Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/69

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THE HINDU CALENDAR.

53

tions for true intercalated and suppressed months were first made according to the method and Tables published by Prof. Jacobi (in the Ind. Ant., Vol. XVII., pp. 145 to 181) as corrected by the errata list printed in the same volume. We based our calculations on his Tables 1 to 10, and the method given in his example 4 on pp. 152—53,^[1] but with certain differences, the necessity of which must now be explained. Prof Jacobi's Tables 1 to 4, which give the dates of the commencement of the solar months, and the hour and minute, were based on the Ârya-Siddhânta, while Tables 5 to 10 followed the Sûrya-Siddhânta, and these two Siddhântas differ. In consequence several points had to be attended to. First, in Prof. Jacobi's Tables l to 4 the solar months are supposed to begin exactly at Ujjain mean sunset, while in fact they begin (as explained by himself at p. 147) at or shortly after mean sunset. This state of things is harmless as regards calculations made for the purpose for which the Professor designed and chiefly uses these Tables, but such is not the case when the task is to determine an intercalary month, where a mere fraction may make all the difference, and where the exact moment of a saṅkrânti must positively be ascertained. Secondly, the beginning of the solar year, i.e., the moment of the Mesha-saṅkrânti, differs when calculated according to those two Siddhântas, as will be seen by comparing cols. 15 to 17 with cols. 15a to 17a of our Table I., the difference being nil in A.D. 496 and 6 gh 23 pa. 41.4 pra. vi. in 1900 A.D. Thirdly, even if we suppose the year to begin simultaneously by both Siddhântas, still the collective duration of the months from the beginning of the year to the end of the required solar month is not the same,^[2] as will be seen by comparing cols. 6 or 7 with cols. 8 or 9 of our Table III. We have applied all the corrections necessitated by these three differences to the figures obtained from Prof Jacobi's Tables and have given the final results in cols. 9 and 11. We know of no independent test which can be applied to determine the accuracy of the results of our calculations for true added and suppressed months; but the first calculations were made exceedingly carefully and were checked and rechecked. They were made quite independently of any previously existing lists of added and suppressed months, and the results were afterwards compared with Prof. Chhatre's list; and whenever a difference appeared the calculations were completely re-examined. In some cases of expunged months the difference between the two lists is only nominal, but in other cases of difference it can be said with certainty that Prof. Chhatre's list is wrong. (See note to Art. 46.) Moreover, since the greatest possible error in the value of the tithi-index that can result by use of Prof. Jacobi's Table is 7 (see his Table p. 164), whenever the tithi-index for added and suppressed months obtained by our computation fell within 7 of 10,000, i.e., whenever the resulting index was below 7 or over 9993, the results were again tested direct by the Sûrya-Siddhânta.^[3]

As regards mean intercalations every figure in our cols, 9a to 12a was found correct by independent test. The months and the times of the saṅkrântis expressed in tithi-indices and tithis were calculated by the present Sûrya-Siddhânta, and the results are the same whether

↑ For finding the initial date of the luni-solar years Prof, Jacobi's Tables I. to XI. were used, and in the course of the calculations it was necessary to introduce a few alterations, and to correct some misprints which had crept in in addition to those noted in the already published errata-list. Thus, the earliest date noted in Tables I. to IV., being A.D. 354, these Tables had to be extended backwards by adding two lines more of figures above those already given. In Table VI., as corrected by the errata, the bîja is taken into account only from A.D. 1601, whereas we consider that it should be introduced from A.D. 1501 (see Art. 21). In Table VI. the century correction is given for the New (Gregorian) Style from A.D 1600 according to the practice in the most part of Europe. I have preferred, however, to introduce the New Style into our Tables from Sept. A.D. 1752 to suit English readers, and this necessitated an alteration in the century data for two centuries. [R. S.]
↑ It is the same according to Warren, but in this respect he is in error. (See note to Art. 24.)
↑ 42 calculations were thus made direct by the Sûrya-Siddhânta with and without the bîja, with the satisfactory result that the error in the final figure of the tithi-index originally arrived at was generally only of 1 or 2 units, while in some cases it was nil. It was rarely 3, and only once 4. It never exceeded 4. It may therefore be fairly assumed that our results are accurate. [S. B. D.]

[1] For finding the initial date of the luni-solar years Prof, Jacobi's Tables I. to XI. were used, and in the course of the calculations it was necessary to introduce a few alterations, and to correct some misprints which had crept in in addition to those noted in the already published errata-list. Thus, the earliest date noted in Tables I. to IV., being A.D. 354, these Tables had to be extended backwards by adding two lines more of figures above those already given. In Table VI., as corrected by the errata, the bîja is taken into account only from A.D. 1601, whereas we consider that it should be introduced from A.D. 1501 (see Art. 21). In Table VI. the century correction is given for the New (Gregorian) Style from A.D 1600 according to the practice in the most part of Europe. I have preferred, however, to introduce the New Style into our Tables from Sept. A.D. 1752 to suit English readers, and this necessitated an alteration in the century data for two centuries. [R. S.]

[2] It is the same according to Warren, but in this respect he is in error. (See note to Art. 24.)

[3] 42 calculations were thus made direct by the Sûrya-Siddhânta with and without the bîja, with the satisfactory result that the error in the final figure of the tithi-index originally arrived at was generally only of 1 or 2 units, while in some cases it was nil. It was rarely 3, and only once 4. It never exceeded 4. It may therefore be fairly assumed that our results are accurate. [S. B. D.]

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