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

IX.9 IX. SAURA-SIDDHĀNTA — SOLAR ECLIPSE 207

Fig. IX. 1-a.

The earth E, is the centre of the Orbit-circle, of 'radius' equal to the sine of Three rāśis (120' in this work). O indicates the first point of Meṣa, in the direction EO. EA is the direction of apogee, A, O EA being the longitude of apogee (P is the perigee). X is the centre of the ex-centric circle on which the Sun, Moon or star-planets move uniformly according to the mean motion. X is on EA, at a distance, towards A, equal to the sine of the maxi-minimum Eq. C. S is the position of the body, angle SXO' being the mean longitude of the body. XO' also is directed to the first point of Mesha. EO and XO being practically parallel. ASX = mean longitude – longitude of apogee = mean ano- maly.

SEO is the true longitude, which has got to be found. Since XO' and EO are parallel, SEO = SXO' – XSE, where XSE is the Eq. C. Since XSE changes sign on the right hand side of PA, SEO = SXO' + XSE on that side. Thus we have that in the first case, when the body is from apogee to perigee, i.e. when the anomaly is less than six rāśis, the equation of the centre is subtractive. In the second case, where the mean anomaly is more than six rāśis, is it additive.

Next, for the equation of the centre. If the maximum Eq.C, represented by EX, is small, as in general, then taking SE and SX to be practically equal, sine Eq. C = sine XSE = XE. sine SXE ÷ SE = XE. sine SXA ÷ SX = max Eq.C × sine mean anomaly ÷ 120' (120' being the radius).

In this computation, the astronomers belonging to the school of Āryabhaṭa find the Eq.C using the actual radius vector, SE, in accordance with the geometric representation. But Bhāskaracārya in his Siddhānta Śiromaṇi does not use it, and gives reasons for not using it. Now, if degrees of epicycle are given, as in this Siddhānta, instead of sine maximum Eq. C, these degrees are multiplied by 120' and divided by 360° to get sine maximum Eq. C. (i.e. EX). Therefore, sine Eq. C = (degrees of epi- cycle × 120' ÷ 360°) × sine anomaly ÷ 120'