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34 PAÑCASIDDHĀNTIKĀ II.7
Example 6. The true Sun is 10ʳ 18°, and the true Moon is 5ʳ 22°. Find the nakṣatra and the tithi.
Nakṣatra: The Moon is 5ʳ 22°. Dividing by 4, (5ʳ 22°)/4 = 1ʳ 13°. Multiplying by 9, 9x 1ʳ 13° = 12
– 27, i.e. twelve nakṣatras have gone and in the 13th, (Hasta), 27 muhūrtas have gone.
Tithi: Moon – Sun = 5ʳ 22° – 10ʳ 18° = 7ʳ 4°. Dividing by 2, (7ʳ 4°)/2 = 3ʳ 17°. Multiplying by 5,
3ʳ 17° × 5 = 17 – 25. Seventeen tithis are gone and in the eighteenth (Bahula Tṛtīyā) 25/30 parts
have gone.
[अहर्मानम्]
मकरादौ 'गुण'युक्तो मेषादौ 'तिथि'युतो र(वि)दिवसः ।
कर्कटकादिषु सत्सु 'त्रयस्त्रिकाः' शर्वरीमानम् ॥ ८ ॥
Day-time
8. When the Sun is in the 3 rāśis, Makara etc., the Sun measured in rāśis plus
three is the duration of day-time in muhūrtas. When it is in the 3 rāśis, Meṣa
etc., the Sun plus fifteen is the duration of day-time. When in the 6 rāśis,
Karkaṭaka etc., the Sun plus nine is the duration of the night-time. (To get the
duration of the day-time, this should be subtracted from 30).
Though no measure of time is mentioned here, we can infer that it is the muhūrta (2 nāḍīs)
because by adding the shortest day, 12, and the longest, 18, we get 30 which must be equal to the
whole day, i.e. 60 nāḍikās.
Thus, for the Sun at the beginning of each rāśi, Meṣa etc., the day-time in muhūrtas is 15, 16, 17,
18, 17, 16, 15, 14, 13, 12, 13, 14. The longest day is 18 muhūrtas when the Sun is at the first point
of Karkaṭaka (Cancer) at Summer solstice and the shortest 12 muhūrtas when at the first point of
Makara (Capricorn) at Winter solstice. The day and night are equal at the first points of Meṣa
(Aries) and Tūla (Libra), i.e. at the equinoxes. The daily increase or decrease in day-light is 4 vināḍīs
per day. In essence, the same formula for day-light is found in the Vedāṅga Jyotiṣa and the Paitāmaha
Siddhānta (PS, XII.5),with this difference that here the true Sun is used, but there, because they
have no true Sun but only the mean Sun, the day which is proportionate to the mean Sun, is used.
Evidently not understanding what is given here, TS have made a drastic change in the text, writing
bhūsvarga-tithimito for meṣādau tithiyuto, intending to make this agree with the next verse giving the
noon-day shadow. But, even within that verse, there is contradiction and this need not have been
attempted, at such cost. To crown all their interpretation with their emendation is full of contradiction
within itself, which has been set out in detail by me in a paper entitled 'Vāsiṣṭha Sun and Moon' in the
Journal of Oriental Research, 25 (1955-56) 19 – 41.
The uniform increase and decrease in day-time given here is wrong, of course, and it varies with
the position of the Sun, being greatest at the equinoxes and falling to zero at the solstices. The
maximum or minimum day-time itself varies with the latitude of the place (depending on tan.
8b. A. मेषादौ. C. भूर्स्वर्गातित्थिमितो रखेर्दिवसः c. B2. सत्सु; C.D. षट्सु
A.B.C. रखेः. A2. दिक्कम् । d. B. मानाम्