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

VII.4 VII. PAULIŚA-SIDDHĀNTA — SOLAR ECLIPSE 177 To secure correction 49' in latitude, a correction = 90° × 49/380 = 11°.6, must be applied to Moon ~ Rāhu which can be done by applying it to Rāhu, as the Siddhānta does. The purpose of this replacement is to extend the method of computing the lunar eclipse using Moon ~ Rāhu to the solar eclipse also. So 49' has to be replaced by 11°.6 in the rules, (i), (ii) and (iii). We shall take the rules one by one and derive the Siddhānta rules. (i) = – 11°.6 cos ω sin Ø/120² = – 11°.6 × 109.6 × (degrees of latitude × 120/57.3)/120², (∵ when latitude is not much, its sine ∝ degrees) = – 5 × degrees of latitude ÷ 27, as given. As the Siddhānta has only the north latitudes in view, this part of p.lat is always negative. There- fore Moon's north-latitude must become less, and south latitude more, by the correction. This can be done by increasing Rāhu-Head, i.e. by adding the correction to the Head, and by decreasing Rāhu's Tail, i.e. by subtracting from the Tail, as instructed. (ii) = – 11°.6 sin ω cos. Ø sin (Moon + 90°) sin h. sec δ /120³ = – 11°.6 sin ω . sin (Moon + 90°) × nāḍīs of correction to new moon ÷ (cos ω × 120 × 4), (∵ sin h = 120² × nāḍīs of correction × cos δ ÷ (cos ω × cos Ø × 4), in verse 1). = – 11°.6 × sin declination of point (= Moon + 3 rāśis) × nāḍīs of correction ÷ (109.6 × 4) = – 11°.6 × {Degrees of declination of point (= Moon + 3 rāśis) × 120/57.3} × nāḍīs of correc- tion ÷ (109.6 × 4) = – 'Degrees' of declination of point (= Moon + 3 rāśis) × nāḍīs of correction to new moon ÷ 18. The 'Degrees' are north, i.e. positive for Moon's Uttarāyaṇa, and negative for Dakṣiṇāyana. The nāḍīs stand for positive p-long in the forenoon, and negative p-long in the afternoon as already shown. Thus, for Uttarāyaṇa and forenoon, the p-lat is negative, and so the result of (ii) is to be added to Head, and subtracted from Tail. Clearly, it is the same for Dakṣiṇāyana and afternoon, as then also p-lat is negative. If Uttarāyaṇa and afternoon, or Dakṣiṇāyana and forenoon, p-lat. becomes positive, and so the correction is subtractive to Head, and additive to Tail, as instructed. (iii) = + 11°.6 cos ω. cos Ø. tan δ. cos h/120³. = + 11°.6 × 109.6 × cos Ø × sin δ × cos h ÷ (cos δ × 120³) = + 11°.6 × 109.6 × degrees of Moon's declination × cos h ÷ (120 × 57.3), (∵ sin δ = degrees of declination × 120 ÷ 57.3, nearly, and taking cos Ø/cos δ as equal to unity, δ being not great, and Ø being not great in India) = + 11°.6 × 109.6 × δ × nāḍīs after sunrise or before sunset ÷ (120 × 57.3 × 15), ∵ the Siddhānta, takes cos h as equal to nāḍīs after sunrise or before sunset ÷ 15, being satisfied with approximate values, i.e. Ø not being great, the time from sunrise or sunset to noon is taken as 15 nāḍīs always. Secondly, the angle is taken as ∝ to sine, as often done before. ∴ cos h = sin (90° – h) = (90° – h)/90° = (15 nāḍīs – nāḍīs to meridian)/15 = nāḍīs after sunrise or before sunset ÷ 15 = + δ × nāḍīs after sunrise or before sunset ÷ 80) δ is north, i.e. positive for Moon, 0 to 6 rāśis, and negative for Moon, 6 rāśis to 12 rāśis. The original of the nāḍīs cos h, is positive both forenoon and afternoon. ∴ p.lat is positive for Moon between 0 to 6 rāśis, and so the result is deducted from Head and