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

XIV.6 XIV. ASTRONOMICAL INSTRUMENTS 265 This relation is approximately correct for a place on the equator, and is accurate at an equinox. For any other place it is incorrect, for Rsin z really depends upon Ø, the latitude of the place, and the Sun's declination on the day in question, besides the time of the day elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon. Any such formula must therefore involve these elements. Formula (3) stated above does not occur in any other work on Indian astronomy. But analogous formulae do occur. Of these mention may be made of the following. (i) Vasiṣṭha's formula. Let s₀ denote the gnomonic shadow at midday and s the gnomonic shadow at any other time. Then, in the forenoon: s = 64800 / [(lagna − Sun) in mins.] − 12 + s₀ and in the afternoon s = 64800 / [10800 − (lagna − Sun) in mins.] − 12 + s₀ (see above II.12-13) (ii) Paulīśa's formula s = (6 × day-length) / (day elapsed) − 12 + s₀ (gnomon = 12. See IV. 49. This formula was later restated by Mahāvīra in the form: s = gnomon / (2 day elapsed / day-length) − 12 + s₀ (gnomon = 12. See Gaṇita-sāra-saṅgraha, IX. 18). (iii) Śrīdhara's formula s = (½ gnomon) / d − gnomon, where d = (day elapsed or to elapse) / (day-length) See Triśatikā (ed. Sudhākara Dvivedi), Rule 65. This may be derived from Paulīśa formula by assuming s₀ = 0. Śrīdhara's formula was restated by Nārāyaṇa Paṇḍita in the form: s = { (½ day-length) / (day elapsed or to elpase) − 1 } × gnomon See Gaṇita-kaumudī, Rule 13, p. 207. 5a. A. षड्या भागा; B. ष (B2. श्र) मध्याभागा 6a. B2. छया d. A. B. पश्चाल्लेषा० A. स्तथा C. ॰स्तुया (B2. °सागा) ab. B. ॰भ्यन्तरजा जीवा A. प्राप्नो; B. प्राप; C. [प्राची] b. A. तज्या b. A. षष्ट; B1.2. षष्टं; B3. षष्ठं c. A माध्यंदिनी B समेत्ता c. A. प्राग्यतः; B. प्राग्युता