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

II.6 II. VĀSIṢṬHA-SIDDHĀNTA 31 value, and θ is the anomaly. Note that this is the first term of the series for the equation of the centre in modern astronomy, with its sign reversed, and the reversing is necessary because the ano- maly was reckoned by the ancients from the apogee, not perigee. But in the Vāsiṣṭha it is of the form — (665 — 5P) P/63 for the first two quadrants and + (665 — 5P') P'/63 for the last two. These are derivable from the equation for the Moon’s daily true motion given in III.4, (as we shall show there), which assumes the increase or decrease of motion as uniform. Here we shall assume them and derive the two formulae of II.6. As said before, (e) + (ii) is given by the formulae and (ii) is — (665 — 5P) P/63, for the first formula. Therefore (e) + (ii) = 27 209/248 P — (665 — 5P) P/63 = (63 × 27 209/248 — 665 + 5P) P/63 = (1754 — 665 + 5P) P/63 = (1089 + 5P) P/63 = {1094 + 5 (P — 1)} P/63, which is the first formula. For the second formula (ii) is + (665 — 5P') P'/63. ∴ (e) + (ii) = 27 209/248 P' + (665 — 5P') P'/63 = (27 209/248 P' × 63 + 655 — 5P') P'/63 = (1754 + 665 — 5P') P'/63 = (2419 — 5P') P'/63 = {2414 — 5 (P' — 1)} P'/63 which is the second formula. We have already shown how for the half-gati 6ʳ 0° 4' is got instead of the mean motion 6ʳ 1° 32½'. This means that there is in this an equation of the centre equal to — 88½', combined with it. So, when the equation of the centre given by + (665 — 5P') P'/63 = + 88½, then it is actually zero according to this Siddhānta. Solving this equation, we get P' = 9 or P' = 124. As P' is minus-pada, which is the original padas got less 124, we get that the equation of the centre actually becomes zero at original padas, P= 133, and P = 248. As P = 248, is the end of the gati, this is what we expect, as the anomaly has again become zero. Also, by computation or examination we can get from the equation of the cyclic part of the for- mula for the first half-gati, — (665 — 5P) P/63, the numerically greatest value of the negative equa- tion of the centre, which is — 351', for P = 66½. In the same way, from that the formula for the second half-gati, + (665 — 5P') P'/63 we can get the maximum + 351', for P' = 66½; but as there is a residue of — 88½' in the second half-gati, 351' — 88½' = 262½' is the actual maximum. The numerical mean is 307' which, we see, is very nearly equal to that of the other Hindu Siddhāntas. It is not that VM does not know that zero equation of the centre must occur at P = 124, and not at 133, for in his own Romaka and Saura it is so. Nor is it difficult for VM, a master in the science, to give the two formulae so as to have the equation of the centre zero at P = 124, (so that for a half- gati we get the correct 6ʳ 1° 32½'), retaining, at the same time, the equation of the centre desired by him. If he had given the two formulae in the form (1134 + 5P) P/63, and (2374 — 5P') P'/63, he could have secured this. But adherence to the Siddhānta has prevented him from doing this. So closely does he follow the original that he does not even give the two formulae in the more simplified forms, (1089 — 5P) P/63, and (2419 — 5P') P'/63. The following things are to be noted in connection with this Siddhānta. Of both the Sun and the Moon, the mean motion and the equation of the centre is mixed in a peculiar manner and thereby the true motion is given. We shall see that it is the same in the case of the Pauliśa also. The period of 3031 days called ghana here is the same as what is called kālānala in the Vāk- yakaraṇa, which gives for this period, the mean motion, 11ʳ 7° 31', neglecting full revolutions. The number 248 given here is there mentioned as devara.