Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/72
99 When an intercalary Chaitra occurs by the true system (Arts. 45 etc. above) it must be remembered that the entries in cols. 19 to 25 are for the śukla-pratipadâ of the intercalated, not the true, Chaitra.
100. The first tithi of the year (Chaitra śukla pratipadâ) in Table I., cols. 19 to 25, is taken as an apparent, not mean, tithi, which practice conforms to that of the ordinary native pañchâṅgs. By this system, as worked out according to our methods A and B, the English equivalents of all subsequent tithis will be found as often correct as if the first had been taken as a mean tithi;—probably more often.
101. The figures given in cols. 21 and 22, except in those cases where a minus sign is found prefixed (e.g., Kali 4074 current), constitute a first approximation showing how much of chaitra śukla pratipadâ had expired on the occurrence of mean sunrise at Ujjain on the day given in cols. 19 and 20. Col. 21 gives the expired lunation-parts or tithi-index, and col. 22 shews the same period in tithi-parts, i.e., decimals of a tithi. The meaning of both of these is explained above (Arts. 80 and 81). We differ from the ordinary pañchâṅgs in one respect, viz., that while they give the portion of the tithi which has to run after mean sunrise, we have given, as in some ways more convenient, the portion already elapsed at sunrise. Thus, the entry 286 in col. 21 means that 286 lunation-parts of Chaitra śukla 1st had expired at mean sunrise. The new moon therefore took place 286 lunation-parts before mean sunrise, and by Table X., col. 3, 286 lunation-parts are equal to (14 h. 10 m. + 6 h. 6 m. =) 20 h. 16 m. The new moon therefore took place 20 h. 16 m. before sunrise, or at 9.44 a.m. on the previous day by European reckoning. The ending-moment of Chaitra śukla pratipadâ can be calculated in the same way, remembering that there are 333 lunation-parts to a tithi.
We allude in the last paragraph to those entries in cols. 21 and 22 which stand with a minus sign prefixed. Their meaning is as follows:—Just as other tithis have sometimes to be expunged so it occasionally happens that Chaitra śukla 1st has to be expunged. In other words, the last tithi of Phâlguna, or the tithi called amâvâsyâ, is current at sunrise on one civil day and the 2nd tithi of Chaitra (Chaitra śukla dvitîyâ) at sunrise on the following civil day. In such a case the first of these is the civil day corresponding to Chaitra śukla 1st; and accordingly we give this civil day in cols. 19 and 20. But since the amâvâsyâ-tithi (the last tithi of Phalguna) was actually current at sunrise on that civil day we give in cols. 21 and 22 the lunation-parts and tithiparts of the amâvâsyâ-tithi which have to run after sunrise with a minus sign prefixed to them. Thus, "−12" in col. 21 means that the tithi-index at sunrise was 10,000 − 12 = or 9988, and that the amâvâsyâ-tithi (Phâlguna Kṛishṇa 15 or 30) (Table VIII., col. 3) will end 12 lunation-parts after sunrise, while the next tithi will end 333 lunation-parts after that.
102. (, , , cols. 23, 24, 25). The moment of any new moon, or that moment in each lunation when the sun and moon are nearest together, in other words when the longitudes of the sun and moon are equal, cannot be ascertained without fixing the following three elements,—() The eastward distance of the moon from the sun in mean longitude, () the moon's mean anomaly (Art. 15 and note), which is here taken to be her distance from her perigee in mean longitude, () the sun's mean anomaly, or his distance from his perigee in mean longitude. And thus our "", "", "", have the above meanings; "" being expressed in 10,000ths of a circle reduced by 200.6 for purposes of convenience of use, all calculations being then additive, "" and "" being given in 1000ths of the circle. To take an example. At Ujjain mean sunrise on Chaitra śukla pratipadâ of the Kali year 3402 (Friday. 8th March, A.D. 300), the mean longitudes calculated direct from the Sûrya-Siddhânta were as follow: The sun, 349° 22′ 27″.92.
