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argument 30 is 1 h. 58 m., which differs from the Ind. Cal. result by only 8 m. in the first case. By using argument 40 and stating the time as 2 h. 38 m., he differed from the Ind. Cal. result by 32 m. Again, in the second case he chose for argument the multiple of 10 higher than the Indian Calendar actual. But in the last case, where by the Ind. Cal. we have the argument 45 and time-equivalent 2 h. 57 m., he chose for argument the lower multiple of 10, viz., 40 and not 50; and quoted the time, with argument 40, at 2 h. 38 m. I am at present unable to explain his reason for this.^[1]

123. Nor am I altogether satisfied that the Professor's method is the safest. Thus, working some of these cases by Jacobi's Epig. Ind. General Tables, I find that in the first case where the Ind. Cal. result is 14 h. 14 m., Jacobi's result is 14 h. 10 m.; whereas Kielhorn stated it as 14 h. 27 m. In the same inscription where the Ind. Cal. (Garga) result is 2 h. 6 m., Jacobi's result is 2 h. 3 m.; whereas Kielhorn stated it as 2 h. 38 m. In the second instance where the Ind. Cal. result was 2 h. 14 m., Jacobi's result is 1 h. 53 m., whereas Kielhorn stated it as 2 h. 38 m. So that in these cases Jacobi's result is closer to the Ind. Cal. result than is Prof. Kielhorn's.

124. I believe that Kielhorn's method was based on the hope that by adopting it he would lessen the possible error arising from our multiplication of ${\displaystyle c}$ by 10. Let us examine a case. I take the example given in Ind. Cal., pp. 81 and 97, where ${\displaystyle c=439}$ and the nakshatra-index resulting is 3022, showing (Tables VIII. and X.) that the nakshatra Āślēshā ended at 20 h. 23 m. after mean sunrise on the day in question. Now if instead of 439 as the value of ${\displaystyle c}$ we had had 438 or 440, ${\displaystyle c\times 10}$ would equal 4380 or 4400, and the resulting nakshatra-index ${\displaystyle n}$ would have been 3013 or 3032; the former proving Āślēshā to have ended 20 h. 59 m., the latter 19 h. 44 m. after mean sunrise. In the former case there would have been a difference of 36 m., and in the latter 39 m. between the result and our finding of 20 h. 33 m. We found, for ${\displaystyle c=439}$, that the end of Āślēshā was, in terms of ${\displaystyle n}$, 311 from mean sunrise, and the question is what Prof. Kielhorn would have fixed as its value. He might have taken either 310, the nearest, or 320, the next highest, multiple of ten. In the former case he would have fixed the ending-time of Āślēshā as 20 h. 19 m., in the latter as 20 h. 59 m. after sunrise, and he would have differed from our Ind. Cal. finding by 14 m. or by 26 m. But not being certain that the ${\displaystyle c}$ from which we work was not 438 or 440 instead of 439 he felt, probably, that his result, based on a difference in ${\displaystyle n}$ of less than 10, was more likely to be correct than our own difference, which amounts to 10 either way. It must be noted, however, that supposing he had selected the higher multiple of 10 in the final argument, and supposing the real value of ${\displaystyle c}$ to have been 440, he would have differed from the approximately true result by (20 h. 59 m. − 19 h. 44 m.) 1 h. 15 m. So that I repeat that I am not altogether satisfied that his method is the best.

Prof. Jacobi's method is, as stated above, undoubtedly more accurate than ours, and may be resorted to for testing close or doubtful cases.

125. Nakshatras, when considered with reference to their currency at mean sunrise of a civil day, are subject to nominal intercalations and suppressions in the same way as tithis and lunar months and (in the matter of suppression) Jovian samvatsaras (above, §§ 86–89, 95–103; below, §§ 131, 133). For a nakshatra may begin or end at any moment of a civil day, and it sometimes happens that the same nakshatra is current at two successive sunrises, and sometimes that a nakshatra falls altogether within the period of two successive sunrises. The rule therefore is that a nakshatra during the duration of which the sun rises twice is repeated, and that a nakshatra during which the sun does not rise at all is expunged.

Instances of this are given in the Pañchāṅg extract on p. 14 of the Indian Calendar. On Sunday, September 9th, A.D. 1894, the nakshatra Pūrvā Ashāḍhā ended 58 gh. 11 p. after sunrise, and at that moment Uttarā Ashāḍhā began. The hour was 5.16 a.m. on the Monday, or before sunrise. Uttarā

1. ↑ It was not due to the fact that he selected a higher figure because equation ${\displaystyle c}$ was increasing, and a lower because it was decreasing. In the first two inscription-dates under discussion he selected the higher figure, yet equation ${\displaystyle c}$ was increasing in the first and decreasing in the second.