Page:Sewell Indian chronography.pdf/91

inclination of the ecliptic or to the terrestrial latitude of the observer, the time of the lagna measured from mean sunrise. This is the first approximation, at which alone I aim in the present section.

198. I take the example worked out by Jacobi, i.e., the 6th solar day of Jyēshṭha, K.Y. 4000 expired, the given lagna being the 15th degree of Kanyā, and calculation being made for the horizon lagna. The work is to be done by my own processes. First we require the true longitude of the sun. This is the "s" of our calculations for the nakshatra (§ 119 above) , the formula for finding the value of which is, in the a, b, c system , ${\displaystyle (c\times 10)+7207}$ — equation c. To find c, and therefore equation c, we take the a, b, c for the first civil day of Chaitra at mean sunrise as given in Table I ; add to this the a, b, c for the interval of days to the given day , and so find the c for mean sunrise of the given day. Use the First Ārya Siddhānta.

K.Y. 4000 expired was = A.D. 899–900. By Table I., cols . 13, 17, Mēsha saṁkrānti occurred on day 81, at 13 h. 47 m. By the general rules, therefore (§ 43), the first civil day of solar Vaiśākha, the first month, was day 82. The 6th day of the second month, Jyēshṭha, was 36 days later, or day (82 + 36 = ) 118. We have the value of c on the 75th day given us in col. 25 of the same Table, viz., c = 261 . 118 ― 75 = 43. We add, therefore, from Table IV., the value of c for 43 days, viz .: 118, and we find

that c on the 118th day = (261 +118 ) 379 ; and therefore equation c = (Table VII.) 19. Using the formula ${\displaystyle (c\times 10)+7207}$ — equation c, we find s = 978 = (Table VIII.B) 35° 14′. This is (i.) the apparent longitude of the sun at mean sunrise on the given day.

(ii.) The longitude of the given lagna, viz., of the 15th degree of Kanyā, was, by Table XXII., 165°. As the sun's longitude was 35° 14′ at mean sunrise, the distance between the true sun and the lagna was ( 165° — 35° 14′ ) 129° 46′.

(iii.) We turn this distance into time by calculating at the rate of 4 m. to a degree and 4 s. to a longitudinal minute, and we find that the 129° 46′ take in rising 8 h. 39 m. 4 s.

Hence we have found that roughly (holding the equator and ecliptic to be one plane and taking no account the terrestrial latitude of the place) the 15th degree of Kanyā rose on the day in question at 8 h. 39 m. 4 s. after mean sunrise. Jacobi gives the result by his first approximate process as 21 gh. 40 vin., or 8 h. 40 m.

(See also Example 63 below.)