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

XII.4 XII. PAITĀMAHA SIDDHĀNTA 245 determine whether the anvādhāna or the iṣṭi is to be performed on that day, then the general term, tithi, need not have been used, and it would have been easier to mention the thing. Further this is a matter for the Dharmaśāstras to deal with, not for an astronomical work. Therefore, by fixing the date of the parva, the author means to fix all the subsequent dates following, upto the next parva, and make them convenient for civil use. If the dates are consecutive, one for each day, it will be con- venient for civil reckoning. If there is a jump, omitting one date in the middle (tithikṣaya), it is plainly inconvenient. The instruction in the verse secures that the dates follow without omission in the middle of the fortnight. For, if the moment of full or new moon is after noon, there will be no omitted tithi in the fortnight following, and the corresponding dates will follow one after another each day, beginning from prathamā, next day. But, if the moment of full or new moon is before noon, then there will be an omitted tithi in the fortnight following, since the remainder in getting the omitted days will be greater than 46, increasing by one each day. Therefore, if now the day of full or new moon itself is reckoned as the first date of the fortnight, then the reckoning can be continued to the end of the fortnight without omission. It is bearing in mind this idea implied by the text, that we made a distinction between the astronomical and the civil date, in giving the computation of the 'days from epoch'. The Siddhānta is only repeating here the idea of the Vedāṅga Jyotiṣa in: dyu heyaṃ parva cet pāde pādas triṃśattu saikikā | the term pāde (meaning 'quarter day') corresponding to the term ardhe in our text. The thirty-one parts mentioned form the measure of the pāda, in units of 1/124 parts of a day. We have explained the vyatīpāta in detail, in our commentary on III.20. We must remember here two things that we said there: (1) Vyatīpāta occurs when the Sun and the Moon have the same declination, (both north or both south), and when one is moving northward while the other is moving southward. (2) If the Sun, Moon, and declination are all mean, as here, and if the first point is at the solstice, as here, mid-vyatīpāta-yoga must fall when the Sun + Moon equals 12 rāśis. In the yuga, (of 1830 days) there are 5 + 67 = 72 such yogas, i.e., vyatīpātas. Therefore, for given 'days', there are, 72 × 'days' ÷ 1830 = 12 × 'days' ÷ 305, vyatīpātas, as given here. The quotient obtained are the vyatīpātas gone. But this knowledge is practically useless, and we must take it that the Siddhānta intends here to give when the vyatīpāta occurs, a time extremely propitious for gifts, japa, homa, etc. This can be found easily from the remainder. Divide this by 12. The result is days etc. gone from the last vyatīpāta. Subtracting the remainder from 305 and dividing by 12, we get the days to the middle of the next vyatīpāta. If the remainder is zero or nearly so, it is clear that the vyatīpāta is on. Example 3(a). Given the 'days' 1697, what is the tithi for that day, and the subsequent days, upto the end of the fortnight? The tithis gone = 1697 + 1697 ÷ 61 = 1697 + 27 50/61 = 1724 50/61. Dividing out by 30, the remainder is 14 50/61, i.e. 50/61 part of pūrṇimā has gone, and 11/61 part remains. Since the tithi is equal to 61/62 day, 11/61 tithi equals, 11/61 × 61/62 = 11/62 day. The full Moon ends at 11/62 day, i.e. before noon. Therefore that day itself is Prathamā, (not Pūrṇimā). (The same conclusion follows from the remainder of the omitted day, 51, in this case, (minus zero, for the civil day gone,) being greater than 46. After this, for ten days, the tithis are from the second to the eleventh, for civil purposes, though at sunrise the tithis are from the first to the tenth, the eleventh being the omitted tithi. On the next day the tithi at sunrise is the twelfth, as also the civil tithi, and so on.