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

XVIII.37 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 341 ings by 263, deduct 43 and divide by 829 and the result is the mean Mercury (in revolutions). These will lead to the following: i. 28 1/3 days before the epoch, Mercury rises in the west, after which the countings of the risings begin. ii. One synodic revolution takes (927/8 + 1/240) days. The deduction of 1/4th nāḍīs or 1/240th day per rising is for taking the synodic period as approximately 927/8 days. The balance remaining after division by 927 is the number of eighth parts of a day elapsed since the last rising. So, dividing this by eight, the number of full days are obtained. During a synodic period the motion of mean Mercury is equal to 263/829 revolutions (which is the same for Sun). Hence for one full revolution Sun will take, (927/8 + 1/240) × 829/263 days, or, 365.261708 days, i.e., 365-15-42. iii. At the epoch date, that is 28 1/3 days before 20-3-505 AD., Sun’s longitude is 357-37 minus 27-55 or 329-42. iv. On this date, Mercury’s longitude is given by: (No. of risings (zero) × 263 – 43)/829 or – 43/829 revolutions. This reduces to – (18-40), or 341- 20, which is ahead of Sun by 11-38 as against 12 needed, and therefore acceptable. In verse, 36c, we, also others, have emended the ms. reading muniva.nanaca as muniyamanava to get the correct figure 927. In 37a kṛtvā has been made as hṛtvā. The meaning and rationale of these verses is clear. But NP have made medhā in 36d as śodhyo and have translated it as “Subtract an eighth part of a day (for every synodic period)” etc. and comment, “We find in XVII, 36 a subtraction of 1/8 of a day and a division of the number of risings by 4. We cannot explain these steps which seem in excess of the normal procedure.” It is rather surprising that NP missed the elementary step of dividing the remainder by 8 to get the number of days, particularly when TS have correctly interpreted it. Without the correct number of days (elapsed since the last rising) the further processing does not make sense. Hence we feel that NP have not understood the process at all. In the next step of finding the longitude of Mercury at the time of the last rising, the figures in the verses have been badly corrupted. In 37b tridaśayama has been emended as tridivasapa by TS, and in 38a navavasuyama as navavasurāma, so as to give them a multiplier of 123 and divisor of 389. But this would give the Sun’s period as 366.479641 days which cannot be. NP have made tridaśayama as adridaśayama; rāmārṇava as pāṇḍava and navavasuyama as navavasurasa. They have also changed the meaning so as to subtract pāṇḍava (5) from the divisor 689 rather than to make the deduction from the product. All these they have done just to make these constants agree with those of Babylonian and then claim that “Table 24 reveals exact numeri- cal agreement for the outer planets and Mercury” (!). They forgot that in this process they have obliterated the initial epoch constant of the longitude of Mercury and comment “For Mercury we have no epoch constant giving us directly a longitude.” We have emended tridaśayama as trirasayama, and navavasuyama as navayamavasu. As shown above, these numbers give the sidereal period of Sun as 365-15-42, which is within limits. Of