Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/68
but it should be remembered that their time-equivalent as obtained from Table X. is only approximate for the reason given above (Art. 82.) Since Indian readers are more familiar with tithis than with lunation-parts, and since the expression of time in tithis may be considered desirable by some European workers, we have given the times of all the required saṅkrântis in tithis and decimals in our columns, as well as in lunation-parts; but for turning our figures into time-figures it is easier to work with lunation-parts than with tithi-parts. It may be thought by some readers that instead of recording the phenomena in lunation-parts and tithis it would have been better to have given at once the solar time corresponding to the moments of the saṅkrântis in hours and minutes. But there are several reasons which induced us, after careful consideration, to select the plan we have finally adopted. First, great labour is saved in calculation; for to fix the exact moments in solar time at least five processes must be gone through in each case, as shewn in our Example I. below (Art. 148) It is true that, by the single process used by us, the time-equivalents of the given lunation-parts are only approximate, but the lunation-parts and tithis are in themselves exact. Secondly, the time shewn by our figures in the case of the mean added months is the same by the Original Sûrya, the Present Sûrya, and the Ârya-Siddhânta, as well as by the Present Sûrya-Siddhânta with the bîja, whereas, if converted into solar time, all of these would vary and require separate columns. Thirdly, the notation used by us serves one important purpose. It shews in one simple figure the distance in time of the saṅkrântis from the beginning and end of the added or suppressed month, and points at a glance to the probability or otherwise of there being a difference in the added or suppressed month in the case of the use of another authority. Fourthly, there is a special convenience in our method for working out such problems as are noticed in the following articles.
90. Supposing it is desired to prove the correctness of our added and suppressed months, or to work them out independently, this can easily be done by the following method: The moment of the Mesha saṅkrânti according to the Sûrya-Siddhânta is given in cols. 13, 14 and 15a to 17a for all years from A.D. 1100 to 1900, and for other years it can be calculated by the aid of Table D. in Art. 96 below. Now we wish to ascertain the moment of two consecutive new moons connected with the month in question, and we proceed thus. The interval of time between the beginning of the solar year and the beginning or end of any solar month according to the Sûrya-Siddhânta, is given in Table III., cols. 8 or 9; and by it we can obtain by the rules in Art. 151 below, the tithi-index for the moment of beginning and end of the required solar month, i.e., the moments of the solar saṅkrântis, whose position with reference to the new moon determines the addition or suppression of the luni-solar month. The exact interval also in solar time between those respective saṅkrântis and the new moons (remembering that at new moon "" = 10,000) can be calculated by the same rules. This process will at once shew whether the moon was waning or waxing at the preceding and succeeding saṅkrântis, and this of course determines the addition or suppression of the month. The above, however, applies only to the apparent or true intercalations and suppressions. For mean added months the Śodhya (2 d. 8 gh. 51 p. 15 vi.) must be added (see Art. 26) to the Mesha-saṅkrânti time according to the Ârya-Siddhânta (Table I., col. 15), and the result will be the time of the mean Mesha saṅkrânti. For the required subsequent saṅkrântis all that is necessary is to add the proper figures of duration as given in Art. 24, which shews the mean length of solar months, and to find the "" for the results so obtained by Art. 151. Then add 200 to the totals and the result will be the required tithi-indices.
91. It will of course be asked how our figures in Table I. were obtained, and what guarantee we can give for their accuracy. It is therefore desirable to explain these points. Our calcula-