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

38 PAÑCASIDDHĀNTIKĀ II.11 it would otherwise be, for which the rule has been formulated. As the deduction of the noon- shadow for the day of observation from the shadow would, to some extent, remove this extra length of shadow and bring about an approximation to the ideal condition, the noon-shadow is asked to be deducted from the shadow in the formula. Therefore the increase in lagna is given by 36/ (shadow − noon shadow + 12). As at sunrise the Sun is the lagna, adding the increase to the Sun we get the lagna, i.e. lagna = Sun + 36/(12 + shadow − noon-shadow). This is for the forenoon. In the afternoon, what happens in the forenoon with reference to the shadow is reversed, and therefore the rule gives the part of the lagna to increase from the time of observing the shadow to sunset. So, it is less than the lagna at sunset by what is got from the formula. But the lagna at sunset is the Sun plus six rāśis. Therefore the formula for the afternoon becomes: Sun + 6 − 36/(12 + shadow − noon-shadow). Again let it be remembered that the rules are rough. व्यर्के लग्ने लिप्ताः प्राक्पश्चाच्छोधितास्तु चक्रार्धात् । कार्यश्छेदः 'शून्याम्बराष्टलवणोदषट्कानाम्' ॥ १२ ॥ लब्धं द्वादशहीनं मध्याह्नच्छायया समायुक्तम् । सा विज्ञेया छाया वासिष्ठसमाससिद्धान्ते ॥१३ ॥ 12-13. Deduct the Sun from the lagna and convert the remainder into minutes of arc, if forenoon. If afternoon, deduct the minutes from a half circle, (i.e. from 10,800 minutes), and take these as minutes. Divide 64,800 by the minutes got. Add the result to the noon-shadow of date and deduct 12 from this. This is the shadow at the time of the given lagna. This is according to the succinct Vāsiṣṭha Siddhānta. The formula (a) for the forenoon, and (b) for the afternoon, respectively, are: (a) shadow = {64,800 ÷ (lagna − Sun, in minutes) + noon-shadow − 12}. (b) shadow = 64,800 ÷ {10,800 − (lagna − Sun, in minutes)} + noon-shadow − 12. Example 11. (a) On a certain day at a time in the forenoon, the Sun is 9 rāśis and the lagna 10 rāśis and the noon-shadow of date is 12 digits. Find the shadow for the time. (b) On another day, for a time in the after- noon, the sun is 6 rāśis and the lagna 10 rāśis 25 degrees and the noon shadow of date is 6 digits. Find the shadow. a] Using formula (a), shadow = 64,800 ÷ {(10 − 9) × 1800} − 12 + 12 = 36 digits. b] Using formula (b), shadow = 64,800 ÷ {10,800 − (10 5/6 − 6) × 1800} − 12 + 6 = 64,800 ÷ (10,800 − 8640) − 12 + 6 = 64,800 ÷ 2160 − 12 + 6 = 30 − 12 + 6 = 24 digits. These formulae (a) and (b) can be derived from the previous formulae (a) and (b) of verse 11, for these are only the inverse of the previous operations. 12a. B3.लिप्ता b. A.प्राक्पक्षा A.छोधितास्तु; B.छोधितासु 13. A1.लब्धं; A2.लब्ध. B3.हिनं B1.चक्राद्धति:; B3.चक्रार्धात् । द्वोतिः b. A.B.°ह्रच्छायया. B.समायुक्ता c. A.B.कायछेदः (B3.कायः छेदः) d. A2.वासिष्ट; B1.2.वाशिष्ट; B3.वाशिष्ठ