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

VII.6 VII. PAULIŚA-SIDDHĀNTA — SOLAR ECLIPSE 179 The formulae here are similar to that of VI. 5 as reduced by us, giving the total duration in the lunar eclipse, according to Vāsiṣṭha. Therefore, the explanation is similar. As in the Vasiṣṭha, in the Pauliśa too, the limit of the lunar eclipse is seen to be 13°, giving 55′ latitude. Therefore, in the Pauliśa too, the sine of the semi-diameters of the Shadow and the Moon is 55′, wherefrom their respective semi-diameters may be taken as the same, i.e. 38′ and 17′. The limit of the solar eclipse is seen to be 8°, at which the latitude is 8 × 55′/13 = 33′.8. Therefore the sum of the semi-diameters of the Sun and the Moon is 33′.8, from which the semi-diameter of the Sun is found to be 16′.8. If actually the Moon’s semi-diameter is a little more or less in the Pauliśa, to that extent that of the Sun must be less or more. But we have no means of knowing it exactly, since the original Pauliśa is not extant, the Pauliśa quoted by Bhaṭṭotpala in the Bṛhat Saṁhitā being different, as already mentioned. From the formulae, the minutes of arc pertaining to duration is, 55′ × 2 √(169 − (Moon ~ Rāhu)²)/ 13 in the case of the lunar eclipse. To be correct, the time must be found from this by dividing by the true relative motion, which is not done here. If the mean relative motion is used, we get: {2 × 55 √(169 − 0)/13} × 60 ÷ 731.5 = 9, being the nāḍis for the maximum. But, by the formula, the maximum is, 3√(169 − 0)/4 = 9¾ nāḍis. But this is nearer the correct value. For the solar eclipse the maximum by the formula is, 3 √(64 − 0)/4 = 6 nāḍis. But actually, in the solar eclipse the maximum differs according to the time of new moon, being about 5 nāḍis at sunrise or sunset, and about 10 nāḍis near noon. TS, in their explanation here, take the maximum lat. to be 270′, instead of their taking 240′ for the Vāsiṣṭha. But, by this, the respective sums of semi-diameters must be got as 61′ and 38′. But they give 58′ and 35′, which is quite wrong. They seem to have taken these wrong values deliberately, with a view to deriving the formulae using the mean relative motion. NP too have failed to get the correct meanings and so close their notes on verse 7 with th.e statement “We cannot explain the origin of this discrepancy” (pt. II, p.59), the apparent discrepancy being in the formula for total duration of the eclipse as calculated by them. We shall illustrate the whole thing with two examples. Example (a). In chap. VI, example 3, the Moon at full-moon was given as rā. 5-15-0, and Rāhu at that time as rā. 5-6-36. Compute the lunar eclipse:- The Rāhu corrected for eclipse = rā. 5-6-36 − 1° 36′ = rā. 5-5-0 Moon ~ Rāhu = rā. 5-15-0 − rā. 5-5-0 = 10° Total duration = 3√(169 − 10²)/4 = 3 × 8.307/4 = nā. 6-14. (Compare this with the nāḍis got by Vāsiṣṭha, nā. 5-46). Example (b). The latitude of Pudukkottai in S.India is 10° 24′ N. On a certain day, there, sunrise is nā. 28- 40, after sunset, midday is after nā 44-20, and new moon is after nā. 49-20 The Sun = Moon = rā. 2-0-0, at new moon and Rāhu (Tail) is rā. 2-1-0, Compute the solar eclipse, if any, at Pudukkottai. First, Parallax-corrected new moon:- Time of new moon ~ time of midday = nā. 49-20 − nā. 44-20 = 5 nāḍikās, west. = 5 × 6 = 30°, degrees from meridian west. Correction for new moon = sin 30°/30 = 60/30 = 2, nāḍikās. Degrees being west, adding to new moon, the parallax corrected new moon = nā. 49-20 + nā. 2-0 = nā. 51-20.