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

180
(vii) Lambāṁsa-chāpa is the arc of the colatitude
QS where S is the South point so that Lam-
bajyā is the H sine of QS or H cosine of ZQ.
This Lambajyā will be seen to be the diameter
of a small circle parallel to the Equator and
passing through Z.
Verses 49-51. A different method of obtaining
chara.
This chara can be had by the so-called chara-segments
of the locality using a process similar to that of finding
the H sines of the smaller table of nine H sines using
λ/3 where λ is the Sāyana longitude of the Sun (i.e. The
Hindu longitude plus the arc of ayanāṁśas is called the
Sāyana longitude or the modern longitude measured from
v along the ecliptic to the Sun). Find the charas of 30°,
60° and 90° of the ecliptic measured from v. Subtract the
first from the second, the second from the third. Thus we
have C30°, C60°-C30°, C90°-C60°, (where Cθ° signifies the
chara of θ°) which are called chara-Khandas or chara-seg-
ments. The equinoctial shadow multiplied by 10, 8, 3⅓
gives the approximate values of the chara-segments in
Vinādīs (a sidereal day is divided into 60 nādīs and each
nādī consists of 60 Vinādīs). The chara-segments thus
measured in Vinādīs are rather approximate. If further
exactitude is required, better take the arc in units each
of which rises in ⅙th of a Vinādī (This ⅙th part of a
Vinādī is known as a prāṇa i.e. the duration of the
interval between two inhales of a healthy person reckoned
as 4″ of time).
Comm. The charas of 30°, 60° and 90° of modern
longitude are the values of the arc EA, (Ref. Fig. 21)
when S has longitudes 30°, 60° and 90°. We have the
folmula
Charajyā = R tan δ tan ϕ