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

66 PAÑCASIDDHĀNTIKĀ III.27
Saṅkrānti-kāla
26. The angular diameter of the Sun in minutes, multiplied by sixty and
divided by the daily motion of the Sun, are total sacred nāḍis of Saṅkrānti
(literally ‘crossing’). Half this time before and after the Sun entering a rāśi, is
sacred.
The Pauliśa does not give the angular diameter of the Sun, so it must be the intention of the
author to use the angular diameter given by the Romaka or the Saura.
Example 12. The angular diameter of Sun is 31' and its daily motion 57'. The Saṅkramaṇa is 19 nāḍīs after
sunrise. Find the sacred nāḍis.
Angular diameter × 60 ÷ daily motion = 31' × 60 ÷ 57' = nā. 32-38. Half this is 32-38/2 = nā.
16-19. Therefore nā. 19-0 - nā. 16-19 = nā. 2-41 to nā. 19-0 + 16 - 19 = nā. 35-19 is the sacred
period.
The rule is proved thus: The time of the centre of the Sun’s orb crossing to the next sign is the
time of Saṅkramaṇa. At this time half the orb is in the previous sign and half in the next. The period
when parts of the orb are in both signs is the sacred period. So it begins when the east point of the
orb just enters the next sign and ends when the west point just leaves the previous sign. So, during
the interval the Sun moves a distance equal to its own diameter. This time is got by the proportion:
daily motion: angular diameter :: 60 nāḍikās: the required time. Therefore aṅg. diameter × 60
÷ 60 is the time in nāḍikās. As half this time is required for the mid-point to reach the junction of
the signs, half this period placed on either side of the time of the mid-point crossing over gives the
beginning and end of sacred period.
It must be noted that if the angular diameter is computed according to the old Hindu astronomical
works and used, the sacred period would be constant whatever be the daily motion, and the sacred
period can easily be given as so many nāḍikās before and after saṅkramaṇa. How? Let x be the mean
angular diameter in minutes. According to Hindu astronomy the angular diameter is proportionate
to the daily motion, (because the motion is taken inversely proportionate to the distance and the
angular diameter also is inversely proportionate to the distance) (See VIII. 15, IX 14-16). Therefore
the angular diameter = x multiplied by daily motion ÷ mean daily motion. The period = angular
diameter × 60 ÷ daily motion = x × daily motion × 60 ÷ (daily motion × mean daily motion) = x
× 60 ÷ mean daily motion which is constant. If to avoid this we assume that the mean diameter is
intended to be used in the rule, then the rule is unreasonable. Or we have to accept it on the injunc-
tion of the Dharmaśāstras, throwing the burden on them. We said, “according to the old Hindu
astronomical works”, because actually the angular diameter is not exactly proportional to the daily
motion.
[त्रिदिनस्पृग्योगः]
तिथ्यन्तं यदि सूर्यः स्पृशन्नुदेत्ये (षा) वासरं चाऽपि ।
योगस्तदा त्र्यहस्पृक् तिथित्रयस्पर्शनाद(वमः) ॥ २७ ॥
26a. B1. भुक्षिहताः B2. भुक्षिहता; B3. भुक्षिहता d. B1.2.पुण्यतोद्धेन
b. A1.रबिम्ब०; B.बिम्बककला For चाद्यन्तात्, B1.2. वार्धता कृतिः; B2. न नार्धतात्