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COMPUTATION OF DATES.
beginning. If a few days do not influence the general result, as is usual, the tables here given may be used, applying the correction prescribed for the Arya Siddhanta.
46. The cycle of twelve years.-The years in this cycle take the names of the common months with Mahá prefixed, e.g. Mahakârttika; they are entirely regulated by Jupiter, but on two distinct principles.
47. The mean-sign system. In this system the name of the Jovian year depends on the zodiacal sign in which mean Jupiter is at a given time. The end and beginning of the Jovian years are exactly the same as in the sixty-year cycle. We can therefore use the tables as before.
Rule. Find Jupiter's Samvat.' for the given date according to the Siddhanta to be employed. Divide the figures of the integral part by 12, neglect the quotient, and the remainder is the index of the subjoined table:
0 or 12. Âévayuja,
1. Karttika.
2. Margasira. 3. Pausha.
427
4. Magha.
5. Phalguna.
6. Chaitra.
7. Vaisakha.
8. Jyaishṭha. 9. Ashâḍha.
10. Sravana. 11. Bhadrapada.
E. g. we have found above that Jupiter' according to the Arya Siddhanta about the beginning of 4210 K.Y. was 59-3973. By the above rule we find that then the year Maha-Bhadrapada was running, which ended, as calculated above, on the 3rd Margasira.
48. The heliacal rising system. The year in this system begins with the heliacal rising of Jupiter i.e. his reappearing after his conjunction with the sun: the year is named from the Nakshatra in which the planet rises heliacally, in the same way as the lunar months were named after the Nakshatra in which the moon of a particular month became full. The 27 (or 28) Nakshatras are formed into twelve groups (indicated in Table IX by an asterisk placed after the last Nakshatra in each group). Of the two or three nakshatras in each group, only one (the name of which is spaced in Table IX) gives name to the lunar month or to the Jovian year.
The problem, therefore, is to find the apparent longitude of Jupiter at his heliacal rising, and the time of the rising. If we know the longitude of Jupiter when heliacally rising, we can readily interpret it according to the different systems of the Nakshatras as specialised in Tables IX and X. A strict solution of the problem would entail long and troublesome calculations. As, however, all dates as yet found in this cycle have already been calculated (by Mr. Dikshit, Corpus Inscrip. Ind. vol. III, p. 105), there will only be occasion to solve the problem when new dates occur. We may therefore be content to ascertain the time of Jupiter's heliacal rising within a day from the correct date, and the longitude of Jupiter at that time within a degree of the truth.
2 x 3576 90000
Ex.-Calculate Jupiter's Sam.' for the beginning of the year; e.g. 3576 K. Y., 0.9516-8892 = 17-8392. For the Surya Siddhánta without bija add = 0.0795, making 17 9187, or rejecting the 3rd and 4th decimals-17-92. Subtract 12 or multiples of 12 from the integers, and there results 5.92. Multiply this by 0-083, add the product, 049, to the Jupiter Sam.' found above: 5.92 +0:49 6:41. With the sum apply to Table XII and add to or subtract from it (as directed in the table) the
=
For such problems, however, Professor Kielhorn's tables published in the Indian Antiquary (1889), vol. XVIII, pp. 193ff. and 380ff., and in the Abhandlungen der Königl. Gesellschaft der Wissenschaften zu Göttingen, 1889, supply an easy method of computation.
3 G 2
