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

134 PAÑCASIDDHĀNTIKĀ IV. 56 (ii) Sūryāgrā = 12 × 120' × 60' ÷ (13 × 103' 55") = 63' 57".2 (iii) ‘The Sine’ = aṅg. 2-36.6 × 120 ÷ 13 aṅg = 24' 6". (This is north as shadow is north). (iv) As ‘the sine’ is north, the lower sign is to be used, i.e. the difference is to be found. There, as Sūryāgrā is greater, Agrā = 63' 57".2 – 24' 6" = 39' 51" (The Sun is in the northern hemisphere). (v) The sine of Sun’s longitude = 39' 51" × 103' 55" × 5 ÷ 244 = 84' 51". (vi) The Bhuja degrees D = Arc of 84' 51" = rāśi. 1-15. As the sun is in the northern hemisphere, the longitude is rāśi 1-15, or rāśi 6-0 — rāśi 1-15, i.e. rāśi 4-15. As the Sun is in Uttarāyaṇa, the longi- tude of the sun is rāśi 1-15. Using the simplified method, and taking the lower sign since the distance is north, sin Sun’s long = (12 aṅg × 60' ~ aṅg 2-36.6 × 103' 55") × 150 ÷ (61 × 13 aṅg.) = (720' – 271' 30") × 150 ÷ (61 × 13) = 84' 51". (As 12 × sin lat is greater, the sun is in the northern hemisphere). The rest of the work is the same. Example 26. Of a certain place, sin lat = 60', sin colat = 103' 55". On a Dakṣiṇāyana day, when the shadow is aṅg. 27-30, its tip is found to be aṅg 3-2.15 south of the east-west line. Find the Sun. (i) Shadow-hypotenuse = √(144 + 27½²) = aṅg. 30. (ii) Sūryāgrā = 12 × 120' × 60' ÷ (30 × 103' 55") = 27' 42".8. (iii) ‘The sine’ = aṅg. 3-2.15 × 120 ÷ aṅg. 30 = 12' 8".6 (south, as the shadow is south). (iv) As the sine is south, the upper sign is to be taken, and the Sun is in the northern hemisphere, and therefore, Agrā = 27' 42".8 + 12' 8".6 = 39' 51". (v) Sin longitude of Sun = 39' 51" × 103' 55" × 5 ÷ 244' = 84' 51". (vi) The degrees of Bhuja = Arc 84' 51" = rāśi 1-15 As the Sun is in the northern hemisphere, the longitude is rāśi 1-15 or rāśi 4-15. As it is Dakṣiṇāyana, the Sun is rāśi 4-15. Applying the simplified method for this, as the upper sign is to be taken, since the shadow tip lies south of the east-west line, sin long = (12 × 60 + 103' 55" × 3.2) × 150 ÷ (61 × 30) = 84' 51", and the Sun must be in the northern hemisphere. The rest of the work is the same as done already. Example 27. Of a certain place sin lat = 72', and sin colat = 96'. There, on a certain day in Uttarāyaṇa, when the shadow is aṅg. 27-30, the distance of its tip from the east-west line is aṅg. 16-37.5 north. Find the Sun. (i) Shadow hypotenuse = √(144 + 27½²) = 30. (ii) Sūryāgrā = 12 × 120' × 72' ÷ (30 × 96) = 36'. (iii) ‘The sine’ = aṅg. 16-37.5 × 120 ÷ aṅg. 30 = 66' 30", (north, as the distance is north).