पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

the current month, the total tithis are obtained. These lessened by the number of elided days in the period between the Epoch and the time taken gives the Days from Epoch, for the elided days are the tithis left out of reckoning in one to one correspondence between the tithis and the days. Here the elided days are obtained by the proportion, if for the tithis in the yuga numbering 10,57,500 there are 16,547 elided days, how many elided days are there for the tithis from the Epoch to the taken time; i.e. 10,57,500 : 16,547 :: the intervening tithis : the intervening elided days. So, we have the equation, the intervening tithis × 16,547 ÷ 10,57,500 = the elided days. Here the multiplier for the tithis, viz., the fraction 16,547/10,57,500 can be expressed as a continued fraction to find a suitable smaller fraction for easy work, thus: 1 16547 1057500 63 1 1508 15039 9 1 41 1467 35 1 9 32 3 4 4 5 1 0 1 1 1 1 1 1 1 1 1 1 i.e. 16,547/10,57,500 = ——— ——— ——— ——— ——— ——— ——— ——— ——— 63+ 1+ 9+ 1+ 35+ 1+ 3+ 1+ 4+ The successive convergents obtained from this are: 1/63, 1/64, 10/639, 11/703, 395/25244 etc. Of these the author has taken 11/703 as being simple and, at the same time, sufficiently accurate for the purposes of this work, for even during a period as large as the yuga, the difference in the elided days will be only 10,57,500 (1654/10,57,500 − 11/703) = 1/17, and this is small in comparison with the difference caused by actually using the true tithi in the formula, which we are constrained to use, in the place of the mean tithi which, according to theory we must use. Now, at the time of Epoch there was a fraction of elided day equal to 514/703, and, as this has also to be added, the additive constant 514 is given. As done in the case of the intercalary month, here also we can examine the correctness of the constant, 514, thus: the fraction of elided day is the part of the current tithi gone before the time of beginning of the new day, as in the present case, viz., the Romaka before sunset at Yavanapura. We have seen before that at Epoch there remains 16½ nāḍikās for the mean new moon to end, i.e. about 43 nāḍikās have ended in mean Amāvāsyā tithi. The constant 514 means that 514/703 part of the Amāvāsyā has gone and this is equal to about 43 nāḍikās and thus the constant is practically correct. It is because of the existence of this constant that we have interpreted, caitra-śuklādau as ‘when the first tithi of Caitra was about to begin’. Further, we have seen that at Epoch Amāvāsyā is current and Caturdaśī is gone. But, taking the Amāvāsyā as gone, the tithis to be used in the formula are asked to be reckoned from the first tithi of the month. That is why we gave the instruction to add the tithis from Śukla-Pratipad to the current tithi, though the usual instruction would be to add only the tithis gone. It must be noted that the author’s instruc- tion is simpler and at the same time not incorrect. Also, there is the usual practice of comparing the week day for the obtained Days from Epoch, with the actual week day of the taken time, and adding or subtracting a day from the days got, if necessary, which will take care of everything. Thus the whole thing is explained. The Śaka year is the year of the Śaka era which began at 3179 Kali (elapsed), for the Siddhāntas instruct that 3179 should be added to the Śaka year to get the Kali year. The purpose of mentioning that Caitra Śukla Pratipad occurred near the Epoch is to indicate that the months gone must be