local rule. The rules obtaining are detailed in § 28, p. 12, of the Indian Calendar. They are four in number:—
(i.) The Bengal rule. When a saṁkrānti takes place between sunrise and midnight, or between 0 h. and 18 h. Laṅkā time, the solar month begins next day; when it occurs after midnight the first day of the solar month is the next following, or third, day.
(ii.) The Orissa rule, for Amli and Vilāyatī eras. The first day of the month is the day of the saṁkrānti whenever it occurs. If, for instance, the saṁkrānti occurred at 23 h. 50 m. Laṅkā time, or 23 h. 50 m. after sunrise on a Friday, though this be only 10 m. before sunrise or about 5.50 a.m. on the Saturday, still the first civil day of the month is Friday.
(iii.) The Tamil rule, or general rule for South India. If the saṁkrānti takes place on any day before sunset or 12 h. Laṅkā time that day is the first civil day; if it takes place after sunset, or between 12 h. and 24 h. Laṅkā time, the next day is the first day of the month.
(iv.) The Malabar rule. The day between sunrise and sunset is divided, according to its true length, into five parts; and if the saṁkrānti occurs within the first three of them the month begins on the same day, otherwise it begins on the following day. Thus, if the length of a day from sunrise to sunset is 12 h. 30 m., its fifth part is 2 h. 30 m., and three of these parts is 7 h. 30 m. If a saṁkrānti occurred on a Friday 7 h. 25 m. after sunrise, the first civil day of the month began at sunrise on Friday; but if it occurred at 7h. 35 m. after sunrise, the first civil day of the month began at sunrise on Saturday.
44. The exact time fixed by a calculation according to the Ārya Siddhānta, made for the purpose of testing the date of an inscription, will be found generally to differ from the similar result made by a calculation when the Sūrya Siddhānta is used. There are three reasons for this: (1) The starting point for calculations, which is the astronomical beginning in time of the true solar year, i.e., the moment of true Mēsha saṁkrānti, as fixed by the Ārya, differs, except in A.D. 496, when the two were together,[1] from the same moment as fixed by the Surya Siddhānta.
(2) The lengths of the true solar months according to the former differ slightly from those established by the latter. This is also the case with the mean months, but in them the difference is very small.
(3) In the case of calculation by the sun's mean motion a constant quantity called by us the śōdhya, viz., the difference between the time of the sun's arrival at the Mēsha saṁkrānti point when calculated by his true and his mean motions (§39A above),has to be applied to the time of true Mēsha saṁkrānti; and this śōdhya interval is not quite the same according to the various authorities.
45. These differences necessitate the application, in the case of both true and mean computation, of two out of three corrections to a result obtained by one of these Siddhāntas if we desire to ascertain what that result would be by the other. I proceed to explain them more fully. In "true" calculations Corrections I. and II., in mean calculations Corrections I. and III., must be so applied.
46. The sidereal year of the Ārya Siddhānta is in length 365 d. 6 h. 12 m. 30 s., and that of the Sūrya Siddhānta is 365 d. 6 h. 12 m. 36.56 s. The time of the Mēsha saṁkrānti, according to the latter, Correction I.
Year-lengths. is therefore earlier than it is according to the former by the amount of 6.56 s. per annum in years prior to A.D. 496, when the two were together, and by the same amount later in years subsequent to that date. The time of the true Mēsha saṁkrānti for every year according to the Ārya Siddhānta from A.D. 300 to 1900 is given in the Indian Calendar, Table I., and
- ↑ See the "Additional Notes" at the beginning of this Volume.
