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

202 PAÑCASIDDHĀNTIKĀ IX.6 The Head of Rāhu in revolutions etc. = - (Days × 2700 + 63,13,219) ÷ 1,83,45,827. The tail of Rāhu = the above + 6 rāśis. As for Moon's latitude, for a maximum moon ~Rāhu, equal to 90°, there is the maximum latitude, 270'. For other differences, lat = 270' sin (Moon ~ Rāhu) ÷ 120, as given in verse 25, which reduces to, lat = 9 sin (Moon ~ Rāhu)/4. This is given by the Saura, and followed by all later Siddhāntas. Example 4. Compute Rāhu (a) for Ujjain mean noon prior to Epoch, and (b) for Epoch. (a) In this case, days from Epoch is zero. ∴ Head of Rāhu in revs. = - (0 × 2700 + 63,13,219) ÷ 1,83,45,827 = - rā.4-3-53-3 = rā.7-26-6-57. (b) Since the Epoch is nā. 22-20 later, the motion for this interval, rev. 67/180 × 2,700 ÷ 1,83,45,827 = 1' 11'' has to be deducted. Rāhu-head according to the Saura for the time of Epoch, viz. mean sunset at Yavanapura, is rā. 7-26-5-46. Actually it is rā. 7-26-0, and the difference is within 6'. The calculation of the latitude will be explained in the context of the computation of eclipses. The rule of Rāhu: Like that for the apogee, this rule must be derived from the constants given in the two works that follow Saura since the original Saura is lost. In the Mahāyuga consisting of 1,57,79,17,800 days, there are 2,32,226 revolutions of Rāhu, (i.e. Moon's nodes). Using the rule for Rāhu here, we get, 2700 × 1,57,79,17,800 ÷ 1,83,45,827 = rev. 2,32,226-0-0-46-2 of Rāhu per yuga. This is 46' 2'' more than what we should get, but neglected by author as being small especially in a karaṇa intended to be used for a comparatively short period, considering the fact that even in 10,000 years the error is only 6'', which will not affect the result. That is why the second step of correction is not given, unlike in the case of the mean Moon and apogee. If a correction is wanted here also, multiply the revolutions by 10, divide by 848, and add the resulting seconds to Rāhu. Or, instead of using 1,83,45,827 as divisor use 1,83,45,827.2 i.e., in the rule, take the multiplier to be 27,000, kṣepa 6,31,32,190, and the divisor 18,34,58,272. At the end of 427 Śāka or Kali years 3606, the revolutions to get Rāhu = the longitude at the commencement + the revolutions in 3606 years. = 1/2 + 3606 × 2,32,226 ÷ 43,20,000 = 194 + 1,23,913/3,60,000. Omitting the full revolutions, the parts for the fraction remaining are the kṣepa, for the end of 3606 years Kali. Since there are 1,83,45,827 parts for a revolution, the parts of kṣepa = 1,83,45,827 × 1,23,913/ 3,60,000 = 63,14,684. Since we want the kṣepa for Ujjain mean noon, nā. 33-9 earlier, we have to subtract the parts for this time. Since there are 2700 parts in a day, for nā. 33-9 we have nā. 33-9 × 2700 ÷ nā. 60 = 1492 parts. ∴ the kṣepa for mean noon is 63,14,684 - 1492 = 63,13,192.