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

IX.24 IX. SAURA-SIDDHĀNTA — SOLAR ECLIPSE 223 Repeating the work, the p.c.n. got will be about nā.23-20. The rule is thus explained: It has been shown in the context of the Paulīśa solar eclipse that the relative total parallax is obtained by multiplying the relative horizontal parallax (π) by sine zenith distance of the Sun (dṛgjyā) and dividing by the radius. In this Siddhānta, the horizontal parallaxes of the Sun and the Moon are got separately by dividing by their distances for the sake of exactness. But the Sun's dṛgjyā is used for the Moon too, since the difference is very small in the neighbour- hood of new moon, with the solar eclipse occurring. In fig. 2, dṛgjyā = sin Zs, and the relative parallax = ss'. Its projection on the ecliptic, sl, is the relative parallax in longitude, by which (Moon — Sun) has got to be increased or decreased to get their apparent difference in longitude. In the figure, since s is west of n, it is subtractive, and p.c.n. is later, and therefore the nāḍīs of parallax are additive. (When the Sun is east of n and parallax is additive, clearly the nāḍīs are subtractive.) Since (Moon — Sun) is tithi element, the relative parallax is treated like tithi, and multiplied by 60 and divided by the daily motion to get the nāḍīs of parallax. Now, sl is found thus in this Siddhānta: sl² = ss'² - s'l². (∵ the triangle ss'l is right-angled at l, and so small that it may be considered plane.) = ss'² - ss'².sin² l ss' = ss'² - ss'².sin²Zn ÷ sin² Zs (∵ triangle Zns is right angled at n) = π² dṛgjyā² - π² sin² (z.d. of n) (∵ ss' = π × dṛgjyā = sin zs, and Zn is the z.d. of n) = π² (radius² - Śaṅku² - sin² z.d. of n). (dṛgjyā² = radius² - Śaṅku²) ∴ sl² = π √(120² - śaṅku² - sin² z.d. of n) = π × dṛggati, as given But, π = the Moon's horizontal parallax - the Sun's horizontal parallax. ∴ the dṛggati is multiplied by each and then subtracted. It has been said already, in previous two solar eclipse contexts, that the sine of the horizontal parallax is obtained by dividing the earth's radius by the respective distance. Since the author uses as the divisor not the actual distance but the respective distance divided by 43, the earth's radius also has to be taken divided by 43. The author takes 788 yojanas as the earth's radius, adopting the value of the Āryabhaṭīya and multiplying it by 3/2 to express it in the yojana measure of the Ārdharātrika etc. systems. (These systems give the earth's radius as 800 yojanas.) Dividing it by 43 we get 18.3, and the author gives it as 18, corrected to the nearest unit's place. Further, since Zn is perpendicular to the ecliptic, Zs, the zenith distance of the Sun at any position on the ecliptic, is always greater than Zn, and, accordingly, their sines also, since the arcs are all less than 90°, i.e. (radius² - śaṅku²) is always greater than sin² z.d. of n. Therefore, the interpretation of TS that the former is to be subtracted from the latter is wrong, as mentioned already. The need for successive approximation by repetition of work is plain. [नति:] अविशेषाद् (दृक्क्षे)पं 'वस्वेक'घ्नं विभज्य कक्षाभ्याम् । लब्धान्तरचापांशा मध्यज्यादिग्वशेन नतिः ॥ २४ ॥