[284] That is to say, by the opposition, trine, &c.

[285] On this side of the equator.

[286] Thus (according to the [Table inserted at p. 152]), in the climate or latitude of Lower Ægypt, the times of ascension between the first point of Gemini and the first point of Sagittarius, diametrically opposite, are 205° 18′, which, being divided by 15, give 13 hours 41 minutes and a fraction of equatorial time, as the length of the day of the first point of Gemini. And the same number of times of ascension, divided by 12, give 17° 6′ and a fraction of the equator, as the length of the diurnal temporal hour. In the latitude of Southern Britain, the times of ascension between the same points as above mentioned are 236° 2′, which, divided by 15, give 15 hours 44 minutes and a fraction of equatorial time, as the length of the day of the first point of Gemini; and, if divided by 12, they produce 19° 40′ and a fraction of the equator, as the length of the diurnal temporal hour.

[287] Thus, the aggregate times of ascension, in a right sphere, of the first point of Gemini are 57° 44′; and, in the climate of Lower Ægypt, 45° 5′: the sixth part of the difference between them is 2° 6′ and a fraction, which, added to 15°, again makes the diurnal temporal hour of the first point of Gemini equal to 17° 6′ and a fraction of the equator. In the climate of Southern Britain, the aggregate times of ascension of the first point of Gemini are 29° 43′: the sixth part of the difference between that sum and 57° 44′ of right ascension is 4° 40′ and a fraction, which, added to 15°, makes the diurnal temporal hour of the first point of Gemini, in South Britain, equal to 19° 40′ and a fraction of the equator, as before shown.

[288] For example,

Diurnal horary times of the first point of
 Gemini in the latitude of Alexandria17° 6′ 30″
Number of temporal hours12
15)205 18 0
Diurnal equatorial hours of the first point of
 Gemini in the latitude of Alexandria13 41 12
Diurnal horary times of the first point of
 Gemini in the latitude of Southern Britain19° 40′ 10″
Number of temporal hours12 
15)236 2 0 
Diurnal equatorial hours of the first point of
 Gemini in the latitude of Southern Britain15 44 8 

[289] Let the first point of Gemini be on the meridian above the earth; the number of temporal hours since sunrise will then be 6, by which 17° 6′ 30″ are to multiplied. The product will be 102° 39′: this, added to 45° 5′, the aggregate number of the first point of Gemini in the latitude of Alexandria, will give 147° 44′, which, in the ascensions of the climate in question, will correspond to the 3d degree of Virgo, and show that to be the degree ascending. In the latitude of Southern Britain the total number would still amount to the same, viz. 147° 44′, but it would show 7° and about 30′ of Virgo to be ascending.

[290] Let the first point of Gemini be three temporal hours past the meridian; these hours reduced to degrees, in the latitude of Alexandria, will give 51° 19′, which, added to the right ascension of the first point of Gemini, make 109° 3′, showing the 18th degree of Cancer on the meridian. In the latitude of Southern Britain, these hours would produce 59°, which, added to the right ascension, would make 116° 44′, and show the 25th degree of Cancer on the meridian.

[291] Thus, in the latitude of Alexandria, when the first point of Gemini is three temporal hours past the meridian, the 16th degree of Libra will be on the ascendant, and the aggregate times of ascension of that degree in the said latitude are 109° 3′: by subtracting 90 from this sum, the remainder will be 19° 3′, the right ascension of the mid-heaven answering to the 18th degree of Cancer. In the latitude of Southern Britain, the 18th degree of Libra would be on the ascendant, of which degree the aggregate times of ascension in that latitude are 206° 44′, from which, if 90 be subtracted, the remainder will be 116° 44′, the right ascension of the mid-heaven answering to the 25th degree of Cancer. The converse of these operations seems too obvious to need explanation.

[292] Alexandria.