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

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(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 .
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