पृष्ठम्:लघुभास्करीयम्.djvu/१३६

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vss. 10-12 ] STHITYARDHAS 63 A rule relating to the calculation of the sparsa- and moksa- stkityardhas : 10-12. Diminish the square of half the sum of the diameters of the Moon and the shadow (samparkardha) by the square of the (Moon's) latitude (for the time of opposition of the Sun and Moon) and then take the square root (of that). That divided by the difference between the (true) daily motions (of the Sun and Moon) and multiplied by 60 gives, in nadis, the (first ap- proximation to the sparsa- or moksa-) sthityardha. (Then) multiply those nadls by the true daily motion (of the Moon) and always 1 divide by 60. The resulting minutes should then be severally subtracted from and added to the longitude of the Moon (calculated for the time of opposition) to get the longi- tudes of the Moon for the times of the first and last contacts. From the Moon's longitude (for the first contact as also for the last contact) calculate the Moon's latitude; and from that successively determine the (corresponding sthityardha in terms of) riadis, the corresponding minutes of arc (of the Moon's motion), and the longitude of the Moon (for the first contact as also for the last contact). Repeating this process again and again, find the nearest approximations to the (spar'sa~ and moksa-) sthityardhas? The t#rm samparkardha means "half the sum of (the diameters of) the eclipsed and eclipsing bodies". In the case of a lunar eclipse, it denotes the sum of the diameters of the Moon and the shadow. The term sthityardha means "half the duration (of the eclipse)" and denotes, in the case of a lunar eclipse, the time-interval between the. first contact and opposition or bet- ween opposition and the last contact. The interval between the 6rst con- tact and opposition is called the sparsa-sthityardha (or sparsika sthityardha) and that between opposition and the last contact is called the moksa' sthityardha (or mauksika sthityardha). The above three verses say how to find the sparsa- and moksa- Sthityardhas. The method used is the method of successive approximations and may be ex- plained as follows : 1 i.e., in every approximation. 1 Cf. MBh, v. 74-76(i).