1919.] Ancient Hindu Spherical Astronomy. 163 
have the same true longitude, and it becomes necessary to find 
the longitude of the point of intersection of the circle of posi- 
tion with the ecliptic, when the true longitude of the star is 
known. 
In figure 7, 2’a is a portion of the ecliptic, and aX and a’X 
are respectively the circle of latitude and the circle of position 
through the heavenly body at X. The problem is to find the 
longitude of x’ when that of a is known. 
Let xab be the day circle of the point a and x the point of 
intersection between this day circle and the circle of position, 
then the first step in the solution of the problem is to assume 
that az is sufficiently nearly equal to x’a for the purpose in 
hand. 
Draw the declination circles Px, Pa, Pb through the points 
a, a, and X, the last cutting the day circle in 6, and denote 
We 
solstices aX and aP coincide and ab disappears. The process 
of determining ab is therefore called ayanadrikarma ; while at 
the equator aX and Pb would coincide and then xb would dis- 
appear and the process of determining xb is termed akshadri- 
karma. 
(i) Ayanadrikarma.—The angle PaX between the circle of 
declination Pa and the circle of latitude aX is the ayanavalana 
(see § (h)) and we have 
sin y, = sin aX sin PaX /sin PX 
= sin B sin x/ cos 8. 
(ii) Ayanadrikarma.—The angle PxX is nearly equal to the 
akshavalana, ¢, and sin aX = sin bX /sin Xxb and bX = 8’, 
the polar latitude, so we have 
sin y, = sin xX sin PxX / sin ra 
= sin f’ sin £/cos § sin X2b_ nearly 
and at the horizon the angle Xzb is equal to the colatitude of 
the place. 
The ascensional difference. 
At the equator, where the horizon is at right angles to 
the equator, the apparent daily paths of the stars are circles at 
right angles to the horizon, and we have right ascensions ; 
while at the poles the apparent daily paths are parallel to the 
horizon; but at any other latitude (?) they are inclined to the 
rizon and we have oblique ascensions. The Greek astrono- 
on to the relation between right 
mers paid considerable attention t 
and oblique ascensions and determined therefrom correct rules 
for the calculation of the length of the day, rules and tables 
connected with the rising sign or ascendant or horoscope, 
