166 
Journal of the Asiatic Society of Bengal. 
[N.S 4, 
ength of day.—The difference between the length 
of ‘he as and night is equivalent to twice the angle GCF in 
figure 1, when 
FGR represents the path of the sun. 
Now sin 
GCF or sin Aa has been shown (§ 5(@) v) to be equal to tan » 
tan 6. The length of the day 
in hours is therefore (180° 
+ 2 Aa)/15 and in ghatis it is ‘130° + 2 Aa) /6 where sin ae 
= tan ¢ tan 6, and for the longest day 
ule is given by Paulisa (PS. ii, 11) and Beckinigupis 
and Aryabhata (G19) notes the connexion with the ‘six hour 
1 
circle.’ 
Aa = tan 
® tan w 
No tables of the lengths of days are given in the early 
kos 
Hindu texts: the following is taken from Abt ‘Ali al- Marra- 
hi. 
Longest days for different latitudes. 
Latitude. | 3” 
shes g° ie | 
i 
12 12 13 
hal 12/12 
.. | 10/21/31 
te 
12/44 
| 
ripe 18°|21° 
| 
| 
40 4 2 hg 
13 idl isl 13 14 14 4 15|15 15] 16 
42 53 a ak 29 
24° 
27° 
52 56 58 52. 8 54 4 
The planets. 
27a 9" 36" 30°30 45° 48°|51° 54° 
1256 11 28,45 5 | 27 
hl 
ic 
18 19 
| 
61} 21 33 | 52 
28! 4 4\ 0 
10. All the planets, including the sun and moon, are sup- 
posed to have the same absolute daily aeeeee of about 12,000 
yojanas. The orbit of the moon bei wn, the orbits of the 
other planets are found by (orbit of moat: x ik / ere Ff, 
d revolutions in a cycle of the moon and the 
planet respectively. 
obtained fr 
Whether the elements the moon were 
rom parallax observations or not i 
there is no direct evidente of such pou Teta 
uncertain, but 
The follow- 
ing table is based on the elements of the later Sarya Sid- 
dhanta :— 
t any time employ ‘ temporary ’ muhiirtas or ghatis, but see Albiriini 
(India i, eget 
who discusses this is intresting topic. 
mode: rm op Seta cos h = 
length of of the day 
oJ seated Vedanga rule is :— 
length of day = 12 + 2 (183 — n)/61 muhirtas 
where 7 is the number of days ae from a solstice. The longest day 
ours 24 minutes, pat sail day is 
is therefore 18 muhirtas 
rr muhirtas = 9" 36™ and the fara increase is 2/61 m 
np tan 5 where 2/15 is the 
oe tod 7 ae 
The Paitémaha Siddhanta gives 1 se (= 10" 36” Pits te the short- 
est day and 3 palas for the daily 
22 
28 
32 
| 
