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COMPUTATION OF DATES.
425
The columns headed 'Jupiter's Samvat.' in Tables VI, VII, VIII, furnish the means of ascertaining the Jovian year for any given epoch. The numbers in them must be summed up for the parts into which the given date is divided, e.g., we find for 3542 K.Y., 18th Kârttika:
3500 K.Y.
42 years 18th Kartt.
Jup. Sam. 0.95 42.4914 0.5595
44.0009
The integers give the number of the current cyclic year, Table XXIII; in this case 44 Isvara; the decimals show how much of the Jovian year has elapsed, here 10,000 or about 20 ghatikás. This result however does not refer to the beginning of the day, but to a point of time removed from it by the same interval as separates the beginning of the mean solar year from the beginning of the day. We find the moment in question by the Cor.' of the given year; in this case for 3542 K. Y. the Cor.' is (according to the Surya Siddhanta) + 32 gh. 52 p.-8 gh. 8 p. + 24 gh. 44 p. Therefore the result above refers to 24 gh. 44 p. after mean sunrise at Lanka, and the beginning of the year lévara occurred about 4 gh. after mean sunrise of the 18th Karttika in K.Y. 3542.
The tables yield the Jovian years according to the Surya Siddhanta with btja. To find the same according to the Surya Siddhanta without bija, multiply the year of the Kaliyuga by 2, and divide by 9; the quotient is to be added as 10,000th parts to the value given in the tables. In the present instance 3542x=787. Dividing by 10,000 gives 0-0787, and this added to 44 0009 makes 44-0796,-the value according to the Surya Siddhanta without bija.
For the Arya Siddhánta, divide the year K.Y. by 3, and add the quotient divided by 10,000 to the tabular value. In the example this gives 44.1190.
For the Brahma Siddhanta, multiply the year K.Y. by 0-0000401528; add to the tabular value and subtract 0.0180.
For Siddhanta Siromani, multiply the year K.Y. by 0.0000273639; add to tabular
value and subtract 0.0180.
For the Arya Siddhanta with Lalla's correction subtract 420 from the Saka year (or 3599 from the year of the Kaliyuga); multiply the remainder in 0.00010445; and subtract the product from the 'Jupiter's Sam.' as found for the original Arya Siddhanta.
The tables yield the result correctly within about 2 ghatikás, which in most cases is an accuracy not needed. If, however, for special cases, still greater accuracy should be required, it can be found with a high degree of exactness for the commencement of the solar year, by the help of the above rules, for the various Siddhántas. But it must be calculated for the day of the year by multiplying the ahargana, or number of the day of the year, by 0.00276988 for Surya Siddh.; by 0-00276982 for the same Siddhanta with bija; by 0-00276991 for the Arya Siddhanta :-the product is the Jupiter Sam.' for the beginning of the day under consideration. The fractions here given are the increase of the element in one solar day (60 ghatikás or 24 hours). From these data the increase for any interval in ghatikás or hours can easily be found.
30 If they are larger than 60, subtract 60. The value of Jupiter' in Tables VI and VII, it must be noted, refer to the beginning of the mean solar year.
3 G
