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

III.22 III. PAULIŚA-SIDDHĀNTA 63 occurs when the declinations are the same and the courses are different. The expression half- revolution in that connection is only meant to be approximate, because by the latitude of the Moon it may be a little more or less." Therefore we should examine whether a Vyatīpāta would occur at the neighbourhood of the sum being six signs, because it can occur only there. But sometimes it may not occur at all, because the definition is not satisfied (All this is expounded clearly in works like the Siddhānta Śiromaṇi and we stop with this). One may think that we are making contradictory statements by saying in the history of the origin of the Vyatīpāta, that it occurs at the sum being full revolutions and here that it occurs at half revolu- tions. There is no contradiction because the origin from which the longitudes are measured is different in the two cases. In the former the winter solstice was taken as the origin, and, in the latter, the spring equinox. There is a difference of three signs between the origins, which causes the same difference in each of the two longitudes, with the result that there is a difference of six signs in the sum. That they are the same can be shown thus: The Sun measured from winter solstice, (say, a) = the Sun measured from spring equinox (say, b) + 3 signs. The Moon measured from winter solstice, (say, á) = the Moon measured from spring equinox (say, b́) + 3 signs. Therefore a + a' = b + b' + 6 signs. If a + a' = full revolution, b + b' + 6 signs = full revolution, therefore b + b' = full revolution - 6 signs = half revolution, which proves the sameness. Spring equinox is not men- tioned because at the author's time it was situated at the beginning of Aśvinī and longitudes are reckoned from there. Example 11. The Sun and the Moon at the end of the day are rā. 1-10-0 and rā. 4-23-30, and their daily motion 57' and 783'. Taking the spring equinox to be at the beginning of Aśvinī, i.e. the winter solstice at the beginning of Capricorn, examine the possibility of Vyatīpāta, in both ways. Because the longitudes are from zero Aśvinī, they are the same as reckoned from spring equinox also, both points being the same in the problem. Therefore sum of longitudes = rā. 1-10-0- + rā. 4-23-30 = rā. 6-3-30. This is 3° 30', i.e. 210', over a half revolution. The sum of the daily motions = 57' + 783' = 840'. Therefore at 210 × 60 ÷ 840 = 15, nāḍīs before the end of the day, the sum is equal to a half revolution or 6 signs, and so Vyatīpāta may occur in its neighbourhood. Otherwise, if the longitudes as measured from winter solstice, the Sun = rā. 1-10-0 - rā. 9-0-0 = rā. 4-10-0. The Moon = rā. 4-23-30 - rā. 9-0-0 = rā. 7-23-30. Their sum = rā. 4-10-0 + rā. 7-23- 30 = rā. 12-3-30, and this is 210' over a full revolution. Therefore 210' × 60 ÷ 840 = 15, nāḍīs before the end of the day. The sum is a full revolution and the Vyatīpāta may occur as its neighbour- hood. (Note that worked in both ways, the time is the same). Now for the readings. In the place of pāto we have taken yāto because the scribe may easily mistake pā for yā. But the correction bhāgo of TS does not agree with the second case in arkakāṣṭhām and deserves to be rejected. The wrong reading, śaśi-savikṣepaḥ has been corrected by us into śaśī savikṣepaḥ, by a simple lengthening of. But TS and NP have made it śaśiravikṣepaḥ which is incorrect and also does not agree with kāṣṭhām. The meaning which they have taken for this verse itself is wrong. Their interpretation of kāṣṭha into 'maximum declination' i.e. 24° (or 23° 20') is not proper, for, in his work (see Chap. IV), kāṣṭhānta is used for maximum declination and kaṣṭhā is taken to mean only declination. Let us concede it is maximum declination and therefore means 24°. Even this does not agree with the meaning given by them because they want and imply 23° 20' only there. If 24° is given roughly for 23° 20', why not 23° which is nearer. They do not seem to have under- stood at all what is sought to be conveyed by the author.