सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

182 For a given place of equinoctial shadow equal to s″, we have to multiply 10, 8, 3⅓, by s, which will be the chara- segments for the place. The meaning of the first half of the verse 49 is as follows.—Let the equinoctial shadow for a place be 3 Angulas. Then the chara-segments for that place are 30, 24, 10. These are three in number for a longitude λ of 90°. If the longitude be 44° (say) then proceed as we have done to find sin 24°, using the method of Bhogya Khanda Sphutīkaraṇa with respect to the table of H sines namely 21, 20, 19, 17, 15, 12, 9, 5, 2. Proceeding as directed the Sphuta Bhogya Khanda for 14° is ( (3 × 14) / 30 = 7/5 ; 30 - 7/5 = 28⅗ ; (14 × 28⅗) / 30 = 2002 / 150 = 13⅓ ; 30 + 13⅓ = 43⅓ ). Proceeding according to the modern formula we have Charajyā = tan δ tan ϕ where ϕ = 3/12, and sin δ = sin 44° sin 24° log sin δ = 9.8418 + 9.6093 = 9.4511; δ = 16°-25 log tan δ = 9.4693 ∴ log sin (chara) = 9.4693 + log tan ϕ = 9.4693 + log 3/12 = 9.4693 - .6021 = 8.8672 ∴ Chara = 4°-14' = 254 / 6 = 42⅓ Vinadis whereas we have got by the Hindu method 43⅓ which is near the truth. Verse 52. To find the durations of day and night. Fifteen ghatis increased or decreased by the Chara- nadis, according as the Sun is in the northern hemi- sphere or southern, gives half the day of the locality and the difference of 30 nādis and the above half-day gives half the duration of night. Comm. Ref. fig. 21. Let S be the Sun rising in the northern hemisphere when his declination is north. Then