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

32 PAÑCASIDDHĀNTIKĀ II.6 We can see that the remark in I.4 about the tithi of the Vāsiṣṭha being very incorrect is appropriate, but it can be shown that it is not due to the error in the Moon, but in the Sun, whose sidereal year is taken as 365-15-0 days. The Moon's motion for 3031 days is in cycles etc. 110-11-7-32 = 110 5063/5400 cycles. In one day the motion is 110 5063/5400 ÷ 3031 = 5,99,063/ (5400 × 3031) cycle. In one day the Sun's motion is 1/365¹/4 = 4/1461 cycle. The relative motion, i.e. their separation per day is 5,99,063/(5400 × 3031) − 4/1461 cycle. The time taken for a separation of one cycle, i.e. the synodic month, is in days, 1/{59,90,63/(5400 × 3031) − 4/1461} = 1461 × 3031 × 5400 ÷ (1461 × 5,99,063 − 4 × 5400 × 3031) = 7,97,09,23,800 ÷ 26,99,20,481 = 29 - 31 - 50 - 17 - 38. But the correct synodic month computed for the time near that of our author is 29 - 31 - 50 - 7 - 47. Therefore in successive synodic months the tithi comes later by days etc. 0-0-0-9-51, according to Vāsiṣṭha. In about 29¹/2 years this will accumulate to one nāḍikā. This is bad indeed, and merits VM's remark in I.4 taditarau dūravibhraṣṭau (i.e., 'The tithis of the other two have slipped far away from the real'.) Now, we have seen that according to this Siddhānta the mean Moon moves revs. 110-11-7-32-0, while the real motion for the period is revs. 110-11-7-32-15. Therefore in 3031 days the Vāsiṣṭha nakṣatra is delayed by a little more than one vināḍi. So a delay of one nāḍi is caused in 440 years only. So the delay of one nāḍi in the tithi per 29¹/2 years mentioned above, must be due almost wholly to the error in the Sun, the result of giving the time per cycle as 365-15-0 days. Again, in every 3031 days, the Vāsiṣṭha Moon lags behind the correct one by 15". A lagging behind by one degree will take place in 3031 × 60 × 60 ÷ 15 days, i.e. in about 2000 years, a very long period indeed. Bearing this in mind, we shall try to answer the question already raised, viz. whether the Vāsiṣṭha Sun and Moon are given for sunrise at Ujjain or sunset at Yavanapura; and, incidentally, we shall show that the kṣepa, 1ʳ 7° 29′ given by śaśi-muninavayāmāśca rāśyādyāḥ and obliterated by TS by their drastic emendation as yama-hṛtāś ca is necessary in II.3. The following is the mean Moon for Epoch (viz. Śaka 427 elapsed, i.e. in A.D. 505), sunset, at Yavanapura, beginning Monday, Caitra Sukla being about to begin. i. Computed for the period according to modern astronomy, assuming the ayanāṁśa to be practically 0 for the time 354° 48′ ii. According to Saura 355° 6′ iii. According to Siddhānta Śiromaṇi 355° 41′ iv. According to Romaka 356° 12′ v. According to Vāsiṣṭha, assuming that the mean Moon is given for Ujjain sunrise 355° 6′ -do- -do- for sunset at Yavanapura 346° 54′ -do- Ujjain sunrise, without Kṣepa 317° 37′ -do- sunset at Yavanapura without Kṣepa 309° 25′ (For use by anyone interested in making the calculations himself, the Kalidina etc. of Epoch is 13,17,122-37-20. Also, the Epoch is 5,09,432-22-40 days before mean sunrise at Ujjain of the first January 1900). An examination of the table will show that the Vāsiṣṭha Moon agrees with that of every other fairly well, taking it as being given for Ujjain sunrise, and taking that the kṣepa is given. If, on the other hand, it is assumed that it is given for sunset at Yavanapura, there is a difference of about 8°, which can happen only in 1600 years, which is very very unlikely; for this to happen the Vāsiṣṭha should