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

198 PAÑCASIDDHĀNTIKĀ IX.4 That is, take the days from Epoch got by the Romaka or Pauliśa rule. The mean Sun at Ujjain mean noon, just preceding the Epoch, (i.e. sunset at Yavanapura beginning Monday), = (days × 800 − 442) ÷ 2,92,207, in revolutions etc. Example 1 (a). Find the mean Sun, given days from epoch, 5,28,931. (This is midday, Ujjain, 21-5-1953 A.D.). (b) Get the mean Sun for Ujjain mean noon, just preceding the Epoch, i.e. for zero day. What is it at Epoch, i.e. sunset at Yavanapura? (a) Mean Sun = (5,28,931 × 800 − 442) ÷ 2,92,207 = revol. 1448-1-5-15.7 = rā 1-5-15.7. (b) Mean Sun at Ujjain mean noon preceding Epoch = (0 × 800 − 442) ÷ 2,92,207 = − 32'.7 = rā 11-29-27-3. Since mean sunset at Yavanapura is nā. 7-20 later than that at Ujjain, the mean motion for nā 22-20, about 22', has to be added, and the required mean Sun at Epoch is rā. 11-29-49.3. (According to modern astronomy it is 11-29-37.2, assuming that at that period the vernal equinox coincided with the First point of Meṣa. See how accurate the value is.) The rule is explained thus: We showed under I.14 that in the Saura yuga of 1,80,000 years, i.e. 1,80,000 mean solar revolutions, there are 6,57,46,575 days. Therefore, the revolutions for the given days = days × 1,80,000 ÷ 6,57,46,575 = days × 800 ÷ 2,92,207, reducing the numerator and denominator by the factor 225. Now, according to the Saura, the revolution of the mean Sun was completed 442/800 days after Ujjain mean-noon prior to Epoch. Therefore 442 eight hundredth parts have to be subtracted from the total number of eight-hundredths, and hence the deduction of 442. Though the original Saura is not obtainable now, yet from the Ārdharātrika system of Āryabhaṭa, and the Khaṇḍakhādyaka following it, we can see that 442/800 day after the said Ujjain- mean noon the mean Sun's revolution was completed. The Epoch was near the end of Śaka 427, i.e. 427 + 3179 = 3606, Kali years gone. Kali began with Friday, Ujjain mean mid-night. For 3606 revolutions, the days (from the beginning of Kali) = 3606 × 2,92,207 ÷ 800 = 13,17,123 42/800. Dividing out by 7, we have the remainder 3 42/800, i.e. 42/800 days after midnight ending Sunday, the revolutions was complete. Since Sunday mid-day is half a day or 400/800 day earlier than midnight, it is 42/800

• 400/800 = 442/800 day earlier, than the time of full revolution, as we have taken and used. Incidentally, we also got that it is Sunday mean noon, agreeing with the fact that the Epoch is at sunset at Yavanapura on that day. Further, we get that according to this Siddhānta the length of the year is 2,92,207 ÷ 800, days = 365 - 15 - 31.5 days. [चन्द्रमध्यं उच्चं च] नवशतसहस्रगुणिते ‘स्वरैकपक्षाम्बरस्वरर्तूने’ । ‘षट्शून्येन्द्रियनववसुविषयजिनै’र्भाजिते चन्द्रः ॥ २ ॥ नवशतगुणिते दद्याद् ‘रसविषयगुणाम्बरर्तुयमपक्षान्’ । ‘नववसुसप्ताष्टाम्बरनवाश्वि’ भक्ते शशाङ्कोच्चम् ॥ ३ ॥ ‘शशिविषय’घ्नानीन्दोः ‘(क्र)कर्मि’हतानि मण्डलानि ऋणम् । स्वोच्चे ‘दि(ग्घ्ना)’नि धनं ‘स्वर(न्ध्र)यमो’द्धृते विकलाः ॥ ४ ॥