Page:Sewell Indian chronography.pdf/84

result. Table XXXIII. thus gives the mean longitude at mean Mēsha saṁkrānti in any year later than K.Y. 0; and Table XXXIV. gives us the increase in his mean longitude for any number of days, hours and minutes elapsed to the given moment from mean Mēsha saṁkrānti of the year concerned.

182. To find the mean longitude of Jupiter, therefore, by the Tables on any day we first find the time of the true Mēsha saṁkrānti of the year in question from Table I., or as shewn below in Examples 1 and 3; add to it the śōdhya interval according to the authority we are using (see foot of Table XXXIV.), and thereby find the moment of mean Mēsha saṁkrānti. Calculating the number of complete years from mean Mēsha saṁkrānti of K.Y. 1 current to the mean Mēsha saṁkrānti of the given year, we find Jupiter's mean longitude at that last moment by Table XXXIII. The corresponding increase in mean longitude during the interval between mean Mēsha saṁkrānti in the given year and the given moment is obtained from Table XXXIV. and is to be added to the mean longitude at mean Mēsha saṁkrānti. We then have Jupiter's mean longitude at the given moment as required. The sun's mean longitude at the given moment is calculated by Table XXXIV. alone, from the interval between mean Mēsha saṁkrānti of the given year and the given moment; since his mean longitude at mean Mēsha saṁkrānti of every year is 0°.

183. We cannot find Jupiter's true or apparent longitude without first determining the mean longitude both of the planet and of the sun. As we must therefore always begin by these operations it will be well to illustrate them by an example.

In E. Burgess's "Sūrya Siddhānta" will be found, on p. 34, a Table, giving amongst other information the mean place of Jupiter according to that authority, both with and without the bīja, at midnight between December 31st, A.D. 1859, and January 1st, A.D. 1860. I proceed to calculate the same by the present Tables, following the Sūrya Siddhanta.

The given moment fell in K.Y. 4961 current (Table I.). The number of whole years from mean Mēsha saṁkrānti K.Y. 0 to mean Mēsha saṁkrānti K.Y. 4961 is 4960. Apparent Mēsha saṁkrānti in K.Y. 4961 took place (Table I.) on April 12th (day 102), A.D. 1859, at 0 h. 16 m. after mean sunrise. Adding the śōdhya interval we find that mean Mēsha saṁkrānti took place 2 d. 4 h. 6 m. later, namely, on April 14th (day 104) at 4 h. 22 m. The interval from April 14th (104), 4 h. 22 m., to December 31st (365) 18 h., or midnight, is 261 d. 13 h. 38 m. We therefore take down the figures from Tables XXXIII and XXXIV. for 4960 y. 261 d. 13 h. 38 m., and add them together. This is the time elapsed from mean Mēsha saṁkrānti K.Y. 1 current, or the epoch of the Kaliyuga, to the given moment.

1. ↑ Remember that there are 30° to 1 sign, and only 12 signs.