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

124 PAÑCASIDDHĀNTIKĀ IV. 50
to convey that the inverse process of finding the time from the Moon’s shadow is also to be done as
from the Sun’s. The time of moonrise required in this work will be given by the author in V. 8-10.
The Moon’s true declination has been given already in IV. 16. The proof of the work is similar to
that of the Sun’s. It must be remembered that in getting the time from the Moon’s shadow, succes-
sive approximation has to be done, as in the case of the sun, for the same reason.
The following should also be noted. If the desired time after sunset for which the shadow is
sought is less than the time of moonrise after sunset, the work need not be done. Or if the moon
sets in the night before the desired time, the work need not be done. Obviously, these should be
examined before commencing the work. Much has to be said here, for which the reader is referred
to works like the Siddhānta Śiromaṇi.
Example 20. The sine of latitude of a place is 45' 56", and thence the sine of colatitude 110' 52". There, on
a particular day the daytime is nā. 32-24. The moonrise is at nā. 27-18 after sunrise. At that time the Moon’s
true declination is 15° south. (i.e. the Moon is in the southern hemisphere). Since Moon’s declination is 31' 4",
and thence the day-diameter 231' 50". The cara-vināḍīs from these for the day is 132. The lunar day, i.e. the
duration of moonrise to moonrise is 62 nāḍīs. Compute the shadow caused by the Moon at nā, 4-8 after sunset.
The time to be taken for computation = the time from moonrise to the given time
= the time from moonrise to sunset +the given time (after sunset)
= nā. 32-24 – nā. 27-18 + 4-8
= nā. 9-14.
The Moon’s cara-vināḍīs = 132, given.
Both should be converted to the lunar measure.
For 62 nāḍīs there is one lunar day, i.e. 60 lunar nāḍīs; so for nā. 9-14, there are 9-14 × 60/62 =
8-56 lunar nāḍīs.
Converting into degrees, we have (8-56) × 6 = 53° 36'.
Similarly, the cara-vināḍis made lunar = 132 × 60/62 = 128.
Converted into degrees, 128/20 = 6° 24'.
Now, using the rules of verses 40-44,
(i) Sin altitude = {sin (53° 36' + 6° 24') – sin 6° 24')} × 231' 50" × 110' 52" ÷ 28,800 (the upper
sign is taken because the Moon is in the southern hemisphere).
= (sin 60° – sin 6° 24') × 231' 50" × 110' 52" ÷ 28,800
= (103' 55" – 13' 23") 231' 50" × 110' 52" ÷ 28,800
= 90' 32" × 231' 50" × 110' 52" ÷ 28,800
= 80' 49".
(ii) gnomonic shadow caused by the Moon = 12√(14,400 – 80' 49"²) ÷ 80' 49" = aṅg. 13, vyaṅg
11.
Example 21. For the same place and the same time of Example 20, find the time, given the shadow caused
by the Moon is aṅg. 13-11, extending the method of verse 45-47 to the Moon.
The required elements already given in Example 20 are: sin lat. 45' 56", sin colat. 110' 52", sin
Moon’s declination 31' 4", sin Moon’s day-diameter 231' 50", time of moonrise nā. 27-18 after sun-
rise, duration of the day nā. 32-24, and the duration of the lunar day = 62 nāḍīs.