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

V. 3 V. PAULISA MOON'S CUSPS 139 also. The Baudhāyanas have to avoid Iṣṭi being performed on the day of the first appearance of the Moon, and do it on the previous day, and the offerings to the manes have to be done on the day pre- vious to the Iṣṭi. The Dharmaśāstras describe the seeing of the first digit of the Moon as meritorious. The Muslims consider their months ending with the first appearance of the Moon, and so this is important to them for calendrical purposes. The observance of the last digit of the Moon was neces- sary in ancient times, for from that they had to determine whether the same day or the next one would be the new moon day, so necessary for their religious rites. The importance can be guessed from the special names they had for the days at new moon, Sinīvālī and Kuhū in which the streak of the Moon will be visible and invisible, respectively. Example 1. At a certain place having lat. 30°N. examine the visibility of the Moon in the evening, given, the Sun at sunset = rāśi 1-0, the Moon at sunset = rāśi 1-15, and the Moon's latitude = 240' south. From the Sun and the Moon, their respective declinations are 704'N and 1004'N (mean). From the latitude 30°N, and Sun's declination the vināḍis of ascension at the place, of Scorpio, the seventh rāśi from Sun and Moon, can be calculated to be 355. From these, i. Diff. in long = rā. 1-15 − rā. 1-0 = rā. 0-15 = 15°. ii. Diff. in dec. = 1004' − 704' = 300' = 5° iii. The square root = √[(15° + 5°) × (15° − 5°)] = 14° 8'.4 iv. The Result = 5° × 4° ÷ 14° 8'.4 = 85'. v. Corrected diff. in long = 15° + 85' = 16° 25', (the lower sign, because the work pertains to the west (evening) and the Moon's latitude is south, while its ayana is north), vi. As the work pertains to the west, the seventh rāśi measure is to be used, which we have found to be 355 vināḍis. Using this, the time taken for 16° 25' to rise is 16° 25' × 355 ÷ 30° = 194 vināḍis. This is more than 2 nāḍis and so the Moon will be visible. As the time found is far above the requirement, we need not repeat the work using the elements of the time of moonset. Example 2. At a certain place (north of the equator) on a particular day in the evening the Sun rā 6-0. The Moon is rā. 6-15. The Moon's latitude is 4° 40'. The equinoctial shadow of the place is 4 digits. Examine for Moon's visibility. From the Sun, its declination is 0', and from the Moon its mean declination is 363' S. From the equinoctial shadow and the Sun's declination, the measure of the ascension of Aries, (seventh from Sun and Moon, since the computation pertains to the west) can be calculated to be 228 vināḍis. Using these, i. diff. in long. = rā 6-15 − rā 6-0 = 15° = 900' ii. diff. in dec. = 363' − 0' = 363'. iii. The square root = √[(900' + 363') × (900' − 363')] = 823'.5 iv. The result = 363' × 280' ÷ 823.5 = 123'.4 v. The corrected diff. in long. = 900' − 123'.4 = 12° 56'.6 (The upper sign because, the work pertains to the west, and the ayana and latitude of the Moon are of the same direction.) vi. As the work refers to the west, using the measure of Aries, the seventh rāśi from Sun and 12