ŚRIPATT'S SECOND INEQUALITY OF THE MOON result; multiply it by 160^ and divide by the radius; the result is called caraphala. Put it down in another place, multiply it by sara(i.e.. R. vers (D-a) or versed sine of the Moon's distance from the apogee) and divide by the difference between the Moon's distance (hypotenuse) and the radius; the result is called parama (cara) phata, which is to be considered positive or negative according as the hypotenuse put down in another place is less or greater than the radius. Multi- ply the "sine of the Moon which has been diminished by the apparent Sun, by the apparent paramaphala and divide by the radius; the final result is to be called caraphala to be applied to Moon negatively or posi- tively as the Moon minus the Sun and the Sun minus the Moon's apogee (diminished by 90°) be of opposite signs; if these latter quantities be of the same signs the new equation should be applied in the inverse order by those who want to make the calculation of the appa- rent Moon agree with observation.¹ Symbolically :- 160 R sin[6-~~(a-90°)]_ M =caraphala R 160' R_sin_[ē– (a–909] x R vers (D – a ) F R H-R = paramaphala according as H>or<R The new equation Rsin ( D - 0 ) R 'Xparamaphala 1. त्रिभविरहितचन्द्रोच्चो नभास्वद भुजज्या | गगन नृप विनिम्नी भन्नयज्या विभक्ता || भवति चरफलाख्यं तत् पृथक स्वं शरध्वं । हृतमुडपतिक त्रिज्ययोरन्तरेण || परमफलमवा संतदूधन पथकस्थे । तुहिन किरयकरों त्रिज्यकोनाधिकेऽथ | स्कुटदिनकर हीना दिन्दुतो या भुजज्या | स्फुटपरमफलानी भाजिता त्रिज्ययाप्तम् ॥ शशिति चरफ्ज़ाख्यं सूयँहीनेन्दुगोला | तहणमुतधनं चेन्डूच्चदीनार्कगोलम् || यदि भगति हि साम्यं व्यस्तमेतद् विधेयम् । स्फुटगणितदृगैक्यं कर्त्तु मिच्चभिरत्र || ★ 117
