INDIAN LUNI-SOLAR ASTRONOMY As to the positive or negative character of the "sine" and the "cosine" he gives the rule:- 116 The mean planet diminished by its ucca, the aposes. aphelion or the Sighra, is called Kendra or mean anomaly; its "sine" from above six signs (180) arises from half circles and are respectively positive or negative, and its "cosine" in different quadrants are respectively positive, negative, negative, and posi- tive.¹ The convention followed is that the "sine" is negative from 0° to 180° and positive from 180° to 360° of the arc and that the cosine is positive betwen 0° and 90%, negative between 90° and 270° and positive between 270° and 360°. We may now symbolically express Manjula's second ineq- uality thus - -(13° 11' 35"-11°)×8° 8′ cos (0-a)×8² 8' sin (D--0) where D stands for the Moon as corrected by the 1st equation; we leave out the correction to the Moon's daily motion as given in the stanzas quoted above. The moon's new equation comes out to be =-143'58" cos (0-a) sin (D-e). This, it will be seen, is exactly the modern form of the evection as combined with a part of the equation of apsis shown before. The difference in the main is that Manjula's constant is 144', a quantity less by 8'. In form the equation is most perfect, it is far superior to Ptolemy's, it is above all praise. It is from this inequality, we trust, that Manjula should have an abiding place in the history of astronomy. The next writer who gives the second equation is Sripati (1028 A.D.). Śripati's Second Inequality of the Moon The following stanzas from Sripati's Siddhanta Sekhara, it is said, were communicated to Sengupta by Pandit Babua Misra. Though they are probably not very correct still the general meaning is clear. They carry the following sense : "From the Moon's apogee subtract 90°, diminish the Sun by the remainder left; take the "sine" of the 1. ग्रहः स्वोच्चोनितः केन्द्र षडूद जो भुजः । धनर्णः पदशः कोटिर्धन धनात्मिका ||
