________________
JUNE, 1888.]
JACOBI'S TABLES FOR HINDU DATES.
157
day come out right. It is therefore doubtful the day of new-moon, the initial day of all whether the dates of those inscriptions are cor- lunar months will be fonnd by adding one to rect. But I find that the date in Vol. XII. the Epact of the new-moon day of the year p. 258, is correct when calculated for the time under consideration. As Cunningham's Table of full-moon.
XVII. gives the initial day of the luni-solar
years, the date taken out from that Table serves PART III.-THE PERPETUAL LUNAR
to find the beginning of all lunar months. But CALENDAR
Canningham's dates are, in many cases, apt to
mislead; for they are calculated for mean midMany chronological questions can be more
night of Ujjain; whereas, in civil reckonings readily solved if the whole lunar year, together the days are accounted to begin with sunrise. with the corresponding English year, is ex- Therefore, if the mean new-moon falls between posed to our view. However, this cannot be midnight and sunrise, Cunningham couples it done without a sacrifice of accuracy ; i.e. we with the following day, whereas, actually, it must rest satisfied with approximate results. belonged to the preceding one. Hence a fourth Where no more than such an approximation is part of Cunningham's dates is a day too late. wanted, the Perpetual Lunar Calendar, exhi- To find with perfect accaracy the date of mean bited in Table 12, will be found useful. In new-moon, my Tables may be used thus, - Table 12, every day is entered with a Roman
Add 200 to the a. of the corresponding year, cypher, the Epact, and one of the seven letters then add the a. for the intervening centuries. a. to g., the Dominical Letter. To begin with Subtract the a. thus found from 10000. The the latter, the Dominical Letters serve to show
remainder is the a. on which the mean newon what day of the week fell any given date of moon occurred throughout the whole year. For any year, in which the week-day of one date is instance, in A.D. 1468 we have 10000—(1800+ known. For instance, let us suppose that, 200 + 9936) = 10000—1936 = 8064. Hence, in a certain year, the 5th March was a Wed
mean now-moon occurred, e.g., late on the 23rd nesday. As the 5th March has the Dominical March, as that day has the next lower a (7768), Letter a., we know at once that all days and Chaitra bu di 1 fell, i.e. ended, on the having the same Dominical Letter a., were 24th March. For the reasons stated above, Wednesdays. What were the week-days of Cunningham gives the 25th March for the the remaining Dominical Letters, will be found beginning of the luni-solar year. by the subsidiary Table 12, which needs no ex. However, without reference to the Tables, the planation. If no week-day is known from day of new.mon in March can be found for any other sources, the week day of the 1st March, given year, and, at the same time, for a good
the value of the Dominical Letter d., many years preceding and following it, by can easily be found by help of Table 14, which Table 13. gives the value of the Dominical Letter d. from The second Part of this Table gives the date A.D. 0 to 2000, Old Style. The Epacts are in March on which new-moon occurred in the arranged in such a way, that the same phase of years A.D. 304 (0) to 379 (75); the fraction gives the moon approximately occurred throughout the complete quarters of the day, after which one English year and the first four months of the conjunction took place. The same dates, in the next, on all days having the same Epact. the same order, are valid for the next 76 years ; For instance, if of some given year the 10th but a quarter of a day must be subtracted from March, having the Epact X., was the day of a each; after 152 years two quarters must be new-moon, a new-moon occurred on all days subtracted; after 228 years, three quarters, having the Epact X., throughout the year, i.e. and after 304 years in A.D. 608 etc.) a on the 9th April, 8th May, etc. As the initial complete day must be retrenched from the date date of the lunar month immediately follows found."
13 The correctness of these rules can easily be demon- 339 = 85. In 304 years it amounts to 335 instead of strated by the above Tables. The difference of the 339, which would be the increase of t. for one completo relative positions of the sun and the moon after 76 years, day. Our error, therefore, is about 20 minutes in 304 is found by subtracting the a. of A.D. 1801 (5188) from years; and even in the 19th century the error is only 1 h. that of A.D. 1876 (5222). The remainder 84 is nearly 25 m., which may be neglected without any practical equal to the fourth part of the increase of a. for one day I consequences.
