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

185 (90-rA), there will be perpetual day. But sin δ = sin λ sin ω so that sin λ = sin δ / sin ω . Putting δ = 90 - ϕ, sin λ = cos ϕ / sin ω ; Sin λ = sin γA = cos AS ∴ cos AS = cos ϕ / sin ω ∴ 2 AS = 2 cos⁻¹(cos ϕ / sin ω). Supposing AS expressed in degrees and assuming the Sun goes along the ecliptic with uniform motion, since he takes 365¼ days to trace 360°, to trace 2 AS, he takes (2 AS / 360) × 365¼ days = 365¼ / 180 × cos⁻¹(cos ϕ / sin ω) which is the length of the perpetual day. Verse 52. The correction known as Chara. The daily motion of the planet being multiplied by the chara expressed in asus and divided by the asus in a day viz. 21659 and the result being subtracted from or added to the planetary position at Sunrise according as the Sun is in the northern or southern hemisphere. The result is to be added to or subtracted from the planetary position at Sunset. Comm. The mean planets computed hold good at the Sun-rise at Lanka i.e. at zero latitude; they have to be converted to hold good at the local Sun-rise. In other words in fig. 21, the mean planet computed is B which is on the Lanka horizon, whereas we have to get S, the same planet on the local horizon. The position of S is earlier than that of B by the time interval indicated by the arc SB which is measured by EA the chara because the position B on the Lanka horizon is later than the position S on the local horizon. If the mean planet moves in a day of 21659 asus by the arc denoting its daily mean motion, by how much does it move in the time of chara expressed in asus? The result is (Chara in Asus × mean daily motion) / 21659 . 24