Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/45

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THE HINDU CALENDAR.

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and suppressed months, may be summed up as follows. That amânta lunar month in which the Mesha saṅkrânti occurs is called Chaitra, and the rest in succession. That amânta lunar month in which there is no saṅkrânti is adhika and receives the name (i) of the preceding natural lunar month by the old Brâhma-Siddhânta rule, (2) of the following natural lunar month by the present rule. When there are two saṅkrântis in one amânta lunar month, the name which would be derived from the first is dropped by the old Brâhma-Siddhânta rule, the name which would be derived from the second is dropped by the present rule.

49. Different results by different Siddhântas. The use of different Siddhântas will sometimes create a difference in the month to be intercalated or suppressed, but only when a saṅkrânti takes place very close^[1] to the end of the amâvâsyâ. Such cases will be rare. Our calculations for added and suppressed months have been made by the Sûrya-Siddhânta, and to assist investigation we have been at the pains to ascertain and particularize the exact moments (given in tithi-indices, and tithis and decimals) of the saṅkrântis preceding and succeeding an added or suppressed month, from which it can be readily seen if there be a probability of any divergence in results if a different Siddhânta be used. The Special Tables published by Professor Jacobi in the Epigraphia Indica (Vol., II., pp. 403 ff.) must not be relied on for calculations of added and suppressed months of Siddhântas other than the Sûrya-Siddhânta. If a different Siddhânta happened to have been used by the original computor of the given Hindu date, and if such date is near to or actually in an added or suppressed month according to our Table I., it is possible that the result as worked out by our Tables may be a whole month wrong. Our mean intercalations from A. D. 300 to 1100 are the same by the original Sûrya-Siddhânta, the present Sûrya-Siddhânta, and the first Ârya-Siddhânta.

50. Some peculiarities. Certain points are worth noticing in connection with our calculations of the added and suppressed months for the 1600 years from A. D. 300 to 1900 according to the Sûrya-Siddhânta.

(a) Intercalations occur generally in the 3rd, 5th, 8th, 11th. 14th, 16th and 19th years of a cycle of 19 years. (b) A month becomes intercalary at an interval of 19 years over a certain period, and afterwards gives way generally to one of the months preceding it, but sometimes, though rarely, to the following one. (c) Out of the seven intercalary months of a cycle one or two are always changed in the next succeeding cycle, so that after a number of cycles the whole are replaced by others. (d) During our period of 1600 years the months Mârgaśîrsha, Pausha, and Mâgha are never intercalary. (e) The interval between years where a suppression of the month occurs is worth noticing. In the period covered by our Tables the first suppressed month is in A.D. 404, and the intervals are thus: 19, 65, 38, 19, 19, 46, 19, 141, 122, 19, 141, 141, 65, 19, 19, 19, 19, 46, 76, 46, 141, 141, and an unfinished period of 78 years. At first sight there seems no regularity, but closer examination shews that the periods group themselves into three classes, viz., (i.) 19, 38, 76; (ii.) 141; and (iii.) 122, 65 and 46 years; the first of which consists of 19 or its multiples, the second is a constant, and the third is the difference between (ii.) and (i.) or between 141 and a multiple of 19. The unfinished period up to 1900 A.D. being 78 years, we are led by these peculiarities to suppose that there will be no suppressed month till at earliest (122 years =)

↑ It is difficult to define the exact limit, because it varies with different Siddhântas, and even for one Siddhânta it is not always the same. It is, however, generally not more than six ghaṭikâs, or about 33 of our tithi-indices ( $t$ ). But in the case of some Siddhântas as corrected with a bîja the difference may amount sometimes to as much as 20 ghaṭikâs, or 113 of our tithi-indices. It would be very rare to find any difference in true added months; but in the case of suppressed months we might expect some divergence, a month suppressed by one authority not being the same as that suppressed by another, or there being no suppression at all by the latter in some cases. Differences in mean added months would be very rare, except in the case of the Brâhma-Siddhânta. (See Art. 88.)

[1] It is difficult to define the exact limit, because it varies with different Siddhântas, and even for one Siddhânta it is not always the same. It is, however, generally not more than six ghaṭikâs, or about 33 of our tithi-indices ( $t$ ). But in the case of some Siddhântas as corrected with a bîja the difference may amount sometimes to as much as 20 ghaṭikâs, or 113 of our tithi-indices. It would be very rare to find any difference in true added months; but in the case of suppressed months we might expect some divergence, a month suppressed by one authority not being the same as that suppressed by another, or there being no suppression at all by the latter in some cases. Differences in mean added months would be very rare, except in the case of the Brâhma-Siddhânta. (See Art. 88.)

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