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

XII.5 XII. PAITĀMAHA SIDDHĀNTA 247 when the northward course begins, and when the southward one. (Perhaps he has said that in this verse, and the corruption of the text has masked it.) When the Sun enters Śraviṣṭhā its northward course begins, and when it is at the middle of Āśleṣā, its southward course begins, or the first half of the year is the northward course, and the second half, the southward one. It can also be inferred from the rule for vyatīpāta. Example 4. Given the 'days' 1722, find the daytime for the day following. 1722 ÷ 366 = 4 258/366. Four years have gone, and 258 days in the fifth. The 183 days of the northward course have gone, and 75 days have elapsed in the southward course. The days to go = 183 − 75 = 108. The duration of daytime in muhūrtas = 12 + 108 × 2 ÷ 61 = 12 + 3 33/61 = 15 33/61. To conclude, it has been said in the introduction to this chapter that the Sun, Moon etc. of this Siddhānta are only mean, not true. Some think it is even worse than this, which we must investigate now. We have seen that, according to this Siddhānta, there are 366 days in the year, 5 years or 1830 days constitute the yuga, and there are 62 synodic months in it. But actually there are about 365 ¹/⁴ days in the year, and also 62 synodic months take 1830.8965 days. Therefore, instead of being at the zero point of Śraviṣṭhā at the beginning of each yuga, the Sun will be advancing by about three degrees per yuga. The synodic month being not completed, it will be really only Caturdaśī then, and at the end of every yuga, the tithi will be preceding by about one per yuga. This is common to both this Siddhānta and the Vedāṅga Jyotiṣa. But accumulation of this error is prevented by tying the Yuga to the correct Śaka year, by the instruction to use the Śaka year for finding the year of the yuga. (This is of the same nature as tying the lunar year to the solar.) It may be said, in passing, that at the period when the VJ was followed, actual observation was used to find out when a correction was wanted and the same made by simply omitting an intercalation, for which, it is possible, they could even have discovered a formula in the long run. We have made this clear in our Notes to the VJ, (Indian National Sc. Ae., New Delhi, 1985) and the during the Seminar on Indian Calendar held by the Institute of Traditional Cultures, University of Madras. (Bulletin of the Institute of Traditional Cultures, Madras, 1968, Part I, page 60.) When thus the accumulation of error is taken care of, giving 366 days to the year is extremely convenient for civil, calendrical, and even religious purposes, since it makes calculations easy in the same way as we, even now, take the year to have 365 days, and the months 31 etc. days. We get 183 days for each ayana, 122 days for each cātarmāsya, and 61 days for each ṛtu, all in whole numbers. There are 61 sāvana months in the yuga. Even the saura month has 30 days and a half, a fraction easy to work with. Further, the fortnight or pakṣa was the unit used then in the place of the modern week. We have shown, in our Notes on verses 2 and 4 above, how it was secured that the dates follow consecutively in the pakṣa, a factor so essential for a civil calendar. The approximateness of the tithis etc. being mean, is of course there, but this is only an advantage in civil reckoning. As for religious purposes, the true tithis etc. required for rites like darśa-pūrṇa-māsa were guessed from earlier observations, as we have said, and there are several indications in the Vedas that such was the case. The abhyudayeṣṭi, enjoined to be performed if the Moon is observable in the east between the anvādhāna on the previous day and the iṣṭi on the next day, is one such indication, for, if the visibility had been properly calculated from the true Sun and Moon, using dṛkkarma etc. there would be no need for abhyudayeṣṭi at all. [इति पञ्चसिद्धान्तिकायां वराहमिहिरविरचितायां पैतामहसिद्धान्तो नाम द्वादशोऽध्यायः ] Thus ends Chapter Twelve entitled 'Paitāmaha Siddhānta' in the Pañcasiddhāntikā composed by Varāhamihira Col. A.D. इति (A om इति) पैतामहसिद्धान्ते द्वादशोध्यायः B. इति पितामहसिद्धान्ते द्वादशोऽध्यायः C. इति पैतामहसिद्धान्तो नाम द्वादशोऽध्यायः