1919,] Ancient Hindu Spherical Astronomy. 155 
(D) Multiply ta latter by the radius and divide by the 
radius of the rnal circle and the quotient is the sine of 
the unnata: i) “this, then, being subtracted from the day 
mete and the remainder turned into are by means of the 
tables of versed sines, the final result is the hour angle.” 
The operations indicated are : 
(A) sinz =rs/H, (B) sin (90°— z) = 4/7? — 43, 
(C) rB/ sin (90°— 9), (D) rC |r cos 5, where 7 cos 64 is 
the ‘radius of the diurnal circle,’ (E) r + r tan ¢ tan 6 — D, 
where r + 7 tan ¢ tan 6 is the ‘ day measure.’ 
This means 
versin h = r + r tan ¢ tan 8 — C/cos 8 
=r+yrtan ¢ tan d —7rB/cos 8 cos ¢ 
=r+rtan ¢ tan d—r cos z/cos 6 cos ¢ 
or cos h = cos z/cos 6 cos ? — tan ¢ tan 8 
when r = l. 
Definitions. 
(a) In figure 1 the horizon (kshitija) is represented by 
NES, ‘the equator (vishuvadvritta) by #Q, the pole is P, the 
zenith (dris) is z, and FGR is the diurnal path of a star. The 
angle PON = ZOQ = ¢ is the terrestial latitude (aksha) of the 
7 
R 
\ 
< 
a \ Pp 
‘\ \ 
a \ 
on * 
5 * 
Ne Me 
\ 74 
\ x 
\ a 
‘ ‘ 
Pd i ~,D N 
ed 1@) G \ 
‘ \ 
\ F 
ee 
£: 
Fig. |. 
place O, the angle ROQ =8 is the eacceros (kranti) of the 
star, and the angle HOF = a) is its amplitude when on the 
