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

184 PAÑCASIDDHĀNTIKĀ VIII.6 The true Moon is got thus:- (i) mean Moon in revolutions = (days × 38,100 - 10,984) ÷ 10,40,953. (ii) mean anomaly in revolutions etc. = (days × 110 + 609) ÷ 3031. This is for sunset at Ujjain. If required for sunset at Yavanapura, 622½ should be used in the place of 609, we shall explain how, later. (iii) The intervals of equation of the centre for the 6 half-signs in a quadrant are, 1° 14' 25", 1° 11' 48", 1° 1' 51", 47' 45", 30' 0" and 9' 59". In the first quadrant these are to be deducted in the given order, in the second they are to be added in the reverse order, in the third they are to be added in the given order, and in the fourth they are to be subtracted in the reverse order. (iv) True Moon = (i) + (iii). Example 2. For days 59, (from sunset at Yavanapura), compute the true Moon. (i) The mean Moon = (59 × 38,100 - 10,984) ÷ 10,40,953 = Rev. 2-1-23-36-30 = rā. 1-23-36-30. (ii) Mean anomaly = (59 × 110 + 622½) ÷ 3031 = rā. 4-4-46. (iii) The equation of the centre = - 1° 14' 25" - 1° 11' 48" - 1° 1' 51" - 47' 45" - 30' 0" - 9' 59"

• 9' 59" + 30' 0" + 4° 46' × 47' 45" ÷ 15° = -4° 0' 39". (iv) True Moon = (i) + (iii) = rā. 1-23-36-30 - 4° 0' 39" = rā. 1-19-36. (Note: This is for sunset at Yavanapura). The rules are explained as in the case of the Sun thus: In I.15, it has been mentioned that in the Romaka yuga of 2850 solar years, there are 1050 intercalary months and 16,547 suppressed tithis. Therefrom it has been shown, that in the yuga there are 2850 × 12 = 34,200 solar months, 34,200
• 1050 = 35,250 synodic months, 35,250 + 2850 = 38,100 lunar revolutions, and 35,250 × 30 - 16,547 = 10,40,953 mean solar or civil days. So, from the proportion: If there are 38,100 lunar revolutions in 10,40,953 days, how many are there in the days from epoch, we have, the number of revolutions = days × 38,100 ÷ 10,40,953. The mean Moon at epoch should be added to the mean Moon or the time by which the Moon completes the current revolution should be omitted from the days. According to the Romaka, by 10,984 ÷ 38,100 days after epoch, the mean Moon is a full revolution, though we cannot verify this, as the original Romaka is lost. Therefore, we have to deduct from the product of days from epoch, (10,984 ÷ 38,100) × 38,100 = 10,984, as instructed. With the given deductive constant we get that the Romaka mean Moon in revolutions at epoch = (0 × 38,100 - 10,984) ÷ 38,100 = rā. 11-26-12. See how close this is to the actual, rā. 11-24-48, to the Saura, rā. 11-25-6, and the Siddhānta Śiro- maṇi's rā. 11-25-49. This is why we corrected the reading, kṛtāṣṭanavakaikā (1984) into kṛtāṣṭanavakhaika (10,984). If the reading is taken as it is as done by TS and NP then the mean Moon at epoch would become rā. 11-29-19, which is improbable, being too far from the actual. We have also shown under I. 8-10 that the mean Moon of the corrected reading alone would agree with the constants there. In the Romaka, as in the Vāsiṣṭha-Pauliśa there are 110 anomalistic revolutions of the Moon in 3031 days. Therefore multiplying the days by 110 and dividing by 3031, the mean anomaly of the Moon in revolutions etc. is got. As, according to the Romaka 609/110 days before sunset at Ujjain, it was a full revolution, we have the additive constant 609. We cannot understand why the anomaly alone is given for sunset at Ujjain, while it could also be given for Epoch, i.e. for sunset at Yavanapura by