180 Journal of the Asiatic Society of Bengal. [N.S., XV, 
the centres of the moon and sun from the centre of the earth, 
then, since the angles are all small, we obtain from (i) 
(ii) R, = R, — R. (R,/ Re — 1) ry / 15. 
The Paulisa Siddhanta simply assumes that R, = 38’: the old 
Surya Siddhanta gives the rule in the form 
Te: | BO 
4h, = 36° — 36’ =/ 
° t / 276 
which * is obtained from (ii) by making 
R, = 18’ and R, = 73-2’; 
while the modern Surya Siddhanta gives it thus— 
R, = Re My + Rem, (Ry / R,) — Ry m, (Ry / By) 
where m,, and m, are the ratios of the true daily motions to 
the mean daily motions of the moon and sun respectively. 
This rule implies two assumptions, neither of which is strictly 
accurate: (a) that the ratio of the true daily motion to the 
mean daily motion is equal to the ratio of the mean distance to 
the true distance; (6) that R,,/R, =7,,/r,, which implies that 
the mean apparent values of the diameters of the sun and 
moon are equal. . 
24. Duration.—In figure 12 let M be the centre of the 
moon when about to enter the shadow, C the centre of the 
shadow whose radius is R,; let AN be the ecliptic and MN 
the moon’s path. If » is the velocity with which the moon 
travels from M to M’ then the duration of the eclipse is 
2 . 60” 
a Go i: 0, 
where 8 is the moon’s latitude at the time of opposition, and 
since there are 60 nadikas in y. 
For the time between the first and last moments of inter- 
nal contact we have 
iv) (=i VR Rae 
(iii) t=2MM’jv= J/ (Rk. + Ry) — 
Here the values are in lengths and the corresponding value of the 
moon’s orbit would be 
800 = 18> 7290 (see table 4). 
To reduce to minutes of arc we must therefore multiply by 360 x 60 +7290. 
+ The time rules (iii) and (iv) may be obtained direct from the 
odern rule 
a = 4/(8 — bt)? + (m — sf 2B, 
where 6 is the rate of the moon’s motion in latitude, and m and s are the 
