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

224 PAÑCASIDDHĀNTIKĀ IX.25 Parallax in latitude 24. Take the sine z.d. of n last got in the successive approximation, multiply by 18, and divide by the respective kakṣās. The respective sine parallax in latitude is got. The arc of their difference is the relative parallax in latitude and its direction is that of sine z.d. of m.e.p. (i.e. of M from Z.) Since the sines are very small, it is immaterial whether the arcs are found first and their difference is taken, or whether the arc of the difference of the sines is taken, both being the same practically. But the latter will entail less work. a) Sine parallax lat. of the Sun = 18 × sin z.d. of n ÷ Sun's kakṣā. b) Sin parallax in lat. of the Moon = 18 × sin z.d. of n ÷ Moon's kakṣā. (b) − (a) is the sine of the relative parallax in lat. whose arc is to be found, and its direction is that of M from Z. Example 16. To continue example 10. The sine z.d. of n, last got in the successive approximation in the last example is 27′ 26″ say. (a) Sun's sine par. in lat. = 18 × 27′ 26″ ÷ 16,641 = 1″.8. (b) Moon's par. in lat. = 18 × 27′ 26″ ÷ 1171.2 = 25″.3. Sin relative par. in lat. = 25″.3. − 1″.8 = 23″.5. Rel. par. in lat. = arc of 23″.5 = 11′.2, north, since M is north. The rule is thus derived: The zenith distance of the nonagesimal, Zn, is the Sun's dṛkkṣepa. In the context of the solar eclipse, according to the Paulīśa, it was shown how the parallax in latitude (p.c.lat) is to be got by multiplying this dṛk-kṣepa by the relative horizontal parallax and using it as a correction to the Moon's latitude to obtain the corrected latitude. Here, the parallax is derived separately for each of the Sun and the Moon, for the sake of greater accuracy. Now, the direction of the nonagesimal and the sine of its zenith distance is the same as that of sine z.d. of M, and the direction of the apparent shifting of the Sun and the Moon by parallax, as resolved on the line of latitude, is the same as that of sine z.d. of n, (as ls' in fig. 2). Therefore, the direction of the parallax correction is the direction of sine z.d. of M, as mentioned by the author. (In the fig. it is north.) Thus everything is explained. ज्याविधिना विक्षेपं तत्कालं प्राप्य तेन सहितोना । स्पष्ट[T] नतिः प्रमाणैः स्वैस्स्वैर्ग्रासं स्थितं च वदेत् ॥ २५ ॥ 25. The Moon's latitude at the time taken is to be got by using the sine (of Moon ~ Rāhu), and this is to be added to or subtracted from the parallax correction in latitude (according to their direction). This is the parallax- corrected latitude (p.c. lat.). This is to be got separately for each of the times separately and from them the times of total obscuration and total duration are to be got. 24a. A. दृक्षेपं; B. दृक्षेप 25a. B. विक्षेप d. A. स्वैस्वैग्रसं; B. स्वैस्वैग्रांमं b. B. चस्वेकग्रं (B2.3.°ग्रं) d. B. ज्याद्विख b. A. प्राथ c. A.B. स्पष्टनति D. स्थिति