पृष्ठम्:महाभास्करीयम्.djvu/२१३

128 TRUE LONGITUDE OF A PLANET northern hemishere; if the Sun is in the southern hemisphere, it should be applied reversely.¹ In the case of other planets, this correction is determined by proportion (with the Sun's ascensional difference and the planet's mean daily motion); the law for its addition or sub- traction (to the planet's true longitude) is the same as in the case of the Sun. The correction due to the Sun's ascensional difference is the fourth and last correction to be applied to the Sun. By this correction llowance is made for the difference between the times of sunrise (or sunset) at the local and the svanirakṣa places. This is applied to the Sun's true longi- tude for true sunrise at the svanirakṣa place to get the Sun's true longitude for true sunrise at the local place. When the Sun is in the northern hemisphere, sunrise at the local place occurs earlier than that at the svanirakṣa place, and sunset at the local place occurs later than that at the svaniraksa place. When the Sun is in the southern hemisphere, it is just the contrary. Hence the law of correction stated in the text. The general formula for the cara correction is³ cara correction (Sun's asc. diff. in asus) x (planet's mean daily motion) 21600 A rule for finding the semi-durations of the day and night: 28. (When the Sun is) in the northern hemisphere, one- fourth of the total duration of the day and night increased by the (Sun's) ascensional difference, and (when the Sun is) in the southern hemisphere, one-fourth of the total duration of the day and night diminished by the (Sun's) ascensional difference is ¹ This rule occurs also in KK (Sengupta's edition ), i. 22; ŠiDV, I, ii. 19; Sisi, I, ii. 53; etc. The local place has been always assumed to be in the northern hemisphere, i.e., to the north of the equator. 8 Sise, iii. 69.