Indian Antiquary Vol 20

Author(s): John Faithfull Fleet, Richard Carnac Temple
Publisher: Swati Publications

Page 47

JANUARY, 1891.]
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the fraction (ghatis, palas), and adds one to the complete number, and counts from Thursday as zero (and Friday as one; see the above example of the luni-solar ahargaṇa worked out on page 243 of the text and p. 66 of the Tables); while, in finding the week-day from the solar ahargana, he neglects the fraction, does not add one to it, and counts from Friday as zero (see the example on p. 240 of the text and p. 65 of the Tables). To add one in the former case, amounts to the same thing as not to add one and to count from the Friday as zero. To the luni-solar ahargana of both the Surya and Arya-Siddhantas, he applied one and the same method, and evidently forgot that the former ahargana is to be counted from Thursday midnight. In the above example (worked on page 243) the complete number of the ahargana according to the Súrya-Siddhanta is 1,798,147; adding one to it, he obtained 1,798,148, which, being divided by seven, gives 2 as the remainder; and counting from Thursday as zero, he gave Saturday as the sootadina or last day of that mean luni-solar year, according to the SuryaSiddhanta; while, adding one to 1,798,146, which is the complete number of the ahargana according to the Arya-Siddhanta, and counting from the Thursday as zero, he gave Friday as the 'sootadina' according to the Arya-Siddhánta. In the Second Chronological Table, against the Kaliyuga year 4923, he gave 1,798,148 as the luni-solar ahargana in column X., and Saturday as the last feria in column IV. In this, he evidently followed the Surya-Siddhanta. But I have just shewn that, even according to the Surya-Siddhanta, the last feria is Friday, and not Saturday. The luni-solar ahargana according to the Surya-Siddhanta is to be counted from the Thursday midnight; but in order to count it as Warren did, from the Thursday as zero (Friday as one), 15 ghats should first be subtracted from it, and then one (day) added," to the complete number of it. In the above example, the luni-solar ahargana according to the SuryaSiddhanta is 1798147-1-49, &c.; subtracting 15 ghails from it, and then adding one (day) to the complete number, we get 1,798,147, which ought to have been given in column X. of the Second Chronological Table against Kaliyuga year 4923; but Warren gave one more, viz. 1,798,148, which is wrong. In his explanation of the Second Chronological Table, Warren omitted to specify the Siddhanta to which the luni-solar ahargana
MISCELLANEA.
• I do not know why Warren made such a nominal distinction between the solar and luni-solar aharganas. It would have been more convenient to follow one and the same course in both the cases.
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in its tenth column belongs. But from the above example it is clear that it is the Surya-Siddhanta; and from several other examples I have fully satisfied myself that it is according to the Sürya, and not the Arya-Siddhânta. Whenever the fraction in the luni-solar ahargana is less than 15 ghatss, the entries in the columns X. and IV. must be wrong; and from several actual calculations, I have ascertained that they are wrong. The English dates in column V. are, as Warren himself stated (p. xii. of the Chronological Tables), derived from the ahargana inserted in column X.; and consequently they also are wrong. For instance, against the Kaliyuga year 4923 current, the English date of the last mean conjunction is given as the 23rd March (A. D. 1822). But it And from any should be the 22nd March. English Tables, we can see that the 22nd March, A. D. 1822, was a Friday, which is the correct last feria of that luni-solar year. In column VI. of the same Table, the sidereal date, in the solar Chaitra (the Tamil Poongoni) for the last conjunction, is given; and to get it, the same wrong luni-solar ahargana was again used, as will be seen from a note on page xii. f. of the Chronological Tables. Consequently, the entries in column VI. must be wrong. In the above example, the sidereal date is not the 13th but the 12th, and the civil date is the 11th of the solar Chaitra (the Tamul Poogoni). Thus, columns IV., V., VI., and X. of the Second Chronological Table are wrong. It is true that the fraction in the luni-solar ahargana does not every year amount to less than 15 ghatis; but, as the fraction is not given in the Table, there are no means of determining in what years the results are right, and in what years they are wrong; and to provide these means now, would amount to preparing a fresh Table. The mistake, however, is not more than one day, one way or the other.
To use, as Warren did, the solar ahargaņa from one authority and the luni-solar from another in the same Table, is unsystematic, and the more so, because the luni-solar ȧharganas from the Surya and the Arya-Siddhantas differ from each other, and have different starting-points. Warren said that "the Tamil astronomers, though computing in solar time, use in preference the luni-solar ahargana according to the SaryaSiddhanta, and for the solar the Arya-Siddhánta" (see pages 64 and 66 of the Tables, and p. 244, para. 2, of the text). But this cannot be a fact.
7 If counted from Friday as zero, the one day need not be added.
This is for the end of the mean amdvdsyd. The apparent amdudsyd ended on the 12th Poongoni, civil account (see p. 90); but the correct result is only accidental.