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

I.16 I. INTRODUCTION OF THE WORK 17 be lost. Therefore we cannot determine whether the period of 2850 years mentioned here is the actual yuga of the original Siddhānta or a minor yuga (i.e. a fraction of it in whole years) given for convenience. Patently, the solar year given here is tropical and agrees with the value given to it by the ancient Greeks, like Ptolemy II and Herodotus. It is so with the duration of the synodic month also. Reducing the number of solar years and intercalary months in the yuga by the factor, 150, we see that there are 7 intercalary months in a period of 19 years or 228 solar months, which is the wellknown Metonic cycle. From all this we can conclude that this Siddhānta is from a Greek source. In the case of the Saura, the period of 1,80,000 years given here is certainly a minor yuga of the original Saura, for by multiplying this by 24 we get the number of years in the yuga of the original, viz., 43,20,000 years. From this we can infer that in the yuga of the original there are 1,80,000 × 24 = 43,20,000 solar revolutions, 6,57,46,575 × 24 = 1,57,79,17,800 civil days and 24,06,389 × 24 = 5,77,53,336 lunar revolutions. We have already mentioned that all these agree with the Ārdharā- trapakṣa of Āryabhaṭa given in the Mahābhāskarīya, with the Khaṇḍakhādyaka which is based on the Ārdharātrapakṣa and with the Pauliśa quoted by Bhaṭṭotpala in his commentary on the Bṛhatsaṃhitā but not with the Modern and well-known Sūrya Siddhānta. Now what is the purpose of our author in giving the yuga-elements of these two Siddhāntas alone? Our author expects that, like the Pauliśa, the Saura also would be used for a long time. So, if the time taken is far from the Epoch, he expects the reader to make his own rule, taking the elements given here, following the method of the Romaka. In the case of the Romaka itself, the accumulation of error in the rule can be prevented by deducting multiplies of 2850 years from the years gone from Epoch and doing the work with the small number of years left. Also, in the case of both, we can use the elements given here to check the constants given in later work, for mistakes. We shall now explain the rules of verse 16, indicating the Sun’s revolution as R, the Moon’s r, the synodic months m, the intercalary months i, the elided days e, the Tithis t, the civil days d, and the sidereal days n. (i) We shall explain the synodic month and derive the relation between the synodic months and lunar revolutions in the yuga. The synodic month is the interval between two consecutive conjunc- tions of the Sun and the Moon. In the Yuga the Moon makes r revolutions and, therefore, in one day makes r/d revolution. In the same way, the Sun makes R/d revolution. In one day they move apart by (r – R)/d revolution. When the separation equals one revolution they are in the next con- junction. The period of separation equal to one revolution, in days = 1/ [(r – R)/d] = d / (r – R) , which is the length in days, of the synodic month ....... (1) For d/(r – R) days, there is one synodic month; for d days (i.e. the days of the yuga) there are d/ {d/(r – R)} = r – R synodic months, i.e. r – R = m, r = m + R.........(2); i.e. adding the Sun’s revolutions to the synodic months, the lunar revolutions are obtained. (ii) The explanation of the intercalary month and its relation to the synodic month: The synodic months, Caitra etc. are those that end in the solar months Meṣa etc., and there is normally one to one correspondence between the two sets. But as the synodic month is shorter than the solar it succes- sively ends earlier and earlier in the solar and when it happens that the synodic month ends so early in the solar that another synodic month also ends within the same solar, obviously it has to be left out of reckoning if the correspondence between the set Caitra etc. with the set Meṣa etc. has to be maintained. This is the Adhikamāsa or intercalary month.