VS. 13] TIMES OF FIRST AND LAST CONTACTS 65 This is the first approximation to the sparsa sthityardha. Let us denote it by t r Now we calculate the displacement of the Moon for the sparsa-sthityardha t v then diminish the Moon's longitude (calculated for the time of opposition) by that displacement, and then with the help of the resulting longitude calculate the Moon's latitude. Treating this as the Moon's latitude for the time of the first contact, we calculate, as before, the sparsa-sthityardha again. This is the second approximation to the sparsa-sthityardha. Let us denote it by t 2 . Repeating the above process, we calculate the successive approximations t,, t 4 , t 5 to the sparsa-sthityardha. It can be easily seen that ^ - . . . 60xL'S tx <t, <t 3 <... <t n <... < — ~ . Therefore, the sequence of the successive approximations to the sparsa- sthityardha is convergent. The convergence is also rapid, so that the third or fourth approximation generally gives a fairly good approximation to the sparsa sthityardha. The method for finding the moksa-sthityardka is similar. The only differ- ence is that in the second and the next successive approximations calculation is made of the Moon's latitude for the time of the last contact instead of that for the first contact. A rule relating to the determination of the times of the first and the last contacts : 13. Diminish and increase the true time of opposition by the {sparsa^ and moksa-) sthityardhas, obtained by the method of successive approximations, (respectively): then are obtained the times of the first and the last contacts. The time of the middle of the eclipse is the same as that (of opposition of the Sun and the Moon). 1 This is how the exact times of the beginning and end of a lunar eclipse are determined. In practice, however, the exact beginning and end of an ' eclipse are not perceived with the unaided eye. A lunar eclipse is seen to begin after a portion of the Moon's disc is already obscured by the shadow.
- Cf. MBh,v. 35.
