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200
THE INDIAN ANTIQUARY.
[JULY, 1889.
1.e. 29th July, A.D. 1387, 6 h. 5.89 m., - beginning of Bhava; end of Bhâva (under 2) 2228 230-2639
+ 360-9730
sum 2228 591-2369, i.e. 20th July, A.D. 1389, 5 h. 41.1 m., - end of Yuvan.
And in a similar manner it would be possible, without starting a new calculation, to ascertain the end of any previous or subsequent year (as will be shown helow, not separated from the year the end of which has already been found, by an expunction), by either subtracting or adding one ordinary Jupiter's year multiplied by the difference in the Sixty-Year Cycle between the year the end of which we know and the year the end of which we wish to find. For instance, given the end of Bhåva (No. 8), we find the end of the year Tarana (No. 18), by adding 360-9730 or 360-97298) X 10, thus :
end of Bhava..... 2228 230-2639 + (360-97298 x 10) = 3 609-7298
sum 2231 839.9937, 1.e. 11th June, A.D. 1398, 23 h. 50-9 m., - end of Tåraņa (No. 18).
4. Were we to calculate the Jupiter's years, e.g., for the expired Saka years 60 and 61, the result would be as follows :
00 * 23* *281 = 2 1893, and 4? = 1 %;
01 * 22 + 4291 = 3 and 48 = 16 Here the namerators of the second fractions and tell us that, at the commencement of Saka 60 expired, the Jupiter's year last expired was No. 2 = Vibhava, and the Jupiter's year current was No. 3 = Sukla ; and that, at the commencement of Saka 61 expired, the Jupiter's year last expired was (not No. 3, but) No. 4 = Pramoda. The year Pramoda accordingly commenced after the beginning of 'Saka 60 expired ; and since it ended before the close of the same year, it was a kshaya or expunged year. And from the first fractions (1893 and 187) we see that the duration of the year preceding the expunged year amounted to exactly one solar year, as may also be clearly demonstrated by the following figures :Numerator 1861 by Table IV. ......... = 362-53141
1.55844 Beginning of 'Saka 60 expired ...... = 1771 536-71873 deduct for 1975 ..............
- 362-53141 End of No. 2 = Vibhava ... 1771 174:18732 Beginning of Saka 61 expired......... = 1771 901-97741
deduct for 15 ..................... - 1.55844
End of No. 4 = Pramoda ... 1771 900-41897 deduct for end of No. 2 = Vibhava, -- 1771 174.18732
remainder............ 726-23165 days; which is made up of one solar year... = 365.25868 + one ordinary Jupiter's year............ = 360-97297
sam ........................ 72623165 days. With the above data, and assuming the occasions of expunged years to be known, we might now of course calculate the end of any of Jupiter's years whatever, taking as our basis the end of any one year which may happen to be already known to us. For instance, the end of the
Expunged years fell within the expired Saka years 60, 145, 231, 316, 401, 486, 571, 657, 742, 827, 912, 998, 1083, 1168, 1953, 1389, 144, 1509, 1594, 1679, 1765.
