TIMES OF RISING OF THE SIGNS If A, B, and C be the last points of the signs Aries, Taurus, and Gemini respectively, then the time of rising of Aries at the equator is equal to the right ascension of A, the time of rising of Taurus at the equator is equal to the right ascension of B minus the right ascension of A, and the time of rising of Gemini at the equator is equal to the right ascension of C minus the right ascension of B. If λ and 8 be the sayana longitude and declination of a point on the ecliptic, then the right ascention of that point is given by the formula:¹ Rsin d - Rcos x Rsin > Rcos & where is the obliquity of the ecliptic. 69 , But, according to Bhāskara I, € = 24°; ² therefore we have Rsin d 3141 x Rsin > day-radius Hence the above rule. Times of rising of the (sayana) signs, Aries, Taurus, and Gemini at the equator and a rule for finding the times of rising of the (sayana) signs at the local place : 10. Those who know astronomical methods have found them (i.e., the times of rising of Aries, Taurus, and Gemini at the equator) to be 1670, 1795, and 1935 (asus respectively). These respectively diminished and the same reversed and increased by the corresponding ascensional differences are the times (in asus) of rising of the six signs beginning with Aries at the local place. (The same in the inverse order are the times of rising of the six signs beginning with Libra at the local place.)³ If a, b, and c denote the ascensional differences of Aries, Taurus and Gemini respectively, then the times of rising of the signs at the local place are given by the following table : ¹ This formula occurs in A, iv. 25. For its rationale see Part I, Chapter IX. 2 See LBh, ii. 16, where Rsin has been stated to be equal to 1397'. 8 This rule occurs also in SüSi, iii. 43-45; LBh, iii. 5-6; SiDV, I, iii. 9; Sise, iv. 17, 15(ii); SiŚi, I, iii. 58-59(i).
