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

THE GUPTA INSCRIPTIONS; APPENDIX III. 169
In the preceding remarks, my object has been to explain concisely the system of the
Twelve-Year Cycle of Jupiter that is based on his heliacal risings; and the three methods
for determining the nakshatra with which the heliacal rising takes place. I have now to
make a few observations of a more general kind; and to introduce the eleven
other authorities of which I have spoken at page 162 above. Before doing so, however,
I must refer more fully to another system, which also has been incidentally mentioned, of
naming the saṁvatsaras of the Twelve-Year Cycle according to Jupiter's passage from one
sign of the zodiac into another, with reference to his mean longitude.
The rule for that which I have named the mean-sign system, is thus given by
Âryabhaṭa in his Ârya-Siddhânta or Âryabhaṭîya, Kâlakriyâpâda, verse 4,—Guru-bhagaṇâ
râśi-guṇâs tv=Âśvayuj-âdyâ Gurôr abdâḥ,—"the revolutions of Jupiter, multiplied by the
signs (twelve), (are) the years of Jupiter, the first of which is Âśvayuja." And it is given,
in very similar words, by Brahmagupta, in his Brahma-Siddhânta, adhyâya xiii. verse 42,—
Guru-varshâṇy=Âśvayujâd dvâdaśa-guṇitâ Gurôr bhagaṇâḥ. In this rule, the revolutions
(bhagaṇa) are meant to be taken from the beginning of the Kalpa, or of a Mahâyuga.
But, for practical purposes, we need not go back so far. One Twelve-Year Cycle is com-
pleted in one revolution. And, therefore, we can determine the saṁvatsara for a given
year, or for any given date in it, by taking Jupiter's signs, including the current sign, of the
current revolution, and counting from Âśvayuja. In this system, the signs are intended to
be taken, and in practice are taken, according to Jupiter's mean longitude. Now, suppose
that on a certain day Jupiter's mean longitude is 9 signs and 12 degrees; i.e. that he is in
the tenth sign. Then, counting from Âśvayuja, we have Âshâḍha, as the current saṁvatsara
for the given day.¹
The names of the saṁvatsaras of the Sixty-Year Cycle also,—according to that
which is usually called the northern system, but which is, in reality, the only truly astrono-

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¹ In his treatment of the Twelve-Year Cycle (Indian Eras, p. 26 ff.), Gen. Sir A. Cun-
ningham opens the subject by quoting Kern's translation (see page 161 above, note 1) of the same
verse in the Bṛihat-Saṁhitâ which I use for the same purpose. But, for the rest, he altogether
ignores the force of the reference to Jupiter's rising, and treats the subject as if the heliacal-rising
system, described by me above, did not exist at all. What he has deduced from the verse, is only the
mean-sign system, which the verse does not really refer to at all; and in respect of which he is wrong
in making the saṁvatsaras of both the Twelve-Year and the Sixty-Year Cycle, begin and end with the
luni-solar years. The rules that he applies give, at the best, only the saṁvatsaras of the Twelve-Year
Cycle by the mean-sign system, and of the Sixty-Year Cycle, that are current at the commencement of a
given solar year; they do not provide for the essential point in both the cycles, viz. the determination
of the exact day on which a given saṁvatsara of either cycle commences—I have not had an
opportunity of seeing the writings of Davis and Warren on this subject. But, with all due deference,
I may safely say that the Twelve-Year Cycle by the heliacal-rising system, has hitherto remained
quite unknown to European scholars.—I would take this opportunity of remarking that I can find no
authority for the introduction, in Kern's translation, of the bracketed words "(during which Jupiter
completes a twelfth part of his revolution)." Jupiter completes a twelfth part (râśi) of his revolution
in about three hundred and sixty-one days; while the interval between two of his heliacal risings is
about four hundred days.
A b