When it has been ascertained what degree of the zodiac is on the mid-heaven, as also which are the preceding and succeeding degrees, the period of whose meeting is to be calculated, the position of the preceding degree, and its distance in temporal hours from the meridian, are next to be noted; because any part of the zodiac, on becoming distant from the meridian in the same temporal hours, must fall on the same individual semicircle.[164] For ascertaining this distance, the number of ascensions, in a right sphere, found in the intermediate space between the said preceding degree and the mid-heaven, either above or under the earth, is to be divided by the number of the diurnal or nocturnal horary times of the said preceding degree: for instance, if that degree be above the earth, by its diurnal horary times; and, by its nocturnal, if it be under the earth. It is then to be discovered in what number of equatorial times the succeeding degree will be distant from the same meridian, by as many similar temporal hours as those by which the preceding degree is distant from it. And, to effect this, the hours in question must be noted, and it must first be observed, by the right ascensions again, how many equatorial times the succeeding degree, at its original position, is distant from the degree on the mid-heaven; and then it must be seen how many equatorial times it will be distant, on coming to the preceding degree’s distance in temporal hours from the said mid-heaven: this will be found, by multiplying those hours by the succeeding degree’s horary times; diurnal, if the future position be above the earth, and nocturnal if under; and the difference in amount, of these two distances, in equatorial times, will present the number of years inquired for. [164] _Vide_ Note ², p. 95. CHAPTER XV EXEMPLIFICATION In order to exemplify the foregoing instructions, let the first point of Aries be supposed as the preceding place, and the first point in Gemini the succeeding; and let the latitude of the country, to which the operation relates, be such as will cause the longest day to consist of fourteen hours[165]; and where the horary magnitude of the beginning of Gemini will be about seventeen equatorial times.[166] [165] This, in the Northern Hemisphere, would be the latitude of Alexandria (where Ptolemy flourished), or, in his own words, that of the 3rd Climate, passing through Lower Egypt, numbered 30° 22′.—_Vide_ extracts from the Tables of the Almagest, inserted in the Appendix. [166] This is the magnitude of the diurnal temporal hour of the first point of Gemini in the latitude prescribed.