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

VII.4 VII. PAULIŚA-SIDDHĀNTA — SOLAR ECLIPSE 175 ZM = z.d., and MM′ is the general parallax. PM′ is the parallax in latitude, and MP, that in longitude ZQ. = latitude of the place, and ZN is the zenith distance of the nonagesimal (z.d.N.). We shall find an expression for PM′, the p.lat. p.lat = PM′ = MM′ × sin M′ MP/120 = 49′ sin ZM × sin ZM N/120² = 49′ sin ZN/120 = 49′ sin zdN/120, (from rt △ MNZ). Similarly for p.long, i.e. MP, p.long = MP = MM′ cos M′ MP/120 = 49′ sin ZM. cos ZMN/120² = 49′ cos ZN × sin MN/120² (from rt △ MNZ) = 49′ cos z.d.N × cos OM/120², OM being (lagnam − Moon). Clearly, this is positive when the Moon is east of the nonagesimal, and negative when west. It is p.long. that we are concerned with in this verse, and it must be given in terms of the hour- angle (h, or natāṃśa) cos z.d.N × cos OM = (i) cos w. cos Ø. sin h. sec δ [δ being the Moon’s declination] + (ii) [sin w × cos Moon’s longitude × {cos Ø × tan δ × sin (nāḍīs after sunrise or before sunset × 6°)/120²} − sin Ø/120]. The Siddhānta omits (ii) which is small in comparison with (i), sin Ø/120 being small in India. For the same reason, and as w and δ cannot exceed 24°, it takes cos w. cos Ø. sec δ as 120. ∴ p.long = 49′ sin h/120. As said before, this is positive, i.e. it increases the Moon’s longitude when h is east, and negative, i.e. it decreases, when h is west. Therefore the corrected time of new moon is earlier and subtractive in the forenoon, and later and additive in the afternoon. Now, 49′ of p-long, converted into time, using the mean relative daily motion of the Sun and the Moon, (731′.5), = 49′ × 60/731′.5 = 4 nāḍīs nearly. ∴ nāḍīs of parallax = 4 × sin h/120 = sin h/30, as given by the text. If (ii) is not neglected, the Moon being east or west of the nonagesimal will be the criterion for the subtraction and addition of the nāḍīkās. [नतिः] पञ्चघ्नात् ‘(त्रि)घना’ऽऽप्तादक्षान्मुखपु(च्छ)योर्धनर्णे तत् | (सशशि)चरणा(पमगुणा) धनर्णनाड्यो ‘[धृति]’विभक्ता ॥ २ ॥ उदगयने पूर्वार्धे धनमृणं दक्षिणे प्राच्याम् | पश्चाद्धनं तु याम्ये (दि)गुदग्गुणं वामतः पुच्छे ॥ ३ ॥ दिनयातशेषनाड्यश्चन्द्रा(पम)संगुणास्त्वशीतिहताः | (मे)षतुलादि ऋणधनं विपरीतं वामतः पुच्छे ॥ ४ ॥