पृष्ठम्:चन्द्रछायागणितम्.djvu/५२

APPENDIX I DERIVATION OF THE HOUR-ANGLE OF THE MOON IN PR AN AS 1 The square root of 144-p/ws-the square of the Shadow is called the 'Shadow-hypotenuse'. The radius of the diurnal circle, diminished or increased, respectively, by the Earth-sine (got in verse 21), as the declination is south or north, is called Antyn. 2, A third of the moon's daily motion in degrees is to be multiplied by the Shadow in ahgulas and added to R. This should be multiplied by the Equinoctical Shadow-hypotenuse and divided by the Shadow-hypotenuse. 3. The result is to be subtracted from the Antya got above and the product multiplied by R, and divided by the radius of the diurnal circle. The arc of this, using the versed-sine, is the Hour-angle in pranas} 1. The three verses here instruct the same thing as given by verses 28-29, with the exception that a correction is made to the first R used in verse 29. This is necessary and does duty for the correction to be made for the sake of the moon's parallax and corresponds to the correction applied in verse 14. See note there.