184 RISING, SETTING AND CONJUNCTION OF PLANETS It follows that the formula given in the text actually gives an approximate value of the arc CM' or AB.¹ The rule stated in the text has been generally used in the cases where the latitude of the body concerned is small. In the cases of fixed stars whose latitudes may be considerable, a more accurate rule is pres- cribed.2 When the Moon's latitude is north, the longitude of the point T is smaller or greater than the longitude of the point L according as the Moon M' is rising or setting; and when the Moon's latitude is south, the longitude of the point T is respectively greater or smaller; hence the rule of addition and subtraction stated in the text. A rule relating to the visibility correction known as ayana- drkkarma : 2(ii)-3. Divide the product of the Rversed-sine of the Moon's longitude diminished by three signs, the Rsine of the Sun's greatest declination, and the Moon's latitude by the square of the radius. Whatever is thus obtained, say the learned, should be subtracted from the Moon's longitude provided that her ayana and latitude are of like direction; in the contrary case, that result should always be added to the Moon's longitude. ¹That this formula gives an approximate value of arc AB may be demonstrated as follows: Since MM' is small, we may treat the triangle M'BA as plane. Then from the triangle M'BA, we have Rsin BM'AXM'A Rsin M'BA Rsin L, BM'AXM'M AB = Rsin M'BA Rsin x Moon's latitude Rsin approx. approx. See E. Burgess, SuSi, vii. 7-12, notes, 2 See BrSpSi, x. 18-19; ŚiDVṛ, I, xi. 12-13; and Siśi, I, vii. 6. Bhāskara II has given a slightly modified formula for small latitudes also. See SiSi, I. vii. 7. The most accurate formula for the aksa-drkkarma occurs in SiTV, vii. 103-104.
- This rule occurs also in SiDVṛ, I, vii. 2-3(i) and Siśe, ix. 4, 5.
The same rule in a modified form occurs in BrSpSi, vi. 3; x. 17 and in MSi, vii. 2, 3. More accurate rules occur in SiSi, I, vii, 4, 5 and in SITV, vii, 77-80.
