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

THE GUPTA INSCRIPTIONS; APPENDIX II. 149
moon in order to find her apparent place; but only one of these, called phala-saṁskâra,
which is 'the equation of the centre,' is taken into account by Hindu astronomers:¹ and
this, as given by them, amounts to a little more than five degrees at the greatest. This
correction varies according to the moon's kêndra or 'anomaly;' which is taken to be her
distance from apogee.² From this correction is calculated the correction in time to be
applied to the mean tithi; it is named parâkhya; and it is given in Table IV., on p. 20,
in the column headed parâkhya. It evidently varies according to the moon's kêndra.
One revolution of the moon's kêndra is completed in 27 days, 33 ghaṭîs, 16·56 palas.
This period is called nîchôchcha-mâsa;³ and is known to English astronomers by the name
of the 'anomalistic month.' This period, converted into tithis,⁴ is equal to 27 tithis, 59
ghaṭîs, 33·36 palas; that is, nearly and practically, 28 tithis. It is converted into tithis
for the sake of convenience; since, the variation in the kêndra is one tithi of kêndra in
one tithi of time; and it is called tithi-kêndra, or 'the anomaly of the tithi, expressed
in tithis.' The moon's mean kêndra at the Mêsha-Saṁkrânti of Śaka-Saṁvat 0 expired,
was 10 signs, 19 degrees, 58·8 minutes (p. 87). This, converted into tithis, is equal to 24
tithis, 52 ghaṭîs, 50 palas;⁵ and this is given (p. 10) as the tithi-madhyama-kêndra, or
'mean anomaly of the tithi,' at the time of the Mêsha-Saṁkrânti of Śaka-Saṁvat 0 expired.
It shews that so many tithis and parts of a tithi had elapsed, up to that Mêsha-Saṁkrânti,
from the moon's preceding arrival at her apogee. The variation in the moon's kêndra, in
one solar year, is 3 signs, 2 degrees, 6·2 minutes (p. 87, col. 3). This, changed into tithis
by the rule of three, viz.—360° : 92° 6'·2 :: ti. 27, gh. 59, p. 33·36 : ti. 7, gh. 9, p. 42,—is
given, therefore, as the variation in the tithi-kêndra in one year (p. 10, col. 5).
A few other points and terms will be explained, as we proceed with the following
example.
To find the Week-Day of a given Tithi.
The process will be best illustrated, step by step, by actually working out an example.
And, at Mr. Fleet's request, I take, as my example, the date of Śaka-Saṁvat 406
¹ The amount of this correction, adopted by Prof. K. L. Chhatre, in finding out tithis in his Kâla-
sâdhana Tables (pp. 1 to 30 of his book), is nearly the same as that adopted by ancient Hindu astro-
nomers. Therefore, the tithis obtained by his method, as described above, should agree very closely
with those obtained from the methods prescribed in Sanskṛit works. But, in the abdapa and other
elements, the Sûrya-Siddhânta and other authorities themselves slightly differ, one from the other.
And, accordingly the difference will be sometimes about five or six ghaṭîs. There are, also, some
other minute causes of difference.
² In European astronomical works, the anomaly is reckoned from perigee or perihelion; but in
Hindu works it is reckoned from apogee or aphelion.
³ In this term nîcha means 'perigee;' and uchcha, 'apogee.' And nîchôchcha-mâsa is the
period in which the moon comes from perigee or apogee to the same point again.
⁴ One tithi is equal to 0·9843529572 of a mean solar day.
⁵ 360 : 319°58'·8 :: ti. 27, gh. 59, p. 33·36 : ti. 24, gh. 52, p. 50.