{"collection":"astro","html_url":"https://unchartedknowledge.5gfusion.net/browse/astro/ptb/ptb77.htm","path":"astro/ptb/ptb77.htm","source_url":"https://sacred-texts.com/astro/ptb/ptb77.htm","text":"THE Reader is desired to refer to the Plate at end of book containing diagrams of the Zodiacal Planisphere, which has been spoken of in the Note in p. 99.\nFig. 1 is the Planisphere adjusted for the northern latitude of 30\u00b0 22' (where the longest day consists of fourteen equatorial hours), agreeably to the \"Exemplification\" given by Ptolemy in Chapter XV, Book 3. It represents that portion of the celestial sphere which is contained between the tropics: the central horizontal line is the equator; the curved line extending longitudinally from east to west is the ecliptic; the central perpendicular line is the meridian, or cusp of the 10th house; the other short lines, cutting the equator transversely, are the cusps of the other houses; that of the 1st house being the eastern horizon; that of the 7th, the western horizon. Hence, the distance from the 1st house to the meridian, or from the meridian to the 7th house, shows the semi-diurnal arc of any parallel of declination in the ecliptic; and the distance of the 7th house to the 4th, or from the 4th to the 1st, shows the semi-nocturnal arc. The distance from the cusp of one house to that of the next, taken on the same parallel, is also equal to two\ntemporal hours; thus, for instance, in the latitude above quoted, the semi-diurnal arc of 0\u00b0 \u264a is 6 h. 50 m., or 102\u00b0 39' of the equator; consequently the diurnal temporal hour is equal to one equatorial hour and eight minutes, or to 17\u00b0 6' of the equator.\nIn his first example, Ptolemy directs 0\u00b0 \u2648 to be placed on the ascendant, so that the beginning of \u2651 may be on the mid-heaven; 0\u00b0 \u264a must, therefore, fall on the point A, distant from the mid-heaven 147\u00b0 44' of the equator, as measured by the line AB; because every point in the sphere always preserves one and the same parallel with the equator; and 6\u00b0 \u264a, in passing to the mid-heaven, must proceed along the line AB. In the present case, however, it is required to know how long 0\u00b0 \u264a will be in coming to the ascendant, the given position of 0\u00b0 \u2648. Now 0\u00b0 \u264a will be on the ascendant when it arrives at the point G; therefore the distance from A to C is the amount of the prorogation between 0\u00b0 \u2648 (when posited on the ascendant) and 0\u00b0 \u264a, and it is equal to 45\u00b0 5' of the equator. In the second example, 0\u00b0 \u2648 is placed on the mid-heaven, which position must be at D, so that 0\u00b0 \u264a must necessarily be at E; and the distance from E to B, equal to 57\u00b0 44' of the equator, is the prorogation between 0\u00b0 \u2648 and 0\u00b0 , when 0\u00b0 \u2648 is on the mid-heaven. In the third example, 0\u00b0 \u2648 supposed to be on the 7th house, descending, at F, so that \u264b is on the mid-heaven, and 0\u00b0 \u264a at the point G, in advance of the mid-heaven 32\u00b0 16' of the equator, as shown by the distance BG. Now it is required to bring 0\u00b0 \u264a to the 7th house (the place of 0\u00b0 \u2648), and it will be there on arriving at H, distant from B 102\u00b0 39' of the equator; but as 0\u00b0 \u264a is already at G, the distance from G to H, equal to 70\u00b0 23' of the equator, is the amount of the prorogation between 0\u00b0 \u2648 and 0\u00b0 \u264a, when 0\u00b0 \u2648 is on the 7th house. The fourth example places 0\u00b0 \u2648 at I, three temporal hours past the meridian; 0\u00b0 \u2648 therefore falls on the point K, at the distance of 13 equatorial degrees before the meridian or mid-heaven, and will be three temporal hours past the meridian (the position of 0\u00b0 \u264a) on arriving at L, distant 51 equatorial degrees from the mid-heaven: the whole distance from K (the first position of 0\u00b0 \u264a) to L, its second position, equal to 64 degrees of the equator, is therefore the prorogation between 0\u00b0 \u2648 and 0\u00b0 \u264a, when 0\u00b0 \u2648 is past the meridian at the distance of three temporal hours. Ptolemy has also instanced two other positions for 0\u00b0 \u2648; viz. at two temporal hours past the meridian, and at two temporal hours before the occidental angle; or, in other words, on the cusp of the 9th house, and on that of the 8th. Now, if 0\u00b0 \u2648 be on the cusp of the 9th house, it must be at M, and 0\u00b0 \u264a will be at N, distant 62 equatorial degrees from Q, which is also on the cusp of the 9th. If 0\u00b0 \u2648 be on the cusp of the 8th, it must be at O, and 0\u00b0 \u264a will be at P, distant 66 equatorial degrees from R, which is also on the cusp of the 8th: these two several numbers of degrees will be the respective prorogations between 0\u00b0 and 0\u00b0 \u264a, when 0\u00b0 \u2648 is placed on the 9th and 8th houses.\nPtolemy's \"Exemplification\" has been followed thus minutely in\norder to show how perfectly Mr. Ranger's invention is adapted to assist (if not to supersede) arithmetical calculation; for, after the Planisphere has once been accurately laid down, a line drawn parallel to the equator, from the significator to the promittor, or to the promittor's pole of position, and measured by degrees of the equator, will accomplish the whole operation of ascertaining the amount of prorogation.\nFig. 2 is the Equator extended, in plana, on a scale proportionate to the planispheres in Figs. 1 and 3: it is divided into 360 degrees, and into equal time, as measured by the 24 hours of the earth's daily rotation on its axis, and by smaller portions of four minutes each, corresponding with degrees of the equator.\nFig. 3 is the Planisphere set for the latitude of Southern Britain, 51\u00b0 30' N., where the longest day is 16 h. 30 m., the semi-diurnal arc of 0\u00b0 being consequently 7 h. 52 m., or 118\u00b0 of the equator, and its diurnal temporal hour equal to one hour and nearly nineteen minutes of equatorial time, or to 19\u00b0 40' of the equator. In applying Ptolemy's examples, given in Chapter XV, Book 3, to this latitude, it will follow that, when 0\u00b0 \u2648 may be on the ascendant, 0\u00b0 \u264a will be at A, and will subsequently arrive at the ascendant at C, after the passage of 29\u00b0 43' of the equator. When 0\u00b0 \u2648 may be on the mid-heaven at D, 0\u00b0 \u264a will be at E, and will arrive at B, on the mid-heaven, after the passage of 57\u00b0 44' of the equator, as in Fig. 1. When 0\u00b0 \u2648 may be on the 7th house, at F, 0\u00b0 \u264a will be at G, and will come to the 7th house, at H, after the passage of 85\u00b0 45' of the equator. If 0\u00b0 \u2648 be three temporal hours past the meridian, at I, 0\u00b0 would be at K, again 13 equatorial degrees before the meridian, as in Fig. 1, and will be three temporal hours past the meridian, a position similar to that assumed for 0\u00b0 \u2648, on arriving at L, distant from the mid-heaven 59 equatorial degrees; thus making the whole distance, from K to L, 17 equatorial degrees. If 0\u00b0 \u2648 be on the 9th house, at M, 0\u00b0 \u264a will be at N, distant from Q (also on the 9th house) about 67 equatorial degrees. If 0\u00b0 \u2648 be on the 8th house, at O, 0\u00b0 \u264a will be at P, distant from R (also on the 8th house) about 76 equatorial degrees.\nBy taking the trouble to calculate the distances between the several positions given by Ptolemy, the Reader may satisfy himself of the sufficiency of this Planisphere for the purpose for which it was first projected; viz. for the more expeditious measurement of the arcs of direction. The Tables of Ascensions, extracted from the Almagest, in p. 152, will show that the arcs, as measured in Figs. 1 and 2 of the plate, exactly tally with the amounts of distance obtained by calculating arithmetically, according to the respective latitudes, as quoted in the Tables.\nThe slight view which has been here given of the Zodiacal Planisphere invented by Mr. Ranger, must not be considered as pretending to\noffer a complete idea of its powers: they are so manifold and various, that another volume would be required to detail them fully; and it has now been used only in order to give a better illustration of Ptolemy's examples of the spaces of prorogation than mere words can do. To persons conversant with the mathematical part of astronomy, the facility with which a complete representation of zodiacal latitude, declination, the poles of position, crepusculine circles, and other phenomena, may be made by this Planisphere, will be sufficiently obvious from the accompanying Figures.\nFINIS\n \nClick to enlarge\nFigures 1-3","title":"Ptolemy's Tetrabiblos: Appendix: No. IV. The Zodiacal Planisphere","type":"page"}