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

III. 16 III. PAULIŚA-SIDDHĀNTA 55
The result are nāḍīs of the incomplete nakṣatra gone in that day. Deduct it from 60. The ending
moment of the nakṣatra gone or last gone on that day is got in nāḍīs from the beginning of the day.
To get the tithi, subtract the Sun's longitude from the Moon's and convert it into minutes. Divide
by 720. The quotient are full tithis gone after new moon. The last tithi gone is the tithi ending before
the incomplete one begins. Multiply the remainder by 60 and divide by the difference of the Sun's
and Moon's motions in minutes, for that day. The result are nāḍīs of the incomplete tithi on that day.
Deduct the nāḍis from 60. The remaining nāḍīs are the ending moment of the tithi ending or last
ending on that day. If the total tithis got are more than 15, count again from one, i.e. Prathamā.
Example 8. At the end of a certain day the Sun is rā. 2-15-10 and its daily motion 57'. The moon is rā.
10-18-30 and its daily motion 827'. Find the nakṣatras etc. for the day.
The Moon = rā. 10-18-30 = 318° 30' = 19,110'. Dividing this by 800 the quotient, i.e. full
nakṣatras gone is 23, and the remainder 710' has gone in the 24th. Multiplying by 60 and dividing
by the daily motion, 710 × 60 ÷ 827 = 51-31, nāḍis, belong to the 24th. Therefore the 23rd, i.e.
Śraviṣṭhā ends 60.0 - 51.31 = 8.29 nāḍis, after the beginning of the day.
The Tithi: Moon - Sun = rā. 10-18-30 - rā. 2-15-10 = rā. 8-3-20 = 243° 20' = 14,600'. Dividing
by 720, the full tithis gone are 20, and the remainder 200' has gone in the next tithi. Multiplying this
by 60 and dividing by the difference of the daily motions, the nāḍis got are 200 × 60 ÷ (827 - 57)
= 200 × 60/770 = 15-35, which is the time occupied by the 21st tithi. Therefore the 20th tithi, i.e.
Bahula Pañcamī ends at 60 nāḍikās - 15.35 nāḍikās, i.e. 44.25 nāḍikās after the beginning of the day.
The length of a nakṣatra is 800' and the Moon's mean daily motion 791', is not much different
from it. The length of a tithi is 720' and its mean daily passage 732 is not very much different from
it. Therefore generally there is one nakṣatra or one tithi ending in a day. But it may happen that the
remainder is so small and the motion or passage for the day so great, that, remainder + length of
a nakṣatra or tithi < the daily motion or passage. In this case, two nakṣatras or two tithis end on the
same day. In the case of the tithi this is called avama, the second ending tithi being immersed in the
day and not counted for reckoning days. On the other hand, the remainder may be greater than the
motion or passage for the day, with the result that no nakṣatra or tithi ends on that day, i.e. they
begin at close of the previous day, extend throughout the day and end at the beginning of the next
day. When this happens in the case of a tithi it is called Tridina-spṛk, literally 'touching three days'.
The explanation of the rules is as follows: The Zodiac consists of 12 rāśis, i.e. 12 × 30 × 60 =
21,600 minutes. It is divided into 27 equal segments called nakṣatras and so there are 21600 ÷ 27
= 800 minutes for each segment. What is called nakṣatra in the verse and sought to be found, is the
segment in which the Moon is situated. Therefore the Moon's longitude in minutes is divided by 800
and the quotient are the segments passed. The remainder is the position of the Moon in the next
segment. The time taken by the Moon to pass that portion is found by the proportion; If the daily
motion takes 60 nāḍikās to pass, how long will the remainder take? Therefore the time when the
Moon has been at the end of the segment just passed, i.e. the end of the nakṣatra passed, falls before
the end of the day by the obtained nāḍikās.
Now for Tithi: When after new moon the Moon leaves the Sun behind for every 12° one tithi is
gone. Therefore by subtracting the Sun from the Moon, the total degrees left behind is found, and
dividing this by 12° or 720' the tithis gone is found. Everyday, i.e. in every 60 nāḍikās, the Sun is left
behind by the difference of their motions. Therefore the time taken for leaving behind the remainder
is: remainder × 60 ÷ difference of the motions. As the remainder is of the incomplete tithi, the
completed tithi ends before the end of the day, by a time equal to the nāḍikās found.