गुप्त अभिलेख संग्रह (जे. एफ. फ्लीट - गुप्त सम्राटों एवं परवर्ती नरेशों के ऐतिहासिक पाषाण व ताम्रलेख)

even in Northern India, where the dark fortnight of the month precedes the bright.¹ In
Pañchâṅgs, the ghaṭīs and palas of tithis are given; and, by them, it is to be under-
stood that the tithis end so many ghaṭīs and palas after sun-rise. In general, the
expression tithi means the end of a tithi; not its beginning, or its duration.
The term tithi-śuddhi, lit. 'the subtraction of tithis,' denotes the number
of tithis that elapse from the beginning of the month Chaitra (March-April) up
to the time of the Mêsha-Saṁkrānti. In Prof. K. L. Chhatre's Tables, this term is
used to shew the number of tithis, calculated from the difference between the moon's
mean longitude and the sun's apparent longitude, that elapse from the beginning of
Chaitra to the time of the sun's spashṭa or 'apparent' Mêsha-Saṁkrānti.² Thus, for Śaka-
Saṁvat 0 expired, at the time of the Mêsha-Saṁkrānti the sun's mean longitude was
11 signs, 20 degrees, 46·1 minutes (p. 46); and the apparent longitude obtained from it,
according to the method given by Prof. K. L. Chhatre, is 11 signs, 22 degrees, 38·9
minutes. The moon's mean longitude at that time was 4 signs, 25 degrees, 42·4 minutes
(p. 87). The difference between the longitudes of the sun and the moon,—the sun's
longitude being subtracted from that of the moon,—is, therefore, 5 signs, 3 degrees (=
153 degrees), 3·5 minutes. Then 153° 3'·5 ÷ 12 = 12 + (9° 3'·5 ÷ 12) tithis; that is,
12 tithis, and about 45 ghaṭīs and 14 palas, had elapsed. This, therefore, is given as
the tithi-śuddhi for Saka-Saṁvat 0 expired. In one solar year, the mean tithis are 371,
and 3 ghaṭīs, 53·4 palas. Dividing 371 by 360, the remainder, 11 tithis, 3 ghaṭīs,
53·4 palas, is given as the variation in the tithi-śuddhi in one year (p. 10, col. 4).
The tithis obtained from the mean places and mean motions of both the sun and the
moon, are madhyama or 'mean' tithis. So, also, those calculated from the apparent
place and motion of the sun and the mean place and motion of the moon,—as in the case
of the tithi-śuddhi and the mean solar equivalents of tithis given in Table III. pp. 13-19,
col. 2,—may be called mean tithis and not apparent. But the tithis, &c., given in
our Pañchâṅgs are always spashṭa or 'apparent;'³ that is, they are calculated from the
apparent places and motions of the sun and the moon. The spashṭa-tithi differs from the
madhyama-tithi sometimes by nearly twenty-five ghaṭīs; and this is chiefly owing to the
fact that the moon's apparent longitude differs from her mean longitude sometimes by
about five degrees.⁴ Many corrections have to be applied to the mean place of the
¹ In astronomical works, it is always the Amânta southern arrangement of the lunar fortnights
that is actually taken for calculations.
² In the Siddhânta-Śirōmaṇi and other works, the term tithi-śuddhi is used in the sense of the
number of tithis, calculated from the mean places of the sun and the moon, that elapse from the
beginning of Chaitra to the time of the sun's madhyama or 'mean' Mêsha-Saṁkrānti.
³ Though not always in the strictest sense. I say so, because, in practice, extreme accuracy is
not, and cannot be, sought. But, in theory, they are required to be 'apparent' in the strictest sense.
⁴ According to European Tables, the difference is sometimes about eight degrees