1919.] Ancier.! Hindu Spherical Astronomy. 161 
The rule for the drikshepa or sin z, is evolved thus: In figure 5 
where Vv # is the ecliptic, v # the equator, HHS the horizon, 
ZMS the meridian and WN the nonagesimal, we have Hy N 
= 90 degrees, Hv HE =o, and rv HH = 90° — 9. From the 
triangle Y HE we obtain sin HE sin YHH = sin YH sin HY E£, or 
(i) sin a; = sin A; sin w/ Cos 9, 
where a; denotes the amplitude of the rising sign or lagna (H) 
and , denotes its longitude (YH). Also HEH = SA, since 
ELS = 90° and HA = 90° and therefore the angle ges = a). 
Now in the triangle ZMN we have MZN =a,, ZN =z, 2M 
=z, and the angle ZNM = 90°; and consequently + sini ZN 
sin ZMN sin ZM, or sinz, = sin ZMN sinz. If now ZMN 
be ‘bensiderad” a plain triangle we have sin ZMN = cos MZN 
= cos a; and finally 
(ii) sin 2, = sin z cos q 
= a/ sin*z — sin*z sin*a, 
as given in the texts. 
h) The valana.—In figure 6, NES is the horizon, CX the 
ecliptic, NXS is the circle of position of X, P is the pole of the 
equator and K is the pole of the ecliptic ; PX = 90° — 8 is the 
hour circle of X and XPZ =h is its hour angle, Z being the 
zenith ; PN = ¢ and PK =o. 
Fig. 6. 
According to the Paulisa siddhanta the valana or angle of 
position of the point X on the ecliptic is the angle NV. XP = é,* 
* Apparently with reference to the use of the ‘ polar latitude’ (see 
§ 5c). 
