1919.] Ancient Hindu Spherical Astronomy. 173 
But E and ¢360° are only apparent dimensions, and t 
change is probably due to a supposed change in the iene 
from the centre of the deferent to the centre of the epicycle, 
and is connected with the “second inequality ’—due to the 
excentricity of the orbits 
he values of EF are re the circumference of the epicycle 
in terms of the circumference of the deferent. For example 
the value 72 for Mars means that 
the circumference of epicycle _ (ee 
the circumference of deferent 360 ape 
or r./T2 = 1/5 where r, is the radius of the epicycle and 7, is 
the radius of the deferent. We shall denote r,/rq by é, or e, 
according as the epicycle of the apsis or the eae. of con- 
junction is employed. 
17. The equation of the centre. —The processes in- 
volved in determining the equation of the centre are generally 
four. If A denotes the mean position of the planet then the 
first correction gives A, = + ¢,/2 where ¢, is the equation 
second correction gives A, = 4; + €,/2 where « is the 23 ee 
derived by employing the epicyele of the apsis; 4, =A + «, 
res again the epicycle of the apsis is employed ; and finally 
4 =A, + «, where the epicycle of conjunction is again em- 
Haped. 
The calculations may be summarised thus :— 
: é,. . sin », 
(i) 4, =A + <,/2 where sin ¢, = : wu 
a/ €-2 + 2, . COS V% + 1 
(ii) A, =A, +q/2. » Se = @, - Sin v," 
(iii) AA =A + © >» Ange €. Sno, 
ivi kd €,. . SIN UV; 
iv) A= Ag + & , 1,2 
/ e,* + 2e,. cos v3 + 1 
where Vy =A AS V3.= Ae — Ags 1 = Aa — A; 
* The oval’ has been applied to the epicycle in this connexion 
but is ihe os her a 
Theo ve teal, at at the oF — of the change in dimension oe hone 
epicycle i. panel In the the moon the effect of the 
inequality was always to aaa ies absolute value vo the first oe, 
particularly in the quadratures. “ The obvious inference was,” writes 
J. L. E. Dre 
ic cle a of lengtl , gre q in 
7 i Ee P Ptolemy the centre of the soto move on @ 
poled el ric so that its distance from the earth varied and co ntly so 
did the apparent dimensions of the epicycle. The excentric appears 
comparatively late in India. See the Siddhanta Stromant, G. v, Tf. 
