1919.] Ancient Hindu Spherical Astronomy. 165 
(i) sin TB =sino, =sin dA cos w/ cos 6 
(ii) sin AB = sinay = tan > tan 6 
(iii) TAi=.0,5 =a,+ Aa 
where a, denotes SE of a) oblique ascension, and Aa 
ascensional differe 
calculate the time of rising of any particular sign we 
have 
(iv) tn = Ay(n) ~~ (Aan Sh A an-1) 
where ¢, is expressed in degrees, and n refers to the n“ sign 
according to the order given in tables 6 an 
The Paulisa Siddhanta gives the ascensional differences in 
the form 20e, 164e, 6e where e is the equi inoctial noonday 
ha 
dhanta gives She ascensions, but none of the early Hindu 
texts appears to give correct tables for oblique area or 
ascensional differences. The fairly accurate tables give 
tables 6 and 7 are taken from Abi ‘Ali al-Marrakoshi (13th 
century). 
8. e lagna.—The point of the ecliptic on the horizon 
(horoscope, Nobenioa) at any time is termed the lagna. Its 
ogee armies may be explained by an example. Suppose that 
7 hours 17 minutes has elapsed since sunrise at a fegoo whose 
latitude is 36°N., and that the longitude of t 
degrees. The tbls of oblique ascensions ‘enti 7), aieded 
into time units, gives for latitude 36° 
dice JY 19%, oP Bl ST ST", bee B21, 
= 2° 28". 
Since the sun has at 12 degrees into the second sign we 
have first to find how much of f, has not been used up. This is 
(1" 31”) x (30° — 12°)/30° = 55 minutes approximately. 
Now 
7°17" = 66" + 1°57" + 2° 21™ + (2° 4"), 
Led last term pene less than fs ane time then corresponds to 
ome point in f, (Leo); and sin 
x /30 = (2° 4 vn 28”) 
gives x = 25° 8’ the npr of the lagna is approximately 
a —— 25 degrees 8 minu 
eon (c. A.D. 380) calculated the lagna 0 or ¢ ‘ horoscope” n the same 
way, tor: with reference to temporary Apparently the Hindus did 
