1919.] Ancient Hindu Spherical Astronomy. 179 
where \ and £ are the stars, geocentric longitude and latitude, 
and A, and 8, are the longitude and latitude of the zenith, and 
tan y = tan B,/cos (Az — A). 
We then have 
(i) 6/15 = p/r nearly ; 
(ii) 7 sin z, = 7 sin B, sin (y — B)/sin y; 
and (iii) 7 cos z, sin (Ay — A’) = 7 cos £, sin (4. — A)/ cos B; 
and as £ is generally considered negligible in these Hindu 
calculations we have 
z, = B, and sin (Ay — A’) = sin (A, — A) 
where 2’ is the apparent longitude ; and as a matter of fact the 
zenith distance (z.) of the nonagesimal is equal to the latitude 
of the zenith (8,), and the longitudes of the zenith (.) and the 
nonagesimal (Ay) are the same. 
Lunar eclipses. 
23. Diameter of the shadow.—In figure 11 we have 
(i) the angle TEM = PTE — POE = PTE — Q’ES 
= PTE — (QES — QEQ’) 
where S, E, and M are the centres of the sun, earth and moon 
respectively, HP and SQ are perperdiculars to OPQ, TM is 
Fig. UI. 
