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JULY, 1889.)
THE SIXTY-YEAR CYCLE OF JUPITER.
199
THE SIXTY-YEAR CYCLE OF JUPITER.
BY PROFESSOR F. KIELHORN, C.I.E.; GÖTTINGEN. W HILE engaged in calculating or verifying Hindu dates in which the year of one era or
V another is coupled with a year of the Sixty-Year Cycle of Jupiter, I have had frequent occasion to resort to the third memoir of Warren's invaluable Kala-Saxkalita, pp. 197-216, and I have often admired the ingenuity and clearness with which that great scholar has treated his subject. At the same time, I cannot but confess that the use of Warren's Tables is somewhat troublesome; and it has appeared to me that the process of finding the exact beginning and end of a cycle-year, according to the different roles, might be simplified by giving certain fractions of days, etc., in decimals of days, and by expressing the epochs of the several eras, as well as other items, in days of the Julian period, a method which has been followed successfully by Dr. Schram in his Hilfstafeln für Chronologie. Besides, Warren's book is now difficult to obtain. The following simple rules and Tables may therefore not be altogether unwelcome to scholars who either do not possess a copy of the Kala-Sankalita themselves, or have no large public library within easy reach. A.-The beginning and end of the Cycle-year according to the surya-Siddhanta. (a) - According to the Súrya-Siddhanta, the epoch of the Kaliyuga, expressed in days of
the Julian period, and in such a manner as to yield current days and hours, etc., after mean sunrise (at Ujjain), in the final results, is -
588 465-7500 days." (6)-The length of one solar year is
365-2587565 days. (c)-The length of one year of Jupiter's cycle, without Blja or correotion, is -
361.02672103 days. (d)-The length of one year of Jupiter's cycle, with Bija or correction, is -
361.0346511 days.
•
Rules.
1. To find the beginning of any year of the Kaliyuga, in accordance with the Súrya. Siddhanta, multiply (6), i.e. the length of one solar year, by the number of years expired, and to the product add 588 463-6024 (i.e. the epoch of the Kaliyuga diminished by 2-1476, the time by which the apparent Mesha-samkrinti at the commencement of the Kaliyaga, according to Warren, preceded the epoch). Convert the result into the European date by Tables I. and II. Thus, for the beginning of Kaliyuga 4871, current, we find
365.2587565 X 4870 1778 810-1441550 + 588 463.6024
2367 273.7466 days of the Julian period, which by Tables I. And II. correspond to
9th April, A.D. 1769, new style, 17 h. 55.1 m. In other words, the solar year Kaliyuga 4871, current, according to the Súrya-Siddhanta, commenced 17 h. 55-1 m. after mean sunrise (at Ujjain) of 9th April, A.D. 1769, new style.
That portion of Dr. Schram's work which has reference to the Hindu luni-solar calendar, has now been re-cast by the author, and will be published in s following number of this Journal. Dr. Sohram's Table for converting a day of the Julian period into the European date, the use of which will appear from the examples given at the end of this article) is, for the sake of ready reference, by the author's permission, appended also to the present paper (Table 1.).
11. 6. midnight between the 17th and 19th February, 3102 B.C.
3 These figures (b), (c), and (d) are based on the following data :-The number of civil days in a Mahiyuga is 1577917828; in the same period there are 4320000 revolutions of the sun revolutions of Jupiter (without correction) 364220; and revolutions of Jupiter, as corrected by the Blja, 861212.
