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

CANDRAŚEKHARA ON THE MOON'S INEQUALITIES 123 and had no acquaintance with English education. His work Siddhānta-darpaṇa was edited by Prof. Jogeschandra Ray, late of the Cuttack College, in 1899.¹ Candraśekhara in his work gives four equations of the Moon which are :- (1) The equation of apsis. (2) The Tungāntra equation or the complement of the equation of apsis in combination with evection. (3) The fortnightly equation or variation. (4) The Digamśa equation or the annual equation (i. e., 1/10 of the Sun's equation). (5) The first equation is of the form [31° 30' - 30' cos (nt - a)]3438 × sin (nt - a) = ─────────────────────────────────────────────── 360° = -300' 49".5 sin (nt - a) + 4' 46".5 sin (nt - a) cos (nt - a) = -300' 49".5(sin nt - a) + 2' 23".25 sin 2 (nt - a) It is seen that Candraśekhara wanted to correct the equa- tion of apsis to the second order of small quantities as in all the Indian authors from Brahmagupta but Candraśekhara's form is correct though his contant is wrong. (2) His second equation is of the form 160' × 3438 sin[a - (θ + 90°)] 3438 sin(D - θ) ────────────────────────────── × ─────────────── 3438 3438 Moon's appt. daily motion² × ────────────────────────── Moon's mean motion = -160' cos (θ - a) sin (D - θ) Moon's appt. daily motion × ───────────────────────── Moon's daily mean motion Here the constant is the same as that of Śrīpati discussed before. The symbol means the Moon as corrected by the equation of apsis. It is readily seen that the constant of the first term of the equation of apsis is increased by 80'. and that the constant of evection is taken at 80'. In both the cases the error is about +4'. (3) Candraśekhara's third equation or Variation 3438' sin 2(D' - θ) = ─────────────────── = 38' 12" sin 2(D' - θ),³ 90

1. Siddhānta-darpaṇa, V, 100-114.
2. Ibid, VI, 7-9
3. Siddhānta-darpaṇa VI. 11-12.