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

88 PAÑCASIDDHĀNTIKĀ IV. 17
Example 3 (b). Sāyana Sun is rāśi 4-7-30. Find its declination.
Sin 4ʳ 7° 30′ = Sin (6ʳ-0-0 – 4ʳ-7-30) = sin 1ʳ-22-30 = 95′ 12″.
Sin Declination = 95′ 12″ × (60 + 1) ÷ 150 = 95′ 12″ × (2/5 + 2/5 × 60) = 38′ 5″ + 38″ = 38′ 43″.
Its arc, 18° 50′, is the declination. Since the sāyana Sun is within 6 rāśis, the declination is north.
Example 3 (c). The sāyana Moon is 9ʳ0°0′. Its latitude is 4°N. Find its declination.
The sāyana longitude being 9ʳ0° 0′, the mean declination is the maximum, south, i.e. 24°S. Its lat.
is 4°N, i.e. of opposite direction. ∴ the true declination is 24° – 4° = 20° S. South because South is
greater.
The author uses the word kāṣṭhā to signify declination, which is uncommon. Sometimes this word
itself is used to mean sine declination.
The rule for sin declination is explained thus: Our siddhāntas take the maximum declination to
be 24°. As the maximun declination occurs when the sāyana longitude is 3 signs, the angle between
the ecliptic and the celestial equator (i.e. the obliquity of the ecliptic) also is 24°. In Fig. 5, take AB
and AC as parts of the ecliptic and celestial equator. Then, A = 24° and AB is the sāyana longitude.
BC is the declination wanted. By formula II under the present verse, sin dec. = long. × sin 24° ÷
120′. But sin 24° ÷ 120′ = 48′ 48′′ ÷ 120′ = 61/150. Hence, sin dec = sin long × (60 + 1)/150, which
is the given rule.
Now for the direction: See Fig. 4. At r the Sun moving along the ecliptic crosses the celestial
equator, and passes from South to North. As great circles bisect one another, till the longitude is 6
sings it moves north of the celestial equator, for which declinations are reckoned, and then moves
south of it. Therefore for longitude 0 to 6 rāśis, the declination is North, and for longitude 6 to 12
rāśīs, it is South.
As the Moon and other planets move in their own orbits inclined to the ecliptic, the declinations
computed from their longitudes reckoned along the ecliptic are only approximate. To get correct
declinations, their distances north or south from the ecliptic points, called their ‘latitudes’, should
be combined in the proper manner as instructed. But the result by thus adding or subtracting will
be only approximate, because the latitudes are directed towards the pole of the ecliptic (Kadamba),
while the declinations are directed towards the Celestial Pole. The maximum error that can occur
thus is about 24′. Combined with the error in latitude due to other factors like proportion by
degrees of the argument of latitude (advocated by the Pauliśa) instead of the sine etc., the error will
be considerable.
Now, for the readings. For syntactical purposes, and getting the proper meaning, śatārmśāśsaikā
has been corrected as śatāṁśaghnaikā, ṣaṣtidineśa as ṣaṣṭirdineśa, kāṣṭhānta as kāṣṭhā jyā, apakramarāśi
as apakramo rāśi and pādenyaḥ as pādebhyaḥ. As for TS, they have not touched this verse and the next
two, saying, in so many words, that they cannot interpret them. NP’s interpretation of the three
verses has also been affected by the highly corrupt text.
लिप्ताशत [क] म (शीत्या) मेषे 'त्रिख' यु (क्त) 'मिन्द्रिय' 'मनू' (न) म् ।
गवि ('मनु') 'भव' 'मुनि' 'रूपै' - श्र [तु] गुणैः संयुतं च शतम् ॥ १७ ॥