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149. In A.D. 1478 the author of an astronomical work or karaṇa called the Makaranda, composed at Benares, introduced a bīja, or correction, to the present Sūrya Siddhānta in regard to Jupiter's revolutions in a Mahāyuga, the number of which he made 364,212 (B) instead of 364,220 as before. No change was made in the number of civil days in a Mahāyuga, viz., 1,577,917,828 (A). Hence the length of one revolution of Jupiter by this authority, or A ÷ B, was corrected to 4332.415812768 days (C); and the length of one of Jupiter's saṁvatsaras, or C ÷ 12, was corrected to 361.034651064 days (D).

150. The correction was adopted generally, but of course in different years in different tracts, till it became prevalent throughout all India. I have therefore calculated the beginnings of Prabhava-years, in other words the beginnings of Jupiter cycles, freshly on this basis from the epoch of the Kaliyuga, and have embodied the results, beginning from K.Y. 4540 expired (A.D. 1439–40) in Table XXVIII. The process is as follows:—

151. To find the moment of beginning of any cycle, or the number of days by which 1 Prabhava began after apparent Mēsha saṁkrānti of any year, we have to add to the moment found for the beginning of the previous cycle 365.258756481 − 253.446325020 days, or 111.812431461 days. And first we have to ascertain the moment of beginning of the first whole cycle, with Prabhava as 1, after the epoch of the Kaliyuga. As before, we begin with the 27 Vijaya which, according to Hindū astronomers, began exactly at mean Mēsha saṁkrānti of K.Y. 1 current (0 expired, or 3102 B.C.). It began by the Sūrya Siddhānta, both with and without the bīja, 2.170694 days after apparent Mēsha saṁkrānti of that year, that being the time-difference, or śōdhya, between apparent and mean Mēsha saṁkrāntis. After this date the first Prabhava-year occurred after 34 saṁvatsaras had run.

From this point there were 76 cycles of 60 saṁvatsaras each till the year K.Y. 4540 (A.D. 1439–40).

For the remaining beginnings of cycles we add for each cycle 111.812431461 days. This explains the figures in Table XXVIII. Those in Table XXVIII.A are similar to those in Table XXVII.A, but for the Sūrya Siddhānta with the bīja.