurdity of the imitation of symbolic reasoning is so lusciously rich,\nthat I shall insert it when I make up my final book. Somebody mastered\nSpanish merely to read Don Quixote: it would be worth while to learn a\nlittle algebra merely to enjoy this a b-istical attack on the windmills.\nThe principle is, Prove something in as roundabout a way as possible,\nmention the circle once or twice irrelevantly in the course of your proof,\nand then make an act of Q. E. D. in words at length. The following is\nhardly caricature:--\n\nTo prove that 2 and 2 make 5. Let a = 2, b = 5: let c = 658, the number of\nthe House: let d = 666, the number of the Beast. Then of necessity d = a +\nb + c + 1; so that 1 is a harmonious and logical quantification of the\nnumber of which we are to take care. Now, b, the middle of our digital\nsystem, is, by mathematical and geometrical combination, a mean between 5 +\n1 and 2 + 2. Let 1 be removed to be taken care of, a thing no real\nmathematician can refuse without serious injury to his mathematical and\ngeometrical reputation. It follows of necessity that 2 + 2 = 5, _quod erat\ndemonstrumhorrendum_. If Simpkin & Marshall have not, after my notice, to\naccount for a gross of copies more than would have gone off without me, the\nworld is not worthy of its James Smith!\n\nThe only fault of the above is, that there is more {238} connection than in\nthe process of Faber Cyclometricus: so much, in fact, that the blunders are\nvisible. The utter irrelevance of premises to conclusion cannot be\nexhibited with the requisite obscurity by any one who is able to follow\nreasoning: it is high art displayed in a certain toning down of the _aegri\nsomnia_, which brings them to a certain look of reproach to reasoning which\nI can only burlesque. Mr. J. S. produces something which resembles argument\nmuch as a chimpanzee in dolor, because balked of his dinner, resembles a\nthinking man at his studies. My humble attempt at imitation of him is more\nlike a monkey hanging by his tail from a tree and trying to crack a\ncocoa-nut by his chatter.\n\nI could forgive Mr. J. S. anything, properly headed. I would allow him to\nprove--_for himself_--that the Quadrature of the Circle is the child of a\nprivate marriage between the Bull Unigenitus and the Pragmatic Sanction,\nclaiming tithe of onions for repeal of the Mortmain Act, before the Bishops\nin Committee under the kitchen table: his mode of imitating reason would do\nthis with ease. But when he puts his imitation into my mouth, to make me\nwhat _he_ calls a \"real mathematician,\" my soul rises in epigram against\nhim. I say with the doll's dressmaker--such a job makes me feel like a\npuppet's tailor myself--\"He ought to have a little pepper? just a few\ngrains? I think the young man's tricks and manners make a claim upon his\nfriends for a little pepper?\" De Faure[380] and Joseph Scaliger[381] come\ninto my head: my reader may look back for them.\n\n \"Three circlesquarers to the manner born,\n  Switzerland, France, and England did adorn,\n  De Faure in equations did surpass,\n  Joseph at contradictions was an ass.\n  Groaned Folly, I'm used up! What shall I do\n  To make James Smith? Grinned Momus, _Join the two_!\"\n\n{239}\n\nAs to my _locus poenitentiae_,[382] the reader who is fit to enjoy the\nletter I have already alluded to will see that I have a soft and easy\nposition; that the thing is really a _pillowry_; and that I am, like\nPerrette's pot of milk,\n\n \"Bien pose sur un coussinet.\"[383]\n\nJoanna Southcott[384] never had a follower who believed in her with more\nhumble piety than Mr. James Smith believes in himself. After all that has\nhappened to him, he asks me with high confidence to \"favor the writer with\na proof\" that I still continue of opinion that \"the best of the argument is\nin my jokes, and the best of the joke is in his arguments.\" I will not so\nfavor him. At the very outset I told him in plain English that he has the\nwhiphand of all the reasoners in the world, and in plain French that _il a\nperdu le droit d'etre frappe de l'evidence_[385]; I might have said\n_pendu_.[386] To which I now add, in plain Latin, _Sapienti pauca, indocto\nnihil_.[387] The law of Chancery says that he who will have equity must do\nequity: the law of reasoning says that he who will have proof must see\nproof.\n\nThe introduction of things quite irrelevant, by way of reproach, is an\nargument in universal request: and it often happens that the argument so\nproduced really tells against the producer. So common is it that we forget\nhow boyish it is; but we are strikingly reminded when it actually comes\nfrom a boy. In a certain police court, certain small boys were arraigned\nfor conspiring to hoot an obnoxious individual on his way from one of their\nschool exhibitions. This proceeding was necessary, because there seemed to\nbe a permanent conspiracy to annoy the gentleman; and the {240} masters did\nnot feel able to interfere in what took place outside the school. So the\nboys were arraigned; and their friends, as silly in their way as\nthemselves, allowed one of them to make the defence, instead of employing\ncounsel; and did not even give them any useful hints. The defence was as\nfollows; and any one who does not see how richly it sets off the defences\nof bigger boys in bigger matters has much to learn. The innocent conviction\nthat there was answer in the latter part is delightful. Of course fine and\nrecognizance followed.\n\nA---- said the boys had received great provocation from B----. He was\nconstantly threatening them with a horsewhip which he carried in his hand\n[the boy did not say what had passed to induce him to take such a weapon],\nand he had repeatedly insulted the master, which the boys could not stand.\nB---- had in his own drawing-room told him (A----) that he had drawn his\nsword against the master and thrown away the scabbard. B---- knew well that\nif he came to the college he would catch it, and then he went off through a\nside door--which was no sign of pluck; and then he brought Mrs. B---- with\nhim, thinking that her presence would protect him.\n\nMy readers may expect a word on Mr. Thom's sermons, after my account of his\nqueer doings about 666. He is evidently an honest and devout man, much\nwanting in discrimination. He has a sermon about private _judgment_, in\nwhich he halts between the logical and legal meanings of the word. He\nloathes those who apply their private judgment to the word of God: here he\nmeans those who decide what it _ought to be_. He seems in other places\naware that the theological phrase means taking right to determine what it\n_is_. He uses his own private judgment very freely, and is strong in the\nconclusion that others ought not to use theirs except as he tells them how;\nhe leaves all the rest of mankind free to think with him. In this he is not\noriginal: his fame must rest on his senary tripod. {241}\n\n\n\nJAMES SMITH ONCE MORE.\n\nMr. James Smith's procedures are not caricature of reasoning; they are\ncaricature of blundering. The old way of proving that 2 = 1 is solemn\nearnest compared with his demonstrations. As follows:[388]\n\n  Let x = 1\n  Then x^2 = x\n  And x^2 - 1 = x - 1\n  Divide both sides by x - 1; then x + 1 = 1; but x = 1, whence 2 = 1.\n\nWhen a man is regularly snubbed, bullied, blown up, walked into, and put\ndown, there is usually some reaction in his favor, a kind of deostracism,\nwhich cannot bear to hear him always called the blunderer. I hope it will\nbe so in this case. There is nothing I more desire than to see _sects_ of\nparadoxers. There are fully five thousand adults in England who ought to be\nthe followers of some one false quadrature. And I have most hope of 3-1/8,\nbecause I think Mr. James Smith better fitted to be the leader of an\norganized infatuation than any one I know of. He wants no pity, and will\nget none. He has energy, means, good humor, strong conviction, character,\nand popularity in his own circle. And, most indispensable point of all, he\nsticks at nothing;\n\n \"In coelum jusseris, ibit.\"[389]\n\nWhen my instructor found I did not print an acceptance of what I have\nquoted, he addressed me as follows (_Corr._, Sept 23):--\n\n\"In this life, however, we must do our duty, and, when {242} necessary, use\nthe rod, not in a spirit of revenge, but for the benefit of the culprit and\nthe good of society. Now, Sir, the opportunity has been thrown in your way\nof slipping out of the pillory without risk of serious injury; but, like an\nobstinate urchin, you have chosen to quarrel with your opportunity and\nremain there, and thus you compel me to deal with you as schoolmasters used\nto do with stupid boys in bygone days--that is to say, you force me to the\nuse of the critic's rod, compel me to put you where little Jack Horner sat,\nand, as a warning to other naughty boys, to ornament you with a dunce's\ncap. The task I set you was a very simple one, as I shall make manifest at\nthe proper time.\"\n\nIn one or more places, as well as this, Mr. Smith shows that he does not\nknow the legend of little Jack Horner, whom he imagines to be put in the\ncorner as a bad boy. This is curious; for there had been many allusions to\nthe story in the journal he was writing in, and the Christmas pie had\nbecome altered into the Seaforth [pi].\n\nMr. Smith is satisfied at last that--what between argument and punishment\nhe has convinced me. He says (_Corr._, Jan. 27, 1866): \"I tell him without\nhesitation that he knows the true ratio of diameter to circumference as\nwell as I do, and if he be wise he will admit it.\" I should hope I do, and\nbetter; but there is no occasion to admit what everybody knows.\n\nI have often wished that we could have a slight glimpse of the reception\nwhich was given to some of the old cyclometers: but we have nothing, except\nthe grave disapprobation of historians. I am resolved to give the New\nZealander a chance of knowing a little more than this about one of them at\nleast; and, by the fortunate entrance into life of the _Correspondent_, I\nam able to do it. I omit sober mathematical answers, of which there were\nseveral. The following letter is grave earnest:\n\n\"Sir,--I have watched Mr. James Smith's writings on this subject from the\nfirst, and I did hope that, as the more {243} he departs from truth the\nmore easy it must be to refute him, [this by no means always true] some of\nyour correspondents would by this time have done so. I own that I am unable\nto detect the fallacy of his argument; and I am quite certain that '[Pi]'\nis wrong, in No. 23, where he declares that Mr. Smith is 'ignorant of the\nvery elements of mathematical truth.' I have observed an immense amount of\ngeometrical reasoning on his part, and I cannot see that it is either fair\nor honest to deny this, which may be regarded as the 'elements' of\nmathematical truth. Would it not be better for '[Pi]' to answer Mr. Smith,\nto refute his arguments, to point out their fallacies, and to save learners\nfrom error, than to plunge into gross insult and unmanly abuse? Would it\nnot be well, also, that Professor De Morgan should favour us with a little\nreasoning?\n\n\"I have hitherto seen no attempt to overthrow Mr. Smith's arguments; I\ntrust that this will not continue, since the subject is one of immense\nimportance to science in general, especially to nautical science, and all\nthat thereto belongs.\n\nYours, etc.,\n\nA CAPTAIN, R.N.\"\n\nOn looking at this homoeopathic treatment of the 3-1/8\nquadrature--remember, homoeopathic, _similia similibus_,[390] not\ninfinitesimal--and at the imputation thrown upon it, I asked myself, what\n_is_ vulgarity? No two agree, except in this, that every one sees vulgarity\nin what is directed against himself. Mark the world, and see if anything be\nso common as the description of the other side's remarks as \"vulgar attempt\nat wit.\" \"I suppose you think that very witty:\" the answer is \"No my\nfriend! your remark shows that you feel it as wit, so that the purpose is\nanswered; I keep my razor for something else than cutting blocks;\" I am\ninclined to think that \"out of place\" is a necessary attribute of true\nvulgarity. And further, it is to be noticed that nothing is {244}\nunproducible--_salvo pudore_[391]--which has classical authority, modern or\nancient, in its favor. \"He is a vulgar fellow; I asked him what he was\nupon, and what do you think he answered, My legs!\"--\"Well, and has he not\njustification? what do you find in Terence? _Quid agitur? Statur._\"[392] I\ndo not even blench from my principle where I find that it brings what is\ncalled \"taking a sight\" within permissible forms of expression: Rabelais\nnot only establishes its antiquity, but makes it English. Our old\ntranslation[393] has it thus (book 2. ch. 19):\n\n\"Then made the Englishman this sign. His left hand, all open, he lifted up\ninto the air, then instantly shut into his fist the four fingers thereof;\nand his thumb extended at length he placed upon the tip of his nose.\nPresently after he lifted up his right hand all open and abased and bent it\ndownwards, putting the thumb thereof in the very place where the little\nfinger of the left hand did close in the fist, and the four right hand\nfingers he softly moved in the air. Then contrarily he did with the right\nhand what he had done with the left, and with the left what he had done\nwith the right.\"\n\nAn impressive sight! The making of a fist of the left hand is a great\naddition of power, and should be followed in modern practice. The gentle\nsullation of the front fingers, with the clenched fist behind them, says as\nplainly as possible, Put _suaviter in modo_ in the van, but don't forget to\nhave _fortiter in re_[394] in the rear.\n\n{245}\n\nMy Budget was announced (March 23, 1867) for completion on the 30th. Mr.\nJames Smith wrote five letters, one before the completion, four after it;\nthe five contained 68 pages of quarto letter paper. Mr. J. S. had picked up\na clerical correspondent, with whom he was in the heat of battle.\n\n\"_March 27._--Dear Sir. Very truly yours. Duty; for my own sake; just time\nleft to retrieve my errors; sends copy of letter to clergyman; new proof\nnever before thought of; merest tyro would laugh if I were to stifle it,\nwhether by rhodomontade or silent contempt; keep your temper. I shall be\nconvinced; and if world be right in supposing me incapable of a foul act, I\nshall proclaim glorious discovery in the _Athenaeum_.\n\n\"_April 15._--Sir,... My dear Sir, Your sincere tutelary. Copy of another\nletter to clergyman; discovery tested by logarithms; reasons such as none\nbut a knave or a sinner can resist. Let me advise you to take counsel\nbefore it is too late! Keep your temper. Let not your _pride_ get the\nbetter of your discretion! Screw up your courage, my good friend, and\n_resolve_ to show the world that you are an _honest_ man....\n\n\"_April 20._--Sir ... Your very sincere and favorite tutelary. I have long\nplayed the _cur_, snapping and snarling...; suddenly lost my power, and\nbecame _half-starved_ dog without _spirit_ to bark; try if air cannot\nrestore me; calls himself the _thistle_ in allusion to my other tutelary,\nthe _thorn_; Would I prefer his next work to be, 'A whip for the\nMathematical Cur, Prof. De M.' In some previous letter which I have\nmislaid, he told me his next would be 'a muzzle for the Mathematical Bull\ndog, Prof. De M.'\n\n\"_April 23._--Sir. Very sincerely yours. More letters to clergyman; you may\nas well knock your head against a stone wall to improve your intellect as\nattempt to controvert my proofs. [I thought so too; and tried neither].\n{246}\n\n\"_May 6._--My dear Sir. Very sincerely yours. All to myself, and nothing to\nnote.\n\n\"_July 2._--No more in this interval. All that precedes is a desperate\nattempt to induce me to continue my descriptions: notoriety at any price.\"\n\nI dare say the matter is finished: the record of so marked an instance of\nself-delusion will be useful.\n\nI append to the foregoing a letter from Dr. Whewell[395] to Mr. James\nSmith. The Master of Trinity was conspicuous as a rough customer, an\nintellectual bully, an overbearing disputant: the character was as well\nestablished as that of Sam Johnson. But there was a marked difference. It\nwas said of Johnson that if his pistol missed fire, he would knock you down\nwith the butt end of it: but Whewell, in like case, always acknowledged the\nmiss, and loaded again or not, as the case might be. He reminded me of\nDennis Brulgruddery, who says to Dan, Pacify me with a good reason, and\nyou'll find me a dutiful master. I knew him from the time when he was my\nteacher at Cambridge, more than forty years. As a teacher, he was anything\nbut dictatorial, and he was perfectly accessible to proposal of objections.\nHe came in contact with me in his slashing way twice in our after joint\nlives, and on both occasions he acknowledged himself overcome, by that\nchange of manner, and apologetic mode of continuance, which I had seen him\nemploy towards others under like circumstances.\n\nI had expressed my wish to have a _thermometer of probability_, with\nimpossibility at one end, as 2 and 2 make 5, and necessity at the other, as\n2 and 2 make 4, and a graduated rise of examples between them. Down came a\nblow: \"What! put necessary and contingent propositions together! It's\nabsurd!\" I pointed out that the two kinds of necessity are but such\nextremes of probability as 0 and [infinity] are of number, and illustrated\nby an urn with 1 white and _n_ black {247} balls, _n_ increasing without\nlimit. It was frankly seen, and the point yielded; a large company was\npresent.\n\nAgain, in a large party, after dinner, and politics being the subject, I\nwas proceeding, in discussion with Mr. Whewell, with \"I think\"...--\"Ugh!\n_you_ think!\" was the answer. I repeated my phrase, and gave as a reason\nthe words which Lord Grey[396] had used in the House of Lords the night\nbefore (the celebrated advice to the Bishops to set their houses in order).\nHe had not heard of this, and his manner changed in an instant: he was the\nrational discutient all the rest of the evening, having previously been\nnothing but a disputant with all the distinctions strongly marked.\n\nI have said that Whewell was gentle with his pupils; it was the same with\nall who wanted teaching: it was only on an armed enemy that he drew his\nweapon. The letter which he wrote to Mr. J. Smith is an instance: and as it\napplies with perfect fidelity to the efforts of unreasoning above\ndescribed, I give it here. Mr. James Smith is skilfully exposed, and felt\nit; as is proved by \"putting the writer in the stocks.\"\n\n\"The Lodge, Cambridge, September 14th, 1862.\n\n\"Sir,--I have received your explanation of your proposition that the\ncircumference of the circle is to its diameter as 25 to 8. I am afraid I\nshall disappoint you by saying that I see no force in your proof: and I\nshould hope that you will see that there is no force in it if you consider\nthis: In the whole course of the proof, though the word cycle occurs, there\nis no property of the circle employed. You may do this: you may put the\nword _hexagon_ or _dodecagon_, or any other word describing a polygon in\nthe place of _Circle_ in your proof, and the proof would be just as good as\nbefore. Does not this satisfy you that you cannot have proved a property of\nthat special figure--a circle? {248}\n\n\"Or you may do this: calculate the side of a polygon of 24 sides inscribed\nin a circle. I think you are a Mathematician enough to do this. You will\nfind that if the radius of the circle be one, the side of this polygon is\n.264 etc. Now, the arc which this side subtends is according to your\nproposition 3.125/12 = .2604, and therefore the chord is greater than its\narc, which you will allow is impossible.\n\n\"I shall be glad if these arguments satisfy you, and\n\n\"I am, Sir, your obedient Servant,\n\n\"W. WHEWELL.\"\n\n\n\nAN M.P.'S ARITHMETIC.\n\nIn the debate of May, 1866, on Electoral Qualifications, a question arose\nabout arithmetical capability. Mr. Gladstone asked how many members of the\nHouse could divide 1330l. 7s. 6d. by 2l. 13s. 8d. Six hundred and\nfifty-eight, answered one member; the thing cannot be done, answered\nanother. There is an old paradox to which this relates: it arises out of\nthe ignorance of the distinction between abstract and concrete arithmetic.\n_Magnitude_ may be divided by _magnitude_; and the answer is number: how\noften does 12d. contain 4d.; answer three times. _Magnitude_ may be divided\nby _number_, and the answer is _magnitude_: 12d. is divided in four equal\nparts, what is each part? Answer three _pence_. The honorable objector,\nwhose name I suppress, trusting that he has mended his ways, gave the\nfollowing utterance:\n\n\"With regard to the division sum, it was quite possible to divide by a sum,\nbut not by money. How could any one divide money by 2l. 16s. 8d.?\n(Laughter.) The question might be asked, 'How many times 2s. will go into\n1l.?' but that was not dividing by money; it was simply dividing 20 by 2.\nHe might be asked, 'How many times will 6s. 8d. go into a pound?' but it\nwas only required to divide 240 by 80. If the right hon. gentleman were to\nask the hon. {249} member for Brighton (Professor Fawcett),[397] or any\nother authority, he would receive the same answer--viz., that it was\npossible to divide by a sum, but not by money. (Hear.)\"\n\nI shall leave all comment for the second edition, if I publish one.[398] I\nshall be sure to have something to laugh at. Anything said from a\nrespectable quarter, or supposed to be said, is sure to find defenders. Sam\nJohnson, a sound arithmetician, comparing himself, and what he alone had\ndone in three years, with forty French Academicians and their forty years,\nsaid it proved that an Englishman is to a Frenchman as 40 x 40 to 3, or as\n1600 to 3. Boswell, who was no great hand at arithmetic, made him say that\nan Englishman is to a Frenchman as 3 to 1600. When I pointed this out, the\nsupposed Johnson was defended through thick and thin in _Notes and\nQueries_.\n\nI am now curious to see whether the following will find a palliator. It is\nfrom \"Tristram Shandy,\" book V. chapter 3. There are two curious idioms,\n\"for for\" and \"half in half\"; but these have nothing to do with my point:\n\n\"A blessing which tied up my father's tongue, and a misfortune which set it\nloose with a good grace, were pretty equal: sometimes, indeed, the\nmisfortune was the better of the two; for, for instance, where the pleasure\nof harangue was as _ten_, and the pain of the misfortune but as _five_, my\nfather gained half in half; and consequently was as well again off as if it\nhad never befallen him.\"\n\nThis is a jolly confusion of ideas; and wants nothing but a defender to\nmake it perfect. A person who invests five {250} with a return of ten, and\none who loses five with one hand and gains ten with the other, both leave\noff five richer than they began, no doubt. The first gains \"half in half,\"\nmore properly \"half _on_ half,\" that is, of the return, 10, the second 5 is\ngain upon the first 5 invested. \"Half _in_ half\" is a queer way of saying\ncent. per cent. If the 5l. invested be all the man had in the world, he\ncomes out, after the gain, twice as well off as he began, with reference to\nhis whole fortune. But it is very odd to say that balance of 5l. gain is\n_twice_ as good as if nothing had befallen, either loss or gain. A\nmathematician thinks 5 an infinite number of times as great as 0. The whole\nconfusion is not so apparent when money is in question: for money is money\nwhether gained or lost. But though pleasure and pain stand to one another\nin the same algebraical relation as money gained and lost, yet there is\nmore than algebra can take account of in the difference.\n\nNext, Ri. Milward[399] (Richard, no doubt, but it cannot be proved) who\npublished Selden's[400] Table Talk, which he had collected while serving as\namanuensis, makes Selden say, \"A subsidy was counted the fifth part of a\nman's estate; and so fifty subsidies is five and forty times more than a\nman is worth.\" For _times_ read _subsidies_, which seems part of the\nconfusion, and there remains the making all the subsidies equal to the\nfirst, though the whole of which they are to be the fifths is perpetually\ndiminished.\n\nThirdly, there is the confusion of the great misomath {251} of our own day,\nwho discovered two quantities which he avers to be identically the same,\nbut the greater the one the less the other. He had a truth in his mind,\nwhich his notions of quantity were inadequate to clothe in language. This\nerroneous phraseology has not found a defender; and I am almost inclined to\nsay, with Falstaff, The poor abuses of the time want countenance.\n\n\n\nERRONEOUS ARITHMETICAL NOTIONS.\n\n\"Shallow numerists,\" as Cocker[401] is made to call them, have long been at\nwork upon the question how to _multiply_ money by money. It is, I have\nobserved, a very common way of amusing the tedium of a sea voyage: I have\nhad more than one bet referred to me. Because an oblong of five inches by\nfour inches contains 5 x 4 or 20 _square_ inches, people say that five\ninches multiplied by four inches _is_ twenty _square_ inches: and, thinking\nthat they have multiplied length by length, they stare when they are told\nthat money cannot be multiplied by money. One of my betters made it an\nargument for the thing being impossible, that there is no _square money_:\nwhat could I do but suggest that postage-stamps should be made legal\ntender. Multiplication must be _repetition_: the repeating process must be\nindicated by _number_ of times. I once had difficulty in persuading another\nof my betters that if you repeat five shillings as often as there are hairs\nin a horse's tail, you do not _multiply five shillings by a\nhorsetail_.[402]\n\nI am very sorry to say that these wrong notions have found support--I think\nthey do so no longer--in the University of Cambridge. In 1856 or 1857, an\nexaminer was displaced by a vote of the Senate. The pretext was that he was\ntoo severe an examiner: but it was well known that {252} great\ndissatisfaction had been expressed, far and wide through the Colleges, at\nan absurd question which he had given. He actually proposed such a fraction\nas\n\n   6s. 3d.\n  --------.\n  17s. 4d.\n\nAs common sense gained a hearing very soon, there is no occasion to say\nmore. In 1858, it was proposed at a college examination, to divide 22557\ndays, 20 hours, 20 minutes, 48 seconds, by 57 minutes, 12 seconds, and also\nto explain the fraction\n\n  32l. 18s. 8d.\n  -------------.\n  62l. 12s. 9d.\n\nAll paradoxy, in matters of demonstration, arises out of muddle about first\nprinciples. Who can say how much of it is to be laid at the door of the\nUniversity of Cambridge, for not taking care of the elements of\narithmetical thought?\n\n\n\nON LITERARY BARGAINS.\n\nThe phenomena of the two ends of society, when brought together, give\ninteresting comparisons: I mean the early beginnings of thought and\nliterature, and our own high and finished state, as we think it. There is\none very remarkable point. In the early day, the letter was matter of the\nclosest adherence, and implied meanings were not admitted.\n\nThe blessing of Isaac meant for Esau, went to false Jacob, in spite of the\nimposition; and the writer of Genesis seems to intend to give the notion\nthat Isaac had no power to pronounce it null and void. And \"Jacob's policy,\nwhereby he became rich\"--as the chapter-heading puts it--in speckled and\nspotted stock, is not considered as a violation of the agreement, which\ncontemplated natural proportions. In {253} the story of Lycurgus the\nlawgiver is held to have behaved fairly when he bound the Spartans to obey\nhis laws until he returned--intimating a short absence--he intending never\nto return. And Vishnoo, when he asked the usurper for three steps of\nterritory as a dwarf, and then enlarged himself until he could bring heaven\nand earth under the bargain, was thought clever, certainly, but quite fair.\n\nThere is nothing of this kind recognized in our day: so far good. But there\nis a bad contrary: the age is apt, in interpretation, to upset the letter\nin favor of the view--very often the after thought--of one side only. The\ncase of John Palmer,[403] the improver of the mail coach system, is\nsmothered. He was to have an office and a salary, and 2-1/2 per cent for\nlife on the increased _revenue_ of the Post-Office. His rights turned out\nso large, that Government would not pay them. For misconduct, real or\npretended, they turned him out of his _office_: but his bargain as to the\npercentage had nothing to do with his future conduct; it was payment for\nhis _plan_. I know nothing, except from the debates of 1808 in the two\nHouses: if any one can redeem the credit of the nation, the field is open.\nWhen I was young, the old stagers spoke of this transaction sparingly, and\ndismissed it speedily.\n\nThe government did not choose to remember what private persons must\nremember, and are made to remember, if needful. When Dr. Lardner[404] made\nhis bargain with the {254} publishers for the _Cabinet Cyclopaedia_ he\nproposed that he, as editor, should have a certain sum for every hundred\nsold above a certain number: the publishers, who did not think there was\nany chance of reaching the turning sale of this stipulation, readily\nconsented. But it turned out that Dr. Lardner saw further than they: the\nreturns under this stipulation gave him a very handsome addition to his\nother receipts. The publishers stared; but they paid. They had no idea of\nstanding out that the amount was too much for an editor; they knew that,\nthough the editor had a percentage, they had all the rest; and they would\nnot have felt aggrieved if he had received ten times as much. But\ngovernments, which cannot be brought to book before a sworn jury, are ruled\nonly by public opinion. John Palmer's day was also the day of Thomas Fyshe\nPalmer,[405] and the governments, in their prosecutions for sedition, knew\nthat these would have a reflex action upon the minds of all who wrote about\npublic affairs.\n\n\n\nDECLARATION OF BELIEF\n\n1864-65.--It often happens that persons combine to maintain and enforce an\nopinion; but it is, in our state of society, a paradox to unite for the\nsole purpose of blaming the opposite side. To invite educated men to do\nthis, and above all, men of learning or science, is the next paradoxical\nthing of all. But this was done by a small combination in 1864. They got\ntogether and drew up a _declaration_, to be signed by \"students of the\nnatural sciences,\" who were to express their \"sincere regret that\nresearches into {255} scientific truth are perverted by some in our own\ntimes into occasion for casting doubt upon the truth and authenticity of\nthe Holy Scriptures.\" In words of ambiguous sophistry, they proceeded to\nrequest, in effect, that people would be pleased to adopt the views of\nchurches as to the _complete_ inspiration of all the canonical books. The\ngreat question whether the Word of God is _in_ the Bible, or whether the\nWord of God is _all_ the Bible, was quietly taken for granted in favor of\nthe second view; to the end that men of science might be induced to blame\nthose who took the first view. The first public attention was drawn to the\nsubject by Sir John Herschel,[406] who in refusing to sign the writ sent to\nhim, administered a rebuke in the _Athenaeum_, which would have opened most\neyes to see that the case was hopeless. The words of a man whose _suaviter\nin modo_ makes his _fortiter in re_[407] cut blocks with a razor are worth\npreserving:\n\n\"I consider the act of calling upon me publicly to avow or disavow, to\napprove or disapprove, in writing, any religious doctrine or statement,\nhowever carefully or cautiously drawn up (in other words, to append my name\nto a religious manifesto) to be an infringement of that social forbearance\nwhich guards the freedom of religious opinion in this country with especial\nsanctity.... I consider this movement simply mischievous, having a direct\ntendency (by putting forward a new Shibboleth, a new verbal test of\nreligious partisanship) to add a fresh element of discord to the already\ntoo discordant relations of the Christian world.... But no nicety of\nwording, no artifice of human language, will suffice to discriminate the\nhundredth part of the shades of meaning in which the most world-wide\ndifferences of thought on such subjects may be involved; or prevent the\nmost gentle worded and apparently justifiable expression of regret, so\nembodied, from grating on the {256} feelings of thousands of estimable and\nwell-intentioned men with all the harshness of controversial hostility.\"\n\nOther doses were administered by Sir J. Bowring,[408] Sir W. Rowan\nHamilton,[409] and myself. The signed declaration was promised for\nChristmas, 1864: but nothing presentable was then ready; and it was near\nMidsummer, 1865, before it was published. Persons often incautiously put\ntheir names without seeing the _character_ of a document, because they\ncoincide in its _opinions_. In this way, probably, fifteen respectable\nnames were procured before printing; and these, when committed, were hawked\nas part of an application to \"solicit the favor\" of other signatures. It is\nlikely enough no one of the fifteen saw that the declaration was, not\n_maintenance_ of their own opinion, but _regret_ (a civil word for _blame_)\nthat others should _think differently_.\n\nWhen the list appeared, there were no fewer than 716 names! But analysis\nshowed that this roll was not a specimen of the mature science of the\ncountry. The collection was very miscellaneous: 38 were designated as\n\"students of the College of Chemistry,\" meaning young men who attended\nlectures in that college. But as all the Royal Society had been applied to,\na test results as follows. Of Fellows of the Royal Society, 600 in number,\n62 gave their signatures; of writers in the _Philosophical Transactions_,\n166 in number, 19 gave their signatures. Roughly speaking, then, only one\nout of ten could be got to express disapprobation of the free comparison of\nthe results of science with the statements of the canonical books. And I am\nsatisfied that many of these thought they were signing only a declaration\nof difference of opinion, not of blame for that difference. The number of\npersons is not small who, when it comes to signing printed documents, would\nput their names to a declaration that the coffee-pot ought to be taken\ndown-stairs, meaning that the teapot ought to be brought {257} up-stairs.\nAnd many of them would defend it. Some would say that the two things are\nnot contradictory; which, with a snort or two of contempt, would be very\neffective. Others would, in the candid and quiet tone, point out that it is\nall one, because coffee is usually taken before tea, and it keeps the table\nclear to send away the coffee-pot before the teapot is brought up.\n\nThe original signatures were decently interred in the Bodleian Library: and\nthe advocates of scattering indefinite blame for indefinite sins of opinion\namong indefinite persons are, I understand, divided in opinion about the\ntime at which the next attempt shall be made upon men of scientific\nstudies: some are for the Greek Calends, and others for the Roman\nOlympiads. But, with their usual love of indefiniteness, they have\ndetermined that the choice shall be argued upon the basis that which comes\nfirst cannot be settled, and is of no consequence.\n\nI give the declaration entire, as a curiosity: and parallel with it I give\na substitute which was proposed in the _Athenaeum_, as worthy to be signed\nboth by students of theology, and by students of science, especially in\npast time. When a new attempt is made, it will be worth while to look at\nboth:\n\n_Declaration._                  _Proposed Substitute._\n\nWe, the undersigned Students    We, the undersigned Students\nof the Natural Sciences,        of Theology and of Nature,\ndesire to express our sincere   desire to express our sincere\nregret, that researches into    regret, that common notions of\nscientific truth are perverted  religious truth are perverted\nby some in our own times into   by some in our own times into\noccasion for casting doubt      occasion for casting reproach\nupon the Truth and              upon the advocates of\nAuthenticity of the Holy        demonstrated or highly\nScriptures.                     probable scientific theories.\n\n                                {258}\nWe conceive that it is          We conceive that it is\nimpossible for the Word of      impossible for the Word of\nGod, as written in the book of  God, as correctly read in the\nnature, and God's Word written  Book of Nature, and the Word\nin Holy Scripture, to           of God, as truly interpreted\ncontradict one another,         out of the Holy Scripture, to\nhowever much they may appear    contradict one another,\nto differ.                      however much they may appear\n                                to differ.\nWe are not forgetful that       We are not forgetful that\nPhysical Science is not         neither theological\ncomplete, but is only in a      interpretation nor physical\ncondition of progress, and      knowledge is yet complete, but\nthat at present our finite      that both are in a condition\nreason enables us only to see   of progress; and that at\nas through a glass darkly,      present our finite reason\n                                enables us only to see both\n                                one and the other as through a\n                                glass darkly [the writers of\n                                the original declaration have\n                                distinctively applied to\n                                physical science the phrase by\n                                which St. Paul denotes the\n                                imperfections of theological\n                                vision, which they tacitly\n                                assume to be quite perfect],\nand we confidently believe,     and we confidently believe,\nthat a time will come when the  that a time will come when the\ntwo records will be seen to     two records will be seen to\nagree in every particular. We   agree in every particular. We\ncannot but deplore that         cannot but deplore that\nNatural Science should be       Religion should be looked upon\nlooked upon with suspicion by   with suspicion by some and\nmany who do not make a study    Science by others, of the\nof it, merely on account of     students of either who do not\nthe unadvised manner in which   make a study of the {259}\nsome are placing it in          other, merely on account of\nopposition to Holy Writ.        the unadvised manner in which\n                                some are placing Religion in\n                                opposition to Science, and\n                                some are placing Science in\n                                opposition to Religion.\nWe believe that it is the duty  We believe that it is the duty\nof every Scientific Student to  of every theological student\ninvestigate nature simply for   to investigate the Scripture,\nthe purpose of elucidating      and of every scientific\ntruth,                          student to investigate Nature,\n                                simply for the purpose of\n                                elucidating truth.\nand that if he finds that some  And if either should find that\nof his results appear to be in  some of his results appear to\ncontradiction to the Written    be in contradiction, whether\nWord, or rather to his own      to Scripture or to Nature, or\n_interpretations_ of it, which  rather to his own\nmay be erroneous, he should     _interpretation_ of one or the\nnot presumptuously affirm that  other, which may be erroneous,\nhis own conclusions must be     he should not affirm as with\nright, and the statements of    certainty that his own\nScripture wrong;                conclusion must be right, and\n                                the other interpretation\n                                wrong:\nrather, leave the two side by   but should leave the two side\nside till it shall please God   by side for further inquiry\nto allow us to see the manner   into both, until it shall\nin which they may be            please God to allow us to\nreconciled;                     arrive at the manner in which\n                                they may be reconciled.\nand, instead of insisting upon  In the mean while, instead of\nthe seeming differences         insisting, and least of all\nbetween Science and the         with acrimony or injurious\nScriptures, it would be as      {260} statements about others,\nwell to rest in faith upon the  upon the seeming differences\npoints in which they agree.     between Science and the\n                                Scriptures, it would be a\n                                thousand times better to rest\n                                in faith as to our future\n                                state, in hope as to our\n                                coming knowledge, and in\n                                charity as to our present\n                                differences.\n\nThe distinctness of the fallacies is creditable to the composers, and shows\nthat scientific habits tend to clearness, even to sophistry. Nowhere does\nit so plainly stand out that the _Written Word_ means the sense in which\nthe accuser takes it, while the sense of the other side is _their\ninterpretation_. The infallible church on one side, arrayed against\nheretical pravity on the other, is seen in all subjects in which men\ndiffer. At school there were various games in which one or another\nadvantage was the right of those who first called for it. In adult argument\nthe same thing is often attempted: we often hear--I cried _Church_ first!\n\nI end with the answer which I myself gave to the application: its revival\nmay possibly save me from a repetition of the like. If there be anything I\nhate more than another it is the proposal to place any persons, especially\nthose who allow freedom to me, under any abridgment of their liberty to\nthink, to infer, and to publish. If they break the law, take the law; but\ndo not make the law: [Greek: agoraioi agontai enkaleitosan allelois.][410]\nI would rather be asked to take shares in an argyrosteretic company (with\nlimited liability) for breaking into houses by night on fork and spoon\nerrands. I should put aside this proposal with _nothing but laughter_. It\nwas a joke against Sam Rogers[411] that his appearance was very like that\nof a corpse. The _John Bull_ {261} newspaper--suppose we now say Theodore\nHook[412]--averred that when he hailed a coach one night in St. Paul's\nChurchyard, the jarvey said, \"Ho! ho! my man; I'm not going to be taken in\nthat way: go back to your grave!\" This is the answer I shall make for the\nfuture to any relics of a former time who shall want to call me off the\nstand for their own purposes. What obligation have I to admit that they\nbelong to our world?\n\n\n\n\"SCRIPTURE AND SCIENCE.\n\n\"_The Writ De Haeretico Commiserando._[413]\n\nNov. 14, 1864.\n\n\"This document was sent to me four days ago. It 'solicits the favor'--I\nthought at first it was a grocer's supplication for tea and sugar\npatronage--of my signature to expression of 'sincere regret' that some\npersons unnamed--general warrants are illegal--differ from what I am\nsupposed--by persons whom it does not concern--to hold about Scripture and\nScience in their real or alleged discrepancies.\n\n\"No such favor from me: for three reasons. First, I agree with Sir. J.\nHerschel that the solicitation is an intrusion to be publicly repelled.\nSecondly, I do _not_ regret that others should differ from me, think what I\nmay: those others are as good as I, and as well able to think, and as much\nentitled to their conclusions. Thirdly, even if I did regret, I should be\nashamed to put my name to bad chemistry made to do duty for good reasoning.\nThe declaration is an awkward attempt to saturate sophism with truism; but\nthe sophism is left largely in excess.\n\n{262}\n\n\"I owe the inquisitors a grudge for taking down my conceit of myself. For\ntwo months I have crowed in my own mind over my friend Sir J. Herschel,\nfancying that the promoters instinctively knew better than to bring their\nfallacies before a writer on logic. Ah! my dear Sir John! thought I, if you\nhad shown yourself to be well up in _Barbara Celarent_,[414] and had ever\nand anon astonished the natives with the distinction between _simpliciter_\nand _secundum quid_, no autograph-hunters would have baited a trap with\n_non sequitur_[415] to catch your signature. What can I say now? I hide my\ndiminished head, diminished by the horns which I have been compelled to\ndraw in.\n\n\"Those who make personal solicitation for support to an opinion about\nreligion are bound to know their men. The king had a right to Brother\nNeale's money, because Brother Neale offered it. Had he put his hand into\npurse after purse by way of finding out all who were of Brother Neale's\nmind, he would have been justly met by a rap on the knuckles whenever he\nmissed his mark.\n\n\"The kind of test before me is the utmost our time will allow of that\ninquisition into opinion which has been the curse of Christianity ever\nsince the State took Providence under its protection. The writ _de haeretico\ncommiserando_ is little more than the smell of the empty cask: and those\nwho issue it may represent the old woman with her\n\n \"O suavis anima, quale in te dicam bonum\n  Antehac fuisse; tales cum sint reliquiae.\"[416]\n\nIt is no excuse that the illegitimate bantling is a very little one. Its\nparents may think themselves hardly treated when they are called lineal\nsuccessors of Tony Fire-the-faggot: {263} but, degenerate though they be,\nsuch is their ancestry. Let every allowance be made for them: but their\nunholy fire must be trodden out; so long as a spark is left, nothing but\nfuel is wanted to make a blaze. If this cannot be done, let the flame be\nconfined to theology, though even there it burns with diminished vigor: and\nlet charity, candor, sense, and ridicule, be ready to play upon it whenever\nthere is any chance of its extending to literature and science.\n\n\"What would be the consequence if this test-signing absurdity were to grow?\nDeep would call unto deep; counter-declaration would answer declaration,\neach stronger than the one before. The moves would go on like the dispute\nof two German students, of whom each is bound to a sharper retort on a\ngraduated scale, until at last comes _dummer Junge_![417]--and then they\nmust fight. There is a gentleman in the upper fifteen of the signers of the\nwrit--the hawking of whose names appears to me very bad taste--whom I met\nin cordial cooperation for many a year at a scientific board. All I knew\nabout his religion was that he, as a clergyman, must in some sense or other\nreceive the 39 Articles:--all that he could know about mine was that I was\nsome kind of heretic, or so reputed. If we had come to signing opposite\nmanifestoes, turn-about, we might have found ourselves in the lowest depths\nof party discussion at our very council-table. I trust the list of\nsubscribers to the declaration, when it comes to be published, will show\nthat the bulk of those who have really added to our knowledge have seen the\nthing in its true light.\n\n\"The promoters--I say nothing about the subscribers--of the movement will,\nI trust, not feel aggrieved at the course I have taken or the remarks I\nhave made. Walter Scott says that before we judge Napoleon by the\ntemptation to which he yielded, we ought to remember how much he may have\nresisted: I invite them to apply this rule to myself; they can have no idea\nof the feeling with which I {264} contemplate all attempts to repress\nfreedom of inquiry, nor of the loathing with which I recoil from the\nproposal to be art and part. They have asked me to give a public opinion\nupon a certain point. It is true that they have had the kindness to tender\nboth the opinion they wish me to form, and the shape in which they would\nhave it appear: I will let them draw me out, but I will not let them take\nme in. If they will put an asterisk to my name, and this letter to the\nasterisk, they are welcome to my signature. As I do not expect them to\nrelish this proposal, I will not solicit the favor of its adoption. But\nthey have given a right to think, for they have asked me to think; to\npublish, for they have asked me to allow them to publish; to blame them,\nfor they have asked me to blame their betters. Should they venture to find\nfault because my direction of disapproval, publicly given, is half a\nrevolution different from theirs, they will be known as having presented a\nloaded document at the head of a traveler in the highway of discussion,\nwith--Your signature or your silence!\"\n\n\n\nTHE FLY-LEAF PARADOX.\n\nThe paradox being the proposition of something which runs counter to what\nwould generally be thought likely, may present itself in many ways. There\nis a _fly-leaf paradox_, which puzzled me for many years, until I found a\nprobable solution. I frequently saw, in the blank leaves of old books,\nlearned books, Bibles of a time when a Bible was very costly, etc., the\nname of an owner who, by the handwriting and spelling, must have been an\nilliterate person or a child, followed by the date of the book itself.\nAccordingly, this uneducated person or young child seemed to be the first\nowner, which in many cases was not credible. Looking one day at a\nBarker's[418] Bible of 1599, I saw an {265} inscription in a child's\nwriting, which certainly belonged to a much later date. It was \"Martha\nTaylor, her book, giuen me by Granny Scott to keep for her sake.\" With this\nthe usual verses, followed by 1599, the date of the book. But it so chanced\nthat the blank page opposite the title, on which the above was written, was\na verso of the last leaf of a prayer book, which had been bound before the\nBible; and on the recto of this leaf was a colophon, with the date 1632. It\nstruck me immediately that uneducated persons and children, having seen\ndates written under names, and not being quite up in chronology, did\nfrequently finish off with the date of the book, which stared them in the\nface.\n\nAlways write in your books. You may be a silly person--for though your\nreading my book is rather a contrary presumption, yet it is not\nconclusive--and your observations may be silly or irrelevant, but you\ncannot tell what use they may be of long after you are gone where\nBudgeteers cease from troubling.\n\nI picked up the following book, printed by J. Franklin[419] at Boston,\nduring the period in which his younger brother Benjamin was his apprentice.\nAnd as Benjamin was apprenticed very early, and is recorded as having\nlearned the mechanical art very rapidly, there is some presumption that\npart of it may be his work, though he was but thirteen at the time. As this\nset of editions of Hodder[420] (by {266} Mose[421]) is not mentioned, to my\nknowledge, I give the title in full:\n\n    \"Hodder's Arithmetick: or that necessary art made most easy: Being\n    explained in a way familiar to the capacity of any that desire to learn\n    it in a little time. By James Hodder, Writing-master. The Five and\n    twentieth edition, revised, augmented, and above a thousand faults\n    amended, by Henry Mose, late servant and successor to the author.\n    Boston: printed by J. Franklin, for S. Phillips, N. Buttolph, B.\n    Elliot, D. Henchman, G. Phillips, J. Elliot, and E. Negus, booksellers\n    in Boston, and sold at their shops. 1719.\"\n\nThe book is a very small octavo, the type and execution are creditable, the\nwoodcut at the beginning is clumsy. It is a perfect copy, page for page, of\nthe English editions of Mose's Hodder, of which the one called seventeenth\nis of London, 1690. There is not a syllable to show that the edition above\ndescribed might not be of Boston in England. Presumptions, but not very\nstrong ones, might be derived from the name of _Franklin_, and from the\nlarge number of booksellers who combined in the undertaking. It chanced,\nhowever, that a former owner had made the following note in my copy:\n\n    \"Wednessday, July y^e 14, 1796, att ten in y^e forenoon we sail^d from\n    Boston, came too twice, once in King Rode, and once in y^e Narrows.\n    Sail^d by y^e lighthouse in y^e even^g.\"\n\n{267}\n\nNo ordinary map would decide these points: so I had to apply to my friend\nSir Francis Beaufort,[422] and the charts at the Admiralty decided\nimmediately for Massachusetts.\n\n\n\nPARADOXES OF ORTHOGRAPHY AND COMPUTATION.\n\nThe French are able paradoxers in their spelling of foreign names. The Abbe\nSabatier de Castres,[423] in 1772, gives an account of an imaginary\ndialogue between Swif, Adisson, Otwai, and Bolingbrocke. I had hoped that\nthis was a thing of former days, like the literal roasting of heretics; but\nthe charity which hopeth all things must hope for disappointments. Looking\nat a recent work on the history of the popes, I found referred to, in the\nmatter of Urban VIII[424] and Galileo, references to the works of two\nEnglishmen, the Rev. Win Worewel and the Rev. Raden Powen. [Wm. Whewell and\nBaden Powell].[425]\n\nI must not forget the \"moderate computation\" paradox. This is the way by\nwhich large figures are usually obtained. Anything surprisingly great is\ngot by the \"lowest computation,\" anything as surprisingly small by the\n\"utmost computation\"; and these are the two great subdivisions of \"moderate\ncomputation.\" In this way we learn that 70,000 persons were executed in one\nreign, and 150,000 persons {268} burned for witchcraft in one century.\nSometimes this computation is very close. By a card before me it appears\nthat all the Christians, including those dispersed in heathen countries,\nthose of Great Britain and Ireland excepted, are 198,728,000 people, and\npay their clergy 8,852,000l. But 6,400,000 people pay the clergy of the\nAnglo-Irish Establishment 8,896,000l.; and 14,600,000 of other\ndenominations pay 1,024,000l. When I read moderate computations, I always\nthink of Voltaire and the \"memoires du fameux eveque de Chiapa, par\nlesquels il parait qu'il avait egorge, ou brule, ou noye dix millions\nd'infideles en Amerique pour les convertir. Je crus que cet eveque\nexaggerait; mais quand on reduisait ces sacrifices a cinq millions de\nvictimes, cela serait encore admirable.\"[426]\n\n\n\nCENTRIFUGAL FORCE.\n\nMy Budget has been arranged by authors. This is the only plan, for much of\nthe remark is personal: the peculiarities of the paradoxer are a large part\nof the interest of the paradox. As to subject-matter, there are points\nwhich stand strongly out; the quadrature of the circle, for instance. But\nthere are others which cannot be drawn out so as to be conspicuous in a\nreview of writers: as one instance, I may take the _centrifugal force_.\n\nWhen I was about nine years old I was taken to hear a course of lectures,\ngiven by an itinerant lecturer in a country town, to get as much as I could\nof the second half of a good, sound, philosophical omniscience. The first\nhalf (and sometimes more) comes by nature. To this end I smelt chemicals,\nlearned that they were different kinds of _gin_, saw young wags try to kiss\nthe girls under the excuse of what was called _laughing gas_--which I was\nsure {269} was not to blame for more than five per cent of the requisite\nassurance--and so forth. This was all well so far as it went; but there was\nalso the excessive notion of creative power exhibited in the millions of\nmiles of the solar system, of which power I wondered they did not give a\nstill grander idea by expressing the distances in inches. But even this was\nnothing to the ingenious contrivance of the centrifugal force. \"You have\nheard what I have said of the wonderful centripetal force, by which Divine\nWisdom has retained the planets in their orbits round the Sun. But, ladies\nand gentlemen, it must be clear to you that if there were no other force in\naction, this centripetal force would draw our earth and the other planets\ninto the Sun, and universal ruin would ensue. To prevent such a\ncatastrophe, the same wisdom has implanted a centrifugal force of the same\namount, and directly opposite,\" etc. I had never heard of Alfonso X of\nCastile,[427] but I ventured to think that if Divine Wisdom had just let\nthe planets alone it would come to the same thing, with equal and opposite\ntroubles saved. The paradoxers deal largely in speculation conducted upon\nthe above explanation. They provide external agents for what they call the\ncentrifugal force. Some make the sun's rays keep the planets off, without a\nthought about what would become of our poor eyes if the _push_ of the light\nwhich falls on the earth were a counterpoise to all its gravitation. The\ntrue explanation cannot be given here, for want of room.\n\n\n\nCAMBRIDGE POETS.\n\nSometimes a person who has a point to carry will assert a singular fact or\nprediction for the sake of his point; and {270} this paradox has almost\nobtained the sole use of the name. Persons who have reputation to care for\nshould beware how they adopt this plan, which now and then eventuates a\nspanker, as the American editor said. Lord Byron, in \"English Bards, etc.\"\n(1809), ridiculing Cambridge poetry, wrote as follows:\n\n \"But where fair Isis rolls her purer wave,\n  The partial muse delighted loves to lave;\n  On her green banks a greener wreath she wove,\n  To crown the bards that haunt her classic grove;\n  Where Richards[428] wakes a genuine poet's fires,\n  And modern Britons glory in their sires.\"[429]\n\nThere is some account of the Rev. Geo. Richards, Fellow of Oriel and Vicar\nof Bampton, (M.A. in 1791) in the _Living Authors_ by Watkins[430] and\nShoberl[431] (1816). In Rivers's _Living Authors_, of 1798, which is best\nfitted for citation, as being published before Lord Byron wrote, he is\nspoken of in high terms. The _Aboriginal Britons_ was an Oxford (special)\nprize poem, of 1791. Charles Lamb mentions Richards as his school-fellow at\nChrist's Hospital, \"author of the _Aboriginal Britons_, the most spirited\nof the Oxford Prize Poems: a pale, studious Grecian.\"\n\nAs I never heard of Richards as a poet,[432] I conclude that his fame is\ndefunct, except in what may prove to be a very ambiguous kind of\nimmortality, conferred by Lord Byron. The awkwardness of a case which time\nhas broken down {271} is increased by the eulogist himself adding so\npowerful a name to the list of Cambridge poets, that his college has placed\nhis statue in the library, more conspicuously than that of Newton in the\nchapel; and this although the greatness of poetic fame had some serious\ndrawbacks in the moral character of some of his writings. And it will be\nfound on inquiry that Byron, to get his instance against Cambridge, had to\ngo back eighteen years, passing over seven intermediate productions, of\nwhich he had either never heard, or which he would not cite as waking a\ngenuine poet's fires.\n\nThe conclusion seems to be that the _Aboriginal Britons_ is a remarkable\nyouthful production, not equalled by subsequent efforts.\n\nTo enhance the position in which the satirist placed himself, two things\nshould be remembered. First, the glowing and justifiable terms in which\nByron had spoken,--a hundred and odd lines before he found it convenient to\nsay no Cambridge poet could compare with Richards,--of a Cambridge poet who\ndied only three years before Byron wrote, and produced greatly admired\nworks while actually studying in the University. The fame of Kirke\nWhite[433] still lives; and future literary critics may perhaps compare his\nwritings and those of Richards, simply by reason of the curious relation in\nwhich they are here placed alongside of each other. And it is much to\nByron's credit that, in speaking of the deceased Cambridge poet, he forgot\nhis own argument and its exigencies, and proved himself only a paradoxer\n_pro re nata_.\n\nSecondly, Byron was very unfortunate in another passage of the same poem:\n\n{272}\n\n \"What varied wonders tempt us as they pass!\n  The cow-pox, tractors, galvanism, and gas.\n  In turns appear, to make the vulgar stare,\n  Till the swoln bubble bursts--and all is air!\"\n\nThree of the bubbles have burst to mighty ends. The metallic tractors are\ndisused; but the force which, if anything, they put in action, is at this\nday, under the name of mesmerism, used, prohibited, respected, scorned,\nassailed, defended, asserted, denied, declared utterly obscure, and\nuniversally known. It was hard lines to select for candidates for oblivion\nnot one of whom got in. I shall myself, I am assured, be some day cited for\nlaughing at the great discovery of ----: the blank is left for my reader to\nfill up in his own way; but I think I shall not be so unlucky in four\ndifferent ways.\n\n\n\nFALSIFIED PREDICTION.\n\nThe narration before the fact, as prophecy has been called, sometimes quite\nas true as the narration after the fact, is very ridiculous when it is\nwrong. Why, the pre-narrator could not know; the post-narrator might have\nknown. A good collection of unlucky predictions might be made: I hardly\nknow one so fit to go with Byron's as that of the Rev. Daniel Rivers,\nalready quoted, about Johnson's biographers. Peter Pindar[434] may be\nexcused, as personal satire was his object, for addressing Boswell and Mrs.\nPiozzi[435] as follows:\n\n \"Instead of adding splendor to his name,\n  Your books are downright gibbets to his fame;\n  You never with posterity can thrive,\n 'Tis by the Rambler's death alone you live.\"\n\nBut Rivers, in prose narrative, was not so excusable. He says:\n\n{273}\n\n\"As admirers of the learning and moral excellence of their hero, we glow at\nalmost every page with indignation that his weaknesses and his failings\nshould be disclosed to public view.... Johnson, after the luster he had\nreflected on the name of Thrale ... was to have his memory tortured and\nabused by her detested itch for scribbling. More injury, we will venture to\naffirm, has been done to the fame of Johnson by this Lady and her late\nbiographical helpmate, than his most avowed enemies have been able to\neffect: and if his character becomes unpopular with some of his successors,\nit is to those gossiping friends he is indebted for the favor.\"\n\nPoor dear old Sam! the best known dead man alive! clever, good-hearted,\nlogical, ugly bear! Where would he have been if it had not been for Boswell\nand Thrale, and their imitators? What would biography have been if Boswell\nhad not shown how to write a life?\n\nRivers is to be commended for not throwing a single Stone at Mrs. Thrale's\nsecond marriage. This poor lady begins to receive a little justice. The\nliterary world seems to have found out that a blue-stocking dame who keeps\nopen house for a set among them has a right, if it so please her, to marry\nagain without taking measures to carry on the cake-shop. I was before my\nage in this respect: as a boy-reader of Boswell, and a few other things\nthat fell in my way, I came to a clearness that the conduct of society\ntowards Mrs. Piozzi was _blackguard_. She wanted nothing but what was in\nthat day a woman's only efficient protection, a male relation with a brace\nof pistols, and a competent notion of using them.\n\n\n\nBYRON AND WORDSWORTH.\n\nByron's mistake about Hallam in the Pindar story may be worth placing among\nabsurdities. For elucidation, suppose that some poet were now to speak--\n{274}\n\n \"Of man's first disobedience, and the fruit\n  Eve gave to Adam in his birthday suit--\"\n\nand some critic were to call it nonsense, would that critic be laughing at\nMilton? Payne Knight,[436] in his _Taste_, translated part of Gray's _Bard_\ninto Greek. Some of his lines are\n\n  [Greek: therma d' ho tengon dakrua stonachais]\n  [Greek: oulon melos phoberai]\n  [Greek: eeide phonai.]\n\nLiterally thus:\n\n \"Wetting warm tears with groans,\n  Continuous chant with fearful\n  Voice he sang.\"\n\nOn which Hallam remarks: \"The twelfth line [our first] is nonsense.\" And so\nit is, a poet can no more wet his tears with his groans than wet his ale\nwith his whistle. Now this first line is from Pindar, but is only part of\nthe sense; in full it is:\n\n  [Greek: therma de tengon dakrua stonachais]\n      [Greek: horthion phonase.]\n\nPindar's [Greek: tengon] must be Englished by _shedding_, and he stands\nalone in this use. He says, \"shedding warm tears, he cried out loud, with\ngroans.\" Byron speaks of\n\n \"Classic Hallam, much renowned for Greek:\"\n\nand represents him as criticising _the Greek_ of all Payne's lines, and not\ndiscovering that \"the lines\" were Pindar's {275} until after publication.\nByron was too much of a scholar to make this blunder himself: he either\naccepted the facts from report, or else took satirical licence. And why\nnot? If you want to laugh at a person, and he will not give occasion, whose\nfault is it that you are obliged to make it? Hallam did criticise some of\nPayne Knight's Greek; but with the caution of his character, he remarked\nthat possibly some of these queer phrases might be \"critic-traps\" justified\nby some one use of some one author. I remember well having a Latin essay to\nwrite at Cambridge, in which I took care to insert a few monstrous and\nunusual idioms from Cicero: a person with a Nizolius,[437] and without\nscruples may get scores of them. So when my tutor raised his voice against\nthese oddities, I was up to him, for I came down upon him with Cicero,\nchapter and verse, and got round him. And so my own solecisms, many of\nthem, passed unchallenged.\n\nByron had more good in his nature than he was fond of letting out: whether\nhe was a soured misanthrope, or whether his _vein_ lay that way in poetry,\nand he felt it necessary to fit his demeanor to it, are matters far beyond\nme. Mr. Crabb Robinson[438] told me the following story more than once. He\nwas at Charles Lamb's chambers in the Temple when Wordsworth came in, with\nthe new _Edinburgh Review_ in his hand, and fume on his countenance. \"These\nreviewers,\" said he, \"put me out of patience! Here is a young man--they say\nhe is a lord--who has written a volume of poetry; and these fellows, just\nbecause he is a lord, set upon him, laugh at him, and sneer at his writing.\nThe young man will do something, if he goes on as he has begun. But these\nreviewers seem to think {276} that nobody may write poetry, unless he lives\nin a garret.\" Crabb Robinson told this long after to Lady Byron, who said,\n\"Ah! if Byron had known that, he would never have attacked Wordsworth. He\nwent one day to meet Wordsworth at dinner; when he came home I said, 'Well,\nhow did the young poet get on with the old one?' 'Why, to tell you the\ntruth,' said he, 'I had but one feeling from the beginning of the visit to\nthe end, and that was--_reverence_!'\" Lady Byron told my wife that her\nhusband had a very great respect for Wordsworth. I suppose he would have\nsaid--as the Archangel said to his Satan--\"Our difference is po[li =\ne]tical.\"\n\nI suspect that Fielding would, if all were known, be ranked among the\nunlucky railers at supposed paradox. In his _Miscellanies_ (1742, 8vo) he\nwrote a satire on the Chrysippus or Guinea, an animal which multiplies\nitself by division, like the polypus. This he supposes to have been drawn\nup by Petrus Gualterus, meaning the famous usurer, Peter Walter. He calls\nit a paper \"proper to be read before the R----l Society\": and next year,\n1743, a quarto reprint was made to resemble a paper in the _Philosophical\nTransactions_. So far as I can make out, one object is ridicule of what the\nzoologists said about the polypus: a reprint in the form of the\n_Transactions_ was certainly satire on the Society, not on Peter Walter and\nhis knack of multiplying guineas.\n\nOld poets have recognized the quadrature of the circle as a well-known\ndifficulty. Dante compares himself, when bewildered, to a geometer who\ncannot find the principle on which the circle is to be measured:\n\n \"Quale e 'l geometra che tutto s' affige\n  Per misurar lo cerchio, e non ritruova,\n  Pensando qual principio ond' egli indige.\"[439]\n\n{277} And Quarles[440] speaks as follows of the _summum bonum_:\n\n \"Or is't a tart idea, to procure\n  An edge, and keep the practic soul in ure,\n  Like that dear chymic dust, or puzzling quadrature?\"\n\nThe poetic notion of the quadrature must not be forgotten. Aristophanes, in\nthe _Birds_, introduces a geometer who announces his intention to _make a\nsquare circle_. Pope, in the _Dunciad_, delivers himself as follows, with a\nGreek pronunciation rather strange in a translator of Homer. Probably Pope\nrecognized, as a general rule, the very common practice of throwing back\nthe accent in defiance of quantity, seen in o'rator, au'ditor, se'nator,\nca'tenary, etc.\n\n \"Mad _Mathesis_ alone was unconfined,\n  Too mad for mere material chains to bind,--\n  Now to pure space lifts her ecstatic stare,\n  Now, running round the circle, finds it square.\"\n\nThe author's note explains that this \"regards the wild and fruitless\nattempts of squaring the circle.\" The poetic idea seems to be that the\ngeometers try to make a square circle. Disraeli quotes it as \"finds _its_\nsquare,\" but the originals do not support this reading.\n\n\n\nDE BECOURT.\n\nI have come in the way of a work, entitled _The Grave of Human\nPhilosophies_ (1827), translated from the French of R. de Becourt[441] by\nA. Dalmas. It supports, but I suspect not very accurately, the views of the\nold Hindu books. {278} That the sun is only 450 miles from us, and only 40\nmiles in diameter, may be passed over; my affair is with the state of mind\ninto which persons of M. Becourt's temperament are brought by a fancy. He\nfully grants, as certain, four millions of years as the duration of the\nHindu race, and 1956 as that of the universe. It must be admitted he is not\nwholly wrong in saying that our errors about the universe proceed from our\nignorance of its origin, antiquity, organization, laws, and final\ndestination. Living in an age of light, he \"avails himself of that\nopportunity\" to remove this veil of darkness, etc. The system of the\nBrahmins is the only true one: he adds that it has never before been\nattempted, as it could not be obtained except by him. The author requests\nus first, to lay aside prejudice; next, to read all he says in the order in\nwhich he says it: we may then pronounce judgment upon a work which begins\nby taking the Brahmins for granted. All the paradoxers make the same\nrequests. They do not see that compliance would bring thousands of systems\nbefore the world every year: we have scores as it is. How is a poor candid\ninquirer to choose. Fortunately, the mind has its grand jury as well as its\nlittle one: and it will not put a book upon its trial without a _prima\nfacie_ case in its favor. And with most of those who really search for\nthemselves, that case is never made out without evidence of knowledge,\nstanding out clear and strong, in the book to be examined.\n\n\n\nBEQUEST OF A QUADRATURE.\n\nThere is much private history which will never come to light, _caret quia\nvate sacro_,[442] because no Budgeteer comes across it. Many years ago a\nman of business, whose life was passed in banking, amused his leisure with\nquadrature, was successful of course, and bequeathed the result in a sealed\nbook, which the legatee was enjoined not to sell {279} under a thousand\npounds. The true ratio was 3.1416: I have the anecdote from the legatee's\nexecutor, who opened the book. That a banker should square the circle is\nvery credible: but how could a City man come by the notion that a thousand\npounds could be got for it? A friend of mine, one of the twins of my\nzodiac, will spend a thousand pounds, if he have not done it already, in\nblack and white cyclometry: but I will answer for it that he, a man of\nsound business notions, never entertained the idea of [pi] recouping him,\nas they now say. I speak of individual success: of course if a company were\nformed, especially if it were of unlimited lie-ability, the shares would be\ntaken. No offence; there is nothing but what a pun will either sanctify,\njustify, or nullify:\n\n \"It comes o'er the soul like the sweet South\n  That breathes upon a bank of _vile hits_.\"\n\nThe shares would be at a premium of 3-1/8 on the day after issue. If they\npresented me with the number of shares I deserve, for suggestion and\nadvertisement, I should stand up for the Archpriest of St. Vitus[443] and\n3-1/5, with a view to a little more gold on the bridge.\n\nI now insert a couple of reviews, one about Cyclopaedias, one about\nepistolary collections. Should any reader wish for explanation of this\ninsertion, I ask him to reflect a moment, and imagine me set to justify all\nthe additions now before him! In truth these reviews are the repositories\nof many odds and ends: they were not made to the books; the materials were\nin my notes, and the books came as to a ready-made clothes shop, and found\nwhat would fit them. Many remember Curll's[444] bequest of some very good\ntitles {280} which only wanted treatises written to them. Well! here were\nsome tolerable reviews--as times go--which only wanted books fitted to\nthem. Accordingly, some tags were made to join on the books; and then as\nthe reader sees.\n\nI should find it hard to explain why the insertion is made in this place\nrather than another. But again, suppose I were put to make such an\nexplanation throughout the volume. The improver who laid out grounds and\nalways studied what he called _unexpectedness_, was asked what name he gave\nit for those who walked over his grounds a second time. He was silenced;\nbut I have an answer: It is that which is given by the very procedure of\ntaking up my book a second time.\n\n\n\nREVIEW OF CYCLOPAEDIAS.\n\n    October 19, 1861. _The English Cyclopaedia._ Conducted by Charles\n    Knight.[445] 22 vols.: viz., _Geography_, 4 vols.; _Biography_, 6\n    vols.; _Natural History_, 4 vols.; _Arts and Sciences_, 8 vols.\n    (Bradbury & Evans.)\n\n    _The Encyclopaedia Britannica: a Dictionary of Arts, Sciences, and\n    General Literature._ Eighth Edition. 21 vols. and Index. (Black.)\n\nThe two editions above described are completed at the same time: and they\nstand at the head of the two great branches into which pantological\nundertakings are divided, as at once the largest and the best of their\nclasses.\n\nWhen the works are brought together, the first thing that strikes the eye\nis the syllable of difference in the names. The word _Cyclopaedia_ is a bit\nof modern purism. Though [Greek: enkuklopaideia][446] is not absolutely\nGreek of Greece, we learn from both Pliny[447] and Quintilian[448] that the\ncircle {281} of the sciences was so called by the Greeks, and\nVitruvius[449] has thence naturalized _encyclium_ in Latin. Nevertheless we\nadmit that the initial _en_ would have euphonized but badly with the word\n_Penny_: and the _English Cyclopaedia_ is the augmented, revised, and\ndistributed edition of the _Penny Cyclopaedia_. It has indeed been said that\nCyclopaedia should mean the education _of_ a circle, just as Cyropaedia is\nthe education _of_ Cyrus. But this is easily upset by Aristotle's word\n[Greek: kuklophoria],[450] motion _in_ a circle, and by many other cases,\nfor which see the lexicon.\n\nThe earliest printed Encyclopaedia of this kind was perhaps the famous\n\"myrrour of the worlde,\" which Caxton[451] translated from the French and\nprinted in 1480. The original Latin is of the thirteenth century, or\nearlier. This is a collection of very short treatises. In or shortly after\n1496 appeared the _Margarita Philosophica_ of Gregory Reisch,[452] the same\nwe must suppose, who was confessor to the Emperor Maximilian.[453] This is\nagain a collection of treatises, of much more pretension: and the\nestimation formed of it is proved by the number of editions it went\nthrough. In 1531 appeared the little collection of _works_ of\nRingelberg,[454] which is truly called an Encyclopaedia by {282} Morhof,\nthough the thumbs and fingers of the two hands will meet over the length of\nits one volume. There are more small collections; but we pass on to the\nfirst work to which the name of _Encyclopaedia_ is given. This is a\nponderous _Scientiarum Omnium Encyclopaedia_ of Alsted,[455] in four folio\nvolumes, commonly bound in two: published in 1629 and again in 1649; the\ntrue parent of all the Encyclopaedias, or collections of treatises, or works\nin which that character predominates. The first great _dictionary_ may\nperhaps be taken to be Hofman's _Lexicon Universale_[456] (1677); but\nChambers's[457] (so called) _Dictionary_ (1728) has a better claim. And we\nsupport our proposed nomenclature by observing that Alsted accidentally\ncalled his work _En_cyclopaedia, and Chambers simply Cyclopaedia.\n\nWe shall make one little extract from the _myrrour_, and one from\nRingelberg. Caxton's author makes a singular remark for his time; and one\nwell worthy of attention. The grammar rules of a language, he says, must\nhave been invented by foreigners: \"And whan any suche tonge was perfytely\nhad and usyd amonge any people, than other people not used to the same\ntonge caused rulys to be made wherby they myght lerne the same tonge ...\nand suche rulys be called the gramer of that tonge.\" Ringelberg says that\nif the right nostril bleed, the little finger of the right hand should be\ncrooked, and squeezed with great force; and the same for the left.\n\n{283}\n\nWe pass on to _the_ Encyclopedie,[458] commenced in 1751; the work which\nhas, in many minds, connected the word _encyclopaedist_ with that of\n_infidel_. Readers of our day are surprised when they look into this work,\nand wonder what has become of all the irreligion. The truth is, that the\nwork--though denounced _ab ovo_[459] on account of the character of its\nsupporters--was neither adapted, nor intended, to excite any particular\nremark on the subject: no work of which D'Alembert[460] was co-editor would\nhave been started on any such plan. For, first, he was a real _sceptic_:\nthat is, doubtful, with a mind not made up. Next, he valued his quiet more\nthan anything; and would as soon have gone to sleep over an hornet's nest\nas have contemplated a systematic attack upon either religion or\ngovernment. As to Diderot[461]--of whose varied career of thought it is\ndifficult to fix the character of any one moment, but who is very\nfrequently taken among us for a pure atheist--we will quote one sentence\nfrom the article \"_Encyclopedie_,\" which he wrote himself:--\"Dans le moral,\nil n'y a que Dieu qui doit servir de modele a 1'homme; dans les art, que la\nnature.\"[462]\n\nA great many readers in our country have but a very hazy idea of the\ndifference between the political Encyclopaedia, as we may call it, and the\n_Encyclopedie Methodique_,[463] which we always take to be meant--whether\nrightly or not we cannot tell--when we hear of the \"great French\nEncyclopaedia.\" This work, which takes much from its {284} predecessor,\nprofessing to correct it, was begun in 1792, and finished in 1832. There\nare 166 volumes of text, and 6439 plates, which are sometimes incorporated\nwith the text, sometimes make about 40 more volumes. This is still the\nmonster production of the kind; though probably the German Cyclopaedia of\nErsch and Gruber,[464] which was begun in 1818, and is still in progress,\nwill beat it in size. The great French work is a collection of\ndictionaries; it consists of Cyclopaedias of all the separate branches of\nknowledge. It is not a work, but a collection of works, one or another\ndepartment is to be bought from time to time; but we never heard of a\ncomplete set for sale in one lot. As ships grow longer and longer, the\nquestion arises what limit there is to the length. One answer is, that it\nwill never do to try such a length that the stern will be rotten before the\nprow is finished. This wholesome rule has not been attended to in the\nmatter before us; the earlier parts of the great French work were\nantiquated before the whole were completed: something of the kind will\nhappen to that of Ersch and Gruber.\n\nThe production of a great dictionary of either of the kinds is far from an\neasy task. There is one way of managing the _En_cyclopaedia which has been\nlargely resorted to; indeed, we may say that no such work has been free\nfrom it. This plan is to throw all the attention upon the great treatises,\nand to resort to paste and scissors, or some process of equally easy\ncharacter, for the smaller articles. However it may be done, it has been\nthe rule that the Encyclopaedia of treatises should have its supplemental\nDictionary of a very incomplete character. It is true that the treatises\nare intended to do a good deal; and that the Index, if it be good, knits\nthe treatises and the dictionary into one whole of reference. Still there\nare two stools, and between them a great deal will fall to the ground. The\ndictionary portion of the _Britannica_ is not to be compared with its {285}\ntreatises; the part called Miscellaneous and Lexicographical in the\n_Metropolitana_[465] is a great failure. The defect is incompleteness. The\nbiographical portion, for example, of the Britannica is very defective: of\nmany names of note in literature and science, which become known to the\nreader from the treatises, there is no account whatever in the dictionary.\nSo that the reader who has learnt the results of a life in astronomy, for\nexample, must go to some other work to know when that life began and ended.\nThis defect has run through all the editions; it is in the casting of the\nwork. The reader must learn to take the results at their true value, which\nis not small. He must accustom himself to regard the Britannica as a\nsplendid body of treatises on all that can be called heads of knowledge,\nboth greater and smaller; with help from the accompanying dictionary, but\nnot of the most complete character. Practically, we believe, this defect\ncannot be avoided: two plans of essentially different structure cannot be\nassociated on the condition of each or either being allowed to abbreviate\nthe other.\n\nThe defect of all others which it is most difficult to avoid is inequality\nof performance. Take any dictionary you please, of any kind which requires\nthe association of a number of contributors, and this defect must result.\nWe do not merely mean that some will do their work better than others; this\nof course: we mean that there will be structural differences of execution,\naffecting the relative extent of the different parts of the whole, as well\nas every other point by which a work can be judged. A wise editor will not\nattempt any strong measures of correction: he will remember that if some\nportions be below the rest, which is a disadvantage, it follows that some\nportions must be above the rest, which is an advantage. The only practical\nlevel, if {286} level there must be, is that of mediocrity, if not of\nabsolute worthlessness: any attempt to secure equality of strength will\nresult in equality of weakness. Efficient development may be cut down into\nmeager brevity, and in this way only can apparent equality of plan be\nsecured throughout. It is far preferable to count upon differences of\nexecution, and to proceed upon the acknowledged expectation that the\nprominent merits of the work will be settled by the accidental character of\nthe contributors; it being held impossible that any editorial efforts can\nsecure a uniform standard of goodness. Wherever the greatest power is\nfound, it should be suffered to produce its natural effect. There are,\nindeed, critics who think that the merit of a book, like the strength of a\nchain, is that of its weakest part: but there are others who know that the\nparallel does not hold, and who will remember that the union of many\nwriters must show exaggeration of the inequalities which almost always\nexist in the production of one person. The true plan is to foster all the\ngood that can be got, and to give development in the directions in which\nmost resources are found: a Cyclopaedia, like a plant, should grow towards\nthe light.\n\nThe _Penny Cyclopaedia_ had its share of this kind of defect or excellence,\naccording to the way in which the measure is taken. The circumstance is not\nso much noticed as might be expected, and this because many a person is in\nthe habit of using such a dictionary chiefly with relation to one subject,\nhis own; and more still want it for the pure dictionary purpose, which does\nnot go much beyond the meaning of the word. But the person of full and\nvaried reference feels the differences; and criticism makes capital of\nthem. The Useful Knowledge Society was always odious to the organs of\nreligious bigotry; and one of them, adverting to the fact that geography\nwas treated with great ability, and most unusual fullness, in the _Penny\nCyclopaedia_, announced it by making it the sole merit of {287} the work\nthat, with sufficient addition, it would make a tolerably good gazetteer.\n\nSome of our readers may still have hanging about them the feelings derived\nfrom this old repugnance of a class to all that did not associate direct\ndoctrinal teaching of religion with every attempt to communicate knowledge.\nI will take one more instance, by way of pointing out the extent to which\nstupidity can go. If there be an astronomical fact of the telescopic\ncharacter which, next after Saturn's ring and Jupiter's satellites, was\nknown to all the world, it was the existence of multitudes of double stars,\ntreble stars, etc. A respectable quarterly of the theological cast, which\nin mercy we refrain from naming, was ignorant of this common\nknowledge,--imagined that the mention of such systems was a blunder of one\nof the writers in the _Penny Cyclopaedia_, and lashed the presumed ignorance\nof the statement in the following words, delivered in April, 1837:\n\n    \"We have forgotten the name of that Sidrophel who lately discovered\n    that the fixed stars were not single stars, but appear in the heavens\n    like soles at Billingsgate, in pairs; while a second astronomer, under\n    the influence of that competition in trade which the political\n    economists tell us is so advantageous to the public, professes to show\n    us, through his superior telescope, that the apparently single stars\n    are really three. Before such wondrous mandarins of science, how\n    continually must _homunculi_ like ourselves keep in the background,\n    lest we come between the wind and their nobility.\"\n\nCertainly these little men ought to have kept in the background; but they\ndid not: and the growing reputation of the work which they assailed has\nchronicled them in literary history; grubs in amber.\n\nThis important matter of inequality, which has led us so far, is one to\nwhich the _Encyclopaedia_ is as subject as the _Cyclopaedia_; but it is not\nso easily recognized as a fault. {288} We receive the first book as mainly\na collection of treatises: we know their authors, and we treat them as\nindividuals. We see, for instance, the names of two leading writers on\nOptics, Brewster[466] and Herschel.[467] It would not at all surprise us if\neither of these writers should be found criticising the other by name, even\nthough the very view opposed should be contained in the same _Encyclopaedia_\nwith the criticism. And in like manner, we should hold it no wonder if we\nfound some third writer not comparable to either of those we have named. It\nis not so in the _Cyclopaedia_: here we do not know the author, except by\ninference from a list of which we never think while consulting the work. We\ndo not dissent from this or that author: we blame the book.\n\nThe _Encyclopaedia Britannica_ is an old friend. Though it holds a proud\nplace in our present literature, yet the time was when it stood by itself,\nmore complete and more clear than anything which was to be found elsewhere.\nThere must be studious men alive in plenty who remember when they were\nstudious boys, what a literary luxury it was to pass a few days in the\nhouse of a friend who had a copy of this work. The present edition is a\nworthy successor of those which went before. The last three editions,\nterminating in 1824, 1842, and 1861, seem to show that a lunar cycle cannot\npass without an amended and augmented edition. Detailed criticism is out of\nthe question; but we may notice the effective continuance of the plan of\ngiving general historical dissertations on the progress of knowledge. Of\nsome of these dissertations we have had to take separate notice; and all\nwill be referred to in our ordinary treatment of current literature.[468]\n\nThe literary excellence of these two extensive undertakings is of the same\nhigh character. To many this will {289} need justification: they will not\neasily concede to the cheap and recent work a right to stand on the same\nshelf with the old and tried magazine, newly replenished with the best of\neverything. Those who are cognizant by use of the kind of material which\nfills the _Penny Cyclopaedia_ will need no further evidence: to others we\nshall quote a very remarkable and certainly very complete testimony. The\n_Cyclopaedia of the Physical Sciences_, published by Dr. Nichol[469] in 1857\n(noticed by us, April 4), is one of the most original of our special\ndictionaries. The following is an extract from the editor's preface:\n\n    \"When I assented to Mr. Griffin's proposal that I should edit such a\n    Cyclopaedia, I had it in my mind that I might make the _scissors_\n    eminently effective. Alas! on narrowly examining our best Cyclopaedias,\n    I found that the scissors had become blunted through too frequent and\n    vigorous use. One great exception exists: viz., the _Penny Cyclopaedia_\n    of Charles Knight.[470] The cheapest and the least pretending, it is\n    really the most philosophical of our _scientific_ dictionaries. It is\n    not made up of a series of treatises, some good and many indifferent,\n    but is a thorough _Dictionary_, well proportioned and generally written\n    by the best men of the time. The more closely it is examined, the more\n    deeply will our obligation be felt to the intelligence and\n    conscientiousness of its projector and editor.\"\n\nAfter Dr. Nichol's candid and amusing announcement of his scissorial\npurpose, it is but fair to state that nothing of the kind was ultimately\ncarried into effect, even upon the work in which he found so much to\npraise. I quote this testimony because it is of a peculiar kind.\n\n{290}\n\nThe success of the _Penny Magazine_ led Mr. Charles Knight in 1832 to\npropose to the Useful Knowledge Society a Cyclopaedia in weekly penny\nnumbers. These two works stamp the name of the projector on the literature\nof our day in very legible characters. Eight volumes of 480 pages each were\ncontemplated; and Mr. Long[471] and Mr. Knight were to take the joint\nmanagement. The plan embraced a popular account of Art and Science, with\nvery brief biographical and geographical information. The early numbers of\nthe work had some of the _Penny Magazine_ character: no one can look at the\npictures of the Abbot and Abbess in their robes without seeing this. By the\ntime the second volume was completed, it was clearly seen that the plan was\nworking out its own extension: a great development of design was submitted\nto, and Mr. Long became sole editor. Contributors could not be found to\nmake articles of the requisite power in the assigned space. One of them\ntold us that when he heard of the eight volumes, happening to want a shelf\nto be near at hand for containing the work as it went on, he ordered it to\nbe made to hold twenty-five volumes easily. But the inexorable logic of\nfacts beat him after all: for the complete work contained twenty-six\nvolumes and two thick volumes of Supplement.\n\nThe penny issue was brought to an end by the state of the law, which\nrequired, in 1833, that the first and last page of everything sold\nseparately should contain the name and address of the printer. The penny\nnumbers contained this imprint on the fold of the outer leaf: and _qui\ntam_[472] informations were laid against the agents in various towns. {291}\nIt became necessary to call in the stock; and the penny issue was\nabandoned. Monthly parts were substituted, which varied in bulk, as the\ndemands of the plan became more urgent, and in price from one sixpence to\nthree. The second volume of Supplement appeared in 1846, and during the\nfourteen years of issue no one monthly part was ever behind its time. This\nresult is mainly due to the peculiar qualities of Mr. Long, who unites the\ntalents of the scholar and the editor in a degree which is altogether\nunusual. If any one should imagine that a mixed mass of contributors is a\npunctual piece of machinery, let him take to editing upon that hypothesis,\nand he shall see what he shall see and learn what he shall learn.\n\nThe _English_ contains about ten per cent more matter than the _Penny\nCyclopaedia_ and its supplements; including the third supplementary volume\nof 1848, which we now mention for the first time. The literary work of the\ntwo editions cost within 500l. and 50,000l.: that of the two editions of\nthe _Britannica_ cost 41,000l. But then it is to be remembered that the\n_Britannica_ had matter to begin upon, which had been paid for in the\nformer editions. Roughly speaking, it is probable that the authorship of a\npage of the same size would have cost nearly the same in one as in the\nother.\n\nThe longest articles in the _Penny Cyclopaedia_ were \"Rome\" in 98 columns\nand \"Yorkshire\" in 86 columns. The only article which can be called a\ntreatise is the Astronomer Royal's \"Gravitation,\" founded on the method of\nNewton in the eleventh section, but carried to a much greater extent. In\nthe _English Cyclopaedia_, the longest article of geography is \"Asia,\" in 45\ncolumns. In natural history the antelopes demand 36 columns. In biography,\n\"Wellington\" uses up 42 columns, and his great military opponent 41\ncolumns. In the division of Arts and Sciences, which includes much of a\nsocial and commercial character, the length of articles often depends upon\nthe state of the {292} times with regard to the subject. Our readers would\nnot hit the longest article of this department in twenty guesses: it is\n\"Deaf and Dumb\" in 60 columns. As other specimens, we may cite Astronomy,\n19; Banking, 36; Blind, 24; British Museum, 35; Cotton, 27; Drama, 26;\nGravitation, 50; Libraries, 50; Painting, 34; Railways, 18; Sculpture, 36;\nSteam, etc., 37; Table, 40; Telegraph, 30; Welsh language and literature,\n39; Wool, 21. These are the long articles of special subdivisions: the\nwords under which the _En_cyclopaedia gives treatises are not so prominent.\nAs in Algebra, 10; Chemistry, 12; Geometry, 8; Logic, 14; Mathematics, 5;\nMusic, 9. But the difference between the collection of treatises and the\ndictionary may be illustrated thus: though \"Mathematics\" have only five\ncolumns, \"Mathematics, recent terminology of,\" has eight: and this article\nwe believe to be by Mr. Cayley,[473] who certainly ought to know his\nsubject, being himself a large manufacturer of the new terms which he\nexplains. Again, though \"Music\" _in genere_, as the schoolmen said, has\nonly nine columns, \"Temperament and Tuning,\" has eight, and \"Chord\" alone\nhas two. And so on.\n\nIn a dictionary of this kind it is difficult to make a total clearance of\n_personality_: by which we mean that exhibition of peculiar opinion which\nis offensive to taste when it is shifted from the individual on the\ncorporate book. The treatise of the known author may, as we have said,\ncarry that author's controversies on its own shoulders: and even his\ncrotchets, if we may use such a word. But {293} the dictionary should not\nput itself into antagonism with general feeling, nor even with the feelings\nof classes. We refer particularly to the ordinary and editorial teaching of\nthe article. If, indeed, the writer, being at issue with mankind, should\nconfess the difference, and give abstract of his full grounds, the case is\naltered: the editor then, as it were, admits a correspondent to a statement\nof his own individual views. The dictionary portion of the Britannica is\nquite clear of any lapses on this point, so far as we know: the treatises\nand dissertations rest upon their authors. The Penny Cyclopaedia was all but\nclear: and great need was there that it should have been so. The Useful\nKnowledge Society, starting on the principle of perfect neutrality in\npolitics and religion, was obliged to keep strict watch against the\nentrance of all attempt even to look over the hedge. There were two--we\nbelieve only two--instances of what we have called personality. The first\nwas in the article \"Bunyan.\" It is worth while to extract all that is\nsaid--in an article of thirty lines--about a writer who is all but\nuniversally held to be the greatest master of allegory that ever wrote:\n\n    \"His works were collected in two volumes, folio, 1736-7: among them\n    'The Pilgrim's Progress' has attained the greatest notoriety. If a\n    judgment is to be formed of the merits of a book by the number of times\n    it has been reprinted, and the many languages into which it has been\n    translated, no production in English literature is superior to this\n    coarse allegory. On a composition which has been extolled by Dr.\n    Johnson, and which in our own times has received a very high critical\n    opinion in its favor [probably Southey], it is hazardous to venture a\n    disapproval, and we, perhaps, speak the opinion of a small minority\n    when we confess that to us it appears to be mean, jejune and\n    wearisome.\"\n\n--If the unfortunate critic who thus individualized himself had been a\nsedulous reader of Bunyan, his power over {294} English would not have been\nso _jejune_ as to have needed that fearful word. This little bit of\ncriticism excited much amusement at the time of its publication: but it was\nso thoroughly exceptional and individual that it was seldom or never\ncharged on the book. The second instance occurred in the article\n\"Socinians.\" It had been arranged that the head-words of Christian sects\nshould be intrusted to members of the sects themselves, on the\nunderstanding that the articles should simply set forth the accounts which\nthe sects themselves give of their own doctrines. Thus the article on the\nRoman Church was written by Dr. Wiseman.[474] But the Unitarians were not\nallowed to come within the rule: as in other quarters, they were treated as\nthe gypsies of Christianity. Under the head \"Socinians\"--a name repudiated\nby themselves--an opponent was allowed not merely to state their alleged\ndoctrines in his own way, but to apply strong terms, such as \"audacious\nunfairness,\" to some of their doings. The protests which were made against\nthis invasion of the understanding produced, in due time, the article\n\"Unitarians,\" written by one of that persuasion. We need not say that these\nerrors have been amended in the English Cyclopaedia: and our chief purpose\nin mentioning them is to remark, that this is all we can find on the points\nin question against twenty-eight large volumes produced by an editor whose\ntask was monthly, and whose issue was never delayed a single hour. How much\nwas arrested before publication none but himself can say. We have not\nalluded to one or two remonstrances on questions of absolute fact, which\nare beside the present purpose.\n\nBoth kinds of encyclopaedic works have been fashioned upon predecessors,\nfrom the very earliest which had a predecessor to be founded upon; and the\nundertakings before us will be themselves the ancestors of a line of\nsuccessors. Those who write in such collections should be {295} careful\nwhat they say, for no one can tell how long a mis-statement may live. On\nthis point we will give the history of a pair of epithets. When the\nhistorian De Thou[475] died, and left the splendid library which was\ncatalogued by Bouillaud[476] and the brothers Dupuis[477] (Bullialdus and\nPuteanus), there was a manuscript of De Thou's friend Vieta,[478] the\n_Harmonicon Coeleste_, of which it is on record, under Bouillaud's hand,\nthat he himself lent it to Cosmo de' Medici,[479] to which must be added\nthat M. Libri[480] found it in the Magliabecchi Library at Florence in our\nown day. Bouillaud, it seems, entirely forgot what he had done. Something,\nprobably, that Peter Dupuis said to Bouillaud, while they were at work on\nthe catalogue, remained on his memory, and was published by him in 1645,\nlong after; to the effect that Dupuis lent the manuscript to Mersenne,[481]\nfrom whom it was procured by some intending plagiarist, who would not give\nit back. This was repeated by Sherburne,[482] in 1675, who speaks of the\nwork, which \"being communicated to Mersennus was, by some perfidious\nacquaintance of that honest-minded person, surreptitiously taken from him,\nand irrecoverably lost or suppressed, to the unspeakable detriment of the\nlettered world.\" Now let the {296} reader look through the dictionaries of\nthe last century and the present, scientific or general, at the article,\n\"Vieta,\" and he will be amused with the constant recurrence of\n\"honest-minded\" Mersenne, and his \"surreptitious\" acquaintance. We cannot\nhave seen less than thirty copies of these epithets.\n\n\n\nREVIEW OF MACCLESFIELD LETTERS.\n\n    October 18, 1862. _Correspondence of Scientific Men of the Seventeenth\n    Century, in the Collection of the Earl of Macclesfield._[483] 2 vols.\n    (Oxford, University Press.)\n\nThough the title-page of this collection bears the date 1841, it is only\njust completed by the publication of its Table of Contents and Index.\nWithout these, a work of the kind is useless for consultation, and cannot\nmake its way. The reason of the delay will appear: its effect is well known\nto us. We have found inquirers into the history of science singularly\nignorant of things which this collection might have taught them.\n\nIn the same year, 1841, the Historical Society of Science, which had but a\nbrief existence, published a collection of letters, eighty-three in number,\nedited by Mr. Halliwell,[484] of English men of science, which dovetails\nwith the one before us, and is for the most part of a prior date. The two\nshould be bound up together. The smaller collection runs from 1562 to 1682;\nthe larger, from 1606 to past 1700. We shall speak of the two as the Museum\ncollection and the Macclesfield collection. And near them should be placed,\nin every scientific library, the valuable collection published, by Mr.\nEdleston,[485] for Trinity College, in 1850.\n\n{297}\n\nThe history of these letters runs back to famous John Collins, the\nattorney-general of the mathematics, as he has been called, who wrote to\neverybody, heard from everybody, and sent copies of everybody's letter to\neverybody else. He was in England what Mersenne[486] was in France: as\nearly as 1671, E. Bernard[487] addresses him as \"the very Mersennus and\nintelligence of this age.\" John Collins[488] was never more than accountant\nto the Excise Office, to which he was promoted from teaching writing and\nciphering, at the Restoration: he died in 1682. We have had a man of the\nsame office in our own day, the late Prof. Schumacher,[489] who made the\nlittle Danish Observatory of Altona the junction of all the lines by which\nastronomical information was conveyed from one country to another. When the\ncollision took place between Denmark and the Duchies, the English\nGovernment, moved by the Astronomical Society, instructed its diplomatic\nagents to represent strongly to the Danish Government, when occasion should\narise, the great importance of the Observatory of Altona to the\nastronomical communications of the whole world. But Schumacher had his own\ncelebrated journal, the _Astronomische Nachrichten_, by which to work out\npart of his plan; private correspondence was his supplementary assistant.\nCollins had only correspondence to rely on. Nothing is better known than\nthat it was Collins's collection which furnished the materials put forward\nby the Committee of the Royal Society in 1712, as a defence of Newton\nagainst the partisans of Leibnitz. The noted _Commercium Epistolicum_ is\nbut the abbreviation of a title which runs on with \"D. Johannis Collins et\naliorum ...\"\n\nThe whole of this collection passed into the hands of {298} William\nJones,[490] the father of the Indian Judge of the same name, who died in\n1749. Jones was originally a teacher, but was presented with a valuable\nsinecure by the interest of George, second Earl of Macclesfield, the mover\nof the bill for the change of style in Britain, who died President of the\nRoyal Society. This change of style may perhaps be traced to the union of\nenergies which were brought into concert by the accident of a common\nteacher: Lord Macclesfield and Lord Chesterfield,[491] the mover and the\nseconder, and Daval,[492] who drew the bill, were pupils of De Moivre.[493]\nJones, who was a respectable mathematician though not an inventor,\ncollected the largest mathematical library of his day, and became possessor\nof the papers of Collins, which contained those of Oughtred[494] and\nothers. Some of these papers passed into the custody of the Royal Society:\nbut the bulk was either bequeathed to, or purchased by, Lord Macclesfield;\nand thus they found their way to Shirburn Castle, where they still remain.\n\nA little before 1836, this collection attracted the attention of a\nsearching inquirer into points of mathematical history, the late Professor\nRigaud,[495] who died in 1839. He examined the whole collection of letters,\nobtained Lord Macclesfield's consent to their publication, and induced the\nOxford Press to bear the expense. It must be particularly remembered that\nthere still remains at Shirburn Castle a {299} valuable mass of\nnon-epistolary manuscripts. So far as we can see, the best chance of a\nfurther examination and publication lies in public encouragement of the\ncollection now before us: the Oxford Press might be induced to extend its\noperations if it were found that the results were really of interest to the\nliterary and scientific world. Rigaud died before the work was completed,\nand the publication was actually made by one of his sons, S. Jordan\nRigaud,[496] who died Bishop of Antigua. But this publication was little\nnoticed, for the reasons given. The completion now published consists of a\nsufficient table of contents, of the briefest kind, by Professor De Morgan,\nand an excellent index by the Rev. John Rigaud.[497] The work is now fairly\nstarted on its career.\n\nIf we were charged to write a volume with the title \"Small things in their\nconnection with great,\" we could not do better than choose the small part\nof this collection of letters as our basis. The names, as well as the\ncontents, are both great and small: the great names, those which are known\nto every mathematician who has any infusion of the history of his pursuit,\nare Briggs,[498] Oughtred, Charles Cavendish,[499] Gascoigne,[500] Seth\nWard,[501] Wallis,[502] {300} Hu[y]gens,[503] Collins,[504] William\nPetty,[505] Hooke,[506] Boyle,[507] Pell,[508] Oldenburg,[509]\nBrancker,[510] Slusius,[511] Bertit,[512] Bernard,[513] Borelli,[514]\nMouton,[515] Pardies,[516] Fermat,[517] Towneley,[518] Auzout,[519] {301}\nD. Gregory,[520] Halley,[521] Machin,[522] Montmort,[523] Cotes,[524]\nJones,[525] Saunderson,[526] Reyneau,[527] Brook Taylor,[528]\nMaupertuis,[529] Bouguer,[530] La Condamine,[531] Folkes,[532]\nMacclesfield,[533] {302} Baker,[534] Barrow,[535] Flamsteed,[536] Lord\nBrounker,[537] J. Gregory,[538] Newton[539] and Keill.[540] To these the\nMuseum collection adds the names of Thomas Digges,[541] Dee,[542] Tycho\nBrahe,[543] Harriot,[544] Lydyat,[545] Briggs,[546] Warner,[547] Tarporley,\nPell,[548] Lilly,[549] Oldenburg,[550] Collins,[551] Morland.[552]\n\n{303}\n\nThe first who appears on the scene is the celebrated Oughtred, who is\nrelated to have died of joy at the Restoration: but it should be added, by\nway of excuse, that he was eighty-six years old. He is an animal of extinct\nrace, an Eton mathematician. Few Eton men, even of the minority which knows\nwhat a sliding rule is, are aware that the inventor was of their own school\nand college: but they may be excused, for Dr. Hutton,[553] so far as his\nDictionary bears witness, seems not to have known it any more than they. A\nglance at one of his letters reminds us of a letter from the Astronomer\nRoyal on the discovery of Neptune, which we printed March 20, 1847. Mr.\nAiry[554] there contends, and proves it both by Leverrier[555] and by\nAdams,[556] that the limited publication of a private letter is more\nefficient than the more general publication of a printed memoir. The same\nmay be true of a dead letter, as opposed to a dead book. Our eye was caught\nby a letter of Oughtred (1629), containing systematic use of contractions\nfor the words _sine_, _cosine_, etc., prefixed to the symbol of the angle.\nThis is so very important a step, simple as it is, that Euler[557] is\njustly held to have greatly advanced trigonometry by its introduction.\nNobody that we know of has noticed that Oughtred was master of the\nimprovement, and willing to have taught it, if people would have learnt.\nAfter looking at his dead letter, we naturally turned to his dead book on\ntrigonometry, and there we found the abbreviations _s_, _sco_, _t_, _tco_,\n_se_, _seco_, regularly established as part of the system of the work. But\nnot one of those who have investigated the contending claims of Euler and\nThomas {304} Simpson[558] has chanced to know of Oughtred's\n\"Trigonometrie\": and the present revival is due to his letter, not to his\nbook.\n\nA casual reader, turning over the pages, would imagine that almost all the\nletters had been printed, either in the General Dictionary, or in\nBirch,[559] etc.: so often does the supplementary remark begin with \"this\nletter has been printed in ----.\" For ourselves we thought, until we\ncounted, that a large majority of the letters had been given, either in\nwhole or in part. But the positive strikes the mind more forcibly than the\nnegative: we find that all of which any portion has been in type makes up\nvery little more than a quarter; the cases in which the whole letter is\ngiven being a minority of this quarter. The person who has been best\nransacked is Flamsteed: of 36 letters from him, 34 had been previously\ngiven in whole or in part. Of 59 letters to and from Newton, only 17 have\nbeen culled.\n\nThe letters have been modernized in spelling, and, to some extent, in\nalgebraical notation; it also seems that conjectural methods of introducing\ninterpolations into the text have been necessary. For all this we are\nsorry: the scientific value of the collection is little altered, but its\nliterary value is somewhat lowered. But it could not be helped: the\nprinters could not work from the originals, and Professor Rigaud had to\ncopy everything himself. A fac-simile must have been the work of more time\nthan he had to give: had he attempted it, his death would have cut short\nthe whole undertaking, instead of allowing him to prepare everything but a\npreface, and to superintend the printing of one of the volumes. We may also\nadd, that we believe we have notices of _all_ the letters in the\nMacclesfield collection. We judge this because several which are too\ntrivial to print are numbered and described; and those would certainly not\nhave been noticed if _any_ omissions had {305} been made. And we know that\nevery letter was removed from Shirburn Castle to Oxford.\n\nTwo persons emerge from oblivion in this series of letters. The first is\nMichael Dary,[560] an obscure mathematician, who was in correspondence with\nNewton and other stars. He was a gauger at Bristol, by the interest of\nCollins; afterwards a candidate for the mathematical school at Christ's\nHospital, with a certificate from Newton: he was then a gunner in the\nTower, and is lastly described by Wallis as \"Mr. Dary, the tobacco-cutter,\na knowing man in algebra.\" In 1674, Dary writes to Newton at Cambridge, as\nfollows:--\"Although I sent you three papers yesterday, I cannot refrain\nfrom sending you this. I have had fresh thoughts this morning.\" Two months\nafterwards poor Newton writes to Collins, \"Mr. Dary is very solicitous\nabout mathematics\": but in spite of the persecution, he subscribes himself\nto Dary \"your loving friend.\" Dary's _problem_ is that of finding the rate\nof interest of an annuity of which the value and term are given. Dary's\n_theorem_, which he seems to have invented specially for the solution of\nhis problem, though it is of wide range, can be exhibited to mathematical\nreaders even in our columns. In modern language, it is that the limit of\n[phi]^{_n_}_x_, when _n_ increases without limit, is a solution of [phi]_x_\n= _x_. We have mentioned the I. Newton to whom Dary looked up; we add a\nword about the one on whom he looked down. Dr. John Newton,[561] a sedulous\npublisher of logarithms, tables of interest, etc., who began his career\nbefore Isaac Newton, sometimes puzzles those who do not know him, when\ndescribed as I. Newton. The scientific world was of opinion that all that\nwas valuable in one of his works was taken from Dary's private\ncommunications.\n\n{306}\n\nThe second character above alluded to is one who carried mathematical\nresearches a far greater length than Newton himself: the assistance which\nhe rendered in this respect, even to Newton, has never been acknowledged in\nmodern times: though the work before us shows that his contemporaries were\nfully aware of it, and never thought of concealing it. In his theory of\ngravitation, in which, so far as he went, we have every reason to believe\nhe was prior to Newton, he did not extend his calculations to the distance\nof the moon; his views in this matter were purely terrestrial, and led him\nto charge according to weight. He was John Stiles, the London and Cambridge\ncarrier: his name is a household word in the Macclesfield Letters, and is\neven enshrined in the depths of Birch's quartos. Dary informs Newton--let\nus do his memory this justice--that he had paid John Stiles for the\ncarriage. At the time when the railroad to Cambridge was opened, a\ncorrespondent recommended the directors, in our columns, to call an engine\nby the name of John Stiles, and never to let that name go off the road. We\ndo not know whether the advice was followed: if not, we repeat it.\n\nLittle points of life and manners come out occasionally. Baker, the author\nof a work on algebra much esteemed at the time, wrote to Collins that their\ncircumstances are alike, \"having a just and equal number of chargeable\nolive-branches, and being in the same predicament and blessed condemnation\nwith you, not more preaching than unpaid, and preaching the art of\ncontentment to others, am forced to practise it.\" But the last sentence of\nhis letter runs as follows: \"I have sent by the bearer ... twenty\nshillings, as a token to you; desiring you to accept of it, as a small\ntaste from Yours, Thos. Baker.\" In our day, men of a station to pay parish\ntaxes do not offer their friends hard money to buy liquor. But\nFlamsteed[562] writes to Collins as follows: \"Last week he sent us down the\ncounterpart, which {307} my father has scaled, and I return up to you by\nthe carrier, with 5l. to be paid to Mr. Leneve for the writing, I have\nadded 2s. 6d. over, which will pay the expenses and serve to drink, with\nhim.\" This would seem as odd to us as it would have seemed thirty years ago\nthat half-a-crown should pay carriage for a deed from Derby to London, and\nleave margin for a bottle of wine: in our day, the Post-office and the\nFrench treaty would just manage it between them. But Flamsteed does not\nlimit his friend to one bottle; he adds, \"If you expend more than the\nhalf-crown, I will make it good after Whitsuntide.\" Collins does not\nremember exactly where he had met James Gregory, and mentions two equally\nlikely places thus: \"Sir, it was once my good hap to meet with you in an\nalehouse or in Sion College.\" There is a little proof how universally the\ndinner-hour was twelve o'clock. Astronomers well know the method of finding\ntime by equal altitudes of the sun before and after noon: Huyghens calls it\n\"le moyen de deux egales hauteurs du soleil devant et apres _diner_.\"[563]\n\nThere is one mention of \"Mr. Cocker,[564] our famous English graver and\nwriter, now a schoolmaster at Northampton.\" This is the true Cocker: his\ngenuine works are specimens of writing, such as engraved copy-books,\nincluding some on arithmetic, with copper-plate questions and space for the\nworking; also a book of forms for law-stationers, with specimens of legal\nhandwriting. It is recorded somewhere that Cocker and another, whose name\nwe forget, competed with the Italians in the beauty of their flourishes.\nThis was his real fame: and in these matters he was great. The eighth\nedition of his book of law forms (1675), published shortly after Cocker's\ndeath, has a preface signed \"J. H.\" This was John Hawkins, who became\npossessed of Cocker's papers--at least he said so--and {308} subsequently\nforged the famous Arithmetic,[565] a second work on Decimal Arithmetic, and\nan English dictionary, all attributed to Cocker. The proofs of this are set\nout in De Morgan's _Arithmetical Books_. Among many other corroborative\ncircumstances, the clumsy forger, after declaring that Cocker to his dying\nday resisted strong solicitation to publish his Arithmetic, makes him write\nin the preface _Ille ego qui quondam_[566] of this kind: \"I have been\ninstrumental to the benefit of many, by virtue of those useful arts,\nwriting and engraving; and do _now_, with the same _wonted alacrity_, cast\nthis my arithmetical mite into the public treasury.\" The book itself is not\ncomparable in merit to at least half-a-dozen others. How then comes Cocker\nto be the impersonation of Arithmetic? Unless some one can show proof,\nwhich we have never found, that he was so before 1756, the matter is to be\naccounted for thus.\n\nArthur Murphy,[567] the dramatist, was by taste a man of letters, and ended\nby being the translator of Tacitus; though many do not know that the two\nare one. His friends had tried to make him a man of business; and no doubt\nhe had been well plied with commercial arithmetic. His first dramatic\nperformance, the farce of \"The Apprentice,\" produced in 1756, is about an\nidle young man who must needs turn actor. Two of the best known books of\nthe day in arithmetic were those of Cocker and Wingate.[568] Murphy chooses\n_Wingate_ to be the name of an old merchant who {309} delights in vulgar\nfractions, and _Cocker_ to be his arithmetical catchword--\"You read\nShakespeare! get Cocker's Arithmetic! you may buy it for a shilling on any\nstall; best book that ever was wrote!\" and so on. The farce became very\npopular, and, as we believe, was the means of elevating Cocker to his\npresent pedestal, where Wingate would have been, if his name had had the\ndroller sound of the two to English ears.\n\nA notoriety of an older day turns up, Major-General Lambert.[569] The\ncommon story is that he was banished to Guernsey, where he passed thirty\nyears in confinement, rearing and painting flowers. But Baker, in 1678,\nrepresents him as a prisoner at Plymouth, sending equations for solution as\na challenge: probably his place of confinement was varied, and his\noccupation also.\n\n[General Lambert was removed to Plymouth, probably about 1668. His daughter\ncaptured the son of the Governor of Guernsey, who therefore probably was\nreckoned an unsafe custodier thenceforward; though he assured the king that\nhe had turned the young couple out of doors, and had never given them a\npenny. Great importance was attached to Lambert's safe detention: probably\nthe remaining republicans looked upon him as to be their next Cromwell, if\nsuch a thing were to be. There were standing orders to shoot him at once on\nthe first appearance of any enemy before the island. See _Notes and\nQueries_, 3d S. iv. 89.]\n\nCollins informs James Gregory that \"some of the Royal Academy wrote over to\nMr. Oldenburg, who was desired to impart the same to the Council of the\nRoyal Society, that the French King was willing to allow pensions to one or\ntwo learned Englishmen, but they never made any answer {310} to such a\nproposal.\" This was written in 1671, and the thing probably happened\nseveral years before. Mr. De Morgan communicated the account of the\nproposal to Lord Macaulay, who replied that he did not think that any\nEnglishman _received_ a literary pension from Louis; but that there is a\ncurious letter, about 1664, from the French Ambassador, in which he says\nthat he has, by his master's orders, been making inquiries as to the state\nof learning in England, and that he is sorry to find that the best writer\nis _the infamous Miltonus_. On two such independent testimonies it may be\nheld proved that the French King had attempted to buy a little adherence\nfrom English literature and science; and the silent contempt of the Royal\nSociety is an honorable fact in their history.\n\nAnother little bit of politics is as follows. Oughtred is informed that\n\"Mr. Foster,[570] our Lecturer on Astronomy at Gresham College, is put out\nbecause he will not kneel down at the communion-table. A Scotsman [Mungo\nMurray], one that is _verbi bis minister_,[571] is now lecturer in Mr.\nFoster's place.\" Ward in his work on the Gresham Professors,[572]\nsuppresses the reason, and the suppression lowers the character of his\nbook. Foster was expelled in 1636, and re-elected on a vacancy in 1641,\nwhen Puritanism had gained strength.\n\nThe correspondence of Newton would require deeper sifting than could be\ngiven in such an article as the present. The first of the letters (1669) is\ncurious, as presenting the {311} appearance of forms belonging to the great\ncalculus which, in this paragraph, we ought to call that of fluxions. We\nfind, of the date February 18, 1669-70, what we believe is the earliest\nmanifestation of that morbid part of Newton's temperament which has been so\nvariously represented. He had solved a problem--being that which we have\ncalled Dary's--on which he writes as follows: \"The solution of the annuity\nproblem, if it will be of any use, you have my leave to insert into the\n_Philosophical Transactions_, so it be without my name to it. For I see not\nwhat there is desirable in public esteem, were I able to acquire and\nmaintain it. It would perhaps increase my acquaintance, the thing which I\nchiefly study to decline.\"\n\nThree letters touch upon \"the experiment of glass rubbed to cause various\nmotions in bits of paper underneath\": they are supplements to the account\ngiven by Newton to the Royal Society, and printed by Birch. It was Newton,\nso far as appears, who added _glass_ to the substances known to be\nelectric. Soon afterwards we come to a little bit of the history of the\nappointment to the Mint. It has appeared from the researches of late years\nthat Newton was long an aspirant for public employment: the only coolness\nwhich is known to have taken place between him and Charles Montague[573]\n[Halifax] arose out of his imagining that his friend was not in earnest\nabout getting him into the public service. March 14, 1696, Newton writes\nthus to Halley: \"And if the rumour of preferment for me in the Mint should\nhereafter, upon the death of Mr. Hoar [the comptroller], or any other\noccasion, be revived, I pray that you would {312} endeavour to obviate it\nby acquainting your friends that I neither _put in_ for _any_ place in the\nMint, nor would meddle with _Mr. Hoar's place_, were it offered to me.\"\nThis means that Mr. Hoar's place had been suggested, which Newton seems to\nhave declined. Five days afterwards, Montague writes to Newton that he is\nto have the _Wardenship_. It is fair to Newton to say that in all\nprobability this was not--or only in a smaller degree--a question of\npersonal dignity, or of salary. It must by this time have been clear to him\nthat the minister, though long bound to make him an object of patronage,\nwas actually seeking him for the Mint, because he wanted both Newton's name\nand his talents for business--which he knew to be great--in the weighty and\ndangerous operation of restoring the coinage. It may have been, and\nprobably was, the case that Newton had a tolerably accurate notion of what\nhe would have to do, and of what degree of power would be necessary to\nenable him to do it in his own way.\n\nWe have said that the non-epistolary manuscripts are still unexamined.\nThere is a chance that one of them may answer a question of two centuries'\nstanding, which is worth answering, because it has been so often asked.\nAbout 1640, Warner,[574] afterwards assisted by Pell,[575] commenced a\ntable of _antilogarithms_, of the kind which Dodson[576] afterwards\nconstructed anew and published. In the Museum collection there is inquiry\nafter inquiry from Charles Cavendish,[577] first, as to when the\n_Analogics_, as he called them, would be finished; next, when they would be\nprinted. Pell answers, in 1644, that Warner left his papers to a kinsman,\nwho had become bankrupt, and proceeds thus:\n\n\"I am not a little afraid that all Mr. Warner's papers, {313} and no small\nshare of my labours therein, are seazed upon, and most unmathematically\ndivided between the sequestrators and creditors, who (not being able to\nballance the account where there appeare so many numbers, and much troubled\nat the sight of so many crosses and circles in the superstitious Algebra\nand that black art of Geometry) will, no doubt, determine once in their\nlives to become figure-casters, and so vote them all to be throwen into the\nfire, if some good body doe not reprieve them for pye-bottoms, for which\npurposes you know analogicall numbers are incomparably apt, if they be\naccurately calculated.\"\n\nPell afterwards told Wallis[578] that the papers had fallen into the hands\nof Dr. Busby,[579] and Collins[580] writes that they were left in the hands\nof Dr. Thorndike,[581] a prebendary of Westminster; whence Rigaud[582]\nseems to say that Thorndike had left them to Dr. Busby. Birch[583] says\nthat he procured for the Royal Society four boxes from Busby's trustees,\ncontaining papers of Warner and Pell: but there is no other tradition of\nsuch things in the Society. But in the Birch manuscripts at the British\nMuseum, there turns up, as printed in what we call the Museum collection, a\nlist of Warner's papers, with _Collins's_ receipt to Dr. Thorndike at the\nbottom, and engagement to restore them on demand. The date is December 14,\n1667; Wallis's statement being in 1693. It is possible that Busby may be a\nmistake altogether: he was very unlikely to have had charge of any\nmathematical papers: there may have been a confusion between the Prebendary\nof Westminster and the Head Master of Westminster School. If so, in all\nprobability Thorndike handed {314} the cumbrous lot over to the notorious\ncollector of mathematical papers, blessing himself that he got rid of them\nin a manner which would insure their return if he were called upon by the\nowners to restore them. It is much against this hypothesis that Dodson, who\ncertainly recalculated, can say nothing more about Warner than a repetition\nof Wallis's story: though, had Collins kept the papers, they would probably\nhave been in Jones's possession at the very time when Dodson, who was a\nfriend of Jones and a user of his library, was engaged on his own\ncomputations. But even books, and still more manuscripts, are often\nsingularly overlooked; and it remains not very improbable that Warner's\ntable is now at Shirburn Castle, among the unexamined manuscripts.\n\n\n\nCYCLOMETRY AND STEEL PENS.\n\n_Redit labor actus in orbem._[584] Among the matters which have come to me\nsince the Budget opened, there is a pamphlet of quadrature of two pages and\na half from Professor Recalcati,[585] already mentioned. It ends with\n\"Quelque objection qu'on fasse touchant les raisonnements ci-dessus on\ntombera toujours dans l'absurde.\"[586] A civil engineer--so he says--has\nmade the quadrature \"no longer a problem, but an axiom.\" As follows: \"Take\nthe quadrant of a circle whose circumference is given, square the quadrant\nwhich gives the true square of the circle. Because 30 / 4 = 7.5 x 7.5 =\n56.25 = the positive square of a circle whose circumference is 30.\"\nBrevity, the soul of wit, is the \"wings of mighty-winds\" to quadrature, and\nsends it \"flying all abroad.\" A _surbodhicary_--something like M.A. or\nLL.D., I understand--at Calcutta, published in 1863 the division of an\n{315} angle into any odd number of parts, demonstration and all in--when\nthe diagram is omitted--one page, good-sized, well-leaded type, small\nduodecimo. But in the Preface he acknowledges \"sheer inability\" to execute\nhis task. Mr. William Dean, of Todmorden, in 1863, announced 3-9/64 as\nproved both practically and geometrically: he has been already mentioned\nanonymously. Next I have the tract of Don Juan Larriva, published at Leiria\nin 1856, and dedicated to Queen Victoria. Mr. W. Peters,[587] already\nmentioned, who has for some months been circulating diagrams on a card,\npublishes (August, 1865) _The Circle Squared_. He agrees with the\nArchpriest of St. Vitus. He hints that a larger publication will depend\npartly on the support he receives, and partly on the castigation, for which\nlast, of course, he looks to me. Cyclometers have their several styles of\nwit; so have anticyclometers too, for that matter. Mr. Peters will not\nallow me any extra-journal being: I am essentially a quotation from the\n_Athenaeum_; \"A. De Morgan\" _et praeterea nihil_.[588] If he had to pay for\nkeeping me set up, he would find out his mistake, and would be glad to\ncompound handsomely for a stereotype. Next comes a magnificent sheet of\npasteboard, printed on both sides. Having glanced at it and detected\nquadrature, I began methodically at the beginning--\"By Royal Command,\" with\nthe lion and unicorn, and all that comes between. Mercy on us! thought I to\nmyself: has Her Majesty referred the question to the Judicial Committee of\nthe Privy Council, where all the great difficulties go now-a-days, and is\nthis proclamation the result? On reading further I was relieved by finding\nthat the first side is entirely an advertisement of Joseph Gillott's[589]\nsteel pens, with engraving of his {316} premises, and notice of novel\napplication of his unrivalled machinery. The second side begins with \"the\ncircle rectified\" by W. E. Walker,[590] who finds [pi] =\n3.141594789624155.... This is an off-shoot from an accurate geometrical\nrectification, on which is to be presumed Mr. Gillott's new machinery is\nfounded. I have no doubt that Mr. Walker's error, which is only in the\nsixth place of decimals, will not hurt the pens, unless it be by the\nslightest possible increase of the tendency to open at the points. This\narises from Mr. Walker having rectified above proof by .000002136034362....\n\nLastly, I, even I myself, who have long felt that I was a quadrature below\npar, have solved the problem by means which, in the present state of the\nlaw of libel, I dare not divulge. But the result is permitted; and it goes\nfar to explain all the discordances. The ratio of the circumference to the\ndiameter is not always the same! Not that it varies with the radius; the\ngeometers are right enough on that point: but it varies with the time, in a\nmanner depending upon the difference of the true longitudes of the Sun and\nMoon. A friend of mine--at least until he misbehaved--insisted on the mean\nright ascensions: but I served him as Abraham served his guest in\nFranklin's parable. The true formula is, A and a being the Sun's and Moon's\nlongitudes,\n\n  [pi] = 3-13/80 + 3/80 cos(A - a).\n\nMr. James Smith obtained his quadrature at full moon; the Archpriest of St.\nVitus and some others at new moon. Until I can venture to publish the\ndemonstration, I recommend the reader to do as I do, which is to adopt\n3.14159..., and to think of the matter only at the two points of the lunar\nmonth at which it is correct. The _Nautical Almanac_ will no doubt give\nthese points in a short time: I am in correspondence with the Admiralty,\nwith nothing {317} to get over except what I must call a perverse notion on\nthe part of the Superintendent of the _Almanac_, who suspects one\ncorrection depending on the Moon's latitude; and the Astronomer Royal leans\ntowards another depending on the date of the Queen's accession. I have no\npatience with these men: what can the Moon's node of the Queen's reign\npossibly have to do with the ratio in question? But this is the way with\nall the regular men of science; Newton is to them etc. etc. etc. etc.\n\nThe following method of finding the circumference of a circle (taken from a\npaper by Mr. S. Drach[591] in the _Phil. Mag._, Jan. 1863, Suppl.) is as\naccurate as the use of 3.14159265. From three diameters deduct\n8-thousandths and 7-millionths of a diameter; to the result add five per\ncent. We have then not quite enough; but the shortcoming is at the rate of\nabout an inch and a sixtieth of an inch in 14,000 miles.\n\n\n\nJACOB BEHMEN.\n\nThough I have met with nothing but a little tract from the school of Jacob\nBehmen[592] (or Boehme; I keep to the old English version of his name), yet\nthere has been more, and of a more recent date. I am told of an\n\"Introduction to Theosophy [_Theo_ private, I suppose, as in theological];\nor, the Science of the Mystery of Christ,\" published in 1854, mostly from\nthe writings of William Law[593]: and also of a volume of 688 pages, of the\nsame year, printed for private circulation, containing notes for a\nbiography of William Law. The editor of the first work wishes to grow \"a\n{318} generation of perfect Christians\" by founding a Theosophic College,\nfor which he requests the public to raise a hundred thousand pounds. There\nis a good account of Jacob Behmen in the _Penny Cyclopaedia_. The author\nmentions inaccurate accounts, one of which he quotes, as follows: \"He\nderived all his mystical and rapturous doctrine from Wood's[594] _Athenae\nOxonienses_, Vol. I, p. 610, and _Hist. et Antiq. Acad. Oxon._, Vol. II, p.\n308.\" On which the author remarks that Wood was born after Behmen's death.\nThere must have been a few words which slipped out: what is meant is that\nBehmen \"derived his doctrine from _Robert Fludd_,[595] _for whom see_\nWood's etc. etc.\" Even this is absurd enough: for Behmen began to publish\nin 1610, and Fludd in 1616. Fludd was a Rosicrucian, and a mystic of a\ndifferent type from Behmen. I have some of his works, and could produce out\nof them paradoxes enough, according to our ways of thinking, to fit out a\nhost. But the Rosicrucian system was a recognized school of its day, and\nFludd, a man of great learning, had abettors enough in all which he\nadvanced, and predecessors in most of it.\n\n[A Correspondent has recently sent a short summary of the claims of Jacob\nBehmen to rank higher than I have placed him. I shall gladly insert this\nsummary in the book I contemplate, as a statement of what is said of Behmen\nfar less liable to suspicion of exaggeration than anything I could write. I\nshall add a few extracts from Behmen himself, in support of his right to be\nin my list.]\n\n\"_Jacob Behmen._--That Prof. De Morgan classes Jacob Behmen among\nparadoxers can only be attributed to the fact of his being avowedly\nunacquainted with the writings {319} of that author. Perhaps you may think\na few words from one who knows them well of sufficient interest to the\nlearned Professor, and your readers in general, to be worthy of space in\nyour columns. The metaphysical system of Behmen--the most perfect and only\ntrue one--still awaits a qualified commentator. Behmen's countryman,\nDionysius Andreas Freher,[596] who spent the greater part of his life in\nthis country, and whose exposition of Behmen exists only in MS., filling\nmany volumes, written in English, with the exception of two, written in\nGerman, with numerous beautiful, highly ingenious, and elaborate\nillustrations,--copies of some of which are in the British Museum, but all\nthe originals of which are in the possession of the gentleman who is the\neditor of the two works alluded to by Professor De Morgan,--this Freher was\nthe first to philosophically expound Behmen's system, which was afterwards,\nwith the help of these MSS., as it were, popularized by William Law; but\nboth Freher and Law confined themselves chiefly to its theological aspect.\nIn Behmen, however, is to be found, not only the true ground of all\ntheology, but also that of all physical science. He demonstrated with a\nfullness, accuracy, completeness and certainty that leave nothing to be\ndesired, the innermost ground of Deity and Nature; and, confining myself to\nthe latter, I can from my own knowledge assert, that in Behmen's writings\nis to be found the true and clear demonstration of every physical fact that\nhas been discovered since his day. Thus, the science of electricity, which\nwas not yet in existence when he wrote, is there anticipated; and not only\ndoes Behmen describe all the now known phenomena of that force, but he even\ngives us the origin, generation and birth of electricity itself. Again,\npositive evidence can be adduced that Newton derived all his knowledge of\ngravitation and its {320} laws from Behmen, with whom gravitation or\nattraction is, and very properly so, as he shows us, the first of the seven\nproperties of Nature. The theory defended by Mr. Grove,[597] at the\nNottingham meeting of last year, that all the apparently distinct causes of\nmoral and physical phenomena are but so many manifestations of one central\nforce, and that Continuity is the law of nature, is clearly laid down, and\nits truth demonstrated, by Behmen, as well as the distinction between\nspirit and matter, and that the moral and material world is pervaded by a\nsublime unity. And though all this was not admitted in Behmen's days,\nbecause science was not then sufficiently advanced to understand the deep\nsense of our author, many of his passages, then unintelligible, or\napparently absurd, read by the light of the present age, are found to\ncontain the positive enunciation of principles at whose discovery and\nestablishment science has only just arrived by wearisome and painful\ninvestigations. Every new scientific discovery goes to prove his profound\nand intuitive insight into the most secret workings of nature; and if\nscientific men, instead of sharing the prejudice arising from ignorance of\nBehmen's system, would place themselves on the vantage ground it affords,\nthey would at once find themselves on an eminence whence they could behold\nall the arcana of nature. Behmen's system, in fact, shows us the _inside_\nof things, while modern physical science is content with looking at the\n_outside_. Behmen traces back every outward manifestation or development to\nits one central root,--to that one central energy which, as yet, is only\nsuspected; every link in the chain of his demonstration is perfect, and\nthere is not one link wanting. He carries us from the out-births of the\ncircumference, along the radius to the center, {321} or point, and beyond\nthat even to the zero, demonstrating the constitution of the zero, or\nnothing, with mathematical precision. C. W. H.\"\n\nAnd so Behmen is no subject for the Budget! I waited until I should chance\nto light on one of his volumes, knowing that any volume would do, and\nalmost any page. My first hap was on the second volume of the edition of\n1664 (4to, published by M. Richardson) and opening near the beginning, a\nturn or two brought me to page 13, where I saw about _sulphur_ and\n_mercurius_ as follows:\n\n\n\n\"Thus SUL is the soul, in an herb it is the oil, and in man also, according\nto the spirit of _this_ world in the third principle, which is continually\ngenerated out of the anguish of the will in the mind, and the\nBrimstone-worm is the Spirit, which hath the fire and _burneth_: PHUR is\nthe sour wheel in itself which causeth that.\n\n\"_Mercurius_ comprehendeth all the four forms, even as the life springeth\nup, and yet hath not its dark beginning in the Center as the PHUR hath, but\nafter the flash of fire, when the sour dark form is terrified, where the\nhardness is turned into pliant sharpness, and where the second will (_viz._\nthe will of nature, which is called the Anguish) ariseth, there Mercurius\nhath its original. For MER is the shivering wheel, very horrible, sharp,\nvenomous, and hostile; which assimulateth it thus in the sourness in the\nflash of fire, where the sour wrathful life _ariseth_. The syllable CU is\nthe pressing out, of the _Anxious_ will of the mind, from Nature: which is\nclimbing up, and _willeth_ to be out aloft. RI is the comprehension of the\nflash of fire, which in MER giveth a clear sound and tune. For the flash\nmaketh the tune, and it is the Salt-Spirit which _soundeth_, and its form\n(or quality) is gritty like sand, and herein arise noises, sounds and\nvoices, and thus CU comprehendeth the flash, and so the pressure is as a\n_wind_ which thrusteth, and giveth a spirit to the flash, so that it liveth\nand burneth. Thus the {322} syllable US is called the burning fire, which\nwith the spirit continually driveth itself forth: and the syllable CU\npresseth continually upon the flash.\"\n\n\n\nShades of Tauler[598] and Paracelsus,[599] how strangely you do mix! Well\nmay Hallam call Germany the native soil of Mysticism. Had Behmen been the\nleast of a scholar, he would not have divided _sulph-ur_ and _merc-ur-i-us_\nas he has done: and the inflexion _us_, that boy of all work, would have\nbeen rejected. I think it will be held that a writer from whom hundreds of\npages like the above could be brought together, is fit for the Budget. If\nSampson Arnold Mackay[600] had tied his etymologies to a mystical\nChristology, instead of a mystical infidelity, he might have had a school\nof followers. The nonsense about Newton borrowing gravitation from Behmen\npasses only with those who know neither what Newton did, nor what was done\nbefore him.\n\nThe above reminds me of a class of paradoxers whom I wonder that I forgot;\nthey are without exception the greatest bores of all, because they can put\nthe small end of their paradox into any literary conversation whatever. I\nmean the people who have heard the local pronunciation of celebrated names,\nand attempt not only to imitate it, but to impose on others their broken\nGerman or Arabic, or what not. They also learn the vernacular names of\nthose who are generally spoken of in their Latin forms; at least, they\nlearn a few cases, and hawk them as evidences of erudition. They are\nmiserably mistaken: scholarship, as a rule, {323} always accepts the\nvernacular form of a name which has vernacular celebrity. Hallam writes\nBehmen: his index-maker, rather superfluously, gives \"_Behmen_ or Boehm.\"\nAnd he retains Melanchthon,[601] the name given by Reuchlin[602] to his\nlittle kinsman Schwartzerd, because the world has adopted it: but he will\nnone of Capnio, the name which Reuchlin fitted on to himself, because the\nworld has not adopted it. He calls the old forms pedantry: but he sees that\nthe rejection of well-established results of pedantry would be greater\npedantry still. The paradoxers assume the question that it is more\n_correct_ to sound a man by lame imitation of his own countrymen than as\nusual in the country in which the sound is to be made. Against them are,\nfirst, the world at large; next, an overpowering majority of those who know\nsomething about surnames and their history. Some thirty years ago--a\nfact--there appeared at the police-office a complainant who found his own\nlaw. In the course of his argument, he asked, \"What does Kitty\nsay?\"--\"Who's Kitty?\" said the magistrate, \"your wife, or your\nnurse?\"--\"Sir! I mean Kitty, the celebrated lawyer.\"--\"Oh!\" said the\nmagistrate, \"I suspect you mean Mr. Chitty,[603] the author of the great\nwork on pleading.\"--\"I do sir! But Chitty is an Italian name, and ought to\nbe pronounced _Kitty_.\" This man was a full-blown flower: but there is many\na modest bud; and all ought either to blush when seen or to waste their\npronunciation on the desert air.\n\n{324}\n\n\n\nA PLEA FOR KING CUSTOM.\n\nI stand up for King Custom, or _Usus_, as Horace called him, with whom is\n_arbitrium_ the decision, and _jus_ the right, and _norma_ the way of\ndeciding, simply because he has _potestas_ the power. He may admit one and\nanother principle to advise: but Custom is not a constitutional king; he\nmay listen to his cabinet, but he decides for himself: and if the ministry\nshould resign, he blesses his stars and does without them. We have a\nglorious liberty in England of owning neither dictionary, grammar, nor\nspelling-book: as many as choose write by either of the three, and decide\nall disputed points their own way, those following them who please.\n\nThroughout this book I have called people by the names which denote them in\ntheir books, or by our vernacular names. This is the intelligible way of\nproceeding. I might, for instance (Vol. I, p. 44), have spoken of Charles\nde Bovelles,[604] of Lefevre d'Etaples,[605] of Pelerin,[606] and of\nEtienne.[607] But I prefer the old plan. Those who like another plan\nbetter, are welcome to substitute with a pen, when they know what to write;\nwhen they do not, it is clear that they would not have understood me if I\nhad given modern names.\n\nThe principal advisers of King Custom are as follows. First, there is\nEtymology, the _chiffonnier_, or general rag-merchant, who has made such a\nfortune of late years in his own business that he begins to be considered\nhighly respectable. He gives advice which is more thought of than followed,\npartly on account of the fearful extremes into which he runs. He lately\nasked some boys of sixteen, at a matriculation examination in _English_, to\nwhat branch of {325} the Indo-Germanic family they felt inclined to refer\nthe Pushto language, and what changes in the force of the letters took\nplace in passing from Greek into Moeso-Gothic. Because all syllables were\nonce words, he is a little inclined to insist that they shall be so still.\nHe would gladly rule English with a Saxon rod, which might be permitted\nwith a certain discretion which he has never attained: and when opposed, he\ndefends himself with analogies of the Aryan family until those who hear him\nlong for the discovery of an Athanasyus. He will transport a word beyond\nseas--he is recorder of Rhematopolis--on circumstantial evidence which\nlooks like mystery gone mad; but, strange to say, something very often\ncomes to light after sentence is passed which proves the soundness of the\nconviction.\n\nThe next adviser is Logic, a swearing old justice of peace, quorum, and\nrotulorum, whose excesses brought on such a fit of the gout that for many\nyears he was unable to move. He is now mending, and his friends say he has\nsown his wild oats. He has some influence with the educated subjects of\nCustom, and will have more, if he can learn the line at which interference\nought to stop: with them he has succeeded in making an affirmative of two\nnegatives; but the vulgar won't never have nothing to say to him. He has\nalways railed at Milton for writing that Eve was the fairest of her\ndaughters; but has never satisfactorily shown what Milton ought to have\nsaid instead.\n\nThe third adviser has more influence with the mass of the subjects of King\nCustom than the other two put together; his name is Fiddlefaddle, the\ntoy-shop keeper; and the other two put him forward to do their worst work.\nIn return, he often uses their names without authority. He took Etymology\nto witness that _means_ to an end must be plural: and he would have any one\nmethod to be a _mean_. But Etymology proved him wrong, King Custom referred\nhim to his Catechism, in which is \"a means whereby we receive the same,\"\nand Analogy--a subordinate of {326} Etymology--asked whether he thought it\na great _new_ to hear that he was wrong. It was either this Fiddlefaddle,\nor Lindley Murray[608] his traveler, who persuaded the Miss Slipslops, of\nthe Ladies Seminary, to put \"The Misses Slipslop\" over the gate. Sixty\nyears ago, this bagman called at all the girls' schools, and got many of\nthe teachers to insist on the pupils saying \"Is it not\" and \"Can I not\" for\n\"Isn't it\" and \"Can't I\": of which it came that the poor girls were\ndreadfully laughed at by their irreverent brothers when they went home for\nthe holidays. Had this bad adviser not been severely checked, he might by\nthis time have proposed our saying \"The Queen's of England son,\" declaring,\nin the name of Logic, that the prince was the Queen's son, not England's.\n\nLastly, there is Typography the metallurgist, an executive officer who is\nalways at work in secret, and whose lawless mode of advising is often done\nby carrying his notions into effect without leave given. He it is who never\nceases suggesting that the same word is not to occur in a second place\nwithin sight of the first. When the Authorized Version was first printed,\nhe began this trick at the passage, \"Let there be light, and there was\nlight;\" he drew a line on the proof under the second _light_, and wrote\n\"_luminosity?_\" opposite. He is strongest in the punctuations and other\nsigns; he has a pepper-box full of commas always by his side. He puts\neverything under marks of quotation which he has ever heard before. An\nearnest preacher, in a very moving sermon, used the phrase Alas! and alack\na day! Typography stuck up the inverted commas because he had read the old\nAnglo-Indian toast, \"A lass and a lac a day!\" If any one should have the\nsense to leave out of his Greek {327} the unmeaning scratches which they\ncall accents, he goes to a lexicon and puts them in. He is powerful in\nroutine; but when two routines interlace or overlap, he frequently takes\nthe wrong one.\n\nSubject to bad advice, and sometimes misled for a season, King Custom goes\non his quiet way and is sure to be right at last.\n\n \"Treason does never prosper: what's the reason?\n  Why, when it prospers, none dare call it treason.\"\n\nLanguage is in constant fermentation, and all that is thrown in, so far as\nit is not fit to assimilate, is thrown off; and this without any obvious\nstruggle. In the meanwhile every one who has read good authors, from\nShakspeare downward, knows what is and what is not English; and knows,\nalso, that our language is not one and indivisible. Two very different\nturns of phrase may both be equally good, and as good as can be: we may be\nrelieved of the consequences of contempt of one court by _habeas corpus_\nissuing out of another.\n\n\n\nTEST OF LANGUAGE.\n\nHallam remarks that the Authorized Version of the Bible is not in the\nlanguage of the time of James the First: that it is not the English of\nRaleigh or of Bacon. Here arises the question whether Raleigh and Bacon are\nthe true expositors of the language of their time; and whether they were\nnot rather the incipient promoters of a change which was successfully\nresisted by--among other things--the Authorized Version of the Testaments.\nI am not prepared to concede that I should have given to the English which\nwould have been fashioned upon that of Bacon by imitators, such as they\nusually are, the admiration which is forced from me by Bacon's English from\nBacon's pen. On this point we have a notable parallel. Samuel Johnson {328}\ncommands our admiration, at least in his matured style: but we nauseate his\nfollowers. It is an opinion of mine that the works of the leading writers\nof an age are seldom the proper specimens of the language of their day,\nwhen that language is in its state of progression. I judge of a language by\nthe colloquial idiom of educated men: that is, I take this to be the best\nmedium between the extreme cases of one who is ignorant of grammar and one\nwho is perched upon a style. Dialogue is what I want to judge by, and plain\ndialogue: so I choose Robert Recorde[609] and his pupil in the _Castle of\nKnowledge_, written before 1556. When Dr. Robert gets into his altitudes of\ninstruction, he differs from his own common phraseology as much as probably\ndid Bacon when he wrote morals and philosophy. But every now and then I\ncome to a little plain talk about a common thing, of which I propose to\nshow a specimen. Anything can be made to look old by such changes as\n_makes_ into _maketh_, with a little old spelling. I shall invert these\nchanges, using the newer form of inflexion, and the modern spelling: with\nno other variation whatever.\n\n\"_Scholar._ Yet the reason of that is easy enough to be conceived, for when\nthe day is at the longest the Sun must needs shine the more time, and so\nmust it needs shine the less time when the day is at the shortest: this\nreason I have heard many men declare.\n\n_Master._ That may be called a crabbed reason, for it {329} goes backward\nlike a crab. The day makes not the Sun to shine, but the Sun shining makes\nthe day. And so the length of the day makes not the Sun to shine long,\nneither the shortness of the day causes not [_sic_] the Sun to shine the\nlesser time, but contrariwise the long shining of the Sun makes the long\nday, and the short shining of the Sun makes the lesser day: else answer me\nwhat makes the days long or short?\n\n_Scholar._ I have heard wise men say that Summer makes the long days, and\nWinter makes the long nights.\n\n_Master._ They might have said more wisely, that long days make summer and\nshort days make winter.\n\n_Scholar._ Why, all that seems one thing to me.\n\n_Master._ Is it all one to say, God made the earth, and the earth made God?\nCovetousness overcomes all men, and all men overcome covetousness?\n\n_Scholar._ No, not so; for here the effect is turned to be the cause, and\nthe agent is made the patient.\n\n_Master._ So is it to say Summer makes long days, when you should say: Long\ndays make summer.\n\n_Scholar._ I perceive it now: but I was so blinded with the vulgar error,\nthat if you had demanded of me further what did make the summer, I had been\nlike to have answered that green leaves do make summer; and the sooner by\nremembrance of an old saying that a year should come in which the summer\nshould not be known but by the green leaves.\n\n_Master._ Yet this saying does not import that green leaves do make summer,\nbut that they betoken summer; so are they the sign and not the cause of\nsummer.\"\n\nI have taken a whole page of our author, without omission, that the reader\nmay see that I do not pick out sentences convenient for my purpose. I have\ndone nothing but alter the third person of the verb and the spelling: but\ngreat is the effect thereof. We say \"the Sun shining makes the day\";\nRecorde, \"the Sonne shynynge maketh the daye.\" {330} These points apart, we\nsee a resemblance between our English and that of three hundred years ago,\nin the common talk of educated persons, which will allow us to affirm that\nthe language of the authorized Bible must have been very close to that of\nits time. For I cannot admit that much change can have taken place in fifty\nyears: and the language of the version represents both our common English\nand that of Recorde with very close approximation. Take sentences from\nBacon and Raleigh, and it will be apparent that these writers will be held\nto differ from all three, Recorde, the version, and ourselves, by\ndifferences of the same character. But we speak of Recorde's conversation,\nand of our own. We conclude that it is the plain and almost colloquial\ncharacter of the Authorized Version which distinguishes it from the English\nof Bacon and Raleigh, by approximating it to the common idiom of the time.\nIf any one will cast an eye upon the letters of instruction written by\nCecil[610] and the Bishop of London to the translators themselves, or to\nthe general directions sent to them in the King's name, he will find that\nthese plain business compositions differ from the English of Bacon and\nRaleigh by the same sort of differences which distinguish the version\nitself.\n\n\n\nPRONUNCIATION.\n\nThe foreign word, or the word of a district, or class of people, passes\ninto the general vernacular; but it is long before the specially learned\nwill acknowledge the right of those with whom they come in contact to\nfollow general usage. The rule is simple: so long as a word is technical or\nlocal, those who know its technical or local pronunciation may reasonably\nemploy it. But when the word has become general, the specialist is not very\nwise if he refuse to follow {331} the mass, and perfectly foolish if he\ninsist on others following him. There have been a few who demanded that\nEuler should be pronounced in the German fashion:[611] Euler has long been\nthe property of the world at large; what does it matter how his own\ncountrymen pronounce the letters? Shall we insist on the French pronouncing\n_Newton_ without that final _tong_ which they never fail to give him? They\nwould be wise enough to laugh at us if we did. We remember that a pedant\nwho was insisting on all the pronunciations being retained, was met by a\nmaxim in contradiction, invented at the moment, and fathered upon\nKaen-foo-tzee,[612] an authority which he was challenged to dispute. Whom\ndid you speak of? said the bewildered man of accuracy. Learn your own\nsystem, was the answer, before you impose it on others; Confucius says that\ntoo.[613]\n\nThe old English has _fote_, _fode_, _loke_, _coke_, _roke_, etc., for\n_foot_, etc. And _above_ rhymes in Chaucer to _remove_. Suspecting that the\nbroader sounds are the older, we may surmise that _remove_ and _food_ have\nretained their old sounds, and that _cook_, once _coke_, would have rhymed\nto our _Luke_, the vowel being brought a little nearer, perhaps, to the _o_\nin our present _coke_, the fuel, probably so called as used by cooks. If\nthis be so, the Chief Justice _Cook_[614] of our lawyers, and the _Coke_\n(pronounced like the fuel) of the greater part of the world, are equally\nwrong. The lawyer has no right whatever to fasten his pronunciation upon\nus: even leaving aside the general custom, he cannot prove himself right,\nand is probably wrong. Those who {332} know the village of Rokeby\n(pronounced Rookby) despise the world for not knowing how to name Walter\nScott's poem: that same world never asked a question about the matter, and\nthe reception of the parody of _Jokeby_, which soon appeared, was a\nsufficient indication of their notion. Those who would fasten the hodiernal\nsound upon us may be reminded that the question is, not what they call it\nnow, but what it was called in Cromwell's time. Throw away general usage as\na lawgiver, and this is the point which emerges. Probably _R[=u]ke-by_\nwould be right, with a little turning of the Italian [=u] towards [=o] of\nmodern English.\n\n[Some of the above is from an old review. I do not always notice such\ninsertions: I take nothing but my own writings. A friend once said to me,\n\"Ah! you got that out of the _Athenaeum_!\" \"Excuse me,\" said I. \"the\n_Athenaeum_ got that out of me!\"]\n\n\n\nAPOLOGIES TO CLUVIER.\n\nIt is part of my function to do justice to any cyclometers whose methods\nhave been wrongly described by any orthodox sneerers (myself included). In\nthis character I must notice _Dethlevus Cluverius_,[615] as the Leipzig\nActs call him (probably Dethleu Cluvier), grandson of the celebrated\ngeographer, Philip Cluvier. The grandson was a Fellow of the Royal Society,\nelected on the same day as Halley,[616] November 30, 1678: I suppose he\nlived in England. This {333} man is quizzed in the Leipzig Acts for 1686;\nand, if Montucla insinuate rightly, by Leibnitz, who is further suspected\nof wanting to embroil Cluvier with his own opponent Nieuwentiit,[617] on\nthe matter of infinitesimals. So far good: I have nothing against Leibnitz,\nwho though he was ironical, told us what he laughed at. But Montucla has\nbehaved very unfairly: he represents Cluvier as placing the essence of his\nmethod in the solution of the problem _construere mundum divinae menti\nanalogum_, to construct a world corresponding to the divine mind. Nothing\nto begin with: no way of proceeding. Now, it ought to have been _ex data\nlinea construere_,[618] etc.: there is a given line, which is something to\ngo on. Further, there is a way of proceeding: it is to find the product of\n1, 2, 3, 4, etc. for ever. Moreover, Montucla charges Cluvier with\n_unsquaring_ the parabola, which Archimedes had squared as tight as a\nglove. But he never mentions how very nearly Cluvier agrees with the Greek:\nthey only differ by 1 divided by 3n^2, where n is the infinite number of\nparts of which a parabola is composed. This must have been the conceit that\ntickled Leibnitz, and made him wish that Cluvier and Nieuwentiit should\nfight it out. Cluvier, was admitted, on terms of irony, into the Leipzig\nActs: he appeared on a more serious footing in London. It is very rare for\none cyclometer to refute another: _les corsaires ne se battent pas_.[619]\nThe only instance I recall is that of M. Cluvier, who (_Phil. Trans._,\n1686, No. 185) refuted M. Mallemont de Messange,[620] who {334} published\nat Paris in 1686. He does it in a very serious style, and shows himself a\nmathematician. And yet in the year in which, in the _Phil. Trans._, he was\na geometer, and one who rebukes his squarer for quoting Matthew xi. 25, in\nthat very year he was the visionary who, in the Leipzig Acts, professed to\nbuild a world resembling the divine mind by multiplying together 1, 2, 3,\n4, etc. up to infinity.\n\n\n\nTHE RAINBOW PARADOX.\n\nThere is a very pretty opening for a paradox which has never found its\nparadoxer in print. The philosophers teach that the rainbow is not\nmaterial: it comes from rain-drops, but those rain-drops do not _take_\ncolor. They only _give_ it, as lenses and mirrors; and each one drop gives\n_all_ the colors, but throws them in different directions. Accordingly, the\nsame drop which furnishes red light to one spectator will furnish violet to\nanother, properly placed. Enter the paradoxer whom I have to invent. The\nphilosopher has gulled you nicely. Look into the water, and you will see\nthe reflected rainbow: take a looking-glass held sideways, and you see\nanother reflection. How could this be, if there were nothing colored to\nreflect? The paradoxer's facts are true: and what are called the reflected\nrainbows are _other_ rainbows, caused by those _other_ drops which are\nplaced so as to give the colors to the eye after reflection, at the water\nor the looking-glass. A few years ago an artist exhibited a picture with a\nrainbow and its apparent reflection: he simply copied what he had seen.\nWhen his picture was examined, some started the idea that there could be no\nreflection of a rainbow; they were right: they inferred that the artist had\nmade a mistake; they were wrong. When it was explained, some agreed and\nsome dissented. Wanted, {335} immediately, an able paradoxer: testimonials\nto be forwarded to either end of the rainbow, No. 1. No circle-squarer need\napply, His Variegatedness having been pleased to adopt 3.14159... from Noah\ndownwards.\n\n\n\nTYCHO BRAHE REVIVED.\n\nThe system of Tycho Brahe,[621] with some alteration and addition, has been\nrevived and contended for in our own day by a Dane, W. Zytphen,[622] who\nhas published _The Motion of the Sun in the Universe_, (second edition)\nCopenhagen, 1865, 8vo, and _Le Mouvement Sideral_, 1865, 8vo. I make an\nextract.\n\n\"How can one explain Copernically that the velocity of the Moon must be\nadded to the velocity of the Earth on the one place in the Earth's orbit,\nto learn how far the Moon has advanced from one fixed star to another; but\nin another place in the orbit these velocities must be subtracted (the\nmovements taking place in opposite directions) to attain the same result?\nIn the Copernican and other systems, it is well known that the Moon,\nabstracting from the insignificant excentricity of the orbit, always in\ntwenty-four hours performs an equally long distance. Why has Copernicus\nnever been denominated Fundamentus or Fundator? Because he has never\nconvinced anybody so thoroughly that this otherwise so natural epithet has\noccurred to the mind.\"\n\nReally the second question is more effective against Newton than against\nCopernicus; for it upsets gravity: the first is of great depth.\n\n{336}\n\n\n\nJAMES SMITH WILL NOT DOWN.\n\nThe _Correspondent_ journal makes a little episode in the history of my\nBudget (born May, 1865, died April, 1866). It consisted entirely of letters\nwritten by correspondents. In August, a correspondent who signed \"Fair\nPlay\"--and who I was afterwards told was a lady--thought it would be a good\njoke to bring in the Cyclometers. Accordingly a letter was written,\ncomplaining that though Mr. Sylvester's[623] demonstration of Newton's\ntheorem--then attracting public attention--was duly lauded, the possibly\ngreater discovery of the quadrature seemed to be blushing unseen, and\nwasting etc. It went on as follows:\n\n\"Prof. De Morgan, who, from his position in the scientific world, might\nfairly afford to look favourably on less practised efforts than his own,\nseems to delight in ridiculing the discoverer. Science is, of course, a\nvery respectable person when he comes out and makes himself useful in the\nworld [it must have been a lady; each sex gives science to the other]: but\nwhen, like a monk of the Middle Ages, he shuts himself up [it must have\nbeen a lady; they always snub the bachelors] in his cloistered cell,\nrepeating his mumpsimus from day to day, and despising the labourers on the\noutside, we begin to think of Galileo,[624] Jenner,[625] Harvey,[626] and\nother glorious trios, who have been contemned ...\"\n\nThe writer then called upon Mr. James Smith[627] to come {337} forward. The\nirony was not seen; and that day fortnight appeared the first of more than\nthirty letters from his pen. Mr. Smith was followed by Mr. Reddie,[628]\nZadkiel,[629] and others, on their several subjects. To some of the letters\nI have referred; to others I shall come. The _Correspondent_ was to become\na first-class scientific journal; the time had arrived at which truth had\nan organ: and I received formal notice that I could not stifle it by\nsilence, nor convert it into falsehood by ridicule. When my reader sees my\nextracts, he will readily believe my declaration that I should have been\nthe last to stifle a publication which was every week what James Mill[630]\nwould call a dose of capital for my Budget. A few anti-paradoxers brought\nin common sense: but to the mass of the readers of the journal it all\nseemed to be the difference between Tweedledum and Tweedledee. Some said\nthat the influx of scientific paradoxes killed the journal: but my belief\nis that they made it last longer than it otherwise would have done. Twenty\nyears ago I recommended the paradoxers to combine and publish their views\nin a common journal: with a catholic editor, who had no pet theory, but a\nstern determination not to exclude anything merely for absurdity. I suspect\nit would answer very well. A strong title, or motto, would be wanted: not\nso coarse as was roared out in a Cambridge mob when I was an\nundergraduate--\"No King! No Church! No House of Lords! No nothing, blast\nme!\"--but something on that _principle_.\n\nAt the end of 1867 I addressed the following letter to the _Athenaeum_:\n\nPSEUDOMATH, PHILOMATH, AND GRAPHOMATH.\n\n_December 31, 1867_\n\nMany thanks for the present of Mr. James Smith's letters {338} of Sept. 28\nand of Oct. 10 and 12. He asks where you will be if you read and digest his\nletters: you probably will be somewhere first. He afterwards asks what the\nWE of the _Athenaeum_ will be if, finding it impossible to controvert, it\nshould refuse to print. I answer for you, that We-We of the _Athenaeum_, not\nbeing Wa-Wa the wild goose, so conspicuous in \"Hiawatha,\" will leave what\ncontroverts itself to print itself, if it please.\n\n_Philomath_ is a good old word, easier to write and speak than\n_mathematician_. It wants the words between which I have placed it. They\nare not well formed: _pseudomathete_ and _graphomathete_ would be better:\nbut they will do. I give an instance of each.\n\nThe _pseudomath_ is a person who handles mathematics as the monkey handled\nthe razor. The creature tried to shave himself as he had seen his master\ndo; but, not having any notion of the angle at which the razor was to be\nheld, he cut his own throat. He never tried a second time, poor animal! but\nthe pseudomath keeps on at his work, proclaims himself clean-shaved, and\nall the rest of the world hairy. So great is the difference between moral\nand physical phenomena! Mr. James Smith is, beyond doubt, the great\npseudomath of our time. His 3-1/8 is the least of a wonderful chain of\ndiscoveries. His books, like Whitbread's barrels, will one day reach from\nSimpkin & Marshall's to Kew, placed upright, or to Windsor laid\nlength-ways. The Queen will run away on their near approach, as Bishop\nHatto did from the rats: but Mr. James Smith will follow her were it to\nJohn o' Groats.\n\nThe _philomath_, for my present purpose, must be exhibited as giving a\nlesson to presumption. The following anecdote is found in Thiebault's[631]\n_Souvenirs de vingt ans de sejours a Berlin_, published in 1804. The book\nitself got a high character for truth. In 1807 Marshal Mollendorff[632]\n{339} answered an inquiry of the Duc de Bassano,[633] by saying that it was\nthe most veracious of books, written by the most honest of men. Thiebault\ndoes not claim personal knowledge of the anecdote, but he vouches for its\nbeing received as true all over the north of Europe.[634]\n\nDiderot[635] paid a visit to Russia at the invitation of Catherine the\nSecond. At that time he was an atheist, or at least talked atheism: it\nwould be easy to prove him either one thing or the other from his writings.\nHis lively sallies on this subject much amused the Empress, and all the\nyounger part of her Court. But some of the older courtiers suggested that\nit was hardly prudent to allow such unreserved exhibitions. The Empress\nthought so too, but did not like to muzzle her guest by an express\nprohibition: so a plot was contrived. The scorner was informed that an\neminent mathematician had an algebraical proof of the existence of God,\nwhich he would communicate before the whole Court, if agreeable. Diderot\ngladly consented. The mathematician, who is not named, was Euler.[636] He\ncame to Diderot with the gravest air, and in a tone of perfect conviction\nsaid, \"_Monsieur!_\n\n  (a + b^n)/n = x\n\n_donc Dieu existe; repondez!_\"[637] Diderot, to whom algebra was Hebrew,\nthough this is expressed in a very roundabout way by Thiebault--and whom we\nmay suppose to have expected some verbal argument of alleged algebraical\ncloseness, was disconcerted; while peals of laughter sounded on all sides.\nNext day he asked permission to return to France, which was granted. An\nalgebraist would have {340} turned the tables completely, by saying,\n\"Monsieur! vous savez bien que votre raisonnement demande le developpement\nde x suivant les puissances entieres de n\".[638] Goldsmith could not have\nseen the anecdote, or he might have been supposed to have drawn from it a\nhint as to the way in which the Squire demolished poor Moses.\n\nThe _graphomath_ is a person who, having no mathematics, attempts to\ndescribe a mathematician. Novelists perform in this way: even Walter Scott\nnow and then burns his fingers. His dreaming calculator, Davy Ramsay,\nswears \"by the bones of the immortal Napier.\" Scott thought that the the\nphilomaths worshiped relics: so they do, in one sense. Look into\nHutton's[639] Dictionary for _Napier's Bones_, and you shall learn all\nabout the little knick-knacks by which he did multiplication and division.\nBut never a bone of his own did he contribute; he preferred elephants'\ntusks. The author of _Headlong Hall_[640] makes a grand error, which is\nquite high science: he says that Laplace proved the precession of the\nequinoxes to be a periodical inequality. He should have said the variation\nof the obliquity. But the finest instance is the following: Mr.\nWarren,[641] in his well-wrought tale of the martyr-philosopher, was\nincautious enough to invent the symbols by which his _savant_ satisfied\nhimself Laplace[642] was right on a doubtful point. And this is what he put\ntogether--\n\n  [sqrt]-3a^2, [rectangle]y^2 / z^2 + 9 - n = 9, n x log e.\n\nNow, to Diderot and the mass of mankind this might be Laplace all over:\nand, in a forged note of Pascal, would {341} prove him quite up to\ngravitation. But I know of nothing like it, except in the lately received\nstory of the American orator, who was called on for some Latin, and\nperorated thus: \"Committing the destiny of the country to your hands,\nGentlemen, I may without fear declare, in the language of the noble Roman\npoet,\n\n  E pluribus unum,\n  Multum in parvo,\n  Ultima Thule,\n  Sine qua non.\"[643]\n\nBut the American got nearer to Horace than the martyr-philosopher to\nLaplace. For all the words are in Horace, except _Thule_, which might have\nbeen there. But [rectangle] is not a symbol wanted by Laplace; nor can we\nsee how it could have been; in fact, it is not recognized in algebra. As to\nthe junctions, etc., Laplace and Horace are about equally well imitated.\n\nFurther thanks for Mr. Smith's letters to you of Oct. 15, 18, 19, 28, and\nNov. 4, 15. The last of these letters has two curious discoveries. First,\nMr. Smith declares that he has _seen_ the editor of the _Athenaeum_: in\nseveral previous letters he mentions a name. If he knew a little of\njournalism he would be aware that editors are a peculiar race, obtained by\nnatural selection. They are never seen, even by their officials; only heard\ndown a pipe. Secondly, \"an ellipse or oval\" is composed of four arcs of\ncircles. Mr. Smith has got hold of the construction I was taught, when a\nboy, for a pretty four-arc oval. But my teachers knew better than to call\nit an ellipse: Mr. Smith does not; but he produces from it such\nconfirmation of 3-1/8 as would convince any _honest_ editor.\n\nSurely the cyclometer is a Darwinite development of a spider, who is always\nat circles, and always begins again when his web is brushed away. He\ninforms you that he {342} has been privileged to discover truths unknown to\nthe scientific world. This we know; but he proceeds to show that he is\nequally fortunate in art. He goes on to say that he will make use of you to\nbring those truths to light, \"just as an artist makes use of a dummy for\nthe purpose of arranging his drapery.\" The painter's lay-figure is for\nflowing robes; the hairdresser's dummy is for curly locks. Mr. James Smith\nshould read Sam Weller's pathetic story of the \"four wax dummies.\" As to\n_his_ use of a dummy, it is quite correct. When I was at University\nCollege, I walked one day into a room in which my Latin colleague was\nexamining. One of the questions was, \"Give the lives and fates of Sp.\nMaelius,[644] and Sp. Cassius.\"[645] Umph! said I, surely all know that\nSpurius Maelius was whipped for adulterating flour, and that Spurius Cassius\nwas hanged for passing bad money. Now, a robe arranged on a dummy would\nlook just like the toga of Cassius on the gallows. Accordingly, Mr. Smith\nis right in the drapery-hanger which he has chosen: he has been detected in\nthe attempt to pass bad circles. He complains bitterly that his geometry,\ninstead of being read and understood by you, is handed over to me to be\ntreated after my scurrilous fashion. It is clear enough that he would\nrather be handled in this way than not handled at all, or why does he go on\nwriting? He must know by this time that it is a part of the institution\nthat his \"untruthful and absurd trash\" shall be distilled into mine at the\nrate of about 3-1/8 pages of the first to one column of the second. Your\nreaders will never know how much they gain by the process, until Mr. James\nSmith publishes it all in a big book, or until they get hold of what he has\nalready published. I have six pounds avoirdupois of pamphlets and letters;\nand there is more than half a pound of letters {343} written to you in the\nlast two months. Your compositor must feel aggrieved by the rejection of\nthese clearly written documents, without erasures, and on one side only.\nYour correspondent has all the makings of a good contributor, except the\nknowledge of his subject and the sense to get it. He is, in fact, only a\nmask: of whom the fox\n\n \"O quanta species, inquit, cerebrum non habet.\"[646]\n\nI do not despair of Mr. Smith on any question which does not involve that\nunfortunate two-stick wicket at which he persists in bowling. He has\npublished many papers; he has forwarded them to mathematicians: and he\ncannot get answers; perhaps not even readers. Does he think that he would\nget more notice if you were to print him in your journal? Who would study\nhis columns? Not the mathematician, we know; and he knows. Would others?\nHis balls are aimed too wide to be blocked by any one who is near the\nwicket. He has long ceased to be worth the answer which a new invader may\nget. Rowan Hamilton,[647] years ago, completely knocked him over; and he\nhas never attempted to point out any error in the short and easy method by\nwhich that powerful investigator condescended to show that, be right who\nmay, he must be wrong. There are some persons who feel inclined to think\nthat Mr. Smith should be argued with: let those persons understand that he\nhas been argued with, refuted, and has never attempted to stick a pen into\nthe refutation. He stated that it was a remarkable paradox, easily\nexplicable; and that is all. After this evasion, Mr. James Smith is below\nthe necessity of being told that he is unworthy of answer. His friends\ncomplain that I do nothing but _chaff_ him. Absurd! I winnow him; and if\nnothing but chaff results, whose fault is that? I am usefully employed: for\nhe is the type of a class which ought to be known, and which I have done\nmuch to make known.\n\n{344}\n\nNothing came of this until July 1869, when I received a reprint of the\nabove letter, with a comment, described as Appendix D of a work in course\nof publication on the geometry of the circle. The _Athenaeum_ journal\nreceived the same: but the Editor, in his private capacity, received the\nwhole work, being _The Geometry of the Circle and Mathematics as applied to\nGeometry by Mathematicians, shown to be a mockery, delusion, and a snare_,\nLiverpool, 8vo, 1869. Mr. J. S. here appears in deep fight with Professor\nWhitworth,[648] and Mr. Wilson,[649] the author of the alleged amendment of\nEuclid. How these accomplished mathematicians could be inveigled into\ncontinued discussion is inexplicable. Mr. Whitworth began by complaining of\nMr. Smith's attacks upon mathematicians, continued to correspond after he\nwas convinced that J. S. proved an arc and its chord to be equal, and only\nretreated when J. S. charged him with believing in 3-1/8, and refusing\nacknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defense\nof his geometry from the assaults of the _Athenaeum_. This the editor would\nnot publish; so J. S. sent a copy to Mr. Wilson himself. Some\ncorrespondence ensued, but Mr. Wilson soon found out his man, and withdrew.\n\nThere is a little derision of the _Athenaeum_ and a merited punishment for\n\"that unscrupulous critic and contemptible mathematical twaddler, De\nMorgan.\"\n\n\n\nMR. REDDIE'S ASTRONOMY.\n\nAt p. 183 I mentioned Mr. Reddie,[650] the author of _Vis Inertiae Victa_\nand of _Victoria toto coelo_,[651] which last is not {345} an address to\nthe whole heaven, either from a Roman Goddess or a British Queen, whatever\na scholar may suppose. Between these Mr. Reddie has published _The\nMechanics of the Heavens_, 8vo, 1862: this I never saw until he sent it to\nme, with an invitation to notice it, he very well knowing that it would\ncatch. His speculations do battle with common notions of mathematics and of\nmechanics, which, to use a feminine idiom, he blasphemes so you can't\nthink! and I suspect that if you do not blaspheme them too, _you_ can't\nthink. He appeals to the \"truly scientific,\" and would be glad to have\nreaders who have read what he controverts, i.e., Newton's _Principia_: I\nwish he may get them; I mean I hope he may obtain them. To none but these\nwould an account of his speculations be intelligible: I accordingly\ndisposed of him in a very short paragraph of description. Now many\nparadoxers desire notice, even though it be disparaging. I have letters\nfrom more than one--besides what have been sent to the Editor of the\n_Athenaeum_--complaining that they are not laughed at; although they deserve\nit, they tell me, as much as some whom I have inserted. Mr. Reddie informs\nme that I have not said a single word against his books, though I have\ngiven nearly a column to sixteen-string arithmetic, and as much to\nanimalcule universes. What need to say anything to readers of Newton\nagainst a book from which I quoted that revolution by gravitation is\n_demonstrably_ impossible? It would be as useless as evidence against a man\nwho has pleaded guilty. Mr. Reddie derisively thanks me for \"small\nmercies\"; he wrote me private letters; he published them, and more, in the\n_Correspondent_. He gave me, _pro viribus suis_,[652] such a dressing you\ncan't think, both for my Budget non-notice, and for reviews which he\nassumed me to have written. He outlawed himself by declaring\n(_Correspondent_, Nov. 11, 1856) that I--in a review--had made a quotation\nwhich was \"garbled, evidently on purpose {346} to make it appear that\" he\n\"was advocating solely a geocentric hypothesis, which is not true.\" In\nfact, he did his best to get larger \"mercy.\" And he shall have it; and at a\nlength which shall content him, unless his mecometer be an insatiable\napparatus. But I fear that in other respects I shall no more satisfy him\nthan the Irish drummer satisfied the poor culprit when, after several times\nchanging the direction of the stroke at earnest entreaty, he was at last\nprovoked to call out, \"Bad cess to ye, ye spalpeen! strike where one will,\nthere's no _plasing_ ye!\"\n\nMr. Reddie attaches much force to Berkeley's[653] old arguments against the\ndoctrine of fluxions, and advances objections to Newton's second section,\nwhich he takes to be new. To me they appear \"such as have been often made,\"\nto copy a description given in a review: though I have no doubt Mr. Reddie\ngot them out of himself. But the whole matter comes to this: Mr. Reddie\nchallenged answer, especially from the British Association, and got none.\nHe presumes that this is because he is right, and cannot be answered: the\nAssociation is willing to risk itself upon the counter-notion that he is\nwrong, and need not be answered; because so wrong that none who could\nunderstand an answer would be likely to want one.\n\nMr. Reddie demands my attention to a point which had already particularly\nstruck me, as giving the means of showing to _all_ readers the kind of\nconfusion into which paradoxers are apt to fall, in spite of the clearest\ninstruction. It is a very honest blunder, and requires notice: it may\notherwise mislead some, who may suppose that no one able to read could be\nmistaken about so simple a matter, {347} let him be ever so wrong about\nNewton. According to his own mis-statement, in less than five months he\nmade the Astronomer Royal abandon the theory of the solar motion in space.\nThe announcement is made in August, 1865, as follows: the italics are not\nmine:\n\n    \"The third (_Victoria ..._), although only published in September,\n    1863, has already had its triumph. _It is the book that forced the\n    Astronomer Royal of England, after publicly teaching the contrary for\n    years, to come to the conclusion, \"strange as it may appear,\" that \"the\n    whole question of solar motion in space is at the present time in doubt\n    and abeyance.\"_ This admission is made in the Annual Report of the\n    Council of the Royal Astronomical Society, published in the Society's\n    _Monthly Notices_ for February, 1864.\"\n\nIt is added that solar motion is \"full of self-contradiction, which \"the\nastronomers\" simply overlooked, but which they dare not now deny after\nbeing once pointed out.\"\n\nThe following is another of his accounts of the matter, given in the\n_Correspondent_, No. 18, 1865:\n\n    \"... You ought, when you came to put me in the 'Budget,' to have been\n    aware of the Report of the Council of the Royal Astronomical Society,\n    where it appears that Professor Airy,[654] with a better appreciation\n    of my demonstrations, had admitted--'strange,' say the Council, 'as it\n    may appear,'--that 'the whole question of solar motion in space [and\n    here Mr. Reddie omits some words] is now in _doubt and abeyance_.' You\n    were culpable as a public teacher of no little pretensions, if you were\n    'unaware' of this. If aware of it, you ought not to have suppressed\n    such an important testimony to my really having been 'very successful'\n    in drawing the teeth of the pegtops, though you thought them so firmly\n    fixed. And if you still suppress {348} it, in your Appendix, or when\n    you reprint your 'Budget,' you will then be guilty of a _suppressio\n    veri_, also of further injury to me, who have never injured you....\"\n\nMr. Reddie must have been very well satisfied in his own mind before he\nventured such a challenge, with an answer from me looming in the distance.\nThe following is the passage of the Report of the Council, etc., from which\nhe quotes:\n\n    \"And yet, strange to say, notwithstanding the near coincidence of all\n    the results of the before-mentioned independent methods of\n    investigation, the inevitable logical inference deduced by Mr. Airy is,\n    that the whole question of solar motion in space, _so far at least as\n    accounting for the proper motion of the stars is concerned_, [I have\n    put in italics the words omitted by Mr. Reddie] appears to remain at\n    this moment in doubt and abeyance.\"\n\nMr. Reddie has forked me, as he thinks, on a dilemma: if unaware, culpable\nignorance; if aware, suppressive intention. But the thing is a _trilemma_,\nand the third horn, on which I elect to be placed, is surmounted by a\ndoubly-stuffed seat. First, Mr. Airy has not changed his opinion about the\n_fact_ of solar motion in space, but only suspends it as to the sufficiency\nof present means to give the amount and direction of the motion. Secondly,\nall that is alluded to in the Astronomical Report was said and printed\nbefore the Victoria proclamation appeared. So that the author, instead of\ndrawing the tooth of the Astronomer Royal's pegtop, has burnt his own\ndoll's nose.\n\nWilliam Herschel,[655] and after him about six other astronomers, had aimed\nat determining, by the proper motions of the stars, the point of the\nheavens towards which the solar system is moving: their results were\ntolerably accordant. Mr. Airy, in 1859, proposed an improved method, and,\napplying it to stars of large proper motion, produced {349} much the same\nresult as Herschel. Mr. E. Dunkin,[656] one of Mr. Airy's staff at\nGreenwich, applied Mr. Airy's method to a very large number of stars, and\nproduced, again, nearly the same result as before. This paper was read to\nthe Astronomical Society in _March_, 1863, was printed in abstract in the\n_Notice_ of that month, was printed in full in the volume then current, and\nwas referred to in the Annual Report of the Council in _February_, 1864,\nunder the name of \"the Astronomer Royal's elaborate investigation, as\nexhibited by Mr. Dunkin.\" Both Mr. Airy and Mr. Dunkin express grave doubts\nas to the sufficiency of the data: and, regarding the coincidence of all\nthe results as highly curious, feel it necessary to wait for calculations\nmade on better data. The report of the Council states these doubts. Mr.\nReddie, who only published in _September_, 1863, happened to see the Report\nof February, 1864, assumes that the doubts were then first expressed, and\ndeclares that his book of September had the triumph of forcing the\nAstronomer Royal to abandon the _fact_ of motion of the solar system by the\nFebruary following. Had Mr. Reddie, when he saw that the Council were\navowedly describing a memoir presented some time before, taken the\nprecaution to find out _when_ that memoir was presented, he would perhaps\nhave seen that doubts of the results obtained, expressed by one astronomer\nin March, 1863, and by another in 1859, could not have been due to his\npublication of September, 1863. And any one else would have learnt that\nneither astronomer doubts the _solar motion_, though both doubt the\nsufficiency of present means to determine its _amount_ and _direction_.\nThis is implied in the omitted words, which Mr. Reddie--whose omission\nwould have been dishonest if he had seen their meaning--no doubt took for\npleonasm, superfluity, overmuchness. The rashness which pushed him headlong\n{350} into the quillet that _his_ thunderbolt had stopped the chariot of\nthe Sun and knocked the Greenwich Phaeton off the box, is the same which\nbetrayed him into yet grander error--which deserves the full word,\n_quidlibet_--about the _Principia_ of Newton. There has been no change of\nopinion at all. When a person undertakes a long investigation, his opinion\nis that, at a certain date, there is _prima facie_ ground for thinking a\nsound result may be obtained. Should it happen that the investigation ends\nin doubt upon the sufficiency of the grounds, the investigator is not put\nin the wrong. He knew beforehand that there was an alternative: and he\ntakes the horn of the alternative indicated by his calculations. The two\nsides of this case present an instructive contrast. Eight astronomers\nproduce nearly the same result, and yet the last two doubt the sufficiency\nof their means: compare them with the what's-his-name who rushes in where\nthing-em-bobs fear to tread.\n\nI was not aware, until I had written what precedes, that Mr. Airy had given\na sufficient answer on the point. Mr. Reddie says (_Correspondent_, Jan.\n20, 1866):\n\n    \"I claim to have forced Professor Airy to give up the notion of 'solar\n    motion in space' altogether, for he admits it to be 'at present in\n    doubt and abeyance.' I first made that claim in a letter addressed to\n    the Astronomer Royal himself in June, 1864, and in replying, very\n    courteously, to other portions of my letter, he did not gainsay that\n    part of it.\"\n\nMr. Reddie is not ready at reading satire, or he never would have so missed\nthe meaning of the courteous reply on one point, and the total silence upon\nanother. Mr. Airy must be one of those peculiar persons who, when they do\nnot think an assertion worth notice, let it alone, without noticing it by a\nnotification of non-notice. He would never commit the bull of \"Sir! I will\nnot say a word on that subject.\" He would put it thus, \"Sir! I will only\nsay ten words on that subject,\"--and, having thus said them, would {351}\nproceed to something else. He assumed, as a matter of form, that Mr. Reddie\nwould draw the proper inference from his silence: and this because he did\nnot care whether or no the assumption was correct.\n\nThe _Mechanics of the Heavens_, which Mr. Reddie sends to be noticed, shall\nbe noticed, so far as an extract goes:\n\n\n\n\"My connection with this subject is, indeed, very simply explained. In\nendeavoring to understand the laws of physical astronomy as generally\ntaught, I happened to entertain some doubt whether gravitating bodies could\nrevolve, and having afterwards imbibed some vague idea that the laws of the\nuniverse were chemical and physical rather than mechanical, and somehow\nconnected with electricity and magnetism as opposing correlative\nforces--most probably suggested to my mind, as to many others, by the\ntranscendent discoveries made in electro-magnetism by Professor\nFaraday[657]--my former doubts about gravitation were revived, and I was\nled very naturally to try and discover whether a gravitating body really\ncould revolve; and I became convinced it could not, before I had ever\npresumed to look into the demonstrations of the _Principia_.\"\n\n\n\nThis is enough against the book, without a word from me: I insert it only\nto show those who know the subject what manner of writer Mr. Reddie is. It\nis clear that \"presumed\" is a slip of the pen; it should have been\n_condescended_.\n\nMr. Reddie represents me as dreaming over paltry paradoxes. He is right;\nmany of my paradoxes are paltry: he is wrong; I am wide awake to them. A\nsingle moth, beetle, or butterfly, may be a paltry thing; but when a\ncabinet is arranged by genus and species, we then begin to admire the {352}\ninfinite variety of a system constructed on a wonderful sameness of leading\ncharacteristics. And why should paradoxes be denied that collective\nimportance, paltry as many of them may individually be, which is accorded\nto moths, beetles, or butterflies? Mr. Reddie himself sees that \"there is a\nmethod in\" my \"mode of dealing with paradoxes.\" I hope I have atoned for\nthe scantiness of my former article, and put the demonstrated impossibility\nof gravitation on that level with Hubongramillposanfy arithmetic and\ninhabited atoms which the demonstrator--not quite without reason--claims\nfor it.\n\nIn the Introduction to a collected edition of the three works, Mr. Reddie\ndescribes his _Mechanism of the Heavens_, from which I have just quoted,\nas--\n\n\n\n\"a public challenge offered to the British Association and the\nmathematicians at Cambridge, in August, 1862, calling upon them to point to\na single demonstration in the _Principia_ or elsewhere, which even attempts\nto prove that Universal Gravitation is possible, or to show that a\ngravitating body could possibly revolve about a center of attraction. The\nchallenge was not accepted, and never will be. No such demonstration\nexists. And the public must judge for themselves as to the character of a\nso-called \"certain science,\" which thus shrinks from rigid examination, and\ndares not defend itself when publicly attacked: also of the character of\nits teachers, who can be content to remain dumb under such circumstances.\"\n\n\n\nON PARADOXERS IN GENERAL.\n\nThe above is the commonplace talk of the class, of which I proceed to speak\nwithout more application to this paradoxer than to that. It reminds one of\nthe funny young rascals who used, in times not yet quite forgotten, to\nabuse the passengers, as long as they could keep up with the {353} stage\ncoach; dropping off at last with \"Why don't you get down and thrash us?\nYou're afraid, you're afraid!\" They will allow the public to judge for\nthemselves, but with somewhat of the feeling of the worthy uncle in _Tom\nJones_, who, though he would let young people choose for themselves, would\n_have them_ choose wisely. They try to be so awfully moral and so ghastly\nsatirical that they must be answered: and they are best answered in their\nown division. We have all heard of the way in which sailors cat's-pawed the\nmonkeys: they taunted the dwellers in the trees with stones, and the\nmonkeys taunted them with cocoa-nuts in return. But these were silly\ndendrobats: had they belonged to the British Association they would have\nsaid--No! No! dear friends; it is not in the itinerary: if you want nuts,\nyou must climb, as we do. The public has referred the question to Time: the\nprocedure of this great king I venture to describe, from precedents, by an\nadaptation of some smart anapaestic tetrameters--your anapaest is the foot\nfor satire to halt on, both in Greek and English--which I read about twenty\nyears ago, and with the point of which I was much tickled. Poetasters were\nlaughed at; but Mr. Slum, whom I employed--Mr. Charles Dickens obliged me\nwith his address--converted the idea into that of a hit at\nmathematicasters, as easily as he turned the Warren acrostic into Jarley.\nAs he observed, when I settled his little account, it is cheaper than any\nprose, though the broom was not stolen quite ready made:\n\n  _Forty stripes save one for the smaller Paradoxers._\n\n  Hark to the wisdom the sages preach\n  Who never have learnt what they try to teach.\n  We are the lights of the age, they say!\n  We are the men, and the thinkers we!\n  So we build up guess-work the livelong day,\n  In a topsy-turvy sort of way,\n  Some with and some wanting _a_ plus b.\n  Let the British Association fuss;\n  What are theirs to the feats to be wrought by us?\n  {354}\n  Shall the earth stand still? Will the round come square?\n  Must Isaac's book be the nest of a mare?\n  Ought the moon to be taught by the laws of space\n  To turn half round without right-about-face?\n  Our whimsey crotchets will manage it all;\n  Deep! Deep! posterity will them call!\n  Though the world, for the present, lets them fall\n  Down! Down! to the twopenny box of the stall!\n\n  Thus they--But the marplot Time stands by,\n  With a knowing wink in his funny old eye.\n  He grasps by the top an immense fool's cap,\n  Which he calls a philosophaster-trap:\n  And rightly enough, for while these little men\n  Croak loud as a concert of frogs in a fen,\n  He first singles out one, and then another,\n  Down goes the cap--lo! a moment's pother,\n  A spirit like that which a rushlight utters\n  As just at the last it kicks and gutters:\n  When the cruel smotherer is raised again\n  Only snuff, and but little of that, will remain.\n\n  But though _uno avulso_ thus comes every day\n  _Non deficit alter_ is also in play:\n  For the vacant parts are, one and all,\n  Soon taken by puppets just as small;\n  Who chirp, chirp, chirp, with a grasshopper's glee,\n  We're the lamps of the Universe, We! We! We!\n  But Time, whose speech is never long,--\n  He hasn't time for it--stops the song\n  And says--Lilliput lamps! leave the twopenny boxes,\n  And shine in the Budget of Paradoxes!\n\nWhen a paradoxer parades capital letters and diagrams which are as good as\nNewton's to all who know nothing about it, some persons wonder why science\ndoes not rise and triturate the whole thing. This is why: all who are fit\nto read the refutation are satisfied already, and can, if they please,\ndetect the paradoxer for themselves. Those who are not fit to do this would\nnot know the difference between the true answer and the new capitals and\ndiagrams on which the delighted paradoxer would declare {355} that he had\ncrumbled the philosophers, and not they him. Trust him for having the last\nword: and what matters it whether he crow the unanswerable sooner or later?\nThere are but two courses to take. One is to wait until he has committed\nhimself in something which all can understand, as Mr. Reddie has done in\nhis fancy about the Astronomer Royal's change of opinion: he can then be\nput in his true place. The other is to construct a Budget of Paradoxes,\nthat the world may see how the thing is always going on, and that the\npicture I have concocted by cribbing and spoiling a bit of poetry is drawn\nfrom life. He who wonders at there being no answer has seen one or two: he\ndoes not know that there are always fifty with equal claims, each of whom\nregards his being ranked with the rest as forty-nine distinct and several\nslanders upon himself, the great Mully Ully Gue. And the fifty would soon\nbe five hundred if any notice were taken of them. They call mankind to\nwitness that science _will not_ defend itself, though publicly attacked in\nterms which might sting a pickpocket into standing up for his character:\nscience, in return, allows mankind to witness or not, at pleasure, that it\n_does not_ defend itself, and yet receives no injury from centuries of\nassault. Demonstrative reason never raises the cry of _Church in Danger_!\nand it cannot have any Dictionary of Heresies except a Budget of Paradoxes.\nMistaken claimants are left to Time and his extinguisher, with the\napprobation of all thinking non-claimants: there is no need of a succession\nof exposures. Time gets through the job in his own workmanlike manner as\nalready described.\n\nOn looking back more than twenty years, I find among my cuttings the\nfollowing passage, relating to a person who had signalized himself by an\neffort to teach comets to the conductor of the _Nautical Almanac_:\n\n\n\n\"Our brethren of the literary class have not the least idea of the small\namount of appearance of knowledge {356} which sets up the scientific\ncharlatan. Their world is large, and there are many who have that moderate\nknowledge, and perception of what is knowledge, before which extreme\nignorance is detected in its first prank. There is a public of moderate\ncultivation, for the most part sound in its judgment, always ready in its\ndecisions. Accordingly, all their successful pretenders have _some\npretension_. It is not so in science. Those who have a right to judge are\nfewer and farther between. The consequence is, that many scientific\npretenders have _nothing but pretension_.\"\n\n\n\nThis is nearly as applicable now as then. It is impossible to make those\nwho have not studied for themselves fully aware of the truth of what I have\nquoted. The best chance is collection of cases; in fact, a Budget of\nParadoxes. Those who have no knowledge of the subject can thus argue from\nthe seen to the unseen. All can feel the impracticability of the\nHubongramillposanfy numeration, and the absurdity of the equality of\ncontour of a regular pentagon and hexagon in one and the same circle. Many\nmay accordingly be satisfied, on the assurance of those who have studied,\nthat there is as much of impracticability, or as much of absurdity, in\nthings which are hidden under\n\n \"Sines, tangents, secants, radius, cosines\n  Subtangents, segments and all those signs;\n  Enough to prove that he who read 'em\n  Was just as mad as he who made 'em.\"\n\nNot that I mean to be disrespectful to mathematical terms: they are short\nand easily explained, and compete favorably with those of most other\nsubjects: for instance, with\n\n \"Horse-pleas, traverses, demurrers,\n  Jeofails, imparlances, and errors,\n  Averments, bars, and protestandos,\n  And puis d'arreign continuandos.\"\n\n{357}\n\nFrom which it appears that, taking the selections made by satirists for our\nsamples, there are, one with another, four letters more in a law term than\nin one of mathematics. But pleading has been simplified of late years.\n\nAll paradoxers can publish; and any one who likes may read. But this is not\nenough; they find that they cannot publish, or those who can find they are\n_not_ read, and they lay their plans athwart the noses of those who, they\nthink, ought to read. To recommend them to be content with publication,\nlike other authors, is an affront: of this I will give the reader an\namusing instance. My good nature, of which I keep a stock, though I do not\nuse it all up in this Budget, prompts me to conceal the name.\n\nI received the following letter, accompanied by a prospectus of a work on\nmetaphysics, physics, astronomy, etc. The author is evidently one whom I\nshould delight to honor:\n\n\"Sir,--A friend of mine has mentioned your name in terms of panigeric\n[_sic_], as being of high standing in mathematics, and of greatly original\nthought. I send you the enclosed without comment; and, assuming that the\nbent of your mind is in free inquiry, shall feel a pleasure in showing you\nmy portfolio, which, as a mathematician, you will acknowledge to be deeply\ninteresting, even in an educational point of view. The work is complete,\nand the system so far perfected as to place it above criticism; and, so far\nas regards astronomy, as will Ptolemy beyond rivalry [_sic_: no doubt some\nwords omitted]. Believe me to be, Sir, with the profoundest respect, etc.\nThe work is the result of thirty-five years' travel and observation, labor,\nexpense, and self-abnegation.\"\n\nI replied to the effect that my time was fully occupied, and that I was\nobliged to decline discussion with many persons who have views of their\nown; that the proper way is to publish, so that those who choose may read\nwhen they can find leisure. I added that I should advise a precursor in the\nshape of a small pamphlet, as two octavo volumes {358} would be too much\nfor most persons. This was sound advice; but it is not the first, second,\nor third time that it has proved very unpalatable. I received the following\nanswer, to which I take the liberty of prefixing a bit of leonine wisdom:\n\n \"Si doceas stultum, laetum non dat tibi vultum;\n  Odit te multum; vellet te scire sepultum.[658]\"\n\n\"Sir,--I pray you pardon the error I unintentionally have fallen into;\ndeceived by the F.R.S. [I am not F.R.S.] I took you to be a man of science\n[_omnis homo est animal, Sortes est homo, ergo Sortes est animal_][659]\ninstead of the mere mathematician, or human calculating-machine. Believe\nme, Sir, you also have mistaken your mission, as I have mine. I wrote to\nyou as I would to any other man well up in mathematics, with the intent to\ncall your attention to a singular fact of omission by Euclid, and other\ngreat mathematicians: and, in selecting you, I did you an honor which, from\nwhat I have just now heard, was entirely out of place. I think, considering\nthe nature of the work set forth in the prospectus, you are guilty of both\nfolly and presumption, in assuming the character of a patron; for your own\nsense ought to have assured you that was such my object I should not have\nsought him in a De Morgan, who exists only by patronage of others. On the\nother hand, I deem it to be an unpardonable piece of presumption in\noffering your advice upon a subject the magnitude, importance, and real\nutility of which you know nothing about: by doing so you have offered me a\ndirect insult. The system is a manual of Philosophy, a one inseparable\nwhole of metaphysics and physic; embracing points the most interesting,\nlaws the most important, {359} doctrines the most essential to advance man\nin accordance with the spirit of the times. I may not live to see it in\nprint; for, at ----, life at best is uncertain: but, live or die, be\nassured Sir, it is not my intention to debase the work by seeking\npatronage, or pandering to the public taste. Your advice was the less\nneeded, seeing I am an old-established ----. I remain, etc.--P.S. You will\noblige me by returning the prospectus of my work.\"\n\n\n\nMy reader will, I am sure, not take this transition from the \"profoundest\nrespect\" to the loftiest insolence for an _apocraphical_ correspondence, to\nuse a word I find in the Prospectus: on my honor it is genuine. He will be\nbetter employed in discovering whether I exist by patronizing others, or by\nbeing patronized by them. I make any one who can find it out a fair offer:\nI will give him my patronage if I turn out to be Bufo, on condition he\ngives me his, if I turn out to be Bavius.[660] I need hardly say that I\nconsidered the last letter to be one of those to which no answer is so good\nas no answer.\n\nThese letters remind me in one respect of the correspondents of the\nnewspapers. My other party wrote because a friend had pointed me out: but\nhe would not have written if he had known what another friend told him just\nin time for the second letter. The man who sends his complaint to the\nnewspaper very often says, in effect, \"Don't imagine, Sir, that I read your\ncolumns; but a friend who sometimes does has told me ...\" It is worded\nthus: \"My attention {360} has been directed to an article in your paper of\n...\" Many thanks to my friend's friends for not mentioning the Budget: had\nmy friend's attention been directed to it I might have lost a striking\nexample of the paradoxer in search of a patron. That my Friend was on this\nscent in the first letter is revealed in the second. Language was given to\nman to conceal his thoughts; but it is not every one who can do it.\n\nAmong the most valuable information which my readers will get from me is\ncomparison of the reactions of paradoxers, when not admitted to argument,\nor when laughed at. Of course, they are misrepresented; and at this they\nare angry, or which is the same thing, take great pains to assure the\nreader that they are not. So far natural, and so far good; anything short\nof concession of a case which must be seriously met by counter-reasons is\nsure to be misrepresentation. My friend Mr. James Smith and my friend Mr.\nReddie are both terribly misrepresented: they resent it by some\ninsinuations in which it is not easy to detect whether I am a conscious\nsmotherer of truth, or only muddle-headed and ignorant. [This was written\nbefore I received my last communication from Mr. James Smith. He tells me\nthat I am wrong in saying that his work in which I stand in the pillory is\nall reprint: I have no doubt I confounded some of it with some of the\nmanuscript or slips which I had received from my much not-agreed-with\ncorrespondent. He adds that my mistake was intentional, and that my reason\nis obvious to the reader. This _is_ information, as the sea-serpent said\nwhen he read in the newspaper that he had a mane and tusks.]\n\n\n\nTHE DOUBLE VAHU PROCESS.\n\nMy friend Dr. Thorn[661] sees deeper into my mystery. By the way, he still\nsends an occasional touch at the old {361} subject; and he wants me\nparticularly to tell my readers that the Latin numeral letters, if M be\nleft out, give 666. And so they do: witness DCLXVI. A person who thinks of\nthe origin of symbols will soon see that 666 is our number because we have\nfive fingers on each hand: had we had but four, our mystic number would\nhave been expressed by 555, and would have stood for our present 365. Had n\nbeen the number on each hand, the great number would have been\n\n  (n + 1) (4n^2 + 2n + 1)\n\nWith no finger on each hand, the number would have been 1: with one finger\nless than none at all on each hand, it would have been 0. But what does\nthis mean? Here is a question for an algebraical paradoxer! So soon as we\nhave found out how many fingers the inhabitants of any one planet have on\neach hand, we have the means of knowing their number of the Beast, and\nthence all about them. Very much struck with this hint of discovery, I\nturned my attention to the means of developing it. The first point was to\nclear my vision of all the old cataracts. I propose the following\nexperiment, subject of course to the consent of parties. Let Dr. Thorn\nDouble-Vahu Mr. James Smith, and Thau Mr. Reddie: if either be deparadoxed\nby the treatment, I will consent to undergo it myself. Provided always that\nthe temperature required be not so high as the Doctor hints at: if the\nTurkish Baths will do for this world, I am content.\n\nThe three paradoxers last named and myself have a pentasyllable convention,\nunder which, though we go far beyond civility, we keep within civilization.\nThough Mr. James Smith pronounced that I must be dishonest if I did not see\nhis argument, which he knew I should not do [to say nothing of recent\naccusation]; though Dr. Thorn declared me a competitor for fire and\nbrimstone--and my wife, too, which doubles the joke: though Mr. Reddie\n{362} was certain I had garbled him, evidently on purpose to make falsehood\nappear truth; yet all three profess respect for me as to everything but\npower to see truth, or candor to admit it. And on the other hand, though\nthese were the modes of opening communication with me, and though I have no\ndoubt that all three are proper persons of whom to inquire whether I should\ngo up-stairs or down-stairs, etc., yet I am satisfied they are thoroughly\nrespectable men, as to everything but reasoning. And I dare say our several\nprofessions are far more true in extent than in many which are made under\nmore parliamentary form. We find excuses for each other: they make\nallowances for my being hoodwinked by Aristotle, by Newton, by the Devil;\nand I permit them to feel, for I know they cannot get on without it, that\ntheir reasons are such as none but a knave or a sinner can resist. But\n_they_ are content with cutting a slice each out of my character: neither\nof them is more than an uncle, a Bone-a-part; I now come to a dreadful\nnephew, Bone-the-whole.\n\nI will not give the name of the poor fellow who has fallen so far below\nboth the _honestum_ and the _utile_, to say nothing of the _decorum_ or the\n_dulce_.[662] He is the fourth who has taken elaborate notice of me; and my\nadvice to him would be, _Nec quarta loqui persona laboret_.[663] According\nto him, I scorn humanity, scandalize learning, and disgrace the press; it\nadmits of no manner of doubt that my object is to mislead the public and\nsilence truth, at the expense of the interests of science, the wealth of\nthe nation, and the lives of my fellow men. The only thing left to be\nsettled is, whether this is due to ignorance, natural distaste for truth,\npersonal malice, a wish to curry favor with the Astronomer Royal, or mere\ntoadyism. The only accusation which has truth in it is, that I have made\nmyself a \"public scavenger of science\": the assertion, which is the {363}\nmost false of all is, that the results of my broom and spade are \"shot\nright in between the columns of\" the _Athenaeum_. I declare I never in my\nlife inserted a word between the columns of the _Athenaeum_: I feel huffed\nand miffed at the very supposition. I _have_ made myself a public\nscavenger; and why not? Is the mud never to be collected into a heap? I\nlook down upon the other scavengers, of whom there have been a few--mere\nhistorical drudges; Montucla, Hutton, etc.--as not fit to compete with me.\nI say of them what one crossing-sweeper said of the rest: \"They are well\nenough for the common thing; but put them to a bit of fancy-work, such as\nsweeping round a post, and see what a mess they make of it!\" Who can touch\nme at sweeping round a paradoxer? If I complete my design of publishing a\nseparate work, an old copy will be fished up from a stall two hundred years\nhence by the coming man, and will be described in an article which will end\nby his comparing our century with his own, and sighing out in the best New\nZealand pronunciation--\n\n \"Dans ces tems-la\n  C'etait deja comme ca!\"[664]\n\n\n\nORTHODOX PARADOXERS.\n\nAnd pray, Sir! I have been asked by more than one--do your orthodox never\nfall into mistake, nor rise into absurdity? They not only do both, but they\nadmit it of each other very freely; individually, they are convinced of\nsin, but not of any particular sin. There is not a syndoxer among them all\nbut draws his line in such a way as to include among paradoxers a great\nmany whom I should exclude altogether from this work. My worst specimens\nare but exaggerations of what may be found, occasionally, in the thoughts\nof sagacious investigators. At the end of the {364} glorious dream, we\nlearn that there is a way to Hell from the gates of Heaven, as well as from\nthe City of Destruction: and that this is true of other things besides\nChristian pilgrimage is affirmed at the end of the Budget of Paradoxes. If\nD'Alembert[665] had produced _enough_ of a quality to match his celebrated\nmistake on the chance of throwing head in two throws, he would have been in\nmy list. If Newton had produced _enough_ to match his reception of the\nstory that Nausicaa, Homer's Phaeacian princess, invented the celestial\nsphere, followed by his serious surmise that she got it from the\nArgonauts,--then Newton himself would have had an appearance entered for\nhim, in spite of the _Principia_. In illustration, I may cite a few words\nfrom _Tristram Shandy_:\n\n\n\n\"'A soldier,' cried my uncle Toby, interrupting the Corporal, 'is no more\nexempt from saying a foolish thing, Trim, than a man of letters.'--'But not\nso often, an' please your honor,' replied the Corporal. My uncle Toby gave\na nod.\"\n\n\n\nI now proceed to die out. Some prefatory remarks will follow in time.[666]\nI shall have occasion to insist that all is not barren: I think I shall\nfind, on casting up, that two out of five of my paradoxers are not to be\nutterly condemned. Among the better lot will be found all gradations of\nmerit; at the same time, as was remarked on quite a different subject,\nthere may be little to choose between the last of the saved and the first\nof the lost. The higher and better class is worthy of blame; the lower and\nworse class is worthy of praise. The higher men are to be reproved for not\ntaking up things in which they could do some good: the lower men are to be\ncommended for taking up things in which they can do no great harm. The\ncircle problem is like Peter Peebles's lawsuit:\n\n{365}\n\n\n\n\"'But, Sir, I should really spoil any cause thrust on me so hastily.'--'Ye\ncannot spoil it, Alan,' said my father, 'that is the very cream of the\nbusiness, man,--... the case is come to that pass that Stair or Arniston\ncould not mend it, and I don't think even you, Alan, can do it much harm.'\"\n\n\n\nI am strongly reminded of the monks in the darker part of the Middle Ages.\nTo a certain proportion of them, perhaps two out of five, we are indebted\nfor the preservation of literature, and their contemporaries for good\nteaching and mitigation of socials evils. But the remaining three were the\nfleas and flies and thistles and briars with whom the satirist lumps them,\nabout a century before the Reformation:\n\n \"Flen, flyys, and freris, populum domini male caedunt;\n  Thystlis and breris crescentia gramina laedunt.\n  Christe nolens guerras qui cuncta pace tueris,\n  Destrue per terras breris, flen, flyys, and freris.\n  Flen, flyys, and freris, foul falle hem thys fyften yeris,\n  For non that her is lovit flen, flyys ne freris.\"[667]\n\nI should not be quite so savage with my second class. Taken together, they\nmay be made to give useful warning to those who are engaged in learning\nunder better auspices: aye, even useful hints; for bad things are very\noften only good things spoiled or misused. My plan is that of a predecessor\nin the time of Edward the Second:\n\n \"Meum est propositum genti imperitae\n  Artes frugi reddere melioris vitae.\"[668]\n\nTo this end I have spoken with freedom of books as books, of opinions as\nopinions, of ignorance as ignorance, of {366} presumption as presumption;\nand of writers as I judge may be fairly inferred from what they have\nwritten. Some--to whom I am therefore under great obligation--have\npermitted me to enlarge my plan by assaults to which I have alluded;\nassaults which allow a privilege of retort, of which I have often availed\nmyself; assaults which give my readers a right of partnership in the\namusement which I myself have received.\n\nFor the present I cut and run: a Catiline, pursued by a chorus of Ciceros,\nwith _Quousque tandem? Quamdiu nos? Nihil ne te?_[669] ending with, _In te\nconferri pestem istam jam pridem oportebat, quam tu in nos omnes jamdiu\nmachinaris!_ I carry with me the reflection that I have furnished to those\nwho need it such a magazine of warnings as they will not find elsewhere; _a\nsignatis cavetote_:[670] and I throw back at my pursuers--_Valete, doctores\nsine doctrina; facite ut proxima congressu vos salvos corporibus et sanos\nmentibus videamus._[671] Here ends the Budget of Paradoxes.\n\n{367}\n\n       *       *       *       *       *\n\n\nAPPENDIX.\n\nI think it right to give the proof that the ratio of the circumference to\nthe diameter is incommensurable. This method of proof was given by\nLambert,[672] in the _Berlin Memoirs_ for 1761, and has been also given in\nthe notes to Legendre's[673] Geometry, and to the English translation of\nthe same. Though not elementary algebra, it is within the reach of a\nstudent of ordinary books.[674]\n\nLet a continued fraction, such as\n\n  a\n  -----\n  b + c\n      -----\n      d + e\n          -\n          f + etc.,\n\nbe abbreviated into a/b+ c/d+ e/f+ etc.: each fraction being understood as\nfalling down to the side of the preceding sign +. In every such fraction we\nmay suppose b, d, f, etc. {368} positive; a, c, e, &c. being as required:\nand all are supposed integers. If this succession be continued ad\ninfinitum, and if a/b, c/d, e/f, etc. all lie between -1 and +1, exclusive,\nthe limit of the fraction must be incommensurable with unity; that is,\ncannot be A/B, where A and B are integers.\n\nFirst, whatever this limit may be, it lies between -1 and +1. This is\nobviously the case with any fraction p/(q + [omega]), where [omega] is\nbetween +-1: for, p/q, being < 1, and p and q integer, cannot be brought up\nto 1, by the value of [omega]. Hence, if we take any of the fractions\n\n  a/b, a/b+ c/d, a/b+ c/d+ e/f, etc.\n\nsay a/b+ c/d+ e/f+ g/h we have, g/h being between +-1, so is e/f+ g/h, so\ntherefore is c/d+ e/f+ g/h; and so therefore is a/b+ c/d+ e/f+ g/h.\n\nNow, if possible, let a/b+ c/d+ etc. be A/B at the limit; A and B being\nintegers. Let\n\n  P = A c/d+ e/f+ etc., Q = P e/f+ g/h+ etc., R = Q g/h + i/k + etc.\n\nP, Q, R, etc. being integer or fractional, as may be. It is easily shown\nthat all must be integer: for\n\n{369}\n\n  A/B = a/b+ P/A, or, P = aB - bA\n\n  P/A = c/d+ Q/P, or, Q = cA - dP\n\n  Q/P = e/f+ R/Q, or, R = eP - fQ\n\netc., etc. Now, since a, B, b, A, are integers, so also is P; and thence Q;\nand thence R, etc. But since A/B, P/A, Q/P, R/Q, etc. are all between -1\nand +1, it follows that the unlimited succession of integers P, Q, R, are\neach less in numerical value than the preceding. Now there can be no such\n_unlimited_ succession of _descending_ integers: consequently, it is\nimpossible that a/b+ c/d+, etc. can have a commensurable limit.\n\nIt easily follows that the continued fraction is incommensurable if a/b,\nc/d, etc., being at first greater than unity, become and continue less than\nunity after some one point. Say that i/k, l/m,... are all less than unity.\nThen the fraction i/k+ l/m+ ... is incommensurable, as proved: let it be\n[kappa]. Then g/(h + [kappa]) is incommensurable, say [lambda]; e/(f +\n[lambda]) is the same, say [mu]; also c/(d + [mu]), say [nu], and a/(b +\n[nu]), say [rho]. But [rho] is the fraction a/b+ c/d+ ... itself; which is\ntherefore incommensurable.\n\nLet [phi]z represent\n\n      a     a^2          a^3\n  1 + - + ------- + -------------- + ....\n      z   2z(z+1)   2.3.z(z+1)(z+2)\n\n{370} Let z be positive: this series is convergent for all values of a, and\napproaches without limit to unity as z increases without limit. Change z\ninto z + 1, and form [phi]z - [phi](z+1): the following equation will\nresult--\n\n                        a\n  [phi]z-[phi](z+1) = ------([phi](z+2))\n                      z(z+1)\n\n         a [phi](z+1)       a [phi](z+1)    a  [phi](z+2)\n  or a = - ---------- . z + - ---------- . --- ----------\n         z   [phi]z         z   [phi]z     z+1 [phi](z+1)\n\n  a = [psi]z(z+[psi](z+1))\n\n[psi]z being (a/z)([phi](z+1)/[phi]z); of which observe that it diminishes\nwithout limit as z increases without limit. Accordingly, we have\n\n  [psi]z = a/z+ [psi](z+1) = a/z+ a/(z+1)+ [psi](z+2)\n                           = a/z+ a/(z+1)+ a/(z+2)+ [psi](z+3), etc.\n\nAnd, [psi](z + n) diminishing without limit, we have\n\n  a/z . [phi](z+1)/[phi]z = (a/z+) (a/(z+1)+) (a/(z+2)+) (a/((z+3)+ ...))\n\nLet z = 1/2; and let 4a = -x^2. Then (a/z)[phi](z+1) is -(x^2/2) ( 1 -\nx^2/(2.3) + x^4/(2.3.4.5...)) or -(x/2) sin x. Again [phi]z is 1 - x^2/2 +\nx^4/(2.3.4) or cos x: and the continued fraction is\n\n  (1/4)x^2/(1/2)+ (1/4)x^2/(3/2)+ (1/4)x^2/(5/2)+ ...\n   or -x/2 x/1+ -x^2/3+ -x^2/5+\n      ...\n\n{371} whence tan x = x/1+ -x^2/3+ -x^2/5+ -x^2/7+ ...\n\nOr, as written in the usual way,\n\n  tan x = x\n          -------\n          1 - x^2\n              -------\n              3 - x^2\n                  -------\n                  5 - x^2\n                      -------\n                      7 - ...\n\nThis result may be proved in various ways: it may also be verified by\ncalculation. To do this, remember that if\n\n  a_1/b_1+ a_2/b_2+ a_3/b_3+ ...  a_n/b_n = P_n/Q_n; then\n\n  P_1=a_1, P_2=b_2 P_1,     P_3=b_3 P_2+a_3 P_1, P_4=b_4 P_3+a_4 P_2, etc.\n  Q_1=b_1, Q_2=b_2 Q_1+a_2, Q_3=b_3 Q_2+a_3 Q_1, Q_4=b_4 Q_3+a_4 Q_2, etc.\n\nin the case before us we have\n\n  a_1=x, a_2=-x^2, a_3=-x^2, a_4=-x^2, a_5=-x^2, etc.\n  b_1=1, b_2=3,    b_3=5,    b_4=7,    b_5=9, etc.\n\n  P_1=x                     Q_1=1\n  P_2=3x                    Q_2=3-x^2\n  P_3=15x-x^3               Q_3=15-6x^2\n  P_4=105x-10x^3            Q_4=105-45x^2+x^4\n  P_5=945x-105x^3+x^5       Q_5=945-420x^2+15x^4\n  P_6=10395x-1260x^3+21x^5  Q_6=10395-4725x^2+210x^4-x^6\n\nWe can use this algebraically, or arithmetically. If we divide P_n by Q_n,\nwe shall find a series agreeing with the known series for tan x, _as far\nas_ n _terms_. That series is\n\n  x + x^3/3 + 2x^5/15 + 17x^7/315 + 62x^9/2835 + ...\n\n{372} Take P_5, and divide it by Q_5 in the common way, and the first five\nterms will be as here written. Now take _x_ = .1, which means that the\nangle is to be one tenth of the actual unit, or, in degrees 5 deg..729578.\nWe find that when x = .1, P_6 = 1038.24021, Q_6 = 10347.770999; whence P_6\ndivided by Q_6 gives .1003346711. Now 5 deg..729578 is 5 deg.43'46-1/2\";\nand from the old tables of Rheticus[675]--no modern tables carry the\ntangents so far--the tangent of this angle is .1003347670.\n\nNow let x = (1/4)[pi]; in which case tan x = 1. If (1/4)[pi] be\ncommensurable with the unit, let it be (m/n), m and n being integers:\nwe know that (1/4)[pi] < 1. We have then\n\n  1=(m/n)/1- (m^2/n^2)/3- (m^2/n^2)/5- ...  = m/n- m^2/3n- m^2/5n- m^2/7n-\n      ...\n\nNow it is clear that m^2/3n, m^2/5n, m^2/7n, etc. must at last become and\ncontinue severally less than unity. The continued fraction is therefore\nincommensurable, and cannot be unity. Consequently [pi]^2 cannot be\ncommensurable: that is, [pi] is an incommensurable quantity, and so also\nis [pi]^2.\n\n\n\nI thought I should end with a grave bit of appendix, deeply mathematical:\nbut paradox follows me wherever I go. The foregoing is--in my own\nlanguage--from Dr. (now Sir David) Brewster's[676] English edition of\nLegendre's Geometry, (Edinburgh, 1824, 8vo.) translated by some one who is\nnot named. I picked up a notion, which others had at Cambridge in 1825,\nthat the translator was the late Mr. Galbraith,[677] then known at\nEdinburgh as a writer and teacher.\n\n{373} But it turns out that it was by a very different person, and one\ndestined to shine in quite another walk; it was a young man named Thomas\nCarlyle.[678] He prefixed, from his own pen, a thoughtful and ingenious\nessay on Proportion, as good a substitute for the fifth Book of Euclid as\ncould have been given in the space; and quite enough to show that he would\nhave been a distinguished teacher and thinker on first principles. But he\nleft the field immediately.\n\n       *       *       *       *       *\n\n(The following is the passage referred to at Vol. II, page 54.)\n\nMichael Stifelius[679] edited, in 1554, a second edition of the Algebra\n(_Die Coss._), of Christopher Rudolff.[680] This is one of the earliest\nworks in which + and - are used.\n\nStifelius was a queer man. He has introduced into this very work of Rudolff\nhis own interpretation of the number of the Beast. He determined to fix the\ncharacter of Pope Leo: so he picked the numeral letters from LEODECIMVS,\nand by taking in X from LEO X. and striking out M as standing for\n_mysterium_, he hit the number exactly. This discovery completed his\nconversion to Luther, and his determination to throw off his monastic vows.\nLuther dealt with him as straight-forwardly as with Melanchthon about his\nastrology: he accepted the conclusions, but told him to clear his mind of\nall the premises about the Beast. Stifelius {374} did not take the advice,\nand proceeded to settle the end of the world out of the prophet Daniel: he\nfixed on October, 1533. The parishioners of some cure which he held, having\nfull faith, began to spend their savings in all kinds of good eating and\ndrinking; we may charitably hope this was not the way of preparing for the\nevent which their pastor pointed out. They succeeded in making themselves\nas fit for Heaven as Lazarus, so far as beggary went: but when the time\ncame, and the world lasted on, they wanted to kill their deceiver, and\nwould have done so but for the interference of Luther. {375}\n\n       *       *       *       *       *\n\n\nINDEX.\n\nPages denoted by numerals of this kind (_287_) refer to biographical notes,\nchiefly by the editor. Numerals like 426 refer to books discussed by De\nMorgan, or to leading topics in the text. Numerals like 126 indicate minor\nreferences.\n\n  Abbott, Justice, I, _181_.\n  Abernethy, J., II, _219_.\n  Aboriginal Britons, a poem, II, 270.\n  Academy of Sciences, French, I, 163.\n  Adair, J., I, _223_.\n  Adam, M., I, _65_.\n  Adams, J. C., I, _43_, 82, 385, 388; II, 131, 135, 140, 303.\n  Ady, Joseph, II, 42, _42_.\n  Agnew, H. C., I, 328.\n  Agricola, J., I, 394.\n  Agricultural Laborer's letter, II, 16.\n  Agrippa, H. C., I, _48_, 48.\n  Ainsworth, W. H., II, _132_.\n  Airy, I, _85_, 88, 152, 242; II, 85, 140, 150, 303, 347.\n  Alchemy, I, 125.\n  Alfonso X (El Sabio), II, _269_.\n  Alford, H., II, _221_.\n  Alfred, King, Ballad of, II, 22.\n  Algebra, I, 121.\n  Algebraic symbols, I, 121.\n  Almanac, I, 300; II, 147, 148, 207.\n    (_See Easter._)\n  Aloysius Lilius, I, 362.\n  Alsted, J. H., II, _282_.\n  Ameen Bey, II, 15.\n  Amicable Society, I, 347.\n  Ampere, I, 86.\n  Amphisbaena serpent, I, 31.\n  Anagrams, De Morgan, I, 138.\n  Anaxagoras, II, _59_.\n  Anghera, II, 60, _60_, 61, 279.\n  Annuities, Fallacies of, I, 157.\n  Antichrist, I, 130.\n  Antimony, I, 125.\n  Antinewtonism, I, 162.\n  Antinomians, I, 394.\n  Antiphon, II, _59_.\n  Antonie, F., I, _126_, 126.\n  Apollonius, I, 41, 107.\n  Apparitions, II, 47.\n  Arago, I, _243_, 390.\n  Aratus, II, _167_.\n  Arbuthnot, I, _133_, 134.\n  Archer, H., II, 90.\n  Archimedes,  I, 5, 11, 42, 83, 107.\n  Archytas, I, _53_.\n  Argoli, I, _104_.\n  Aristocrat, as a scientist, I, 131.\n  Aristotle, I, 5, 331.\n  Arnobius, II, _73_.\n  Arson, P. J., II, _207_.\n  Ashton, R., II, _99_.\n  Astrology, I, 118, 127, 128, 350; II, 43.\n  Astronomer's Drinking Song, I, 380.\n  Astronomical Aphorisms, I, 398.\n    Paradox, I, 394.\n    Police Report, I, 390.\n    Society. (_See Royal Astronomical Society._)\n  Astronomy, Bailly's exaggerated view of, I, 166.\n  Astunica, Didacas, I, 90.\n  Athanasian Creed, I, 371.\n  Atheists, Philosophical, I, 1.\n  Atoms, II, 191.\n  {376}\n  Attraction, I, 136, 151, 155.\n  Augustine, St., II, _23_.\n  Aurora borealis, I, 134.\n  Austen, Jane, I, 191.\n  Auzout, A., II, _300_.\n  Aviation, Early ideas of, II, 8.\n\n  Babbage, C., I, _207_, 290, 291; II, 181.\n  Bachet, de Meziriac, I, _161_.\n  Bacon, F., I, 5, _75_, 75, 76, 79, 89, 145, 331.\n  Bacon, R., I, 5, _126_, 126, 360; II, 94.\n  Baconian controversy, I, 141.\n  Baden Powell, II, _267_.\n  Bailly, J. S., I, 166, _166_, 308.\n  Baily, F., I, 308, _309_; II, 16, 143, 188.\n  Baily, R., II, 16.\n  Baker, T., II, _302_.\n  Bakewell, F. C., II, 156, _156_.\n  Banks, J., I, 28.\n  Barberini, M., II, _267_.\n  Barker, C., II, _262_.\n  Baronius, I, 33, 35; II, _62_.\n  Barreme, I, _42_.\n  Barrett, G., II, _188_.\n  Barrow, I., I, _160_; II, 302.\n  Baruel, de, I, 165.\n  Bassano, Duc de, II, 3, 339.\n  Baxter, T., I, 146.\n  Bayle, P., II, _73_.\n  Beaufort, F., II, _267_.\n  Beaugrand, I, 119, _121_.\n  Beaulieu, I, _119_, 119, 121.\n  Beaune, de, II, _59_.\n  Becourt, R., II, 277.\n  Bedford, Duke of, (6th), I, _182_.\n  Behmen, I, _168_, 254; II, 317.\n  Bellenden, W., I, _175_.\n  Bentley, I, _110_.\n  Berkeley, G., II, 346.\n  Bernard, E., II, _297_, 300.\n  Bernardus Trevisanus, I, _126_, 126.\n  Bernoullis, I, 130, _150_, _335_, 336.\n  Bertius, P., II, _300_.\n  Bese, I, _66_.\n  Bessel, I, _384_; II, 2.\n  Bethune, I, _99_, 279, 291.\n  Bettesworth, I, 19.\n  Beza. (_See Bese._)\n  Bickersteth, E. H., I, _238_.\n  Bidder, I, _86_.\n  Biden, J., II, 158, _160_.\n  Bidle, (Biddle), I, 239.\n  Biot, I, _85_.\n  Birch, T., I, _108_; II, 304, 313.\n  Birks, T. R., II, 158, _158_.\n  Bishop, G., I, _386_.\n  Bishops as Paradoxers, I, 226.\n  Boccaccio, I, 38.\n  Boethius, I, _42_, 45.\n  Boehme. (_See Behmen._)\n  Boncompagni, I, _298_.\n  Boniface, St., I, 32.\n  Bonnycastle, J., II, _16_.\n  Booker, I, 115.\n  Boole, G., I, _261_, 332; II, 75, 79.\n    --A tribute to, II, 79.\n  Borelli, G. A., II, _300_.\n  Borello, I, _69_.\n  Boreman,  I, 113.\n  Borron, Mrs., II, 7.\n  Boscovich, I, _156_, 164.\n  Bouguer, II, _301_.\n  Bouillaud, I, _87_; II, 295.\n  Bouvard, A., I, _327_.\n  Bovillus, I, _44_; II, 324.\n    --Epitome of, I, 44.\n  Bowdler, H. M., I, _194_.\n  Bowring, J., I, _352_; II, 256.\n  Boyle, R., I, 24, _125_; II, 300.\n  Bradley, I, 24.\n  Bradwardine, I, _227_, 228, 229.\n  Brahe. (_See Tycho B._)\n  Brancker, I, 107; II, _300_.\n  Brenan, J., I, 330, _330_.\n  Brewster, D., I, 39, _137_, 140; II, 214, 288, 372.\n  Briggs, I, _69_; II, 299, 302.\n  Bright, J., II, _235_.\n  Brinkley, J., I, _311_.\n  Britannicus, D., II, 8.\n  British Museum library, I, 151.\n  Brothers, R., I, _315_; II, 97.\n  Brougham, Henry, Lord, I, _191_.\n  Brouncker (Brounker), I, _132_; II, 302.\n  Brown, W., II, _168_.\n  Browne, T., I, 31.\n  Brucker, I, _61_.\n  Brunet, I, _402_.\n  Bruennow, I, _386_.\n  Bruno, I, _59_, 59.\n  Bryson, II, _59_.\n  Buergi, I, 52.\n  Buffon, I, _282_.\n  Bulstrode, II, 84.\n  Bungus, I, _55_, 55, 57.\n  Buoncompagno, U., I, _362_.\n  {377}\n  Burgon, J. W., II, _30_.\n  Buridan, I, _37_.\n    --Questiones morales, I, 37.\n  Buridan's Ass, I, 37.\n  Burke, E., I, _173_.\n  Burlesque, Frend's, I, 208.\n  Burnet, G., I, _107_.\n  Burney, Frances, I, _190_.\n  Burton, Frances B., I, 374.\n  Busby, R., II, _313_.\n  Buteo, I, _51_.\n  Butler, G., I, _199_.\n  Butler, S., II, _218_.\n  Buxton, J., I, _86_.\n  Byrgius. (_See Buergi._)\n  Byrne, O., I, _329_; II, 186, 190.\n  Byron, I, 186; II, 270, 273.\n\n  Cabbala, I, 272.\n  Calculating Boys, I, 86.\n  Calculus, I, 129.\n  Calendar. (_See Easter._)\n  Cambridge Poets, II, 269.\n  Campanus, I, 42, _43_.\n  Canning, Geo., II, _145_.\n  Carcavi, I, _106_.\n  Cardanus, II, _59_.\n  Carlile, R., I, _271_.\n  Carlyle, T., II, _373_.\n  Carnot, I, 107.\n  Caroline tables, I, 124.\n  Casaubon, I, _111_.\n  Case, J., I, _128_, 128.\n  Cassini, J., I, _172_.\n  Castel, I, _148_, 148.\n  Castiglioni, I, _139_.\n  Castlereagh, I, 185, _186_.\n  Cataldi, I, _69_, 69.\n  Catcott, A., I, _237_.\n  Causans, de, I, _298_.\n  Cavalieri, I, _106_.\n  Cavendish, C., I, _106_; II, 299, 312.\n  Cavendish, W., I, _290_.\n  Caxton, W., II, _281_.\n  Cayley, A., II, _292_.\n  Cecil, R. (1st Earl of Salisbury), II, _330_.\n  Centrifugal force, II, 268.\n  Ceulen. (_See Van Ceulen._)\n  Challis, J., I, _390_; II, 141.\n  Chalmers, I, _102_; II, 219.\n  Chambers, E., II, _282_.\n  Chambers, R., I, _344_, 344.\n  Charles IX, II, 94.\n  Charles X, II, 1.\n  Chasles, I, _39_, 229.\n  Chesterfield, Earl of (4th), II, _298_.\n  Chiffinch, W., II, _50_.\n  Ch'in Chiu-shang, II, 66.\n  Chitty, J., II, _323_.\n  Chiu-chang, Suan-shu, II, 67.\n  Christian Evidence Society, I, 270.\n  Christie, I, 27.\n  Christmann, I, 272, _272_.\n  Church question, I, 62.\n  Church, The word, II, 30.\n  Circle squarers. (_See Squaring the Circle._)\n  Circulating media of mathematics, I, 107.\n  Ciruelo. (_See Sanchez._)\n  Clairaut, I, _219_, 382.\n  Clarence, Duke of, I, 179.\n  Clarke, R., I, _255_.\n  Clavius, I, 11, _69_, 111, 112, 335, 362, 363, 372; II,\n      59.\n  Clayton., Geo., II, _98_.\n  Cluvier, D., II, 332, _332_.\n  Cobb, Mary, II, 117.\n  Cobbett, W., I, _177_, 200, 399.\n  Cobden, R., II, 217.\n  Cocker, I, _42_; II, 64, 173, 251, 307.\n  Cody, P., II, 208.\n  Coke, E., II, _331_.\n  Colburn, Z., I, _86_.\n  Colenso, I, _63_, 247; II,  191.\n  Collins, J., I, _107_; II, 297, 300,  302, 313.\n  Colvill, W. H., II, 68.\n  Cometic astrology, I, 128.\n  Comets, I, 128; II, 68, 83.\n  Cominale, C., I, _162_, 162.\n  Compton, S. J. A., II, _19_.\n  Computation, Paradoxes of, II, 251, 267.\n  Condamine, C. M. de la, II, _301_.\n  Conduitt, John, I, _397_.\n  Conduitt, Mrs., I, _136_.\n  Congregation of the Index, I, 90.\n  Converse propositions, I, 295.\n  Convocation at Oxford, I, 96.\n  Cooke, Margaret, I, _310_.\n  Cooper, A. A. (Shaftsbury), II, _181_.\n  Copernicus, I, 5, 6, _76_, 90, 121, 172, 380; II, 165, 335.\n  Copley, J. S., I, _198_.\n  Cormouls, I, 225.\n  Cosmology, I, 172.\n  {378}\n  Cotes, R., II, _301_.\n  Cottle, Mrs., II, 97, _97_, 161.\n  Craig, J., I, _129_, 129.\n  Creed, Mathematics of a, I, 329.\n  Cribb, T., I, _314_.\n  Crotus, J., I, 318.\n  Cruickshank, G., I, _186_.\n  Cube, Duplication of, I, 349.\n  Cumyns, Eliza, I, 299.\n  Cunningham, I, 172, _172_.\n  Curabelle, I, _221_.\n  Curious Calculations, II, 66.\n  Curll, E., II, _279_.\n  Cusa, I, _44_, 47, 360.\n  Custom, II, 324.\n  Cyclometry, II, 208. (_See  Squaring of the Circle._)\n  Cyclopaedias, Review of, II, 280.\n\n  D'Alembert, I, _382_; II, 283, 364.\n  Dalgarno, I, 116, _117_.\n  Dalton, J., I, _255_.\n  D'Arblay, Mme., I, _190_.\n  Darwin, E., II, _8_.\n  Darwinism, Primitive, I, 344.\n  Dary, M., II, _305_.\n  Daval, P., II, _298_.\n  Davies, T. S., II, 151, _151_, 188.\n  Day, A., I, 295, _295_.\n  De Baruel, I, 165.\n  De Beaune. (_See Beaune._)\n  De Becourt, II, 277, _277_.\n  Debenham, J., I, _393_.\n  De Causans. (_See Causans._)\n  Dechales. (_See de Challes._)\n  De Challes, I, _45_.\n  Decimal coinage, II, 80, 168, 169.\n  Decimals run riot, II, 80.\n  Dee, J., II, _302_.\n  De Faure, I, 149.\n  De la Leu, I, _297_.\n  Delambre, I, _160_, 167, 354; II, 165.\n  Democritus, II, _34_.\n  De Moivre, I, 24, _376_; II, 298.\n  De Molieres, I, _220_.\n  De Molina, I, _297_.\n  Demonville, I, 291, 293.\n  De Morgan, A., I, 191, 383; II, 194.\n    --Refusal of LL. D., I, 191.\n  De Morgan, G. C., I, 383.\n  De Morgan, Mrs., I, _196_; II, 194.\n  Denison, J., I, 348, 353.\n  Desaguliers, I, _153_, 156, 157.\n  Desargues, I, _119_, 221.\n  Descartes, I, 5, 59, 105, 132, 165, 204, 220; II, 94.\n  De Serres, II, _60_.\n  De Sluse. (_See Sluse._)\n  De Thou, I, 51, _111_, 113; II, 295.\n  De Vausenville, I, 12.\n  Devonshire, Duke of (7th), I, _290_.\n  Diamandi, I, 86.\n  Didacus Astunica, I, 90.\n  Diderot, II, _4_, 283, 339.\n  Digby, K., I, _108_.\n  Digges, T., and L., II, _302_.\n  Dionysius Exiguus, I, _360_.\n  Dircks, H., II, 138, _138_.\n  Discoverers and discoveries, II, 206.\n  Discovery, Basis of, I, 85.\n  D'Israeli, I., I, _115_, 118, 136, 188, 227.\n  Ditton, I, _133_, 133.\n  Division, Nature of, II, 248.\n  Dobson, J., I, _234_, 234.\n  Dodson, J., II, _312_.\n  Dodt, I, _52_.\n  Doggerel verse, I, 341.\n  Dolland, I, _377_.\n  Double Vahu Process, II, 360.\n  Douglas, G., I, _232_.\n  Drach, S. M., II, _317_.\n  Drayson, G. A. W., II, _132_, 132.\n  Dryden, II, _71_.\n  Dual arithmetic, II, 186.\n  Duchesne, I, _52_.\n  Dumortier, I, 313.\n  Duncan, A., I, _179_.\n  Dunkin, E., II, _349_.\n  Duodecimal scale, II, 68.\n  Duplication Problem, I, 349.\n  Dupuy, J. and P., II, _295_.\n  Dutens, L., II, _90_.\n  Dyer, G., I, _178_.\n\n  Earth, Figure of, II, 54.\n  Easter, I, 359.\n  Easter Day Paradoxes, I, 353.\n  Ebrington, Thos., I, _247_.\n  Edgeworth, Maria, I,  _191_.\n  Editorial System, I, 15.\n  Edleston, I, _140_; II, 296.\n  Edwards, J., I, _144_.\n  Edwards, T., I, _112_.\n  Eirenaeus Philalethes, I, _125_, 125, 126.\n  Eldon, Lord (1st), II, _197_.\n  Elephant story, I, 58.\n  Elizabeth, Queen, I, 128.\n  Ellenborough, Baron, I, _181_.\n  {379}\n  Ellicot, I, 24.\n  Ellis, I, _76_, 82.\n  Engel, I, 230.\n  English language, Origin of, I, 215.\n  Enriques, F., II, _367_.\n  Epps, J., I, _153_; II, 143.\n  Equation of fifth degree, I, 250, 373.\n  Erasmus, I, 110.\n  Erastus, I, _65_.\n  Erichsen, I, 163.\n  Ersch, II, _193_, 282.\n  Erskine, T., II, _127_.\n  Esperanto, Forerunner of, I, 116.\n  Euclid, I, 5, 43; II, 118, 151.\n    --Without Axioms, I, 287.\n  Eudoxus, II, _164_.\n  Euler, I, 221, _382_; II, 3, 4, 303, 331, 339.\n  Eusebius, II, _220_.\n  Eustace, J. C., II, _46_.\n  Eutocius, I, _41_; II, 60.\n  Evelyn, J., I, _108_.\n  Everett, J., I, _346_.\n  Evidence, I, 57, 58.\n\n  Faber. (_See Stapulensis._)\n  Fairfax, Mary, I, _242_.\n  Falco, I, 53.\n  Faraday, M., II, _351_.\n  Faure, de, I, 149; II, 238.\n  Fawcett, H., II, _249_.\n  Ferguson, J., II, _20_.\n  Fermat, I, 122, 221; II, _300_.\n  Ferrari, S., II, 68.\n  Fiction, New era in, I, 189.\n  Fienus, I, _74_, 74.\n  Filopanti, Q. B., II, _93_.\n  Finaeus, I, _50_, 50, 113.\n  Finleyson, J., I, 314, _314_.\n  Flamsteed, I, _87_, 309; II, 45, 143, 302, 306.\n  Fletcher, I, 378.\n  Fludd, II, _318_.\n  Fly-leaf Paradox, II, 264.\n  Folkes, M., I, _136_; II, 301.\n  Fontenelle, I, _103_.\n  Forbes, D., I, _237_.\n  Forman, W., I, 296, _296_, 306.\n  Forster, T. I. M., I, 320, _320_.\n  Foscarini, I, _90_.\n  Foster, S., II, _310_.\n  Fourier, II, _66_.\n  Fox, G., I, _397_.\n  Francis, P., II, _96_.\n  Francoeur, I, _365_.\n  Frankland, W. B., I, 230, 287.\n  Franklin, J., II, _265_.\n  Freedom of opinion, Growth of, I, 265.\n  Freher, A., II, 319.\n  French academy on circle squaring, I, 163.\n  Frend, W., I, _196_, 196, 206, 208, 252.\n  Fresnel, II, _48_.\n  Fromondus, I, _74_, 74, 99.\n  Frost, I. and J., I, 394.\n  Fry, Elizabeth, I, 224.\n  Fuller, T., I, _86_.\n  Fulton, R., I, _148_.\n\n  Gadbury, J., I, _115_, 115.\n  Galbraith, J. A., II, 372.\n  Galileo, I, 5, 6, 32, _76_, 82, 83, 96, 122, 381.\n  Galle, J. G., I, _386_; II, 7.\n  Galloway, I, _56_, 57; II, 143.\n  Gamblers, I, 280.\n  Garrick, I, 21.\n  Gascoigne, W., II, _299_.\n  Gassendi, I, _107_.\n  Gauss, I, 86, 107, 310.\n  Gemistus, G., I, _188_.\n  Gentleman's Monthly, Miscellany, I, 208.\n  Gephryander. (_See Salicetus._)\n  Gergonne, I, _336_.\n  Ghetaldi, I, _83_; II, 59.\n  Ghost paradox, II, 47.\n  Giddy (Gilbert), II, _174_.\n  Gilbert, Davies, II, 66, _174_.\n  Gilbert, William, I, 6, _68_, 68, 76.\n  Gillot, II, _315_.\n  Glazier (Glazion), II, 7.\n  Godwin, F., I, _103_.\n  Godwin, W., I, _174_.\n  Golius, I, _106_.\n  Gompertz, B., I, _378_.\n  Goulburn, I, _288_.\n  Goulden, S., II, 88.\n  Graham, I, 24.\n  Grandamicus, I, _104_, 104.\n  Granger, J., I, _156_.\n  Grant, A. R., II, 131.\n  Grant, R., I, _392_; II, 131.\n  Grassi, O., I, _262_.\n  Grassini, I, _231_.\n  Graunt, J., I, 113, _114_, 154.\n  Gravity, I, 151, 244, 348, 353.\n  {380}\n    --Newton's apple, I, 136.\n  Greek numerals, II, _77_.\n  Greene, R., I, _135_, 135.\n  Greenhill, Sir G., I, 136.\n  Greenwich observatory,  I, 87.\n  Gregg, T. D., II, 75, _75_.\n  Gregorian Calendar, I, 363.\n  Gregory, D., I, _66_; II, 301.\n  Gregory, J., I, _118_, 118, 207; II, 302.\n  Gregory O., II, _71_.\n  Gregory, Pope, I, 362.\n  Grevil, I, _202_.\n  Grey, C., (2d Earl), I, _315_; II, 247.\n  Grosart, I, _141_, 141, 145.\n  Grove, W. R., II, _320_.\n  Gruber, II, _193_, 282.\n  Gruenberger, I, _70_.\n  Grynaeus, I, _66_.\n  Guaricus, I, _43_.\n  Guillim, J., II, _28_.\n  Guldin, I, _83_.\n  Gumpach, Von, II, 137, _137_.\n  Gunning, H., I, _198_.\n  Gurney. (_See Fry, E._)\n  Guthrie, W., I, _395_.\n\n  Hailes, J. D., II, 135, _135_.\n  Hailesean system of astronomy, II, 135.\n  Hale, M., I, _123_, 123.\n  Hales, S., I, _123_.\n  Hall, B., II, _181_.\n  Hallam, I, 159.\n  Halley, I, 24, _124_, 311; II, 301, 332.\n  Halliwell-Phillips, II, _148_, 296.\n  Hamilton, W., I, _112_, 117, 331, 335, 339, 341, 342; II,\n      52, 53, 111.\n  Hamilton, W. Rowan, I, _332_; II, 104, 256, 343.\n  Hanover, King of, I, 201.\n  Hardy, C., I, _298_.\n  Hardy, T., I, _178_.\n  Harriot, T., II, _302_.\n  Harvey, I, _76_, 78; II, 201.\n  Hauff, I, _230_.\n  Haughton, S., II, 372.\n  Hauksbee, F., I, _156_.\n  Hayes, C., I, _132_, 132.\n  Heath, D. D., I, _76_.\n  Heinfetter, H., II, 94, _94_.\n  Helmont, J. B. van, I, _125_.\n  Henson, II, 8.\n  Heraclitus, II, _34_.\n  Herbart, J. F., I, 253, _253_; II, 78.\n  Herigone, II, _59_.\n  Herschel, J., I, _80_, 299, 326, 383, 386; II, 88, 95, 181,\n      255, 261, 262.\n  Herschel, W., I, _81_, 151, 192, 225, 233, 299; II, 288, 348.\n  Heywood, F., II, _49_.\n  Hicks, J. P., II, _67_.\n  Higgins, G., I, _257_, 274.\n  Hilarius, Pope, I, _359_.\n  Hill, J., I, 21, 22, 23, 24.\n  Hill, Rev. R., I, _192_.\n  Hill, Sir R., I, _165_, 232.\n  Hind, J. R., I, _384_.\n  Hippocrates, II, _59_.\n  Hoax, An interesting, I, 163.\n    --Lunar Caustic, I, 288.\n    --Moon (Herschel), I, 326; II, 131.\n  Hobbes, I, _105_, 109, 143, 144; II, 80.\n  Hobhouse, J. C., II, _126_.\n  Hodder, J., II, _265_.\n  Hodge, C. B., I, 114.\n  Hodges, W., I, 237.\n  Hoffmann, J. J., II, _282_.\n  Hoffmann, J. J. I. von, I, _230_.\n  Holloway, B., I, _237_.\n  Holmes, O. W., I, 109.\n  Holyoake, G. J., I, _399_, 399.\n  Hone, W., I, 124, 180, 184, 185.\n  Hook, T. E., II, _261_.\n  Hooke, I, _77_; II, 300.\n  Hooker, R., II, _201_.\n  Hopkins, J., II, 41.\n  Horace, I, 40.\n  Horne, G., I, _152_, 152, 154, 155, 236.\n  Horne, J., I, _178_.\n  Horner, L., I, _176_.\n  Horner, W. G., II, _66_, 151, 187.\n  Houlston, W., II, 156, _156_.\n  Howard, E., I, 131.\n  Howison, W., I, 256, _256_.\n  Howitt, W., II, 193, _193_.\n  Howley, I, 63.\n  Hulls, I, _147_, 147; II, 8.\n  Hume, J., I, _352_; II, 174.\n  Husain Rifki, II, 16.\n  Hussein Effendi, II, 15.\n  Hutchinson, J., I, 154, _154_.\n  Hutton, C., I, _153_, 161; II, 303, 340.\n  Huyghens, I, _100_, 133; II, 300.\n\n  Imaginary numbers, II, 186.\n  Impalement by request, II, 133.\n  Inaudi, I, 86.\n  Index Expurgatorius, I, 90.\n  {381}\n  Infant prodigies, I, 86.\n  Inglis, J. B., II, _52_.\n  Inglis, R. H., I, _352_.\n  Ingliz Selim Effendi, II, 15.\n  Innocent I., I, _359_.\n  Irving, E., II, _54_.\n  Ivory, J., II, 142, _142_.\n\n  Jabir ben Aflah, II, _59_.\n  Jack, R., I, 149.\n  Jacotot, J., I, 278, _278_.\n  Jameson, Mrs., II, _63_.\n  Jeffreys, G., I, _183_.\n  Jenner, E., II, _205_.\n  Jesuit contributions, I, 164.\n  Johnson, H. C., I, 350.\n  Johnson, S., I, 20, _190_, 259; II, 117.\n  Johnston, W. H., II, 67.\n  Jombert, I, _161_.\n  Jonchere, I, _146_, 146.\n  Jones, W., I, _135_; II, 298, 301.\n  Jones, Rev. W., I, _237_.\n  Jonson, B., I, 13.\n  Journals, Three classes of, II,  144.\n\n  Kantesian Jeweler,  I, 258.\n  Karsten, I, _230_.\n  Kaestner, I, _43_, 110, 112.\n  Kater, I, 11.\n  Keckermann, I, 3.\n  Keill, J., II, _302_.\n  Kepler, I, 52, _76_, 82, 381; II, 166.\n  Kerigan, T., I, _308_, 353.\n  Keroualle, De, II, 50.\n  Kersey, I, 107.\n  King, Wm., I, _246_.\n  Kircher, Adolphe, I, 229.\n  Kircher, Athanasius, I, _103_.\n  Kirkringius, T., I, 125, _125_.\n  Kittle, I, 236.\n  Klein, F., II, 367.\n  Knight, C., II, _109_, 280, 289.\n  Knight, G., I, 151, _151_.\n  Knight, R. P., II, _274_.\n  Knight, Wm., I, _97_.\n  Koenig, S., I, _150_.\n\n  Lacomme, I, 46.\n  La Condamine, II, _301_.\n  Lacroix, I, 41, 159, 207.\n  Lactantius, I, 33, _96_.\n  Lagrange, I, 221, _288_, 313, 382; II, 86.\n  Laing, F. H., II, _186_, 186.\n  Lalande, I, _159_.\n  Lamb, C., I, 178; II, 270.\n  Lambert, J. H., I, _336_; II, 214, 367.\n  Lambert, John, II, _309_.\n  Language, Test of, II, 327.\n  Lansbergius, I, _70_, 70.\n  Laplace, I, 24, _255_, 382; II, 1, 340.\n  Lardner, D., II, _253_.\n  Lardner, N., I, 14; II, _221_.\n  Laud, I, _145_.\n  Lauder, W., I, 297.\n  Laurent, P., I, _309_, 309.\n  Laurie, J., II, 4.\n  Laurie, P., II, _42_.\n  Laurus, I, 381.\n  Law, Edmund, I, _181_.\n  Law, Edward, I, _181_.\n  Law, W., I, 168, _254_; II, 317.\n  Le Coq, I, _86_.\n  Lee, R., I, _66_.\n  Lee, S., I, _131_.\n  Lee, W., I, 157.\n  Legate, I, _59_.\n  Legendre, I, _229_; II, 215, 367.\n  Legh, P., II, _68_, 83.\n  Leibnitz, I, 5, 7; II, 46.\n  Leo, St., I, _359_.\n  Leverrier, I, _43_, 82, 383, 386, 388, 390; II, 7, 135, 140,\n      303.\n  Lewis, G. C., II, 162, _162_.\n  Libri, I, _40_, 62; II, 295.\n  Lilius, Aloysius, I, 362.\n  Lilly, I, _115_; II, 302.\n  Lipen, M., I, _298_.\n  Little, J., I, 206.\n  Livingston, R., I, _148_.\n  Locke, J., I, _142_, 142, 144;\n    --and Socinianism, I, 142.\n  Locke, R., I, 146.\n  Locke, R. A., I, _326_; II, 86, 131.\n  Logan, W. E., I, _337_.\n  Logic, Formal, I, 158; II, 75.\n    --Has no paradoxes, I, 330.\n  London Mathematical Society, I, 383.\n  London, University of, I, 259; II, 71.\n  Long, G., II, _290_.\n  Long, J. St. J., II. _38_, 205.\n  Longitude problems, I, 132, 146, 249.\n  Longley, C. T., I, _325_.\n  Longomontanus, I, _105_, 105.\n  Lottery, I. 281.\n  Lovett, R., I, 165, _166_.\n  Lowe, R., II, _169_.\n  Lowndes, W. T., I. _402_.\n  Lubbock, J., I, _279_; II, 148.\n  {382}\n  Lucas, F., II, _28_.\n  Lucian, I, _102_.\n  Lunar Caustic Joke, I, 288.\n  Lunn, J. R., II, _66_.\n  Lydiat, T., II, _302_.\n  Lyndhurst, I, _198_.\n\n  Macclesfield, Earls of, I, 7; II, _296_, 301.\n  Macclesfield, Letters, II, 296.\n  MacElshender, II, 87.\n  Machin, J., II, _301_.\n  Mackey, John,  I, 349.\n  Mackey, S. A., I, _256_.\n  Maclear, T., II, _181_.\n  Macleod, H. D., II, 184, _184_.\n  Magic, I, 118.\n  Magna Charta, I, 25.\n  Magnus, I, 42.\n  Maitland, S., I, _63_, 163.\n  Malacarne, I, 119.\n  Malden, H., II, _162_.\n  Malius, II, _342_.\n  Mallemens, II, _333_.\n  Mankind gullible, I, 115.\n  Manning, H. E., (Card.), II, _233_.\n  Mansel, H. L., II, _162_.\n  Marcelis, J., I, _129_, 129.\n  Maret, II, _3_.\n  Margarita Philosophica. (_See Reisch._)\n  Marryat, Capt., II, _87_.\n  Marsh, H., I, _199_, 271.\n  Martin, B., I, _152_, 153.\n  Martin, R., II, _236_.\n  Maseres, F., I, _197_, 203.\n  Mason, M., II, _132_.\n  Mathematical Illustrations of Doctrine, II, 70;\n    --Psychology, I, 253;\n    --Society, I, 374, 376, 382;\n    --Theology, I, 149.\n  Mathematics, Condensed history of, II, 58.\n  Matter to Spirit, II, 194.\n  Maty, I, 23.\n  Maupertuis, II, _301_.\n  Maurice, F. D., II, _101_.\n  Maurolycus, I, _121_.\n  Maxwell, A., I, _102_.\n  Meadley, G. W., I, _223_.\n  Mechanics Magazine, II, 141, 145.\n  Medici, Cosmo de, II, _295_.\n  Medicine, Status of, I, 266.\n  Melanchthon, II, _323_.\n  Menestrier, I, _127_, 127.\n  Mercator, G., II, _92_.\n  Mercator's projection, I, 84.\n  Mersenne, I, _106_, 107; II, 295, 297.\n  Meslier, J., II, _195_.\n  Meteorologist, An early, I, 320.\n  Meteorology, I, 327.\n  Metius, A. and P., I, _52_, _99_, 99.\n  Meton, II, 167.\n  Metric System, Forerunner of, I, 171.\n  Meziriac, I, 161.\n  Milbanke, A. I., I, 225.\n  Mill, Jas., I, 260.\n  Miller, Joe, I, _182_.\n  Miller, S., I, 167.\n  Mills, Elizabeth, W., II, 7.\n  Milne, J., I, _286_.\n  Milner, I., I, _251_, 251.\n  Milner, J., II, _23_.\n  Milner's lamp, I, 252.\n  Milward, II, _250_.\n  Miracles _vs_. Nature, II, 6.\n  Mitchell, J., I, _242_.\n  Moliere, I, _232_.\n  Molina, A. C. de, I, _297_.\n  Mollendorff, von, II, _3_, 338.\n  Mondeux, I, 86.\n  Montague, C., II, _311_.\n  Montmort, P. R. de, II, _301_.\n  Montucla, I, 40, 45, 54, 65, 117, 120, 159, 163; II, 60.\n  Moon Hoax, I, 326; II, 131.\n  Moon, Nature of, II, 84;\n    --Rotation of, II, 4, 19, 84, 87.\n  More, Hannah, I, _189_, 192.\n  More, Henry, I, 123.\n  Moore, Dr. John, I, _190_.\n  Moore, Sir John, I, _190_.\n  Morgan, S., I, 6.\n  Morgan, T., I, 191.\n  Morgan, W., I, _223_, 224.\n  Morhof, I, _61_.\n  Morin, I, _99_, 99.\n  Morinus, J. B., I, 149.\n  Morland, S., II, _302_.\n  Mormonism, II, 69.\n  Morrison, R. J., I, _321_; II, 43.\n  Mose, H., II, _266_.\n  Mottelay, I, 68.\n  Motti, II, 60.\n  Mouton, I, _172_; II, 300.\n  Muggleton, I, 394, _395_.\n  Multiplication, Nature of, II, 251.\n  Murchison, R. I., I, _384_.\n  Murhard, I, _43_, 298.\n  {383}\n  Murphy, A., II, _308_.\n  Murphy, J. L., II, 54, _54_.\n  Murphy, P., I, _327_, 398.\n  Murphy, R., I, 349, _349_.\n  Murray, J., I, _186_; II, 145.\n  Murray, L., II, _326_.\n  Murray, Mungo, II, 310.\n  Musgrave, T., I, _324_.\n  Mydorge, I, _298_.\n  Mystrom, J. W., II, 182.\n  Mythological paradoxes, I, 256.\n\n  Names of Religious Bodies, II, 22.\n  Napier, J., I, 5, 66, _67_, 82.\n  Napoleon, Doubts as to, I, 246.\n  Nautical Almanac, I, 300; II, 147.\n  Neal, I, _98_.\n  Negative numbers, I, 196, 203.\n  Neile, W., II, _190_.\n  Neptune, Discovery of, I, 387; II, 140. (_See Adams, Leverrier._)\n  Nesse, C, I, _128_, 128.\n  Newcomb, S., I, 162.\n  Newcomen, T., I, _147_.\n  Newton, Sir Isaac, I, 5, 6, 8, 24, 39, 84, 88, 130,\n      136, 139, 144, 145, 148, 152, 154, 155, 162, 165,\n      167, 197, 225, 237, 242, 257, 282, 296, 297, 309,\n      311, 382, 394, 395, 396, 397; II, 2, 70, 184, 297, _302_,\n      305.\n  Newton, John, II, _305_.\n  Nicene Creed, I, 371.\n  Nichol, J. P., II, _289_.\n  Nicholas. (_See Cusa._)\n  Nichols, J., I, _175_.\n  Nicolas, N. H., I, _354_.\n  Nicollet, I, _326_; II, 131.\n  Nicolson, W., I, _201_.\n  Nieuwentijt, II, _333_.\n  Nizzoli, M., II, 275.\n  Non-Euclidean geometry, II, 83.\n  Northampton, Marquis of (2d), II, _19_.\n  Novum Organum Moralium, II, 74.\n  Number, Mystery of, I, 55, 56, 169.\n  Number of the Beast (666), I, 55, 130, 272, 298, 352; II, 77,\n      159, 217, 218, 361, 373.\n  Numeral system, II, 68.\n  Nursery rhymes, II, 150.\n\n  Occam, Wm. of, II, _40_.\n  Odgers, N., II, 191, _191_.\n  Oinopides of Chios, II, _59_.\n  Oldenburgh, H., II, _300_, 302.\n  Orthodox Paradoxes, II, 363.\n  Orthography, Paradoxes of, II, 267.\n  Ortwinus, I, 319.\n  Oughtred, W., II, _298_, 303.\n  Owenson, I, _191_.\n  Ozanam, I, _161_, 312.\n\n  Pagi, I, 32.\n  Paine, T., I, 173, _173_, 271.\n  Paley, W., I, _222_; II, 226.\n  Palmer, C., I, 225.\n  Palmer, H., I, _141_, 141, 145.\n  Palmer, J., II, _253_.\n  Palmer, T. F., II, _254_.\n  Palmer, W., II, _37_.\n  Palmerston, Viscount (3d), I, _290_, 352.\n  Palmezeaux, I, 167.\n  Panizzi, A., I, _151_.\n  Papist, II, 26.\n  Paracelsus, II, 322.\n  Paradox defined, I, 2, 31.\n  Paradox, religious, I, 236.\n  Paradoxers in general, II, 352.\n  Parallels, Theory of, I, 229, 344.\n  Pardies, I. G., II, _300_.\n  Park, Mungo, II, _91_, 132.\n  Parker, F., II, _94_.\n  Parker, G. (Earl of Macclesfield), II, _296_.\n  Parr, S., I, 173, _173_, 175, 176, 184.\n  Parsey, I, 293, _293_.\n  Partridge, J., I, _305_.\n  Pasbergius, I, 381.\n  Pascal, I, 39, 119, 122, _220_, _221_; II, 73.\n  Pascal's Hexagram, I, 221.\n  Passot, I, 279, _279_.\n  Passover, I, 358, 372.\n  Patriotic paradox, I, 231.\n  Paucton, I, _172_.\n  Paulian, I, 165, _165_.\n  Peacock, Geo., I, _196_, 350.\n  Peacock, T. L., I, _190_, 340.\n  Pearce, A. J., II, 43.\n  Pearne, T., I, _239_.\n  Peel, Sir R., I, 290, _352_.\n  Peel, W. Y., I, _290_.\n  Pelerin, J., II, _324_.\n  Pell, J., I, _105_, 105, 107; II, 300, 302, 312.\n  Pepys, I, _113_, 114.\n  Perigal, H., II, 19, _20_.\n  {384}\n  Perpetual motion, I, 118, 348; II, 55, 138.\n  Perspective, New theory of, I, 293.\n  Peters, W., II, 11, 315.\n  Petitioning Comet, I, 127.\n  Petrie, W. M. F., I, _328_.\n  Petty, I, _114_; II, 300.\n  Philalethes, Eirenaeus, I, _125_, 125, 126.\n  Philalethes, Eugenius, I, _255_.\n  Phillips, R., I, 242, _242_, 245.\n  Philo of Gadara, I, 40, _40_.\n  Philosopher's stone, I, 118, 125.\n  Philosophical atheists, II, 1.\n  Philosophy and Religion, II, 37.\n  Phonetic spelling, II, 81.\n  [pi], values of, I, 11, 43, 45, 46, 52, 69, 100, 110,\n      129, 135, 146, 245, 283, 284, 294, 347, 348, 349,\n      350; II, 60, 63, 105, 110, 118, 135, 156, 209, 279, 315, 316.\n  Pighius, I, _372_.\n  Pike, S., I, 236, _236_.\n  Pindar, P., II, _272_.\n  Piozzi, Mrs., I, _235_; II, 272.\n  Piscator, B., II, 25.\n  Pitman, F., II, 81, _81_.\n  Place, F., I, _199_.\n  Planets inhabitable, I, 100, 102.\n  Plato, I, 5.\n  Platt, H., I, _126_, 126.\n  Playfair, J., I, _233_.\n  Pletho, G., I, _188_.\n  Pliny, II, 280.\n  Ploucquet, I, _336_, 337.\n  Poe, E. A., II, 132.\n  Poincare, I, 136.\n  Poisson, I, _292_; II, 2.\n  Pollock, J. F., II, _174_.\n  Pons, II, _45_.\n  Pope, Wm., I, 277, _277_.\n  Porta, I, _68_, 68, 83.\n  Porteus, B., I, _193_, 203.\n  Porteus, H. F. A., II, 157, _157_.\n  Porus, I, 44.\n  Powell, Baden, II, _267_.\n  Powell, W. S., I, _222_.\n  Pratt, H. F. A., II, 157, _157_.\n  Pratt, O., II, _69_.\n  Predaval, Count de, I, _348_.\n  Prescot, B., I, 270, _270_, 278.\n  Prester John, I, 70, _71_, 152.\n  Price, R., I, _223_.\n  Probability, Discourse on, I, 279.\n  Proclus, I, 188, _188_.\n  Prodigies, Youthful, I, 219, 332.\n  Pronunciation, II, 330.\n  Protestant and Papal Christendom, II, 33.\n  Protimalethes, II, 6.\n  Ptolemy, I, 5, 33, _380_.\n  Pullicino, II, 61, _61_.\n  Pusey, I, _64_.\n  Pyramids, The, I, 328; II, 95, 136.\n  Pythagoras, II, _59_.\n\n  Quadrature problem. (_See Squaring the circle._)\n  Quarles, F., II, _277_.\n  Quintilian, II, 280.\n  Quotem, C., I, 399.\n\n  Rabelais, I, _102_.\n  Rainbow Paradox, II, 334.\n  Ramachandra, Y., I, _374_.\n  Ramchundra, I, 374.\n  Ramus, I, 5.\n  Recalcati, II, 208, 314.\n  Recorde, R., II, _328_.\n  Reddie, Jas., II, 183, _183_, 344, 360.\n  Reeve, J., I, _395_.\n  Regiomontanus, I, _48_, 360.\n  Reisch, I, _45_; II, 281.\n  Religion and Philosophy, II, 37.\n  Religious bodies, Names of, II, 22;\n    --customs, Attacks on, I, 177;\n    --Insurance, I, 345;\n    --Paradox, I, 236;\n    --Tract society, I, 192.\n  Remigius, I, _50_.\n  Reuchlin, J., II, _323_.\n  Revelations, Napier on, I, 66.\n  Revilo, (O. Byrne), I, 241, 329, _329_.\n  Reyneau, C. R., II, _301_.\n  Rheticus, I, _69_; II, 372.\n  Rhonius, II, 300.\n  Ribadeneira, P. de, II, _62_.\n  Riccioli, I, _96_.\n  Richards, G., II, _270_.\n  Rigaud, J., II, _299_.\n  Rigaud, S. J., II, _299_.\n  Rigaud, S. P., I, _140_; II, 298, 313.\n  Ringelbergh, J. S., II, _281_.\n  Ripley, G., I, _126_, 126.\n  Ritchie, W., I, 295, _295_.\n  Ritterhusius, I, _60_.\n  Rive, J.-J., I, _160_.\n  Robertson, Jas., I, _237_.\n  Roberval, I, _105_, 122.\n  {385}\n  Robinson, B., I, _148_, 148.\n  Robinson, H. C., I, _314_; II, 52, 275.\n  Robinson, R., I, _177_.\n  Robinson, T. R., II, _181_.\n  Roblin, J., II, 136.\n  Rogers, S., II, _260_.\n  Roget, P. M., I, _398_.\n  Roomen, A. van, I, _110_.\n  Ross, J. C., I, _303_.\n  Rosse, I, 26.\n  Rossi, G., I, 231, _231_.\n  Rotation of the Moon, II, 4, 19.\n  Rough, W., I, 198.\n  Rowning, J., I, _155_.\n  Royal Astronomical Society, I, 27;\n    --Forerunner of, I, 374.\n  Royal Society, I, 21, 22, 24-30, 56, 57, 136, 153, 163,\n      164, 165.\n  Rudio, I, 159; II, 367.\n  Rudolff, C., II, 373.\n  Russell, Earl (1st), I, _296_.\n  Rutherford, W., II, _109_.\n\n  Sabatier, A., II, _267_.\n  Sabellius, I, _241_.\n  Sacrobosco, I, _360_.\n  Sadler, T., I, _238_, 241.\n  Saint-Martin, I, 167, _168_, 206.\n  St.-Mesmin, M. de., I, 280.\n  St. Vincent, G. de., I, _110_, 117.\n  St. Vitus, Patron of Cyclometers, II, 60.\n  Sales, de, I, 167.\n  Salicetus, I, 64.\n  Salisbury, Earl of (1st), II, _330_.\n  Salmasius, Claudius, II, _168_.\n  Salusbury, Hester, I, _235_.\n  Sanchez, Petro, I, 229, _229_.\n  Sanders, W., I, 207.\n  Sanderson, R., I, _135_.\n  Sara, R., I, _297_.\n  Saunderson, N., I, _377_; II, 301.\n  Scaliger, I, _44_, 110, 111, 112, 113; II, 238.\n  Scevole de St. Marthe, I, 113.\n  Schooten, Van, II, _59_.\n  Schopp, I, _60_.\n  Schott, I, _64_; II, 64.\n  Schumacher, H. C., I, _107_; II, 297.\n  Schwab, I, _230_.\n  Scientific paradoxes, I, 232.\n  Scott, Michael, I, _38_.\n  Scott's Devils, I, 38.\n  Scott, W., I, 20, 27, 38, 39, 155, _191_.\n  Scripture and Science, II, 261.\n  Search, John, I, 247.\n  Selden, J., II, _250_.\n  Senarmont, II, _48_.\n  Serres, De, II, _60_.\n  Shaftesbury, Earl of, II, _181_.\n  Shakespeare, I, 13.\n  Shanks, II, _63_, 65, 109.\n  Shaw, P., I, _142_.\n  Sheepshanks, J., I, _147_.\n  Sheepshanks, R., I, _290_.\n  Shelley, I, 174.\n  Shepherd, S., I, _124_.\n  Sherburne, E., II, _295_.\n  Sheridan, R. B., I, _175_.\n  Sheridan, T., I, _175_.\n  Shoberl, F., II, _270_.\n  Shrewsbury, I, _108_.\n  Siddons, Mrs., I, 189.\n  Simms, W., I, _152_.\n  Simplicius, II, _164_.\n  Simpson, T., I, 377; II, 304.\n  Simson, R., I, _197_, 202, 233.\n  Sinclair, G., I, _207_.\n  Slander Paradoxes, II, 138.\n  Sloane, I, 24.\n  Sluse, R. de, I, _118_, 118; II, 300.\n  Smith, Adam, II, _112_.\n  Smith, Jas., I, _46_; II, 103, _103_, 154, 236, 237, 238, 241, 336,\n      360.\n  Smith, Jas., II, _217_.\n  Smith, Jas. (Shepherd), II, _55_, 193.\n  Smith, Joseph, II, _69_.\n  Smith, Richarda, I, _242_.\n  Smith, Thomas, I, 346, _346_.\n  Smith, Wm., II, _152_.\n  Smyth, C. P., I, _328_; II, 65.\n  Snell, I, _75_, 75.\n  Socinianism, I, 142, 143.\n  Socinus, I, 3, _143_.\n  Socrates Scholasticus, I, _358_.\n  Sohncke, L. A., II, _131_.\n  Somerville, Mrs., I, _242_.\n  South, J., II, _181_.\n  Southcott, Joanna, II, _58_, 97, 239.\n  Spearman, R., I, _237_.\n  Speculative thought in England, I, 374.\n  Spedding, I, _76_, 82, 142.\n  Speed, J., I, _201_.\n  Speke, I, _70_.\n  Spelling, phonetic, II, 81.\n  Spence, W., I, _231_, 231.\n  Spencer, Earl (3d), II, _9_.\n  {386}\n  Spinoza, I, 3, _37_.\n  Spiritualism, II, 47, 55, 207.\n  Spurius Cassius Viscellinus, II, _342_.\n  Spurius Maelius, II, _342_.\n  Squaring the circle, I, 8, 42, 44, 46, 47, 50, 52, 53,\n      69, 70, 75, 109, 117, 119, 129, 135, 146, 149,\n      159, 163, 164, 347, 348, 374; II, 10, 11, 60, 105, 154,\n      156, 208, 278, 314.\n  Staeckel, I, 230.\n  Stanhope, P. D., (Earl of Chesterfield), II, _298_.\n  Stapulensis, I, _44_; II, 324.\n  Star polygons, I, 229.\n  Starkie, G., I, _126_, 126.\n  Statter, D., II, 80.\n  Steamship suggested, I, 147.\n  Steel, Jas., II, 68.\n  Stenography, II, 81.\n  Stephens, I, _44_; II, 324.\n  Stephenson, G., II, _138_.\n  Stephenson, R., II, _138_.\n  Stevin, I, _83_, 313; II, 59.\n  Stewart, D., II, _53_.\n  Stewart, R., I, _186_.\n  Stifel, M., II, _373_.\n  Strafford, Earl of, I, _240_.\n  Stratford, W. S., I, _300_.\n  Street, T., I, _124_.\n  Stukely, W., I, _236_.\n  Suffield, G., II, _66_.\n  Suidas, II, _29_.\n  Sumner, C. R., I, _324_.\n  Sumner, J. B., I, _324_.\n  Sun as an electric space, II, 41.\n  Supernatural, The, II, 193.\n  Suvaroff, II, _85_.\n  Swastika, II, 231.\n  Swedenborg, E., I, _255_.\n  Swift, I, 19, 133.\n  Sylvester, J. J., II, _336_.\n  Symington, W., I, _148_.\n  Symons, II, 4, 5, 20, 84, 85.\n  Sympathetic powder, I, 108.\n  Synesius, I, 125.\n\n  Talbot, G., I, _22_, _108_.\n  Talbot's powder, I, 108.\n  Tartaglia, II, 59.\n  Tasse, I, _106_.\n  Tate, J., I, _199_.\n  Tauler, J., II, _322_.\n  Taylor, Brook, II, _301_.\n  Taylor, John, I, _352_; II, 95.\n  Taylor, Robt., I, _270_.\n  Taylor, T., I, 188, _188_.\n  Teissier, I, _113_.\n  Temple, H. J., I, 290.\n  Tenterden, Chief Justice, I, _181_.\n  Thales, II, _59_, 83.\n  Theism independent of Revelation, I, 399.\n  Thelwall, J., I, _178_.\n  Theodoretus, I, _358_.\n  Theological Paradoxes, I, 316.\n  Theology, Mathematical, I, 129, 149.\n  Theophrastus, II, _167_.\n  Thiebault, II, _3_, 338.\n  Thom, D., II, _226_, 240.\n  Thom, J. H., II, _226_.\n  Thompson, P., I, _7_.\n  Thompson, T. P., I, _252_, 287, 344; II, 83, 185.\n  Thomson, Dr., I, 21.\n  Thomson, W., I, _325_.\n  Thorn, W., II, 158, _158_, 360.\n  Thorndike, H., II, _313_.\n  Thrale, Mrs., I, _235_.\n  Thurlow, Baron, I, _222_.\n  Thyraeus, I, 50.\n  Tides, New theory of, I, 393.\n  Tombstones of mathematicians, I, 106.\n  Tonal System, II, 182.\n  Tooke, H., I, _178_.\n  Torriano, E., I, 250.\n  Towneley, II, 300.\n  Townley, C., II, _300_.\n  Trisection problem, I, 118; II, 10, 12, 13, 15.\n  Troughton, I, _152_.\n  Turnor, E., I, _137_.\n  Tycho Brahe, I, 5, _76_, 381; II, 302, 335.\n\n  Upton, W., II, 12, _12_, 15.\n  Ursus, I, _52_.\n\n  Valentine, B., I, _125_, 125.\n  Van Ceulen, I, 52, 70, 100.\n  Van de Weyer, I, _313_.\n  Van Etten, I, _161_.\n  Van Helmont, I, _125_, 125.\n  Van Roomen, I, _110_.\n  Van Schooten, II, _59_.\n  Vaughan, T., I, _255_.\n  Victorinus, I, _359_.\n  Viete, I, _51_; II, 210, 295.\n  Virgil, St., I, 32, _33_, 34, 99.\n  {387}\n  Virginia, University of, I, 233.\n  Viscellinus, II, _342_.\n  Vitruvius, II, _281_.\n  Vivian, T., I, 172, _172_.\n  Vogel, A. F., I, 373.\n  Voltaire, I, 103, 165, 166, 167, 168, 248; II, 268.\n  Von Gumpach, II, 137, _137_.\n  Von Hutten, I, 318.\n  Von Wolzogen. (_See Wolzogen._)\n  Vyse, R. W. H., I, _328_.\n\n  Walker, W. E., II, _316_.\n  Walkingame, F., II, _173_.\n  Wallich, N., II, _14_.\n  Wallis, J., I, 107, 109, 110; II, 299, 313.\n  Walpole, I, _23_, 131.\n  Walsh, John, I, 260, _260_; II, 157.\n  Wapshare, J., II, _230_.\n  Warburton, H., I, _349_.\n  Warburton, Wm., I, _55_, 112; II, 174.\n  Ward, S., II, _299_.\n  Waring, E., I, _203_, 222.\n  Warner, W., II, _302_, 312.\n  Warren, S., II, _340_.\n  Watkins, J., II, _270_.\n  Watson, Bp., I, _223_.\n  Watt, R., I, _102_, 402.\n  Watts, I., II, 18.\n  Weddle, T., II, _187_.\n  Wentworth, Thos., I, _240_.\n  Wharton, I, 115.\n  Whately, R., I, 246, _246_, 324.\n  Whately's Paradox, I, 246.\n  Whewell, I, _101_, 101, 273, 314, 380; II, 104, 246, 247.\n  Whigs, II, 22.\n  Whiston, J., I, _147_.\n  Whiston, W., I, 133, _133_, 146, 156, 311.\n  White, H. K., II, _271_.\n  White, J. B., I, 248.\n  White, R., I, 11.\n  Whitford, I, 105.\n  Whitworth, W. A., II, _344_.\n  Whizgig, On the, I, 254.\n  Wightman, I, 59.\n  Wilberforce, W., II, _236_.\n  Wilkins, J., I, 96, _100_, 116, 226.\n  Williams, J. B., I, _378_.\n  Williams, T., I, 171, _171_.\n  Wilson, Sir J., I, _221_.\n  Wilson, J. M., II, _344_.\n  Wilson, R., II, 7, _7_.\n  Wilson's Theorem, I, _222_.\n  Wingate, E., II, _308_.\n  Winter, I, 46.\n  Wirgman, T., I, 258, _258_.\n  Wiseman, N. P. S., II, _26_, 61, 294.\n  Wolcot, J. (Peter Pindar), II, _272_.\n  Wollstonecraft, I, 173, _173_.\n  Wolzogen, I, _106_.\n  Wood, A., I, _98_.\n  Wood, John, I, _233_.\n  Wood, Wm., I, 246, _246_.\n  Woodley, W., I, 307, _307_.\n  Wordsworth, II, 273.\n  Wright, E., I, 84.\n  Wright, T., I, 151, _151_, 152, 153.\n  Wright, W., II, 9.\n  Wronski, I, 249, _250_.\n  Wrottesley, J. (Baron), II, _181_.\n\n  Young, B., II, _69_.\n  Young, J. W. A., II, 367.\n  Young, T., I, 24, 30, _250_.\n  Youthful Prodigies, I, 219.\n  Yvon, I, _297_.\n\n  Zach, von, II, _45_, 196.\n  Zachary, Pope, I, 32, 34.\n  Zadkiel, I, _321_; II, 43.\n  Zetetic Astronomy, II, 88.\n  Zodiac, II, 136.\n  Zytphen, II, _335_.\n\n       *       *       *       *       *\n\n\nNotes\n\nTranscriber's note: References to Notes in Volume I are shown as in the\nprinted book, with the resequenced footnote numbers in the Project\nGutenberg Edition (EText-No. 23100) added thus {123}.\n\n[1] See Vol. I, page 255, note 6 {584}.\n\n[2] \"I have no need for this hypothesis.\"\n\n[3] \"Ah, it is a beautiful hypothesis; it explains many things.\"\n\n[4] \"What we know is very slight; what we don't know is immense.\"\n\n[5] Brewster relates (_Life of Sir Isaac Newton_, Vol. II, p. 407) that, a\nshort time before his death, Newton remarked: \"I do not know what I may\nappear to the world, but to myself I seem to have been only like a boy\nplaying on the seashore, and diverting myself in now and then finding a\nsmoother pebble or a prettier shell than ordinary, whilst the great ocean\nof truth lay all undiscovered before me.\"\n\n[6] See Vol. I, p. 292, note 1 {632}.\n\n[7] \"What is all that!\"\n\n[8] \"I have some good news to tell you: at the Bureau of Longitudes they\nhave just received a letter from Germany announcing that M. Bessel has\nverified by observation your theoretical discoveries on the satellites of\nJupiter.\"\n\n[9] \"Man follows only phantoms.\"\n\n[10] See Vol. I, page 382, note 13 {786}.\n\n[11] Dieudonne Thiebault (1733-1807) was a Jesuit in his early life, but he\nleft the order and took up the study of law. In 1765 he went to Prussia and\nbecame a favorite of Frederick the Great. He returned to France in 1785 and\nbecame head of the Lycee at Versailles.\n\n[12] _Memories of Twenty Years of Residence in Berlin._ There was a second\nFrench and an English edition in 1805.\n\n[13] Richard Joachim Heinrich von Mollendorff (1724-1816) began his career\nas a page of Frederick the Great (1740) and became field marshal (1793) and\ncommander of the Prussian army on the Rhine (1794).\n\n[14] Hugues Bernard Maret (1763-1839) was not Duc de Bassano in 1807, this\ntitle not being conferred upon him until 1809. He was ambassador to England\nin 1792 and to Naples in 1793. Napoleon made him head of the cabinet and\nhis special confidant. The Bourbons exiled him in 1816.\n\n[15] Denis Diderot (1713-1784), whose _Lettre sur les aveugles_ (1749)\nintroduced him to the world as a philosopher, and whose work on the\n_Encyclopedie_ is so well known.\n\n[16] \"Sir, (a + b^{n}) / n = x, whence God exists; answer!\"\n\n[17] This was one James Laurie of Musselburgh.\n\n[18] Jelinger Cookson Symons (1809-1860) was an office-holder with a\ndecided leaning towards the improvement of education and social conditions.\nHe wrote _A Plea for Schools_ (1847), _The Industrial Capacities of South\nWales_ (1855), and _Lunar Motion_ (1856), to which last work the critic\nprobably refers.\n\n[19] \"Protimalethes\" followed this by another work along the same line the\nfollowing year, _The Independence of the Testimony of St. Matthew and St.\nJohn tested and vindicated by the theory of chances_.\n\n[20] Wilson had already taken up the lance against science in his\n_Strictures on Geology and Astronomy, in reference to a supposed want of\nharmony between these sciences and some parts of Divine Revelation_,\nGlasgow, 1843. He had also ventured upon poetry in his _Pleasures of\nPiety_, Glasgow, 1837.\n\n[21] Mrs. Borron was Elizabeth Willesford Mills before her marriage. She\nmade an attempt at literature in her _Sibyl's Leaves_, London (printed at\nDevonport), 1826.\n\n[22] See Vol. I, page 386, note 10 {801}.\n\n[23] See Vol. I, page 43, notes 7 {32} and 8 {33}.\n\n[24] His flying machine, designed in 1843, was one of the earliest attempts\nat aviation on any extensive scale.\n\n[25] Erasmus Darwin (1731-1802) was the grandfather of Charles Darwin. The\nwork here mentioned had great influence, being translated into French,\nPortuguese, and Italian. Canning parodied it in his _Loves of the\nTriangles_.\n\n[26] See Vol. I, page 147, note 1 {312}.\n\n[27] The notes on this page were written on the day of the funeral of\nWilbur Wright, June 1, 1912, the man who realized all of these prophecies,\nand then died a victim of municipal crime,--of typhoid fever.\n\n[28] John Charles, third Earl Spencer (1782-1845), to whose efforts the\nReform Bill was greatly indebted for its final success.\n\n[29] This was published in London in 1851 instead of 1848.\n\n[30] This appeared in 1846.\n\n[31] This was done in _The Circle Squared_, published at Brighton in 1865.\n\n[32] It first appeared in 1847, under the title, _The Scriptural Calendar\nand Chronological Reformer, 1848. Including a review of tracts by Dr.\nWardlaw and others on the Sabbath question. By W. H. Black._ The one above\nmentioned, for 1849, was printed in 1848, and was also by Black\n(1808-1872). He was pastor of the Seventh Day Baptists and was interested\nin archeology and in books. He catalogued the manuscripts of the Ashmolean\nMuseum at Oxford.\n\n[33] William Upton, a Trinity College man, Dublin. He also wrote _Upton's\nPhysioglyphics_, London, 1844; _Pars prima. Geometria vindicata;\nantiquorumque Problematum, ad hoc tempus desperatorum, Trisectionis Anguli,\nCirculique Quadraturae, Solutio, per Eucliden effecta, London_ (printed at\nSouthampton), 1847; _The Uptonian Trisection_, London, 1866; and _The\nCircle Squared_, London, 1872.\n\n[34] For example, if [theta] = 90 deg. we should have 3 cos 30 deg. = 1\n+ [root](4 - sin^2 90 deg.), or 3. 1/2 [root]3 = 1 + [root]3, or\n1/2 [root]3 = 1.\n\n[35] Nathaniel Wallich (1786-1854) was surgeon at the Danish settlement at\nSerampore when the East India Company took over the control in 1807. He\nentered the British medical service and was invalided to England in 1828.\nHis _Plantae Asiaticae Rariores_ (3 vols., London, 1830-1832) was\nrecognized as a standard. He became vice-president of the Linnean Society,\nF. R. S., and fellow of the Royal Asiatic Society.\n\n[36] But if [theta] = 90 deg. this asserts that\n\n  cos 30 deg. = (sin 270 deg. . cos 225 deg. + sin^2 90 deg.\n  . sin 225 deg.) / [root](sin^2\n      270 deg. . cos^2 225 deg. + sin^{4} 90 deg. + sin 270 deg.\n      . sin 450 deg. . sin^2 90 deg.),\n\nor that\n\n  1/2 [root]3 = (-1 . (-1 /[root]2) + 1 . (-1/[root]2) / [root]1\n      . 1/2 + 1 - 1 . 1 . 1) = 0 / [root](1/2),\n\nso that De Morgan must have made some error in copying.\n\n[37] John Bonnycastle (died in 1821) was professor of mathematics at\nWoolwich. His edition of Bossut's _History of Mathematics_ (1803), and his\nworks on elementary mathematics were well known.\n\n[38] The bibliographies give Husain Rifki as the translator, a practical\ngeometry as the work, and 1802 as the date.\n\n[39] See Vol. I, page 309, note 2 {670}.\n\n[40] Probably in _The Improvement of the Mind_ which Isaac Watts\n(1674-1748) published in 1741. His _Horae Lyricae_ appeared in 1706, and\nthe _Hymns_, by which he is still well known, in 1707.\n\n[41] Spencer Joshua Alwyne Compton, second Marquis of Northampton\n(1790-1851), was a poet, a scientist, and a statesman. He was president of\nthe Royal Society from 1838 to 1849.\n\n[42] Besides the writings here mentioned Perigal published a work on\n_Geometric Maps_ (London, 1853), and _Graphic Demonstrations of Geometric\nProblems_ (1891).\n\n[43] See Vol. II, page 5, note 18.\n\n[44] James Ferguson (1710-1776) was a portrait painter, an astronomer, and\na popular writer and lecturer on various subjects.\n\n[45] In the old ballad of King Alfred and the Shepherd, when the latter is\ntempting the disguised king into his service, he says:\n\n \"Of whig and whey we have good store,\n  And keep good pease-straw fire.\"\n\n_Whig_ is then a preparation of milk. But another commonly cited derivation\nmay be suspected from the word _whiggamor_ being used before _whig_, as\napplied to the political party; _whig_ may be a contraction. Perhaps both\nderivations conspired: the word _whiggamor_, said to be a word of command\nto the horses, might contract into _whig_, and the contraction might be\nwelcomed for its own native meaning.--A. De M.\n\n[46] This was p. 147 in the first edition.\n\n[47] St. Augustine (354-430) was bishop of Hippo. His _Confessiones_, in\n13 books, was written in 397, and his _De Civitate Dei_ in 426.\n\n[48] \"He was wont to indulge in certain Punic subtleties lest he should\nweary the reader by much speaking.\"\n\n[49] John Milner (1751-1826), bishop of Castabala, a well-known\nantiquarian.\n\n[50] It will be said that when the final happiness is spoken of in \"sure\nand certain hope,\" it is _the_ Resurrection, generally; but when afterwards\napplication is made to the individual, simple \"hope\" is all that is\npredicated which merely means \"wish?\" I know it: but just before the\ngeneral declaration, it is declared that it _has_ pleased God of his great\nmercy to _take unto Himself_, the soul of our dear brother: and between the\n\"hopes\" hearty thanks are given that it _has_ pleased God to deliver our\ndear brother out of the miseries of this wicked world, with an additional\nprayer that the number of the elect may shortly be accomplished. All which\nmeans, that our dear brother is declared to be taken to God, to be in a\nplace not so miserable as this world--a description which excludes the\n\"wicked place\"--and to be of the elect. Yes, but it will be said again! do\nyou not know that when this Liturgy was framed, all who were not in the\nroad to Heaven were excommunicated burial service read over them. Supposing\nthe fact to have been true in old time, which is a very spicy supposition,\nhow does that excuse the present practice? Have you a right _always_ to say\nwhat you believe _cannot always_ be true, because you think it was once\n_always_ true? Yes, but, choose whom you please, you cannot be _certain_ He\nis _not_ gone to Heaven. True, and choose which Bishop you please, you\ncannot be demonstratively _certain_, he is _not_ a concealed unbeliever:\nmay I therefore say of the whole bench, _singulatim et seriatim_, that they\n_are_ unbelievers? No! No! The voice of common sense, of which common logic\nis a part, is slowly opening the eyes of the multitude to the unprincipled\nreasoning of theologians. Remember 1819. What chance had Parliamentary\nReform when the House of Commons thanked the Manchester sabre-men? If you\ndo not reform your Liturgy, it will be reformed for you, and sooner than\nyou think! The dishonest interpretations, by defence of which even the\nminds of children are corrupted, and which throw their shoots into\nliterature and commerce, will be sent to the place whence they came: and\nover the door of the established organization for teaching religion will be\nposted the following notice:\n\n \"Shift and Subterfuge, Shuffle and Dodge,\n  No longer here allowed to lodge!\"\n\nAll this ought to be written by some one who belongs to the Establishment:\nin him, it would be quite prudent and proper; in me, it is kind and\ncharitable.--A. De M.\n\n[51] But few do have access to it, for the work is not at all common, and\nthis Piscator is rarely mentioned.\n\n[52] This derivation has been omitted.--S. E. De M.\n\n[53] A blow for a blow. Roland and Oliver were two of the paladins of\nCharlemagne whose exploits were so alike that each was constantly receiving\ncredit for what the other did. Finally they met and fought for five days on\nan island in the Rhine, but even at the end of that period it was merely a\ndrawn battle.\n\n[54] \"In the name of the church.\"\n\n[55] \"From the chair,\" officially.\n\n[56] Nicholas Patrick Stephen Wiseman (1802-1865), whose elevation to the\narchbishopric of Westminster and the cardinalate (1850) led to the act\nprohibiting Roman Catholics from assuming episcopal titles in England, a\nlaw that was never enforced.\n\n[57] He was born in 1812 and was converted to Catholicism in 1839. He\nfounded the _Tablet_ in London in 1840, removing its office to Dublin in\n1849. He became M. P. in 1852, and at the time of his death (1855) he was\npreparing a memorial to the Pope asking him to annul the proclamation of an\nIrish bishop prohibiting his priests from taking part in politics.\n\n[58] John Guillim (1565-1621) was the first to systematize and illustrate\nthe whole science of heraldry. He published _A display of Heraldrie:\nmanifesting a more easie accesse to the knowledge thereof_ in 1610.\n\n[59] \"Faith.\"\n\n[60] \"Faithful.\"\n\n[61] \"For the faith vindicated.\"\n\n[62] The words are of the same root, and hence our word _fiddle_. Some\nsuppose this root means a _rope_, which, as that to which you trust,\nbecomes, in one divergence, confidence itself--just as a _rock_, and other\nwords, come to mean reliance--and in another, a little string.--A. De M.\n\n[63] The Greek lexicographer, a Christian, living after 1000 A. D. His\nlexicon was first printed at Milan in 1499.\n\n[64] _Skindapsos._\n\n[65] This was John William Burgon (1813-1888), Gresham professor of\ntheology (1867) and dean of Chichester. He was an ultra-conservative,\nopposing the revised version of the New Testament, and saying of the\nadmission of women to the university examinations that it was \"a thing\ninexpedient and immodest.\"\n\n[66] _Ekklesia_, or _ecclesia_.\n\n[67] _Ennomos ekklesia._\n\n[68] \"Without doubt I shall perish forever.\"\n\n[69] \"Every man is an animal.\" \"Sortes is a man.\" \"Sortes is an animal.\"\n\n[70] \"For a special purpose.\"\n\n[71] Heraclitus of Ephesus, the weeping philosopher, 6th century B. C.\n\n[72] Democritus, the laughing philosopher, founder of the atomistic theory,\n5th century B. C.\n\n[73] \"Ends to which.\"\n\n[74] \"Ends from which.\"\n\n[75] \"In just as many syllables,\" \"With just as many letters,\" \"In just as\nmany words.\"\n\n[76] \"I shall make a way,\" \"I shall find a way.\"\n\n[77] The notion that the Evil Spirit is a functionary liable to be\ndismissed for not attending to his duty, is, so far as my reading goes,\nutterly unknown in theology. My first wrinkle on the subject was the remark\nof the Somersetshire farmer upon Palmer the poisoner-- \"Well! if the Devil\ndon't take he, he didn't ought to be allowed to be devil no longer.\"--A. De\nM.\n\nWilliam Palmer (1824-1856) was a member of the Royal College of Surgeons\nand practised medicine at London. He was hanged in 1856 for having poisoned\na friend and was also suspected of having poisoned his wife and brother for\ntheir insurance money, besides being guilty of numerous other murders. His\ntrial was very much in the public attention at the time.\n\n[78] Advantages and dangers.\n\n[79] The old priory of St. Mary of Bethlehem in London, was used as an\nasylum for the insane. The name was corrupted to Bedlam.\n\n[80] Referring to the common English pronunciation of St. John, almost\nSinjin. John St. John Long (1798-1834), an Irishman by birth, practised\nmedicine in London. He claimed to have found a specific for rheumatism and\ntuberculosis, but upon the death of one of his patients in 1830 he was\ntried for manslaughter. He died of tuberculosis four years later, refusing\nto take his own treatment.\n\n[81] William of Occam (d. 1349), so called from his birthplace, Ockham, in\nSurrey. He was a Franciscan, and lectured on philosophy in the Sorbonne.\n\n[82] He signs himself \"James Hopkins, schoolmaster,\" and this seems to have\nbeen his only published effort.\n\n[83] Joseph Ady (1770-1852) was a famous swindler. One of his best-known\nschemes was to send out letters informing the recipients that they would\nlearn something to their advantage on payment of a certain sum. He spent\nsome time in prison.\n\n[84] Sir Peter Laurie (c. 1779-1861) was worth referring to, for he was\nprominent as a magistrate and was honored because of his interest in all\nsocial reforms. He made a fortune as a contractor, became sheriff of London\nin 1823, and was knighted in the following year. He became Lord Mayor of\nLondon in 1832.\n\n[85] See Vol. I, page 321, note 2 {691}. The _Astronomy in a nutshell_\nappeared in 1860. _The Herald of Astrology_ was first published in London\nin 1831, \"by Zadkiel the Seer.\" It was continued as _The Astrological\nAlmanac_ (London, 1834), as _Zadkiel's Almanac and Herald of Astrology_\n(_ibid._, 1835, edited by R. J. Morrison, and subsequently by A. J.\nPearce), and as _Raphael's Prophetic Almanac_ (1840-1855).\n\n[86] See Vol. I, page 172, note 3 {382}.\n\n[87] See Vol. I, page 87, note 4 {133}.\n\n[88] Franz Xaver, Freiherr von Zach (1754-1832) was director of the\nobservatory at Seeberge near Gotha. He wrote the _Tabulae speciales\naberrationis et mutationis_ (1806-7), _Novae et correctae tabulae solis_\n(1792), and _L'attraction des montagnes et ses effets sur le fil a plomb_\n(1814).\n\n[89] Jean Louis Pons (1761-1831) was connected with the observatory at\nMarseilles for thirty years (1789-1819). He later became director of the\nobservatory at Marlia, near Lucca, and subsequently filled the same office\nat Florence. He was an indefatigable searcher for comets, discovering 37\nbetween 1801 and 1827, among them being the one that bears Encke's name.\n\n[90] This hypothesis has now become an established fact.\n\n[91] John Chetwode Eustace (c. 1762-1815) was born in Ireland. Although a\nRoman Catholic priest he lived for a time at Cambridge where he did some\ntutoring. His _Classical Tour_ appeared in 1813 and went through several\neditions.\n\n[92] \"Crimes should be exposed when they are punished, but disgraceful acts\nshould be hidden.\"\n\n[93] Henri Hureau de Senarmont (1808-1862) was professor of mineralogy at\nthe _Ecole des mines_ and examiner at the _Ecole polytechnique_ at Paris.\n\n[94] Augustin Jean Fresnel (1788-1827), \"Ingenieur des ponts et chaussees,\"\ngave the first experimental proofs of the wave theory of light. He studied\nthe questions of interference and polarization, and determined the\napproximate velocity of light.\n\n[95] \"As is my custom.\"\n\n[96] Francis Heywood (1796-1858) made the first English translation of\nKant's _Critick of Pure Reason_ (1838, reprinted in 1848). The _Analysis_\ncame out, as here stated, in 1844.\n\n[97] Louise Renee de Keroualle, Duchess of Portsmouth and Aubigny\n(1649-1734), was a favorite of Charles II. She used her influence to keep\nhim under the control of Louis XIV.\n\n[98] William Chiffinch (c. 1602-1688) was page of the king's bed-chamber\nand keeper of the private closet to Charles II. He was one of the king's\nintimates and was an unscrupulous henchman.\n\n[99] \"Well devised.\"\n\n[100] \"John Bellingham Inglis. His _Philobiblion_ \"translated from the\nfirst edition (of Ricardus d'Aungervile, Bishop of Durham), 1473,\" appeared\nat London in 1832. It was republished in America (Albany, N. Y.) in 1864.\n\n[101] \"What are you laughing at?\"\n\n[102] See Vol. I, page 314, note 4 {681}.\n\n[103] See Vol. I, page 112, note 7 {211}.\n\n[104] Referring to Hamilton's edition of the _Collected Works of Dugald\nStewart_, 10 volumes, Edinburgh, 1854-58. It is not commonly remembered\nthat Stewart (1753-1828) taught mathematics at the University of Edinburgh\nbefore he took up philosophy.\n\n[105] This was Hamilton's edition of the _Works of Thomas Reid_ (2 vols.,\nEdinburgh, 1846-1863). Reid (1710-1796) included mathematics in his work in\nphilosophy at Aberdeen. In 1764 he succeeded Adam Smith at Glasgow.\n\n[106] Edward Irving (1792-1834), the famous preacher. At first he assisted\nDr. Chalmers at Glasgow, but in 1822 he went to London where he met with\ngreat success. A few years later he became mentally unbalanced and was\nfinally expelled from his church (1832) for heresy. He was a great friend\nof Carlyle.\n\n[107] He also wrote a number of other paradoxes, including _An Essay\ntowards a Science of Consciousness_ (1838), _Instinctive Natural Religion_\n(1858), _Popular Treatise on the structure, diseases, and treatment of the\nhuman teeth_ (1837), and _On Headache_ (1859).\n\n[108] James Smith (1801-1857), known as Shepherd Smith, was a socialist and\na mystic, with a philosophy that was wittily described as \"Oriental\npantheism translated into Scotch.\" He was editor of several journals.\n\n[109] Joanna Southcott (1750-1814) was known for her rhyming prophecies in\nwhich she announced herself as the woman spoken of in Revelations xii. She\nhad at one time as many as 100,000 disciples, and she established a sect\nthat long survived her.\n\n[110] Thales, c. 640-548 B. C.\n\n[111] Pythagoras, 580-501 B. C.\n\n[112] Anaxagoras, 499-428 B. C., the last of the Ionian school, teacher of\nEuripides and Pericles. Plutarch speaks of him as having squared the\ncircle.\n\n[113] Oinopides of Chios, contemporary of Anaxagoras. Proclus tells us that\nOinopides was the first to show how to let fall a perpendicular to a line\nfrom an external point.\n\n[114] Bryson and Antiphon, contemporaries of Socrates, invented the\nso-called method of exhaustions, one of the forerunners of the calculus.\n\n[115] He wrote, c. 440 B. C., the first elementary textbook on mathematics\nin the Greek language. The \"lunes of Hippocrates\" are well known in\ngeometry.\n\n[116] Jabir ben Aflah. He lived c. 1085, at Seville, and wrote on astronomy\nand spherical trigonometry. The _Gebri filii Affla Hispalensis de\nastronomia libri_ IX was published at Nuremberg in 1533.\n\n[117] Hieronymus Cardanus, or Girolamo Cardano (1501-1576), the great\nalgebraist. His _Artis magnae sive de regulis Algebrae_ was published at\nNuremberg in 1545.\n\n[118] Nicolo Tartaglia (c. 1500-1557), the great rival of Cardan.\n\n[119] See note 5 {98}, Vol. I, page 69.\n\n[120] See note 10 {124}, Vol. I., page 83.\n\n[121] See note 9 {123}, Vol. I, page 83.\n\n[122] Pierre Herigone lived in Paris the first half of the 17th century.\nHis _Cours mathematique_ (6 vols., 1634-1644) had some standing but was not\nat all original.\n\n[123] Franciscus van Schooten (died in 1661) was professor of mathematics\nat Leyden. He edited Descartes's _La Geometrie_.\n\n[124] Florimond de Beaune (1601-1652) was the first Frenchman to write a\ncommentary on Descartes's _La Geometrie_. He did some noteworthy work in\nthe theory of curves.\n\n[125] See note 3 {23}, Vol. I, page 41.\n\n[126] Olivier de Serres (b. in 1539) was a writer on agriculture. Montucla\nspeaks of him in his _Quadrature du cercle_ (page 227) as having asserted\nthat the circle is twice the inscribed equilateral triangle, although, as\nDe Morgan points out, this did not fairly interpret his position.\n\n[127] Anghera wrote not only the three works here mentioned, but also the\n_Problemi del piu alto interesse scientifico, geometricamente risoluti e\ndimostrati_, Naples, 1861. His quadrature was defended by Giovanni Motti in\na work entitled _Matematica Vera. Falsita del sistema ciclometrico\nd'Archimede, quadratura del cerchio d'Anghera, ricerca algebraica dei lati\ndi qualunque poligono regolare inscritto in un circolo_, Voghera, 1877. The\n_Problemi_ of 1861 contains Anghera's portrait, and states that he lived at\nMalta from 1849 to 1861. It further states that the Malta publications are\nin part reproduced in this work.\n\n[128] This was his friend Paolo Pullicino whose _Elogio_ was pronounced by\nL. Farrugia at Malta in 1890. He wrote a work _La Santa Effegie della Blata\nVergine Maria_, published at Valetta in 1868.\n\n[129] St. Vitus, St. Modestus, and St. Crescentia were all martyred the\nsame day, being torn limb from limb after lions and molten lead had proved\nof no avail. At least so the story runs.\n\n[130] The reference is to Cardinal Wiseman. See Vol. II, page 26, note 56.\n\n[131] \"Worthy of esteem.\"\n\n[132] Pedro de Ribadeneira (Ribadeneyra, Rivadeneira), was born at Toledo\nin 1526 and died in 1611. He held high position in the Jesuit order. The\nwork referred to is the _Flos Sanctorum o libro de las vidas de los\nsantos_, of which there was an edition at Barcelona in 1643. His life of\nLoyola (1572) and _Historia ecclesiastica del Cisma del reino de\nInglaterra_ were well known.\n\n[133] Caesar Baronius (1538-1607) was made a cardinal in 1595 and became\nlibrarian at the Vatican in 1597. The work referred to appeared at Rome in\n1589.\n\n[134] Mrs. Jameson's (1794-1860) works were very popular half a century\nago, and still have some circulation among art lovers. The first edition of\nthe work mentioned appeared in 1848.\n\n[135] The barnyard cock.\n\n[136] Shanks did nothing but computing. The title should, of course, read\n\"to 607 Places of _Decimals_.\" He later carried the computation to 707\ndecimal places. (_Proc. Roy. Society_, XXI, p. 319.) He also prepared a\ntable of prime numbers up to 60,000. (_Proc. Roy. Society_, XXII, p. 200.)\n\n[137] See Vol. I, page 42, note 4 {24}.\n\n[138] See Vol. I, page 64, note 1 {78}.\n\n[139] See Vol. I, page 328, note 1 {704}.\n\n[140] George Suffield published _Synthetic Division in Arithmetic_, to\nwhich reference is made, in 1863.\n\n[141] John Robert Lunn wrote chiefly on Church matters, although he\npublished a work on motion in 1859.\n\n[142] Jean Baptiste Joseph, Baron Fourier (1768-1830), sometime professor\nin the Military School at Paris, and later at the _Ecole polytechnique_. He\nis best known by his _Theorie analytique de la chaleur_ (Paris, 1822), in\nwhich the Fourier series is used. The work here referred to is the _Analyse\ndes equations determinees_ (Paris, 1831).\n\n[143] William George Horner (1786-1837) acquired a name for himself in\nmathematics in a curious manner. He was not a university man nor was he a\nmathematician of any standing. He taught school near Bristol and at Bath,\nand seems to have stumbled upon his ingenious method for finding the\napproximate roots of numerical higher equations, including as a special\ncase the extracting of the various roots of numbers. Davies Gilbert\npresented the method to the Royal Society in 1819, and it was reprinted in\nthe _Ladies' Diary_ for 1838, and in the _Mathematician_ in 1843. The\nmethod was original as far as Horner was concerned, but it is practically\nidentical with the one used by the Chinese algebraist Ch'in Chiu-shang, in\nhis _Su-shu Chiu-chang_ of 1247. But even Ch'in Chiu-shang can hardly be\ncalled the discoverer of the method since it is merely the extension of a\nprocess for root extracting that appeared in the _Chiu-chang Suan-shu_ of\nthe second century B. C.\n\n[144] He afterwards edited Loftus's _Inland Revenue Officers' Manual_\n(London, 1865). The two equations mentioned were x^3 - 2x = 5 and y^3 -\n90y^2 + 2500y - 16,000 = 0, in which y = 30 - 10x. Hence each place of y is\nthe complement of the following place of x with respect to 9.\n\n[145] Probably the John Power Hicks who wrote a memoir on T. H. Key,\nLondon, 1893.\n\n[146] Possibly the one who wrote on the quadrature of the circle in 1881.\n\n[147] As it is. But what a pity that we have not 12 fingers, with\nduodecimal fractions instead of decimals! We should then have 0.6 for 1/2,\n0.4 for 1/3, 0.8 for 2/3, 0.3 for 1/4, 0.9 for 3/4, and 0.16 for 1/8,\ninstead of 0.5, 0.333+, 0.666+, 0.25, 0.75, and 0.125 as we now have\nwith our decimal system. In other words, the most frequently used\nfractions in business would be much more easily represented on the\nduodecimal scale than on the decimal scale that we now use.\n\n[148] He wrote Hints for an _Essay on Anemology and Ombrology_ (London,\n1839-40) and _The Music of the Eye_ (London, 1831).\n\n[149] Brigham Young (1801-1877) was born at Whitingham, Vermont, and\nentered the Mormon church in 1832. In 1840 he was sent as a missionary to\nEngland. After the death of Joseph Smith he became president of the Mormons\n(1847), leading the church to Salt Lake City (1848).\n\n[150] Joseph Smith (1805-1844) was also born in Vermont, and was four years\nthe junior of Brigham Young. The _Book of Mormon_ appeared in 1827, and the\nchurch was founded in 1830. He was murdered in 1844.\n\n[151] Orson Pratt (1811-1881) was one of the twelve apostles of the Mormon\nChurch (1835), and made several missionary journeys to England. He was\nprofessor of mathematics in the University of Deseret (the Mormon name for\nUtah). Besides the paper mentioned Pratt wrote the _Divine Authenticity of\nthe Book of Mormon_ (1849), _Cubic and Biquadratic Equations_ (1866), and a\n_Key to the Universe_ (1866).\n\n[152] \"It does not follow.\"\n\n[153] Dryden (1631-1700) published his _Religio Laici_ in 1682. The use of\nthe word \"proportion\" in the sense of ratio was common before his time, but\nhe uses it in the sense of having four terms; that is, that price is to\nprice as offence is to offence.\n\n[154] Olinthus Gilbert Gregory (1774-1841) succeeded Hutton as professor of\nmathematics at Woolwich. He was, with De Morgan, much interested in\nfounding the University of London. He wrote on astronomy (1793), mechanics\n(1806), practical mathematics (1825), and Christian evidences (1811).\n\n[155] See Vol. I, page 220, note 6 {482}. The _Pensees_ appeared\nposthumously in 1670.\n\n[156] \"The right thing to do is not to wager at all.\" \"Yes, but you ought\nto wager; you have started out; and not to wager at all that God exists is\nto wager that he does not exist.\"\n\n[157] He lived about 300 A.D., in Africa, and wrote _Libri septem adversus\nGentes_. This was printed at Rome in 1542-3.\n\n[158] Pierre Bayle (1647-1706) was professor of philosophy at the\nProstestant University at Sedan from 1675 until its dissolution in 1681. He\nthen became professor at Rotterdam (1681-1693). In 1684 he began the\npublication of his journal of literary criticism _Nouvelles de la\nRepublique des Lettres_. He is best known for his erudite _Dictionnaire\nhistorique et critique_ (1697).\n\n[159] \"But Christ himself does not prove what he promises. It is true. For,\nas I have said, there cannot be any absolute proof of future events.\nTherefore since it is a condition of future events that they cannot be\ngrasped or comprehended by any efforts of anticipation, is it not more\nreasonable, out of two alternatives that are uncertain and that are hanging\nin doubtful expectation, to give credence to the one that gives some hope\nrather than to the one that offers none at all? For in the former case\nthere is no danger if, as is said to threaten, it becomes empty and void;\nwhile in the latter case the danger is greatest, that is, the loss of\nsalvation, if when the time comes it is found that it was not a falsehood.\"\n\n[160] Gregg wrote several other paradoxes, including the following: _The\nAuthentic Report of the extraordinary case of Tresham Dames Gregg ... his\ncommittal to Bridewell for refusing to give his recognizance_ (Dublin,\n1841), _An Appeal to Public Opinion upon a Case of Injury and Wrong ... in\nthe case of a question of prerogative that arose between_ [R. Whately] _...\nArchbishop of Dublin and the author_ (London, 1861), _The Cosmology of Sir\nIsaac Newton proved to be in accordance with the Bible_ (London, 1871),\n_The Steam Locomotive as revealed in the Bible_ (London 1863) and _On the\nSacred Law of 1866, conferring perpetual life with immunity from decay and\ndisease. A cento of decisive scriptural oracles strangely discovered_\n(London and Dublin, 1875). These titles will help the reader to understand\nthe man whom De Morgan so pleasantly satirizes.\n\n[161] See Vol. I, page 261, note 2 {592}.\n\n[162] \"They have found it.\"\n\n[163] The late Greeks used the letters of their alphabet as numerals,\nadding three early alphabetic characters. The letter [chi] represented 600,\n[xi] represented 60, and [digamma] stood for 6. This gives 666, the number\nof the Beast given in the Revelation.\n\n[164] \"Allowing for necessary exceptions.\"\n\n[165] Mr. Gregg is not alone in his efforts to use the calculus in original\nlines, as any one who has read Herbart's application of the subject to\npsychology will recall.\n\n[166] See Vol. I, page 105, note 4 {188}; page 109, note 1 {197}.\n\n[167] The full title shows the plan,--_The Decimal System as a whole, in\nits relation to time, measure, weight, capacity, and money, in unison with\neach other._ But why is this so much worse than the French plan of which we\nhave only the metric system and the decimal division of the angle left?\n\n[168] One of the brothers of Sir Isaac Pitman (1813-1897), the inventor of\nmodern stenography. Of these brothers, Benjamin taught the art in America,\nJacob in Australia, and Joseph, Henry, and Frederick in England.\n\n[169] For example, _The Phonographic Lecturer_ (London, 1871 etc.), _The\nPhonographic Student_ (1867, etc.), and _The Shorthand Magazine_ (1866,\netc.).\n\n[170] See Vol. II, page 68, note 148.\n\n[171] It involves the theory of non-Euclidean geometry, Euclid's postulate\nof parallels being used in proving this theorem.\n\n[172] Referring to the fact that none of the works of Thales is extant.\n\n[173] The author was one B. Bulstrode. Parts 4 and 5 were printed at\nCalcutta.\n\n[174] See Vol. II, page 5, note 18.\n\n[175] See Vol. I, page 85, note 2 {129}.\n\n[176] Alexander Vasilievich Suvaroff (1729-1800), a Russian general who\nfought against the Turks, in the Polish wars, and in the early Napoleonic\ncampaigns. When he took Ismail in 1790 he sent this couplet to Empress\nCatherine.\n\n[177] \"Newton hath determined rightly,\" \"Newton hath not determined\nrightly.\"\n\n[178] See Vol. I, page 288, note 3 {621}.\n\n[179] See Vol. I, page 326, note 1 {700}.\n\n[180] \"With great honor.\"\n\n[181] Apparently unknown to biographers. He seems to have written nothing\nelse.\n\n[182] Captain Marryat (1792-1848) published _Snarley-yow, or the Dog Fiend_\nin 1837.\n\n[183] He is not known to biographers, and published nothing else under this\nname.\n\n[184] See Vol. I, page 80, note 5 {119}.\n\n[185] He published a _Family and Commercial Illustrated Almanack and Year\nBook ... for 1861_ (Bath, 1860).\n\n[186] Louis Dutens (1730-1812) was born at Tours, but went to England as a\nyoung man. He made the first collection of the works of Leibnitz, against\nthe advice of Voltaire, who wrote to him: \"Les ecrits de Leibnitz sont\nepars comme les feuilles de la Sybille, et aussi obscurs que les ecrits de\ncette vieille.\" The work appeared at Geneva, in six volumes, in 1769.\n\n[187] Mungo Park (1771-1806), the first European to explore the Niger\n(1795-6). His _Travels in the Interior of Africa_ appeared in 1799. He died\nin Africa.\n\n[188] Gerhard Mercator (1512-1594) the well-known map maker of Louvain. The\n\"Mercator's Projection\" was probably made as early as 1550, but the\nprinciple of its construction was first set forth by Edward Wright (London,\n1599).\n\n[189] Quirico Barilli Filopanti wrote a number of works and monographs. He\nsucceeded in getting his _Cesare al Rubicone_ and _Degli_ _usi idraulici\ndella Tela_ in the _Memoria letta ... all' Accademia delle Scienze in\nBologna_ (1847, 1866). He also wrote _Dio esiste_ (1881), _Dio Liberale_\n(1880), and _Sunto della memoria sulle geuranie ossia di alcune singolari\nrelazioni cosmiche della terra e del cielo_ (1862).\n\n[190] The periods of disembodiment may be interesting. They will be seen\nfrom the following dates: Descartes (1596-1650), William III (1650-1702);\nRoger Bacon (1214 to c. 1294), Boccaccio (1313-1375). Charles IX was born\nin 1550 and died in 1574.\n\n[191] His real name was Frederick Parker, and he wrote several works on the\nGreek language and on religion. Among these were a translation of the New\nTestament from the Vatican MS. (1864), _The Revealed History of Man_\n(1854), _An Enquiry respecting the Punctuation of Ancient Greek_ (1841),\nand _Rules for Ascertaining the sense conveyed in Ancient Greek\nManuscripts_ (1848, the seventh edition appearing in 1862).\n\n[192] See Vol. I, page 352, second note 1 {736}.\n\nThe literature on the subject of the Great Pyramid, considered from the\nstandpoint of metrology, is extensive.\n\n[193] See Vol. I, page 80, note 5 {119}.\n\n[194] Sir Philip Francis (1740-1818) was a Whig politician. The evidence\nthat he was the author of the _Letters of Junius_ (1769-1772) is purely\ncircumstantial. He was clerk in the war office at the time of their\npublication. In 1774 he was made a member of the Supreme Council of Bengal,\nand was a vigorous opponent of Warren Hastings, the two fighting a duel in\n1780. He entered parliament in 1784 and was among the leaders in the\nagitation for parliamentary reform.\n\n[195] Mrs. Cottle published a number of letters that attracted attention at\nthe time. Among these were letters to the emperor of France and king of\nSardinia (1859) relating to the prophecies of the war between France and\nAustria; to G. C. Lavis and Her Majesty's Ministers (1859) relating to her\nclaims as a prophetess; and to the \"Crowned Heads\" at St. James, the King\nof Prussia, and others (1860), relating to certain passages of Scripture.\nShe also wrote _The Lamb's Book of Life for the New Jerusalem Church and\nKingdom, interpreted for all nations_ (1861).\n\n[196] See Vol. I, page 315, note 2 {685}, and Vol. II, page 58, note 109.\n\n[197] A Congregational minister, who published a number of sermons, chiefly\nobituaries, between 1804 and 1851. His _Frailty of Human Life_, two sermons\ndelivered on the occasion of the death of Princess Charlotte, went through\nat least three editions.\n\n[198] He was secretary of the Congregational Board and editor of the\n_Congregational Year Book_ (from 1846) and the _Congregational Manual_.\n\n[199] Frederick Denison Maurice (1805-1872) began his preaching as a\nUnitarian but entered the Established Church in 1831, being ordained in\n1834. He was professor of English and History at King's College, London,\nfrom 1840 to 1853. He was one of the founders of Queen's College for women,\nand was the first principal of the Working Men's College, London. The\nsubject referred to by De Morgan is his expression of opinion in his\n_Theological Essays_ (1853) that future punishment is not eternal. As a\nresult of this expression he lost his professorship at King's College. In\n1866 he was made Knightbridge Professor of Casuistry, Moral Theology, and\nMoral Philosophy at Cambridge.\n\n[200] See Vol. I, page 46, note 1 {42}. Besides the books mentioned in\nthis list he wrote _The Ratio between Diameter and Circumference\ndemonstrated by angles, and Euclid's Theorem, Proposition 32, Book I,\nproved to be fallacious_ (Liverpool, 1870). This is the theorem which\nasserts that the exterior angle of a triangle is equal to the sum of the\ntwo opposite interior angles, and that the sum of the interior angles\nequals two right angles. He also published his _Curiosities of Mathematics_\nin 1870, a work containing an extensive correspondence with every one who\nwould pay any attention to him. De Morgan was then too feeble to show any\ninterest in the final effort of the subject of some of his keenest satire.\n\n[201] See Vol. I, page 332, note 4 {709}.\n\n[202] See Vol. I, page 101, note 4 {174}.\n\n[203] \"The circle-squaring disease\"; literally, \"the circle-measuring\ndisease.\"\n\n[204] See Vol. II, page 63, note 136.\n\n[205] William Rutherford (c. 1798-1871), teacher of mathematics at\nWoolwich, secretary of the Royal Astronomical Society, editor of _The\nMathematician_, and author of various textbooks. _The Extension of [pi] to\n440 places_, appeared in the _Proceedings_ of the Royal Society in 1853 (p.\n274).\n\n[206] Charles Knight (1791-1873) was associated with De Morgan for many\nyears. After 1828 he superintended the publications of the Society for the\nDiffusion of Useful Knowledge, to which De Morgan contributed, and he\nedited the _Penny Cyclopedia_ (1833-1844) for which De Morgan wrote the\narticles on mathematics.\n\n[207] Sir William Hamilton. See Vol. I, page 112, note 7 {211}.\n\n[208] Adam Smith (1723-1790) was not only known for his _Wealth of Nations_\n(1776), but for his _Theory of Moral Sentiments_ (1759), published while he\nwas professor of moral philosophy at Glasgow (1752-1764). He was Lord\nRector of the university in 1787.\n\n[209] See Vol. I, page 332, note 4 {709}.\n\n[210] \"Whip.\"\n\n[211] \"Terrible lash.\"\n\n[212] \"An accomplished fact [an accomplished fault].\"\n\n[213] See _Extracts from the Diary and Letters of Mrs. Mary Cobb_, London,\n1805.\n\n[214] \"Gentle in manner.\"\n\n[215] \"Brave in action.\" The motto of Earl Newborough was \"Suaviter in\nmodo, fortiter in re.\"\n\n[216] \"Reduction to an absurdity,\" a method of proof occasionally used in\ngeometry and in logic.\n\n[217] \"He has lost the right of being moved (struck) by evidence.\"\n\n[218] For _radix quadratus_. The usual root sign is supposed to be derived\nfrom _r_ (for radix), and at one time _q_ was commonly used for square, as\nin Viete's style of writing Aq for A^2.\n\n[219] The Garde Douloureuse was a castle in the marches of Wales and\nreceived its name because of its exposure to attacks by the Welsh.\n\n[220] \"Out of the fight.\"\n\n[221] \"Hidden.\"\n\n[222] John Cam Hobhouse (1786-1869), Baron Broughton, was committed to\nNewgate for two months in 1819 for his anonymous pamphlet, _A Trifling\nMistake_. This was a great advertisement for him, and upon his release he\nwas at once elected to parliament for Westminster. He was a strong\nsupporter of all reform measures, and was Secretary for War in 1832. He was\ncreated Baron Broughton de Gyfford in 1851.\n\n[223] Thomas Erskine (1750-1823), the famous orator. He became Lord\nChancellor in 1806, but sat in the House of Commons most of his life.\n\n[224] The above is explained in the MS. by a paragraph referring to some\nanagrams, in one of which, by help of the orthography suggested, a\ndesignation for this cyclometer was obtained from the letters of his\nname.--S. E. De M.\n\n[225] \"A personal verb agrees with its subject.\"\n\n[226] See Vol. I, page 326, note 1 {700}.\n\n[227] See Vol. I, page 326, note 2 {701}.\n\n[228] Apparently unknown to biographers.\n\n[229] The _Bibliotheca Mathematica_ of Ludwig Adolph Sohncke (1807-1853),\nprofessor of mathematics at Koenigsberg and Halle, covered the period from\n1830 to 1854, being completed by W. Engelmann. It appeared in 1854.\n\n[230] See Vol. I, page 392, note 2 {805}.\n\n[231] See Vol. I, page 43, note 7 {32}.\n\n[232] See Vol. II, page 91, note 187.\n\n[233] Mason made a notable balloon trip from London to Weilburg, in the\nDuchy of Nassau, in November, 1836, covering 500 miles in 18 hours. He\npublished an account of this trip in 1837, and a work entitled\n_Aeronautica_ in 1838.\n\n[234] William Harrison Ainsworth (1805-1885) the novelist.\n\n[235] On this question see Vol. I, page 326, note 2 {701}.\n\n[236] Major General Alfred Wilks Drayson, author of various works on\ngeology, astronomy, military surveying, and adventure.\n\n[237] Hailes also wrote several other paradoxes on astronomy and circle\nsquaring during the period 1843-1872.\n\n[238] See Vol. I, page 43, note 8 {33}.\n\n[239] See Vol. I, page 43, note 7 {32}.\n\n[240] \"Very small errors are not to be condemned.\"\n\n[241] He seems to have written nothing else.\n\n[242] Besides the paradoxes here mentioned by De Morgan he wrote several\nother works, including the following: _Abriss der Babylonisch-Assyrischen\nGeschichte_ (Mannheim, 1854), _A Popular Inquiry into the Moon's rotation\non her axis_ (London, 1856), _Practical Tables for the reduction of the\nMahometan dates to the Christian kalendar_ (London, 1856), _Grundzuege einer\nneuen Weltlehre_ (Munich, 1860), and _On the historical Antiquity of the\nPeople of Egypt_ (London, 1863).\n\n[243] Dircks (1806-1873) was a civil engineer of prominence, and a member\nof the British Association and the Royal Society of Edinburgh. He wrote\n(1863) on \"Pepper's Ghost,\" an ingenious optical illusion invented by him.\nThere was a second edition of the _Perpetuum Mobile_ in 1870.\n\n[244] George Stephenson (1781-1848), the inventor of the first successful\nsteam locomotive. His first engine was tried in 1814.\n\n[245] Robert Stephenson (1803-1859), the only son of George. Most of the\nearly improvements in locomotive manufacture were due to him. He was also\nwell known for his construction of great bridges.\n\n[246] \"In its proper place.\"\n\n[247] \"A fool always finds a bigger fool to admire him.\"\n\n[248] See Vol. I, page 43, note 7 {32}.\n\n[249] See Vol. I, page 43, note 8 {33}.\n\n[250] See Vol. I, page 85, note 2 {129}.\n\n[251] See Vol. I, page 390, note 1 {390}.\n\n[252] From 1823 to 1852 it was edited by I. C. Robertson; from 1852 to 1857\nby R. A. Brooman; and from 1857 to 1863 by Brooman and E. J. Reed.\n\n[253] Sir James Ivory (1765-1842) was, as a young man, manager of a flax\nmill in Scotland. In 1804 he was made professor of mathematics at the Royal\nMilitary College, then at Marlow and later at Sandhurst. He was deeply\ninterested in mathematical physics, and there is a theorem on the\nattraction of ellipsoids that bears his name. He was awarded three medals\nof the Royal Society, and was knighted together with Herschel and Brewster,\nin 1831.\n\n[254] See Vol. I, page 56, note 1 {64}.\n\n[255] See Vol. I, page 153, note 5 {338}.\n\n[256] See Vol. I, page 309, note 2 {670}.\n\n[257] See Vol. I, page 87, note 4 {133}.\n\n[258] George Canning (1770-1857), the Tory statesman and friend of Scott,\nwas much interested in founding the _Quarterly Review_ (1808) and was a\ncontributor to its pages.\n\n[259] See Vol. I, page 186, note 14 {418}.\n\n[260] See Vol. II, page 141, note 252.\n\n[261] De Morgan had a number of excellent articles in this publication.\n\n[262] See Vol. I, page 279, note 1 {611}.\n\n[263] James Orchard Halliwell (1820-1889), afterwards Halliwell-Phillips,\ncame into prominence as a writer at an early age. When he was seventeen he\nwrote a series of lives of mathematicians for the _Parthenon_. His _Rara\nMathematica_ appeared when he was but nineteen. He was a great bibliophile\nand an enthusiastic student of Shakespeare.\n\n[264] This was written at the age of twenty-two.\n\n[265] The subject of this criticism is of long past date, and as it has\nonly been introduced by the author as an instance of faulty editorship, I\nhave omitted the name of the writer of the libel, and a few lines of\nfurther detail.--S. E. De M.\n\n[266] \"Condemned souls.\"\n\n[267] The editor of the _Mechanics' Magazine_ died soon after the above was\nwritten.--S. E. De M.\n\n[268] Thomas Stephens Davies (1795-1851) was mathematical master at\nWoolwich and F. R. S. He contributed a series of \"Geometrical Notes\" to the\n_Mechanics' Magazine_ and edited the _Mathematician_. He also published a\nnumber of text-books.\n\n[269] See Vol. II, page 66, note 143.\n\n[270] The _Dictionary of Greek and Roman Biography_ (1849), edited by Sir\nWilliam Smith (1813-1893), whose other dictionaries on classical and\nbiblical matters are well known.\n\n[271] \"O J. S.! This is the worst! the greatest possible injury!\"\n\n[272] See Vol. I, page 44, note 9 {34} and page 110, note 5 {201}.\n\n[273]\n\n \"If there's a man whom the judge's pitiless sentence awaiteth,\n  His head condemned to penalties and tribulations,\n  Let neither penitentiaries tire him with laborer's burdens\n  Nor let his stiffened hands be harrassed by work in the mines.\n  He must square the circle! For what else do I care?--all\n  Known punishments this one task hath surely included.\"\n\n[274] Houlston was in the customs service. He also published _Inklings of\nAreal Autometry_, London, 1874.\n\n[275] This is Frederick C. Bakewell. He had already published _Natural\nEvidence of a Future Life_ (London, 1835), _Philosophical Conversations_\n(London, 1833, with other editions), and _Electric Science_ (London, 1853,\nwith other editions).\n\n[276] Henry F. A. Pratt had already published _A Dissertation on the power\nof the intercepted pressure of the Atmosphere_ (London, 1844) and _The\nGenealogy of Creation_ (1861). Later he published a work _On Orbital\nMotion_ (1863), and _Astronomical Investigations_ (1865).\n\n[277] See Vol. I, page 260, note 1 {591}.\n\n[278] Thomas Rawson Birks (1810-1883), a theologian and controversialist,\nfellow of Trinity College, Cambridge, and (1872) professor of moral\nphilosophy in that university. He wrote _Modern Rationalism_ (1853), _The\nBible and Modern Thought_ (1861), _The First Principles of Moral Science_\n(1873), and _Modern Physical Fatalism and the Doctrine of Evolution_\n(1876), the last being an attack on Herbert Spencer's _First Principles_.\n\n[279] Pseudonym for William Thorn. In the following year (1863) he\npublished a second work, _The Thorn-Tree: being a History of Thorn\nWorship_, a reply to Bishop Colenso's work entitled _The Pentateuch and the\nBook of Joshua critically examined_.\n\n[280] Besides _The Pestilence_ (1866) he published _The True Church_\n(1851), _The Church and her destinies_ (1855), _Religious reformation\nimperatively demanded_ (1864), and _The Bible plan unfolded_ (second\nedition, 1872).\n\n[281] See Vol. II, page 97, note 195.\n\n[282] Sir George Cornewall Lewis (1806-1863) also wrote an _Essay on the\nOrigin and Formation of the Romance Languages_ (1835), an _Essay on the\nGovernment of Dependencies_ (1841), and an _Essay on Foreign Jurisdiction\nand the Extradition of Criminals_ (1859). He was Chancellor of the\nExchequer in 1855 and Home Secretary in 1859.\n\n[283] Henry Malden (1800-1876), a classical scholar, fellow of Trinity\nCollege, Cambridge, and professor of Greek at University College\n(1831-1876), then (1831) the University of London. He wrote a _History of\nRome to 390 B. C._ (1830), and _On the Origin of Universities and\nAcademical Degrees_ (1835).\n\n[284] Henry Longueville Mansel (1820-1871), theologian and metaphysician,\nreader in theology at Magdalen College, Oxford (1855), and professor of\necclesiastical history and Dean of St. Paul's (1866). He wrote on\nmetaphysics, and his Bampton Lectures (1858) were reprinted several times.\n\n[285] \"Hejus gave freely, gave freely. God is propitious, God is favorable\nto him who gives freely. God is honored with a banquet of eggs at the cross\nroads, the god of the world. God, with benignant spirit, desired in\nsacrifice a goat, a bull to be carried within the precincts of the holy\nplace. God, twice propitiated, blesses the pit of the sacred libation.\"\n\n[286] Eudoxus of Cnidus (408-355 B. C.) had much to do with the early\nscientific astronomy of the Greeks. The fifth book of Euclid is generally\nattributed to him. His astronomical works are known chiefly through the\npoetical version of Aratus mentioned in note 13, page 167.\n\n[287] Simplicius, a native of Cilicia, lived in the 6th century of our era.\nHe was driven from Athens by Justinian and went to Persia (531), but he\nreturned later and had some fame as a teacher.\n\n[288] See Vol. I, page 160, note 3 {348}.\n\n[289] See Vol. I, page 76, note 3 {112}.\n\n[290] \"Through right and wrong.\"\n\n[291] \"It is therefore to arrive at this parallelism, or to preserve it,\nthat Copernicus feared to be obliged to have recourse to this equal and\nopposite movement which destroys the effect which he attributed so freely\nto the first, of deranging the parallelism.\"\n\n[292] A contemporary of Plato and a disciple of Aristotle.\n\n[293] Meton's solstice, the beginning of the Metonic cycles, has been\nplaced at 432 B. C. Ptolemy states that he made the length of the year\n365-1/4 + 1/72 days.\n\n[294] Aratus lived about 270 B. C., at the court of Antigonus of Macedonia,\nand probably practiced medicine there. He was the author of two\nastronomical poems, the [Greek: Phainomena], apparently based on the lost\nwork of Eudoxus, and the [Greek: Dioseeia] based on Aristotle's\n_Meteorologica_ and _De Signis Ventorum_ of Theophrastus.\n\n[295] \"The nineteen (-year) cycle of the shining sun.\"\n\n[296] Claudius Salmasius (1588-1653), or Claude Saumaise, was a\ndistinguished classicist, and professor at the University of Leyden. The\nword [Greek: eleioio] means Elian, thus making the phrase refer to the\nbrilliant one of Elis.\n\n[297] Sir William Brown (1784-1864). In 1800 the family moved to Baltimore,\nand there the father, Alexander Brown, became prominent in the linen trade.\nWilliam went to Liverpool where he acquired great wealth as a merchant and\nbanker. He was made a baronet in 1863.\n\n[298] Robert Lowe (1811-1892), viscount Sherbrooke, was a fellow of\nMagdalen College, Oxford (1835). He went to Australia in 1842 and was very\nsuccessful at the bar. He returned to England in 1850 and became leader\nwriter on the _Times_. He was many years in parliament, and in 1880 was\nraised to the peerage.\n\n[299] See Vol. I, page 42, note 4 {24}.\n\n[300] Francis Walkingame (fl. about 1751-1785), whose _Tutor's Assistant_\nwent through many editions from 1751-1854.\n\n[301] Davies Gilbert (1767-1839). His family name was Giddy, but he assumed\nhis wife's name. He sat in parliament from 1806 to 1832. In 1819 he secured\nthe establishment of the Cape of Good Hope observatory. He was Treasurer\n(1820-1827) and President (1827-1830) of the Royal Society.\n\n[302] See Vol. I, page 55, note 2 {63}.\n\n[303] Sir Jonathan Frederick Pollock (1783-1870) entered parliament in 1831\nand was knighted in 1834.\n\n[304] Joseph Hume (1777-1855) entered parliament in 1812 and for thirty\nyears was leader of the Radical party.\n\n[305] \"What! when I say, 'Nicole, bring me my slippers,' is that prose?\"\n\n[306] Captain Basil Hall (1788-1844), a naval officer, carried on a series\nof pendulum observations in 1820-1822, while on a cruise of the west coast\nof North America. The results were published in 1823 in the _Philosophical\nTransactions_. He also wrote two popular works on travel that went through\nnumerous editions.\n\n[307] Anthony Ashley Cooper (1801-1885), Earl of Shaftesbury. His name is\nconnected with philanthropic work and factory legislation.\n\n[308] See Vol. I, page 207, note 12 {469}.\n\n[309] See Vol. I, page 80, note 5 {119}.\n\n[310] Sir Thomas Maclear (1794-1879), an Irishman by birth, became\nAstronomer Royal at the Cape of Good Hope in 1833. He was an indefatigable\nobserver. He was knighted in 1860.\n\n[311] Thomas Romney Robinson (1792-1882), another Irish astronomer of\nprominence. He was a deputy professor at Trinity College, Dublin, but took\ncharge of the Armagh observatory in 1823 and remained there until his\ndeath.\n\n[312] Sir James South (1785-1867) was in early life a surgeon, but gave up\nhis practice in 1816 and fitted up a private observatory. He contributed to\nthe science of astronomy, particularly with respect to the study of double\nstars.\n\n[313] Sir John Wrottesley (1798-1867), second Baron Wrottesley. Like Sir\nJames South, he took up the study of astronomy after a professional\ncareer,--in his case in law. He built a private observatory in 1829 and\nmade a long series of observations, publishing three star catalogues. He\nwas president of the Astronomical Society from 1841 to 1843, and of the\nRoyal Society from 1854 to 1857.\n\n[314] He seems to have written nothing else.\n\n[315] See Vol. II, page 68, note 147.\n\n[316] \"The wills are free, and I wish neither the one nor the other.\"\n\n[317] \"The force of inertia conquered.\"\n\n[318] Reddie also wrote _The Mechanics of the Heavens_, referred to later\nin this work. He must not be confused with Judge James Reddie (1773-1852),\nof Glasgow, who wrote on international law, although this is done in the\nprinted edition of the British Museum catalogue, for he is mentioned by De\nMorgan somewhat later as alive in 1862.\n\n[319] Henry Dunning Macleod (1821-1902), a lawyer and writer on political\neconomy, was a Scotchman by birth. He wrote on economical questions, and\nlectured on banking at Cambridge (1877) and at King's College, London\n(1878). He was a free lance in his field, and was not considered orthodox\nby the majority of economists of his time. He was an unsuccessful candidate\nfor the chairs of political economy at Cambridge (1863), Edinburgh (1871),\nand Oxford (1888).\n\n[320] See Vol. I, page 252, note 2 {576}.\n\n[321] Francis Henry Laing (1816-1889) was a graduate of Queen's College,\nCambridge, and a clergyman in the Church of England until 1846, when he\nentered the Church of Rome. He taught in various Jesuit colleges until\n1862, when his eccentricity was too marked to warrant the Church in\nallowing him to continue. He published various controversial writings\nduring his later years. Of course if he had known the works of Wessel,\nGaus, Buee, Argand, and others, he would not have made such a sorry\nexhibition of his ignorance of mathematics.\n\n[322] See Vol. I, page 329, note 1 {705}. The book went into a second\nedition in 1864.\n\n[323] Thomas Weddle (1817-1853) was, at the time of publishing this paper,\na teacher in a private school. In 1851 he became professor of mathematics\nat Sandhurst. He contributed several papers to the _Cambridge and Dublin\nMathematical Journal_, chiefly on geometry.\n\n[324] See Vol. II, page 109, note 205.\n\n[325] See Vol. II, page 66, note 143.\n\n[326] See Vol. II, page 151, note 268.\n\n[327] George Barrett (1752-1821) worked from 1786 to 1811 on a set of life\ninsurance and annuity tables. He invented a plan known as the \"columnar\nmethod\" for the construction of such tables, and as De Morgan states, this\nwas published by Francis Baily, appearing in the appendix to his work on\nannuities, in the edition of 1813. Some of his tables were used in\nBabbage's _Comparative View of the various Institutions for the Assurance\nof Lives_ (1826).\n\n[328] See Vol. I, page 309, note 2 {670}.\n\n[329] This was his _Practical short and direct Method of Calculating the\nLogarithm of any given Number, and the Number corresponding to any given\nLogarithm_ (1849).\n\n[330] This is William Neile (1637-1670), grandson of Richard Neile (not\nNeal), Archbishop of York. At the age of 19, in 1657, he gave the first\nrectification of the semicubical parabola. Although he communicated it to\nBrouncker, Wren, and others, it was not published until 1639, when it\nappeared in John Wallis's _De Cycloide_.\n\n[331] I myself \"was a considerable part.\"\n\n[332] He also wrote _A Glance at the Universe_ (\"2d thousand\" in 1862), and\n_The Resurrection Body_ (1869).\n\n[333] See Vol. I, page 63, note 1 {74}.\n\n[334] As Swift gave it in his _Poetry. A Rhapsody_, it is as follows:\n\n \"So, naturalists observe, a flea\n  Has smaller fleas that on him prey;\n  And these have smaller still to bite 'em.\n  And so proceed _ad infinitum_.\"\n\n[335] Perhaps 1,600,000,000 years, if Boltwood's recent computations based\non radium disintegration stand the test. This would mean, according to\nMacCurdy's estimate, 60,000,000 years since life first appeared on the\nearth.\n\n[336] De Morgan wrote better than he knew, for this work, the _Allgemeine\nEncyclopaedie der Wissenschaften und Kuenste_, begun at Leipsic in 1818, is\nstill (1913) unfinished. Section I, A-G, consists of 99 parts in 56\nvolumes; Section II, H-N, consists of 43 volumes and is not yet completed;\nand Section III, O-Z, consists of 25 volumes thus far, with most of the\nwork still to be done. Johann Samuel Ersch (1766-1828), the founder, was\nhead librarian at Halle. Johann Gottfried Gruber (1774-1851), his\nassociate, was professor of philosophy at the same university.\n\n[337] William Howitt (1792-1879) was a poet, a spiritualist, and a\nmiscellaneous writer. He and his wife became spiritualists about 1850. He\nwrote numerous popular works on travel, nature and history.\n\n[338] See Vol. II, page 55, note 108.\n\n[339] As will be inferred from the text, C. D. was Mrs. De Morgan, and\nA. B. was De Morgan.\n\n[340] Jean Meslier (1678-1733), cure of Estrepigny, in Champagne, was a\nskeptic, but preached only strict orthodoxy to his people. It was only in\nhis manuscript, _Mon Testament_, that was published after his death, and\nthat caused a great sensation in France, that his antagonism to\nChristianity became known.\n\n[341] Baron Zach relates that a friend of his, in a writing intended for\npublication, said _Un esprit doit se frotter contre un autre_. The censors\nstruck it out. The Austrian police have a keen eye for consequences.--A. De\nM.\n\n\"One mind must rub against another.\" On Baron Zach, see Vol. II, page 45,\nnote 4.\n\n[342] Referring to the first Lord Eldon (1751-1838), who was Lord\nChancellor from 1799 to 1827, with the exception of one year.\n\n[343] \"Sleeping power.\"\n\n[344] \"Causes sleep.\"\n\n[345] Richard Hooker (c. 1554-1600), a theologian, \"the ablest living\nadvocate of the Church of England as by law established.\"\n\n[346] See Vol. I, page 76, note 3 {112}.\n\n[347] \"Other I,\"--other self.\n\n[348] This \"utter rejection\" has been repeated (1872) by the same\nwriter.--S. E. De M.\n\n[349] Edward Jenner (1749-1823) was a physician and biologist. His first\nexperiments in vaccination were made in 1796, and his discovery was\npublished in 1798.\n\n[350] See Vol. II, page 38, note 80.\n\n[351] \"You will go most safely in the middle (way).\"\n\n[352] Pierre Joseph Arson was known early in the 19th century for his\ncontroversy with Hoene Wronski the mathematician, whom he attacked in his\n_Document pour l'histoire des grands fourbes qui ont figure sur la terre_\n(1817-1818).\n\n[353] \"We enter the course by night and are consumed by fire.\"\n\n[354] See Vol. I, page 51, note 3 {51}.\n\n[355] See Vol. I, page 336, note 8 {713}.\n\n[356] See Vol. I, page 137, note 8 {286}.\n\n[357] See Vol. I, page 229, note 2 {515}.\n\n[358] Richard Cobden (1804-1865), the cotton manufacturer and statesman who\nwas prominent in his advocacy of the repeal of the Corn Laws.\n\n[359] James Smith (1775-1839), solicitor to the Board of Ordnance. With his\nbrother Horatio he wrote numerous satires. His _Horace in London_ (1813)\nimitated the Roman poet. His works were collected and published in 1840.\n\n[360] Samuel Butler (1612-1680), the poet and satirist, author of\n_Hudibras_ (1663-1678).\n\n[361] \"Is it not fine to be sure of one's action when entering in a combat\nwith another? There, push me a little in order to see. NICOLE. Well! what's\nthe matter? M. JOURDAIN. Slowly. Ho there! Ho! gently. Deuce take the\nrascal! NICOLE. You told me to push. M. JOURDAIN. Yes, but you pushed me\n_en tierce_, before you pushed _en quarte_, and you did not give me time to\nparry.\"\n\n[362] John Abernethy (1764-1831), the famous physician and surgeon.\n\n[363] See Vol. I, page 102, note 5 {175}.\n\n[364] \"With what measure ye mete, it shall be measured to you again.\"\n\n[365] Eusebius of Caesarea (c. 260-340), leader of the moderate party at the\nCouncil of Nicaea, and author of a _History of the Christian Church_ in ten\nbooks (c. 324 A. D.).\n\n[366] Nathaniel Lardner (1684-1768), a non-conformist minister and one of\nthe first to advocate the scientific study of early Christian literature.\n\n[367] Henry Alford (1810-1871) Dean of Canterbury (1857-1871) and editor of\nthe Greek Testament (1849-1861).\n\n[368] The work was _The Number and Names of the Apocalyptic Beasts: with an\nexplanation and application. Part I._ London, 1848, as mentioned below.\nThom also wrote _The Assurance of Faith, or Calvinism identified with\nUniversalism_ (London, 1833), and various other religious works.\n\n[369] See Vol. I, page 222, note 14 {490}.\n\n[370] John Hamilton Thom (1808-1894) was converted to Unitarianism and was\nlong a minister in that church, preaching in the Renshaw Street Chapel from\n1831 to 1866. De Morgan refers to the Liverpool Unitarian controversy\nconducted by James Martineau and Henry Giles in response to a challenge by\nthirteen Anglican Clergy. In 1839 Thom contributed four lectures and a\nletter to this controversy. Among his religious works were a _Life of\nBlanco White_ (1845) and _Hymns, Chants, and Anthems_ (1854).\n\n[371] The spelling of these names is occasionally changed to meet the\ncondition that the numerical value of the letters shall be 666, \"the number\nof the beast\" of Revelations. The names include Julius Caesar; Valerius\nJovius Diocletianus (249-313), emperor from 287 to 305, persecutor of the\nChristians; Louis, presumably Louis XIV; Gerbert (940-1003), who reigned as\nPope Sylvester II from 999 to 1003, known to mathematicians for his abacus\nand his interest in geometry, and accused by his opponents as being in\nleague with the devil; Linus, the second Bishop of Rome, the successor of\nPeter; Camillo Borghese (1552-1621), who reigned as Pope Paul V from 1605\nto 1621, and who excommunicated all Venice in 1606 for its claim to try\necclesiastics before lay tribunals, thus taking a position which he was\nforced to abandon; Luther, Calvin; Laud (see Vol. I, page 145, note 7\n{307}); Genseric (c. 406-477), king of the Vandals, who sacked Rome in 455\nand persecuted the orthodox Christians in Africa; Boniface III, who was\npope for nine months in 606; Beza (see Vol. I, page 66, note 6 {83});\nMohammed; [Greek: braski], who was Giovanni Angelo Braschi (1717-1799), and\nwho reigned as Pope Pius VI from 1775 to 1799, dying in captivity because\nhe declined to resign his temporal power to Napoleon; Bonaparte; and, under\n[Greek: Ion Paune], possibly Pope John XIV, who reigned in 983 and 984\nduring the absence of Boniface VII in Constantinople.\n\n[372] The Greek words and names are also occasionally misspelled so as to\nfit them to the number 666. They are [Greek: Lateinos] (Latin), [Greek: he\nlatine basileia] (the Latin kingdom), [Greek: ekklesia italika] (the\nItalian Church), [Greek: euanthas] (blooming), [Greek: teitan] (Titan),\n[Greek: arnoume] (renounce), [Greek: lampetis] (the lustrous), [Greek: ho\nniketes] (conqueror), [Greek: kakos hodegos] (bad guide), [Greek: alethes\nblaberos] (truthful harmful one), [Greek: palai baskanos] (a slanderer of\nold), [Greek: amnos adikos] (unmanageable lamb), [Greek: antemos]\n(Antemos), [Greek: genserikos] (Genseric), [Greek: euinas] (with stout\nfibers), [Greek: Benediktos] (Benedict), [Greek: Bonibazios g. papa x. e.\ne. e. a.] (Boniface III, pope 68, bishop of bishops I), [Greek: oulpios]\n(baneful), [Greek: dios eimi he heras] (I, a god, am the), [Greek: he missa\nhe papike] (the papal brief), [Greek: loutherana] (Lutheran), [Greek:\nsaxoneios] (Saxon), [Greek: Bezza antitheos] (Beza antigod), [Greek: he\nalazoneia biou] (the illusion of life), [Greek: Maometis] (Mahomet);\n[Greek: Maometes b.] (Mahomet II), [Greek: theos eimi epi gaies] (I am lord\nover the earth), [Greek: iapetos] (Iapetos, father of Atlas), [Greek:\npapeiskos] (Papeiskos), [Greek: dioklasianos] (Diocletian), [Greek: cheina]\n(Cheina = Cain? China?), [Greek: braski] (Braschi, as explained in note\n10), [Greek: Ion Paune] (Paunian violet, but see note 10), [Greek: koupoks]\n(cowpox), [Greek: Bonneparte] (Bonneparte), [Greek: N. Boneparte] (N.\nBoneparte), [Greek: euporia] (facility), [Greek: paradosis] (surrender),\n[Greek: to megatherion] (the megathereum, the beast).\n\n[373] James Wapshare, whose _Harmony of the Word of God in Spirit and in\nTruth_ appeared in 1849.\n\n[374] The literature relating to the _Swastika_ is too extended to permit\nof any adequate summary in these notes.\n\n[375] Henry Edward Manning (1808-1892), at first an Anglican clergyman, he\nbecame a Roman Catholic priest in 1851, and became Cardinal in 1875. He\nsucceeded Cardinal Wiseman as Archbishop of Westminster in 1865. He wrote a\nnumber of religious works.\n\n[376] John Bright (1811-1889), Quaker, cotton manufacturer, and statesman.\nHe worked with Cobden for free trade, peace, and reform of the electorate.\n\n[377] \"The fallacy of many questions.\"\n\n[378] William Wilberforce (1759-1833), best known for his long fight for\nthe abolition of the slave trade.\n\n[379] Richard Martin (1754-1834), high sheriff of County Galway and owner\nof a large estate in Connemara. Curiously enough, he was known both for his\nreadiness in duelling and for his love for animals. He was known as\n\"Humanity Martin,\" and in 1822 secured the passage of an act \"to prevent\nthe cruel and improper treatment of cattle.\" He was one of the founders\n(1824) of the Royal Society for the Prevention of Cruelty to Animals. He is\nusually considered the original of Godfrey O'Malley in Lever's novel,\n_Charles O'Malley_.\n\n[380] See Vol. I, page 149, note 1 {323}, also text on same page.\n\n[381] See Vol. I, page 44, note 9 {34}, also text, Vol. I, page 110.\n\n[382] \"Penitential seat.\"\n\n[383] \"Well placed upon the cushion.\"\n\n[384] See Vol. II, page 58, note 109.\n\n[385] \"He has lost the right of being influenced by evidence.\"\n\n[386] \"Hung up.\"\n\n[387] \"A few things to the wise, nothing to the unlettered.\"\n\n[388] The fallacy results from dividing both members of an equation by 0, x\n- 1 being the same as 1 - 1, and calling the quotients finite.\n\n[389] \"If you order him to the sky he will go.\"\n\n[390] _Similia similibus curanter_, \"Like cures like,\" the homeopathic\nmotto.\n\n[391] \"Without harm to the proprieties.\"\n\n[392] \"What are you doing? I am standing here.\"\n\n[393] Lors feist l'Anglois tel signe. La main gausche toute ouverte il leva\nhault en l'aer, puis ferma au poing les quatres doigtz d'icelle et le\npoulce estendu assit sus la pinne du nez. Soubdain apres leva la dextre\ntoute ouverte, et toute ouverte la baissa, joignant la poulce au lieu que\nfermait le petit doigt de la gausche, et les quatre doigtz d'icelle mouvoit\nlentement en l'aer. Puis au rebours feit de la dextre ce qu'il avoit faict\nde la gausche, et de la gausche ce que avoit faict de la dextre.--A. De M.\n\n[394] _Suaviter in modo, fortiter in re_, \"Gentle in manners, firm in\naction.\"\n\n[395] See Vol. I, page 101, note 4 {174}.\n\n[396] See Vol. I, page 315, note 3 {686}.\n\n[397] Henry Fawcett (1833-1884) became totally blind in 1858, but in spite\nof this handicap he became professor of political economy at Cambridge and\nsat in parliament for a number of years. He championed the cause of reform\nand in particular he was prominent in the protection of the native\ninterests of India. The establishing of the parcels post (1882) took place\nwhile he was postmaster general (1880-1884).\n\n[398] Of course the whole thing depends upon what definition of division is\ntaken. We can multiply 2 ft. by 3 ft. if we define multiplication so as to\nallow it, or 2 ft. by 3 lb, getting foot-pounds, as is done in physics.\n\n[399] Richard Milward (1609-1680), for so the name is usually given, was\nrector of Great Braxted (Essex) and canon of Windsor. He was long the\namanuensis of John Selden, and the _Table Talk_ was published nine years\nafter Milward's death, from notes that he left. Some doubt has been cast\nupon the authenticity of the work owing to many of the opinions that it\nascribes to Selden.\n\n[400] John Selden (1584-1654) was a jurist, legal antiquary, and Oriental\nscholar. He sat in the Long Parliament, and while an advocate of reform he\nwas not an extremist. He was sent to the Tower for his support of the\nresolution against \"tonnage and poundage,\" in 1629. His _History of Tythes_\n(1618) was suppressed at the demand of the bishops. His _De Diis Syriis_\n(1617) is still esteemed a classic on Semitic mythology.\n\n[401] See Vol. I, page 42, note 4 {24}.\n\n[402] See Vol. II, page 249, note 398.\n\n[403] John Palmer (1742-1818) was a theatrical manager. In 1782 he set\nforth a plan for forwarding the mails by stage coaches instead of by\npostmen. Pitt adopted the plan in 1784. Palmer was made comptroller-general\nof the post office in 1786 and was dismissed six years later for\narbitrarily suspending a deputy. He had been verbally promised 2-1/2% on\nthe increased revenue, but Pitt gave him only a pension of L3000. In 1813\nhe was awarded L50,000 in addition to his pension.\n\n[404] Dionysius Lardner (1793-1859), professor of natural philosophy in\nLondon University (now University College). His _Cabinet Cyclopaedia_\n(1829-1849) contained 133 volumes. De Morgan wrote on probabilities, and\nLardner on various branches of mathematics, and there were many other\nwell-known contributors. Lardner is said to have made $200,000 on a lecture\ntour in America.\n\n[405] Thomas Fysche Palmer (1747-1802) joined the Unitarians in 1783, and\nin 1785 took a charge in Dundee. He was arrested for sedition because of an\naddress that it was falsely alleged that he gave before a society known as\nthe \"Friends of Liberty.\" As a matter of fact the address was given by an\nuneducated weaver, and Palmer was merely asked to revise it, declining to\ndo even this. Nevertheless he was sentenced to Botany Bay (1794) for seven\nyears. The trial aroused great indignation.\n\n[406] See Vol. I, page 80, note 5 {119}.\n\n[407] See Vol. II, page 244, note 394.\n\n[408] See Vol. I, page 352, note 1 {731}.\n\n[409] See Vol. I, page 332, note 4 {709}.\n\n[410] \"The lawyers are brought into court; let them accuse each other.\"\n\n[411] Samuel Rogers (1763-1855), the poet and art connoisseur. He declined\nthe laureateship on the death of Wordsworth (1850). Byron, his pretended\nfriend, wrote a lampoon (1818) ridiculing his cadaverous appearance.\n\n[412] Theodore Edward Hook (1788-1841), the well-known wit. He is satirized\nas Mr. Wagg in _Vanity Fair_. The _John Bull_ was founded in 1820 and Hook\nwas made editor.\n\n[413] \"On pitying the heretic.\"\n\n[414] A term of medieval logic. Barbara: All M is P, all S is M, hence all\nS is P. Celarent: No M is P, all S is M, hence no S is P.\n\n[415] \"Simply,\" \"According to which,\" \"It does not follow.\"\n\n[416]\n\n \"O sweet soul, what good shall I declare\n  That heretofore was thine, since such are thy remains!\"\n\n[417] \"Stupid fellow!\"\n\n[418] Christopher Barker (c. 1529-1599), also called Barkar, was the\nQueen's printer. He began to publish books in 1569, but did no actual\nprinting until 1576. In 1575 the Geneva Bible was first printed in England,\nthe work being done for Barker. He published 38 partial or complete\neditions of the Bible from 1575 to 1588, and 34 were published by his\ndeputies (1588-1599).\n\n[419] James Franklin (1697-1735) was born in Boston, Mass., and was sent to\nLondon to learn the printer's trade. He returned in 1717 and started a\nprinting house. Benjamin, his brother, was apprenticed to him but ran away\n(1723). James published the _New England Courant_ (1721-1727), and Benjamin\nis said to have begun his literary career by writing for it.\n\n[420] James Hodder was a writing master in Tokenhouse Yard, Lothbury, in\n1661, and later kept a boarding school in Bromley-by-Bow. His famous\narithmetic appeared at London in 1661 and went through many editions. It\nwas the basis of Cocker's work. (See Vol. I, page 42, note 4 {24}.) It was\nlong thought to have been the first arithmetic published in America, and it\nwas the first English one. There was, however, an arithmetic published much\nearlier than this, in Mexico, the _Sumario compendioso ... con algunas\nreglas tocantes al Aritmetica_, by \"Juan Diaz Freyle,\" in 1556.\n\n[421] Henry Mose, Hodder's successor, kept a school in Sherborne Lane,\nLondon.\n\n[422] Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was\nhydrographer to the Navy from 1829 to 1855. He prepared an atlas that was\nprinted by the Society for the Diffusion of Useful Knowledge.\n\n[423] Antoine Sabatier (1742-1817), born at Castres, was known as the Abbe\nbut was really nothing more than a \"clerc tonsure.\" He lived at Court and\nwas pensioned to write against the philosophers of the Voltaire group. He\nposed as the defender of morality, a commodity of which he seems to have\npossessed not the slightest trace.\n\n[424] Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644. It was\nduring his ambitious reign that Galileo was summoned to Rome to make his\nrecantation (1633), the exact nature of which is still a matter of dispute.\n\n[425] This Baden Powell (1796-1860) was the Savilian professor of geometry\n(1827-1860) at Oxford.\n\n[426] \"Memoirs of the famous bishop of Chiapa, by which it appears that he\nhad butchered or burned or drowned ten million infidels in America in order\nto convert them. I believe that this bishop exaggerated; but if we should\nreduce these sacrifices to five million victims, this would still be\nadmirable.\"\n\n[427] Alfonso X (1221-1284), known as El Sabio (the Wise), was interested\nin astronomy and caused the Alphonsine Tables to be prepared. These table\nwere used by astronomers for a long time. It is said that when the\nPtolemaic system of the universe was explained to him he remarked that if\nhe had been present at the Creation he could have shown how to arrange\nthings in a much simpler fashion.\n\n[428] George Richards (c. 1767-1837), fellow of Oriel (1790-1796), Bampton\nlecturer (1800), Vicar of St. Martin's-in-the-Fields, Westminster (1824),\nand a poet of no mean ability.\n\n[429] The \"Aboriginal Britons,\" an excellent poem, by Richards. (Note by\nByron.)--A. De M.\n\n[430] John Watkins (d. after 1831), a teacher and miscellaneous writer.\n\n[431] Frederic Shoberl (1775-1853), a miscellaneous writer.\n\n[432] He wrote, besides the _Aboriginal Britons_, _Songs of the Aboriginal\nBards_ (1792), _Modern France: a Poem_ (1793), _Odin, a drama_ (1804),\n_Emma, a drama on the model of the Greek theatre_ (1804), _Poems_ (2\nvolumes, 1804), and a _Monody on the Death of Lord Nelson_ (1806).\n\n[433] Henry Kirke White (1785-1806), published his first volume of poems at\nthe age of 18. Southey and William Wilberforce became interested in him and\nprocured for him a sizarship at St. John's College, Cambridge. He at once\nshowed great brilliancy, but he died of tuberculosis at the age of 21.\n\n[434] John Wolcot, known as Peter Pindar (1738-1819), was a London\nphysician. He wrote numerous satirical poems. His _Bozzy and Piozzi, or the\nBritish Biographers_, appeared in 1786, and reached the 9th edition in\n1788.\n\n[435] See Vol. I, page 235, note 8 {532}.\n\n[436] Richard Payne Knight (1750-1824) was a collector of bronzes, gems,\nand coins, many of his pieces being now in the British Museum. He sat in\nparliament for twenty-six years (1780-1806), but took no active part in\nlegislation. He opposed the acquisition of the Elgin Marbles, holding them\nto be of little importance. His _Analytical Inquiry into the Principles of\nTaste_ appeared in 1808.\n\n[437] Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a\ntime professor at the University of Parma. His _Observationes in M. Tullium\nCiceronem_ appeared at Pratalboino in 1535. It was revised by his nephew\nunder the title _Thesaurus Ciceronianus_ (Venice, 1570).\n\n[438] See Vol. I, page 314, note 4 {681}.\n\n[439]\n\n \"Like the geometer, who bends all his powers\n  To measure the circle, and does not succeed,\n  Thinking what principle he needs.\"\n\n[440] Francis Quarles (1592-1644), a religious poet. He wrote paraphrases\nof the Bible and numerous elegies. In the early days of the revolutionary\nstruggle he sided with the Royalists. One of his most popular works was the\n_Emblems_ (1635), with illustrations by William Marshall.\n\n[441] Regnault de Becourt wrote _La Creation du monde, ou Systeme\nd'organisation primitive suivi de l'interpretation des principaux\nphenomenes et accidents que se sont operes dans la nature depuis l'origine\nde univers jusqu'a nos jours_ (1816). This may be the work translated by\nDalmas.\n\n[442] \"Because it lacks a holy prophet.\"\n\n[443] Anghera. See Vol. II, page 60, note 127.\n\n[444] Edmund Curll (1675-1747), a well-known bookseller, publisher, and\npamphleteer. He was for a time at \"The Peacock without Temple Bar,\" and\nlater at \"The Dial and Bible against St. Dunstan's Church.\" He was fined\nrepeatedly for publishing immoral works, and once stood in the pillory for\nit. He is ridiculed in the _Dunciad_ for having been tossed in a blanket by\nthe boys of Westminster School because of an oration that displeased them.\n\n[445] See Vol. II, page 109, note 206.\n\n[446] Encyclopaedia.\n\n[447] Author of the _Historia Naturalis_ (77 A.D.)\n\n[448] Author of the _De Institutione Oratorio Libri_ XII (c. 91 A.D.)\n\n[449] His _De Architectures Libri_ X was not merely a work on architecture\nand building, but on the education of the architect.\n\n[450] Cyclophoria.\n\n[451] William Caxton (c. 1422-c.1492), sometime Governor of the Company of\nMerchant Adventurers in Bruges (between 1449 and 1470). He learned the art\nof printing either at Bruges or Cologne, and between 1471 and 1477 set up a\npress at Westminster. Tradition says that the first book printed in England\nwas his _Game and Playe of Chesse_ (1474). The _Myrrour of the Worlde and\nth'ymage of the same_ appeared in 1480. It contains a brief statement on\narithmetic, the first mathematics to appear in print in England.\n\n[452] See Vol. I, page 45, note 6 {40}. De Morgan is wrong as to the date\nof the _Margarita Philosophica_. The first edition appeared at Freiburg in\n1503.\n\n[453] Reisch was confessor to Maximilian I (1459-1519), King of the Romans\n(1486) and Emperor (1493-1519).\n\n[454] Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philosophy\nand mathematics in various cities of France and Germany. His _Institutionum\nastronomicarum libri III_ appeared at Basel in 1528, his _Cosmographia_ at\nParis in 1529, and his _Opera_ at Leyden in 1531.\n\n[455] Johannes Heinrich Alsted (1588-1638) was professor of philosophy and\ntheology at his birthplace, Herborn, in Nassau, and later at Weissenberg.\nHe published several works, including the _Elementale mathematicum_ (1611),\n_Systema physicae harmonicae_ (1612), _Methodus admirandorum\nmathematicorum_ (1613), _Encyclopaedia septem tomis distincta_ (1630), and\nthe work mentioned above.\n\n[456] Johann Jakob Hoffmann (1635-1706), professor of Greek and history at\nhis birthplace, Basel. He also wrote the _Epitome metrica historiae\nuniversalis civilis et sacrae ab orbe condito_ (1686).\n\n[457] Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but\nkind-hearted freethinker. His _Cyclopaedia, or an Universal Dictionary_ was\ntranslated into French and is said to have suggested the great\n_Encyclopedie_.\n\n[458] _Encyclopedie, ou Dictionnaire raisonne des sciences, des arts et des\nmetiers, par un societe de gens de lettres. Mis en ordre et publie par M.\nDiderot, et quant a la partie mathematique, par M. d'Alembert._ Paris,\n1751-1780, 35 volumes.\n\n[459] \"From the egg\" (state).\n\n[460] See Vol. I, page 382, note 12 {785}.\n\n[461] See Vol. II, page 4, note 15.\n\n[462] \"In morals nothing should serve man as a model but God; in the arts,\nnothing but nature.\"\n\n[463] _Encyclopedie Methodique, ou par ordre de matieres._ Paris,\n1782-1832, 166-1/2 volumes.\n\n[464] See Vol. II, page 193, note 336.\n\n[465] _Encyclopaedia Metropolitana; or, Universal Dictionary of Knowledge._\nLondon, 1845, 29 volumes. A second edition came out in 1848-1858 in 40\nvolumes.\n\n[466] See Vol. I, page 137, note 8 {286}.\n\n[467] See Vol. I, page 80, note 5 {119}.\n\n[468] De Morgan should be alive to satirize some of the statements on the\nhistory of mathematics in the eleventh edition.\n\n[469] John Pringle Nichol (1804-1859), Regius professor of astronomy at\nGlasgow and a popular lecturer on the subject. He lectured in the United\nStates in 1848-1849. His _Views of the Architecture of the Heavens_ (1838)\nwas a very popular work, and his _Planetary System_ (1848, 1850) contains\nthe first suggestion for the study of sun spots by the aid of photography.\n\n[470] See Vol. II, page 109, note 206.\n\n[471] George Long (1800-1879), a native of Poulton, in Lancashire, was\ncalled to the University of Virginia when he was only twenty-four years old\nas professor of ancient languages. He returned to England in 1828 to become\nprofessor of Greek at London University. From 1833 to 1849 he edited the\ntwenty-nine volumes of the _Penny Cyclopaedia_. He was an authority on Roman\nlaw.\n\n[472] A legal phrase, \"Qui tam pro domina regina, quam pro se ipso\nsequitur,\"--\"Who sues as much on the Queen's account as on his own.\"\n\n[473] Arthur Cayley (1821-1895) was a fellow of Trinity College, Cambridge\n(1842-1846) and was afterwards a lawyer (1849-1863). During his fourteen\nyears at the bar he published some two hundred mathematical papers. In 1863\nhe became professor of mathematics at Cambridge, and so remained until his\ndeath. His collected papers, nine hundred in number, were published by the\nCambridge Press in 13 volumes (1889-1898). He contributed extensively to\nthe theory of invariants and covariants. De Morgan's reference to his\ncoining of new names is justified, although his contemporary, Professor\nSylvester, so far surpassed him in this respect as to have been dubbed \"the\nmathematical Adam.\"\n\n[474] See Vol. II, page 26, note 56.\n\n[475] See Vol. I, page 111, note 3 {207}.\n\n[476] See Vol. I, page 87, note 6 {135}.\n\n[477] Pierre Dupuy (1582-1651) was a friend and relative of De Thou. With\nthe collaboration of his brother and Nicolas Rigault he published the 1620\nand 1626 editions of De Thou's History. He also wrote on law and history.\nHis younger brother, Jacques (died in 1656), edited his works. The two had\na valuable collection of books and manuscripts which they bequeathed to the\nRoyal Library at Paris.\n\n[478] See Vol. I, page 51, note 3 {51}.\n\n[479] It was Cosmo de' Medici (1590-1621) who was the patron of Galileo.\n\n[480] See Vol. I, page 40, note 4 {20}.\n\n[481] See Vol. I, page 106, note 4 {188}.\n\n[482] Sir Edward Sherburne (1618-1702), a scholar of considerable\nreputation. The reference by De Morgan is to _The Sphere of Marcus\nManilius_, in the appendix to which is a _Catalogue of Astronomers, ancient\nand modern_.\n\n[483] George Parker, second Earl of Macclesfield (1697-1764). He erected an\nobservatory at Shirburn Castle, Oxfordshire, in 1739, and fitted it out\nwith the best equipment then available. He was President of the Royal\nSociety in 1752.\n\n[484] See Vol. II, page 148, note 263.\n\n[485] See Vol. I, page 140, note 7 {296}.\n\n[486] See Vol. I, page 106, note 4 {188}.\n\n[487] Edward Bernard (1638-1696), although Savilian professor of astronomy\nat Oxford, was chiefly interested in archeology.\n\n[488] See Vol. I, page 107, note 1 {190}.\n\n[489] See Vol. I, page 107, note 1 {190}.\n\n[490] See Vol. I, page 135, note 3 {281}.\n\n[491] Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-1773), well\nknown for the letters written to his son which were published posthumously\n(1774).\n\n[492] Peter Daval (died in 1763), Vice-President of the Royal Society, and\nan astronomer of some ability.\n\n[493] See Vol. I, page 376, note 1 {766}.\n\n[494] William Oughtred (c. 1573-1660), a fellow of King's College,\nCambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-known\narithmetic and trigonometry of his time. His _Arithmeticae in Numero &\nSpeciebus Institutio ... quasi Clavis Mathematicae est_ (1631) went through\nmany editions and appeared in English as _The Key to the Mathematicks new\nforged and filed_ in 1647.\n\n[495] See Vol. I, page 140, note 5 {294}.\n\n[496] Stephen Jordan Rigaud (1816-1859) was senior assistant master of\nWestminster School (1846) and head master of Queen Elizabeth's School at\nIpswich (1850). He was made Bishop of Antigua in 1858 and died of yellow\nfever the following year.\n\n[497] He also wrote a memoir of his father, privately printed at Oxford in\n1883.\n\n[498] See Vol. I, page 69, note 3 {96}.\n\n[499] See Vol. I, page 106, note 4 {188}.\n\n[500] William Gascoigne was born at Middleton before 1612 and was killed in\nthe battle of Marston Moor in 1644. He was an astronomer and invented the\nmicrometer with movable threads (before 1639).\n\n[501] Seth Ward (1617-1689) was deprived of his fellowship at Cambridge for\nrefusing to sign the covenant. He became professor of astronomy at Oxford\n(1649), Bishop of Exeter (1662), Bishop of Salisbury (1667), and Chancellor\nof the Garter (1671). He is best known for his solution of Kepler's problem\nto approximate a planet's orbit, which appeared in his _Astronomia\ngeometrica_ in 1656.\n\n[502] See Vol. I, page 110, note 2 {198}.\n\n[503] See Vol. I, page 100, note 2 {172}.\n\n[504] See Vol. I, page 107, note 1 {190}.\n\n[505] See Vol. I page 114, note 6 {220}.\n\n[506] See Vol. I, page 77, note 4 {118}.\n\n[507] See Vol. I, page 125, note 3 {253}.\n\n[508] See Vol. I, page 105, note 2 {186}.\n\n[509] Heinrich Oldenburgh (1626-1678) was consul in England for the City\nof Bremen, his birthplace, and afterwards became a private teacher in\nLondon. He became secretary of the Royal Society and contributed on\nphysics and astronomy to the _Philosophical Transactions_.\n\n[510] Thomas Brancker, or Branker (1636-1676) wrote the _Doctrinae\nsphaericae adumbratio et usus globorum artificialium_ (1662) and\ntranslated the algebra of Rhonius with the help of Pell. The latter work\nappeared under the title of _An Introduction to Algebra_ (1668), and\nis noteworthy as having brought before English mathematicians the\nsymbol / for division. The symbol never had any standing on the\nContinent for this purpose, but thereafter became so popular in England\nthat it is still used in all the English-speaking world.\n\n[511] See Vol. I, page 118, note 1 {230}.\n\n[512] Pierre Bertius (1565-1629) was a native of Flanders and was educated\nat London and Leyden. He became a professor at Leyden, and later held the\nchair of mathematics at the College de France. He wrote chiefly on\ngeography.\n\n[513] See Vol. II, page 297, note 487.\n\n[514] Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at\nMessina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome\nat the Convent of St. Panteleon. He wrote several works on geometry,\nastronomy, and physics.\n\n[515] See Vol. I, page 172, note 2 {381}.\n\n[516] Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient\nlanguages and later of mathematics and physics at the College of Pau, and\nafterwards professor of rhetoric at the College Louis-le-Grand at Paris. He\nwrote on geometry, astronomy and physics.\n\n[517] Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse,\nand died in 1665. Although connected with the parliament of Toulouse, his\nsignificant work was in mathematics. He was one of the world's geniuses in\nthe theory of numbers, and was one of the founders of the theory of\nprobabilities and of analytic geometry. After his death his son published\nhis edition of Diophantus (1670) and his _Varia opera mathematica_ (1679).\n\n[518] This may be Christopher Townley (1603-1674) the antiquary, or his\nnephew, Richard, who improved the micrometer already invented by Gascoigne.\n\n[519] Adrien Auzout a native of Rouen, who died at Rome in 1691. He\ninvented a screw micrometer with movable threads (1666) and made many\nimprovements in astronomical instruments.\n\n[520] See Vol. I, page 66, note 9 {86}.\n\n[521] See Vol. I, page 124, note 7 {248}.\n\n[522] John Machin (d. 1751) was professor of astronomy at Gresham College\n(1713-1751) and secretary of the Royal Society. He translated Newton's\n_Principia_ into English. His computation of [pi] to 100 places is given in\nWilliam Jones's _Synopsis palmariorum matheseos_ (1706).\n\n[523] Pierre Remond de Montmort (1678-1719) was canon of Notre Dame until\nhis marriage. He was a gentleman of leisure and devoted himself to the\nstudy of mathematics, especially of probabilities.\n\n[524] Roger Cotes (1682-1716), first Plumian professor of astronomy and\nphysics at Cambridge, and editor of the second edition of Newton's\n_Principia_. His posthumous _Harmonia Mensurarum_ (1722) contains \"Cotes's\nTheorem\" on the binomial equation. Newton said of him, \"If Mr. Cotes had\nlived we had known something.\"\n\n[525] See Vol. I, page 135, note 3 {281}.\n\n[526] See Vol. I, page 377, note 4 {769}.\n\n[527] Charles Rene Reyneau (1656-1728) was professor of mathematics at\nAngers. His _Analyse demontree, ou Maniere de resoudre les problemes de\nmathematiques_ (1708) was a successful attempt to popularize the theories\nof men like Descartes, Newton, Leibnitz, and the Bernoullis.\n\n[528] Brook Taylor (1685-1731), secretary of the Royal Society, and student\nof mathematics and physics. His _Methodus incrementorum directa et inversa_\n(1715) was the first treatise on the calculus of finite differences. It\ncontained the well-known theorem that bears his name.\n\n[529] Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut\n(1735) to measure an arc of a meridian in Lapland. He was head of the\nphysics department in the Berlin Academy from 1745 until 1753. He wrote\n_Sur la figure de la terre_ (1738) and on geography and astronomy.\n\n[530] Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and\nwas one of those sent by the Academy of Sciences to measure an arc of a\nmeridian in Peru (1735). The object of this and the work of Maupertuis was\nto determine the shape of the earth and see if Newton's theory was\nsupported.\n\n[531] Charles Marie de la Condamine (1701-1774) was a member of the Paris\nAcademy of Sciences and was sent with Bouguer to Peru, for the purpose\nmentioned in the preceding note. He wrote on the figure of the earth, but\nwas not a scientist of high rank.\n\n[532] See Vol. I, page 136, note 5 {283}.\n\n[533] See Vol. II, page 296, note 483.\n\n[534] Thomas Baker (c. 1625-1689) gave a geometric solution of the\nbiquadratic in his _Geometrical Key, or Gate of Equations unlocked_ (1684).\n\n[535] See Vol. I, page 160, note 5 {350}.\n\n[536] See Vol. I, page 87, note 4 {133}.\n\n[537] See Vol. I, page 132, note 2 {272}.\n\n[538] See Vol. I, page 118, second note 1 {231}.\n\n[539] The name of Newton is so well known that no note seems necessary. He\nwas born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in\n1727.\n\n[540] John Keill (1671-1721), professor of astronomy at Oxford from 1710,\nis said to have been the first to teach the Newtonian physics by direct\nexperiment, the apparatus being invented by him for the purpose. He wrote\non astronomy and physics. His _Epistola de legibus virium centripetarum_,\nin the Philosophical Transactions for 1708, accused Leibnitz of having\nobtained his ideas of the calculus from Newton, thus starting the priority\ncontroversy.\n\n[541] Thomas Digges (d. in 1595) wrote _An Arithmeticall Militare Treatise,\nnamed Stratioticos_ (1579), and completed _A geometrical practise, named\nPantometria_ (1571) that had been begun by his father, Leonard Digges.\n\n[542] John Dee (1527-1608), the most famous astrologer of his day, and\nsomething of a mathematician, wrote a preface to Billingsley's translation\nof Euclid into English (1570).\n\n[543] See Vol. I, page 76, note 3 {112}.\n\n[544] Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter\nRaleigh, who sent him to survey Virginia (1585). He was one of the best\nEnglish algebraists of his time, but his _Artis Analyticae Praxis ad\nAequationes Algebraicas resolvendas_ (1631) did not appear until ten years\nafter his death.\n\n[545] Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life\nchiefly to the study of chronology, writing upon the subject and taking\nissue with Scaliger (1601).\n\n[546] See Vol. I, page 69, note 3 {96}.\n\n[547] Walter Warner edited Harriot's _Artis Analyticae Praxis_ (1631).\nTarporley is not known in mathematics.\n\n[548] See Vol. I, page 105, note 2 {186}.\n\n[549] See Vol. I, page 115, note 3 {224}.\n\n[550] See Vol. II, page 300, note 509.\n\n[551] See Vol. I, page 107, note 1 {190}.\n\n[552] Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some\nyears he was assistant to John Pell, then ambassador to Switzerland. He\nwrote on arithmetical instruments invented by him (1673), on hydrostatics\n(1697) and on church history (1658).\n\n[553] See Vol. I, page 153, note 4 {337}.\n\n[554] See Vol. I, page 85, note 2 {129}.\n\n[555] See Vol. I, page 43, note 8 {33}.\n\n[556] See Vol. I, page 43, note 7 {32}.\n\n[557] See Vol. I, page 382, note 13 {786}. The history of the subject may\nbe followed in Braunmuehl's _Geschichte der Trigonometrie_.\n\n[558] See Vol. I, page 377, note 3 {768}.\n\n[559] See Vol. I, page 108, note 2 {192}.\n\n[560] Michael Dary wrote _Dary's Miscellanies_ (1669), _Gauging epitomised_\n(1669), and _The general Doctrine of Equation_ (1664).\n\n[561] John Newton (1622-1678), canon of Hereford (1673), educational\nreformer, and writer on elementary mathematics and astronomy.\n\n[562] See Vol. I, page 87, note 4 {133}.\n\n[563] \"The average of the two equal altitudes of the sun before and after\ndinner.\"\n\n[564] See Vol. I, page 42, note 4 {24}.\n\n[565] London, 1678. It went though many editions.\n\n[566] \"This I who once ...\"\n\n[567] Arthur Murphy (1727-1805) worked in a banking house until 1754. He\nthen went on the stage and met with some success at Covent Garden. His\nfirst comedy, _The Apprentice_ (1756) was so successful that he left the\nstage and took to play writing. His translation of Tacitus appeared in\n1793, in four volumes.\n\n[568] Edmund Wingate (1596-1656) went to Paris in 1624 as tutor to Princess\nHenrietta Maria and remained there several years. He wrote _L'usage de la\nregle de proportion_ (Paris, 1624, with an English translation in 1626),\n_Arithmetique Logarithmetique_ (Paris, 1626, with an English translation in\n1635), and _Of Natural and Artificial Arithmetick_ (London, 1630, revised\nin 1650-1652), part I of which was one of the most popular textbooks ever\nproduced in England.\n\n[569] John Lambert (1619-1694) was Major-General during the Revolution and\nhelped to draw up the request for Cromwell to assume the protectorate. He\nwas imprisoned in the Tower by the Rump Parliament. He was confined in\nGuernsey until the clandestine marriage of his daughter Mary to Charles\nHatton, son of the governor, after which he was removed (1667) to St.\nNicholas in Plymouth Sound.\n\n[570] Samuel Foster (d. in 1652) was made professor of astronomy at Gresham\nCollege in March, 1636, but resigned in November of that year, being\nsucceeded by Mungo Murray. Murray vacated his chair by marriage in 1641 and\nFoster succeeded him. He wrote on dialling and made a number of\nimprovements in geometric instruments.\n\n[571] \"Twice of the word a minister,\" that is, twice a minister of the\nGospel.\n\n[572] This is _The Lives of the Professors of Gresham College to which is\nprefixed the Life of the Founder, Sir Thomas Gresham_, London, 1740. It was\nwritten by John Ward (c. 1679-1758), professor of rhetoric (1720) at\nGresham College and vice-president (1752) of the Royal Society.\n\n[573] Charles Montagu (1661-1715), first Earl of Halifax, was Lord of the\nTreasury in 1692, and was created Baron Halifax in 1700 and Viscount\nSunbury and Earl of Halifax in 1714. He introduced the bill establishing\nthe Bank of England, the bill becoming a law in 1694. He had troubles of\nhis own, without considering Newton, for he was impeached in 1701, and was\nthe subject of a damaging resolution of censure as auditor of the exchequer\nin 1703. Although nothing came of either of these attacks, he was out of\noffice during much of Queen Anne's reign.\n\n[574] See Vol. II, page 302, note 547.\n\n[575] See Vol. I, page 105, note 2 {186}.\n\n[576] James Dodson (d. 1757) was master of the Royal Mathematical School,\nChrist's Hospital. He was De Morgan's great-grandfather. The\n_Anti-Logarithmic Canon_ was published in 1742.\n\n[577] See Vol. I, page 106, note 4 {188}.\n\n[578] See Vol. I, page 110, note 2 {198}.\n\n[579] Richard Busby, (1606-1695), master of Westminster School (1640) had\namong his pupils Dryden and Locke.\n\n[580] See Vol. I, page 107, note 1 {190}.\n\n[581] Herbert Thorndike (1598-1672), fellow of Trinity College, Cambridge\n(1620-1646), and Prebend of Westminster (1661), was a well-known\ntheological writer of the time.\n\n[582] See Vol. I, page 140, note 5 {294}.\n\n[583] See Vol. I, page 108, note 2 {192}.\n\n[584] \"Labor performed returns in a circle.\"\n\n[585] See Vol. II, page 208.\n\n[586] \"Whatever objections one may make to the above arguments, one always\nfalls into an absurdity.\"\n\n[587] See Vol. II. page 11, note 29. _The Circle Squared; and the solution\nof the problem adapted to explain the difference between square and\nsuperficial measurement_ appeared at Brighton in 1865.\n\n[588] \"And beyond that nothing.\"\n\n[589] Gillott (1759-1873) was the pioneer maker of steel pens by machinery,\nreducing the price from 1s. each to 4d. a gross. He was a great collector\nof paintings and old violins.\n\n[590] William Edward Walker wrote five works on circle squaring (1853,\n1854, 1857, 1862, 1864), mostly and perhaps all published at Birmingham.\n\n[591] Solomon M. Drach wrote _An easy Rule for formulizing all Epicyclical\nCurves_ (London, 1849), _On the Circle area and Heptagon-chord_ (London,\n1864), _An easy general Rule for filling up all Magic Squares_ (London,\n1873), and _Hebrew Almanack-Signs_ (London, 1877), besides numerous\narticles in journals.\n\n[592] See Vol. I, page 168, note 3 {371}.\n\n[593] See Vol. I, page 254, note 2 {580}.\n\n[594] See Vol. I, page 98, note 6 {163}.\n\n[595] Robert Fludd or Flud (1574-1637) was a physician with a large London\npractice. He denied the diurnal rotation of the earth, and was attacked by\nKepler and Mersenne, and accused of magic by Gassendi. His _Apologia\nCompendiania, Fraternitatem de Rosea Cruce suspicionis ... maculis\naspersam, veritatis quasi Fluctibus abluens_ (Leyden, 1616) is one of a\nlarge number of works of the mystic type.\n\n[596] Consult _To the Christianity of the Age. Notes ... comprising an\nelucidation of the scope and contents of the writings ... of Dionysius\nAndreas Freher_ (1854).\n\n[597] Sir William Robert Grove (1811-1896), although called to the bar\n(1835) and to the bench (1853), is best known for his work as a physicist.\nHe was professor of experimental philosophy (1840-1847) at the London\nInstitution, and invented a battery (1839) known by his name. His\n_Correlation of Physical Forces_ (1846) went through six editions and was\ntranslated into French.\n\n[598] Johann Tauler (c. 1300-1361), a Dominican monk of Strassburg, a\nmystic, closely in touch with the Gottesfreunde of Basel. His _Sermons_\nfirst appeared in print at Leipsic in 1498.\n\n[599] Paracelsus (c. 1490-1541). His real name was Theophrastes Bombast von\nHohenheim, and he took the name by which he is generally known because he\nheld himself superior to Celsus. He was a famous physician and pharmacist,\nbut was also a mystic and neo-Platonist. He lectured in German on medicine\nat Basel, but lost his position through the opposition of the orthodox\nphysicians and apothecaries.\n\n[600] See Vol. I, page 256, note 2 {588}.\n\n[601] Philip Schwarzerd (1497-1560) was professor of Greek at Wittenberg.\nHe helped Luther with his translation of the Bible.\n\n[602] Johann Reuchlin (1455-1522), the first great German humanist, was\nvery influential in establishing the study of Greek and Hebrew in Germany.\nHis lectures were mostly delivered privately in Heidelberg and Stuttgart.\nUnlike Melanchthon, he remained in the Catholic Church.\n\n[603] Joseph Chitty (1776-1841) published his _Precedents of Pleading_ in\n1808 and his _Reports of Cases on Practice and Pleading_ in 1820-23 (2\nvolumes).\n\n[604] See Vol. I, page 44, note 1 {35}.\n\n[605] See Vol. I, page 44, note 4 {38}.\n\n[606] Jean Pelerin, also known as Viator, who wrote on perspective. His\nwork appeared in 1505, with editions in 1509 and 1521.\n\n[607] Henry Stephens. See Vol. I, page 44, note 3 {37}.\n\n[608] The well-known grammarian (1745-1826). He was born at Swatara, in\nPennsylvania, and practised law in New York until 1784, after which he\nresided in England. His grammar (1795) went through 50 editions, and the\nabridgment (1818) through 120 editions. Murray's friend Dalton, the\nchemist, said that \"of all the contrivances invented by human ingenuity for\npuzzling the brains of the young, Lindley Murray's grammar was the worst.\"\n\n[609] Robert Recorde (c. 1510-1558) read and probably taught mathematics\nand medicine at Cambridge up to 1545. After that he taught mathematics at\nOxford and practised medicine in London. His _Grounde of Artes_, published\nabout 1540, was the first arithmetic published in English that had any\ninfluence. It went through many editions. The _Castle of Knowledge_\nappeared in 1551. It was a textbook on astronomy and the first to set forth\nthe Copernican theory in England. Like Recorde's other works it was written\non the catechism plan. His _Whetstone of Witte ... containying thextraction\nof Rootes: The Cosike practise, with the rule of Equation: and the woorkes\nof Surde Nombres_ appeared in 1557, and it is in this work that the modern\nsign of equality first appears in print. The word \"Cosike\" is an adjective\nthat was used for a long time in Germany as equivalent to algebraic, being\nderived from the Italian _cosa_, which stood for the unknown quantity.\n\n[610] Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of\nState under Elizabeth (1596-1603) and under James I (1603-1612).\n\n[611] In America the German pronunciation is at present universal among\nmathematicians, as in the case of most other German names. This is due, no\ndoubt, to the great influence that Germany has had on American education in\nthe last fifty years.\n\n[612] The latest transliteration is substantially K'ung-fu-tz[vu].\n\n[613] The tendency seems to be, however, to adopt the forms used of\nindividuals or places as rapidly as the mass of people comes to be prepared\nfor it. Thus the spelling Leipzig, instead of Leipsic, is coming to be very\ncommon in America.\n\n[614] Sir Edward Coke (1552-1634), the celebrated jurist.\n\n[615] Dethlef Cluvier or Cluever (d. 1708 at Hamburg) was a nephew, not a\ngrandson, of Philippe Cluvier, or Philipp Cluever (1580-c. 1623). Dethlef\ntraveled in France and Italy and then taught mathematics in London. He\nwrote on astronomy and philosophy and also published in the _Acta\nEruditorum_ (1686) his _Schediasma geometricum de nova infinitorum\nscientia_. _Quadratura circuli infinitis modis demonstrata_, and his\n_Monitum ad geometras_ (1687). Philippe was geographer of the Academy of\nLeyden. His _Introductionis in universam geographiam tam veterem quam novam\nlibri sex_ appeared at Leyden in 1624, about the time of his death.\n\n[616] See Vol. I, page 124, note 7 {248}.\n\n[617] Bernard Nieuwentijt (1654-1718), a physician and burgomaster at\nPurmerend. His _Considerationes circa Analyseos ad quantitates infinite\nparvas applicatae Principia et Calculi Differentialis usum_ (Amsterdam,\n1694) was attacked by Leibnitz. He replied in his _Considerationes secundae_\n(1694), and also wrote the _Analysis Infinitorum, seu Curvilineorum\nProprietates ex Polygonorum Natura deductae_ (1695). His most famous work\nwas on the existence of God, _Het Regt Gebruik der Werelt Beschouwingen_\n(1718).\n\n[618] \"From a given line to construct\" etc.\n\n[619] \"Pirates do not fight one another.\"\n\n[620] Claude Mallemens (Mallement) de Messanges (1653-1723) was professor\nof philosophy at the College du Plessis, in Paris, for 34 years. The work\nto which De Morgan refers is probably the _Fameux Probleme de la quadrature\ndu cercle, resolu geometriquement par le cercle et a ligne droite_ that\nappeared in 1683.\n\n[621] On Tycho Brahe see Vol. I, page 76, note 3 {112}.\n\n[622] Wilhelm Frederik von Zytphen also published the _Tidens Stroem_, a\nchronological table, in 1840. The work to which De Morgan refers, the\n_Solens Bevaegelse i Verdensrummet_, appeared first in 1861. De Morgan seems\nto have missed his _Nogl Ord om Cirkelens Quadratur_ which appeared in\n1865, at Copenhagen.\n\n[623] James Joseph Sylvester (1814-1897), professor of natural philosophy\nat University College, London (1837-1841), professor of mathematics at the\nUniversity of Virginia (1841-1845), actuary in London (1845-1855),\nprofessor of mathematics at Woolwich (1877-1884) and at Johns Hopkins\nUniversity, Baltimore (1877-1884), and Savilian professor of geometry at\nOxford (1884-1894).\n\n[624] See Vol. I, page 76, note 3 {112}.\n\n[625] See Vol. II, page 205, note 349.\n\n[626] See Vol. I, page 76, note 3 {112}.\n\n[627] See Vol. I, page 46, note 1 {42}.\n\n[628] See Vol. II, page 183, note 318.\n\n[629] See Vol. I, page 321, note 2 {691}.\n\n[630] James Mill, born 1773, died 1836.\n\n[631] See Vol. II, page 3, note 11.\n\n[632] See Vol. II, page 3, note 13.\n\n[633] See Vol. II, page 3, note 14.\n\n[634] This anecdote is printed at page 4 (Vol. II); but as it is used in\nillustration here, and is given more in detail, I have not omitted\nit.--S.E. De M.\n\n[635] See Vol. II, page 4, note 15.\n\n[636] See Vol. I, page 382, note 13 {786}.\n\n[637] \"Monsieur, (a + b^{n})/n = x, whence God exists; answer that!\"\n\n[638] \"Monsieur, you know very well that your argument requires the\ndevelopment of x according to integral powers of n.\"\n\n[639] See Vol. I, page 153, note 4 {337}.\n\n[640] Thomas Love Peacock (1785-1866) an English novelist and poet.\n\n[641] Perhaps Dr. Samuel Warren (1807-1877), the author of _Ten Thousand a\nYear_ (serially in Blackwood's in 1839; London, 1841).\n\n[642] See Vol. I, page 255, note 6 {584}.\n\n[643] \"From many, one; much in little; Ultima Thule (the most remote\nregion); without which not.\"\n\n[644] Spurius Maelius (fl. 440 B. C.), who distributed corn freely among the\npoor in the famine of 440 B. C. and was assassinated by the patricians.\n\n[645] Spurius Cassius Viscellinus, Roman consul in 502, 493, and 486 B. C.\nPut to death in 485.\n\n[646] \"O what a fine bearing, he said, that has no brain.\"\n\n[647] Sir William Rowan Hamilton. See Vol. I, page 332, note 4 {709}.\n\n[648] William Allen Whitworth, the author of the well-known _Choice and\nChance_ (Cambridge, 1867), and other works.\n\n[649] James Maurice Wilson, whose _Elementary Geometry_ appeared in 1868\nand went through several editions.\n\n[650] See Vol. II, page 183, note 315.\n\n[651] \"Force of inertia conquered,\" and \"Victory in the whole heavens.\"\n\n[652] \"With all his might.\"\n\n[653] George Berkeley (1685-1753), Bishop of Cloyne, the idealistic\nphilosopher and author of the _Principles of Human Knowledge_ (1710), _The\nAnalyst, or a Discourse addressed to an Infidel Mathematician_ (1734), and\n_A Defense of Freethinking in Mathematics_ (1735). He asserted that space\ninvolves the idea of movement without the sensation of resistance. Space\nsensation less than the \"minima sensibilia\" is, therefore, impossible. From\nthis he argues that infinitesimals are impossible concepts.\n\n[654] See Vol. I, page 85, note 2 {129}.\n\n[655] See Vol. I, page 81, note 6 {120}.\n\n[656] Edwin Dunkin revised Lardner's _Handbook of Astronomy_ (1869) and\nMilner's _The Heavens and the Earth_ (1873) and wrote _The Midnight Sky_\n(1869).\n\n[657] Michael Faraday (1791-1867) the celebrated physicist and chemist. He\nwas an assistant to Sir Humphrey Davy (1813) and became professor of\nchemistry at the Royal Institution, London, in 1827.\n\n[658] \"If you teach a fool he shows no joyous countenance; he cordially\nhates you; he wishes you buried.\"\n\n[659] \"Every man is an animal, Sortes is a man, therefore Sortes is an\nanimal.\"\n\n[660]\n\n \"May some choice patron bless each grey goose quill;\n  May every Bavius have his Bufo still.\"--POPE, _Prologue to the Satires._\n\nBavius has become proverbial as a bad poet from the lines in Vergil's\n_Eclogues_ (III, 90):\n\n \"Qui Bavium non odit, amet tua carmina, Maevi,\n  Atque idem jungat vulpes, et mulgeat hircos.\"\n\n\"He who does not hate Bavius shall love thy verses, O Maevius; and the same\nshall yoke foxes and shall milk he-goats.\"\n\nBavius and Maevius were the worst of Latin poets, condemned by Horace as\nwell as Vergil.\n\n[661] See Vol. II, page 158, note 279.\n\n[662] \"Honest,\" \"useful,\" \"handsome,\" \"sweet.\"\n\n[663] \"Let not the fourth man attempt to speak.\"\n\n[664]\n\n \"In those old times,--ah\n 'Twas just like this, ah!\"\n\n[665] See Vol. I, page 382, note 12 {785}.\n\n[666] These remarks were never written.--S. E. De M.\n\n[667]\n\n \"Fleas, flies, and friars, are masters who sadly the people abuse,\n  And thistles and briars are sure growing grains to abuse.\n  O Christ, who hatest strife and slayst all things in peace,\n  Destroy where'er are rife, briars, friars, flies and fleas.\n  Fleas, flies, and friars foul fall them these fifteen years\n  For none that there is loveth fleas, flies, nor freres.\"\n\n[668] \"It is my plan to restore to an unskilled race the worthy arts of a\nbetter life.\"\n\n[669] The first sentences of the first oration of Cicero against Catiline:\n\"Quo usque tandem abutere, Catilina, patientia nostra?\" (How long, O\nCatiline, will you abuse our patience?) \"Quamdiu etiam furor iste tuus nos\neludet?\" (How long will this your madness baffle us?) \"Nihilne te nocturnum\npraesidium Palati, ... nihil horum ora voltusque moverunt?\" (Does the night\nwatch of the Palatium, ... do the faces and expressions of all these men\nfail to move you?) \"In te conferri ...\" (This plague should have been\ninflicted upon you long ago, which you have plotted against us so long.)\n\n[670] \"Beware of the things that are marked.\"\n\n[671] \"Farewell, ye teachers without learning! See to it that at our next\nmeeting we may find you strong in body and sound in mind.\"\n\n[672] See Vol. I, page 336, note 8 {713}.\n\n[673] See Vol. I, page 229, note 2 {515}.\n\n[674] This proof, although capable of improvement, is left as in the\noriginal. Those who may be interested in the mathematics of the question,\nmay consult F. Enriques, _Fragen der Elementargeometrie_ (German by\nFleischer), Leipsic, 1907, Part II, p. 267; F. Rudio, _Archimedes_,\n_Huygens_, _Lambert_, _Legendre_. _Vier Abhandlungen ueber die\nKreismessung_, Leipsic, 1892; F. Klein, _Famous Problems of Elementary\nGeometry_ (English by Beman and Smith), Boston, 1895; J. W. A. Young,\n_Monographs on Modern Mathematics_, New York, 1911, Chap. IX (by the editor\nof the present edition of De Morgan.)\n\n[675] See Vol. I, page 69, note 2 {95}.\n\n[676] See Vol. I, page 137, note 8 {286}.\n\n[677] Joseph Allen Galbraith who, with Samuel Haughton, wrote the Galbraith\nand Haughton's _Scientific Manuals_. (Euclid, 1856; Algebra, 1860;\nTrigonometry, 1854; Optics, 1854, and others.)\n\n[678] This note on Carlyle (1795-1881) is interesting. The translation of\nLegendre appeared in the same year (1824) as his translation of Goethe's\n_Wilhelm Meister_.\n\n[679] Michael Stifel (1487-1567), also known as Stiefel, Styfel, and\nStifelius, was an Augustine monk but became a convert to Lutheranism. He\nwas professor of mathematics at Jena (1559-1567). His edition of the _Coss_\nappeared at Koenigsberg in 1553, the first edition having been published in\n1525. The + and - signs first appeared in print in Widman's arithmetic of\n1489, but for purposes of algebra this book was one of the first to make\nthem known.\n\n[680] Christoff Rudolff was born about 1500 and died between 1540 and 1552.\n_Die Coss_ appeared in 1525 and his arithmetic in 1526.\n\n       *       *       *       *       *\n\n\nCorrections made to printed original.\n\nPage 9, \"long-fostered prejudice\": 'perjudice' in original.\n\nPage 73, \"Pensees, ch. 7\": 'Pansees' in original.\n\nPage 127, \"and pulled out a plum\": 'und' in original.\n\nPage 147, \"did not come forward\": 'forword' in original.\n\nPage 172, \"come into general circulation\": 'circulalation' in original.\n\nIbid., \"the more difficult fractions which we have got\": 'he have got' in\noriginal.\n\nPage 192, \"it has been stated\": 'started' in original.\n\nPage 216, \"the obsolete word tetch of the same meaning\": 'meaing' in\noriginal.\n\nPage 228, \"[Greek: dioklasianos]\": 'dioklalasianos' in original.\n\nPage 233. After `Henry E. Manning' were printed two paragraphs `Shilling\nversus Franc.' and `Teutonic Long Hundred 120 versus 100 or the Decimal\nquestion.' These appear to have been set in error, there is no applicable\ncontext.\n\nPage 316, \"in a manner depending upon the difference\": 'maner' in original.\n\nPage 322, \"neither what Newton did, nor what was done before him.\": 'not'\n(for 'nor') in original.\n\nPage 344, \"Victoria toto coelo\": 'tolo' in original.\n\nPage 368, \"cannot be brought up to 1\": 'up to +-' in original.\n\nPage 371, \"Q_2=b_2 Q_1+a_2\": 'Q_2=b_2 Q_1-a_2' in original.\n\nNote 50, \"all who were not in the road to Heaven were excommunicated\":\n'excomunicated' in original.\n\nNote 372, \"[Greek: he alazoneia biou]\": 'alaxoneia' in original.\n\nIbid., \"Iapetos\": 'Ispetos' in original.\n\nIbid., \"Papeiskos\": 'Paspeisoks' in original.\n\nIbid., \"[Greek: dioklasianos]\": 'dioklalasianos' in original.","title":"A Budget of Paradoxes, Volume II","tradition":"philosophy-ethics","translated_text":null,"word_count":134434}