ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

122 INDIAN LUNI-SOLAR ASTRONOMY Hence the new equation = - 34' sin 2 (θ - D), = 34' sin 2 (D - θ). Here the symbol D stands for the Moon as corrected by the ancient Indian equation of apsis and its complement as given by Bhāskara. It is readily seen that Bhāskara is the first of all the Indian astronomers to detect the equation known as "Variation" His constant, 34', is less than the modern value by about 6', and cannot be considered as a serious error. We now see that the sum-total of the Moon's equation as given dy Bhāskara = - 379' 46".8 sin (nt - a) + 34' sin 2(D - θ), the evection term being totally absent. This is a serious defect, and Bhāskara's new equations would make the Moon generally more incorrect at the syzygies and eclipses than what the ancient Indian equation of apsis would do. Perhaps late in life when he was 69 years old in 1105 of Śaka era (= 1183 A.D.) he discovered the inapplicability of his new equations at the times of eclipses and in his Karaṇa-kutu- hala he altogether omitted these new equations which he had given in his Bījopanaya. As to Bhāskara's second inequality which is really the com- plement of the equation of apsis without the evection term, it is far inferior to that of Mañjula and of Śrīpati; as we have seen their form of the second inequality combines the complement of the equation of apsis and evection in the mathematically cor- rect form. For the discovery of such a form of the equation as of these authors, very patient, careful and frequent observation must have been coupled with very careful and nice comparison of observed facts. As to "variation" it was first discovered by Abul-Wefa in 976 A.D.¹ which was quite forgotten when Tycho-Brahe re-dis- covered it in 1580 A.D. Hence Bhāskara, in 1152 A.D., re-dis- covered it in India four centuries before Tycho. Candraśekhara of Orissa on the Moon's Inequalities In connection with lunar inequalities it is nesefsary here to record what were the equations discovered or verified by M.M. Candraśekhara Simha of Orissa in the later half of the last century. He was educated in the orthodox Sanskrit fashion

1. Godfray's Lunar Theory, p. 114.