began at sunrise on March 18th, as entered in Table XXIV. The years A.D. 309–10, 310–11, 311–12, correspond to K.Y. 3411, 3412, 3413 current. A lunar month had to be intercalated by the mean system in K.Y. 3411,[1] in which year there was no intercalation by the true system. In the year K.Y. 3412 Vaiśākha was intercalated under the true system (Table I., col. 8), while there was no intercalation under the mean system; so that the beginning of the luni-solar year K.Y. 3413 was the same (Table I., cols. 19–25) under both systems. The beginnings of the years K.Y. 3411, 3413, therefore, are the same as given in Table I. for both systems, but while that Table for K.Y. 3412 stands if the "true"system is used, Table XXIV. must be substituted for Table I. if the mean system is used.[2]
70. Although, as I have stated, it is most improbable that Hindi calculators ever used the tropical year for the purpose of preparing ordinary calendars, it is necessary to notice them because it is possible that occasionally (though no instance has as yet been discovered) the date of a record may have been associated with a tropical, and not with a sidereal samkranti. And for that reason attention must be called to the fact that whenever, subsequent to the year of coincidence (§ 34), a new-moon falls between the moments of the tropical and sidereal Mīna saṁkrāntis, the tropical luni-solar year will begin a lunar month earlier than the ordinary sidereal luni-solar year of our Tables, for reasons similar to those considered in §§ 66 to 69. There is no need to frame Tables for such years. It is only necessary to call attention to the fact. The point to be remembered is that, though the tithi will, when worked according to rule, be correct by our Tables, the name of the month may be different; the month to which the tithi belongs being, if tropical saṁkrāntis were used, a month later or earlier than the month obtained from our Tables—later in years in which the tropical Mīna saṁkrānti is later than the sidereal Mīna saṁkrānti of the Tables, and earlier when it is earlier.
71. So much being said by way of caution, I return to the ordinary civil beginning of the Chaitrādi luni-solar year, or the year which astronomically begins with the new-moon of amanta Chaitra. Mutatis mutandis, the same principles apply to years which begin with other months. (See § 52, p. 31 of the Indian Calendar.)
72. The civil beginning of such a year is, in amānta reckoning, supposed to be, as already stated, at sunrise (probably taken as true sunrise in local almanacs, but by us as mean sunrise for preparation of general working Tables; and this as representing for time-measurement 6 a.m. on the meridian of Laṅkā, alias of Ujjain, Greenwich east longitude 75° 46′,—time-correction from Greenwich + 5 h. 3 m.) —at sunrise of the day on which the first tithi of the bright half of Chaitra, alias Chaitra śukla pratipadā or Chaitra śukla 1st, is current at sunrise. And in columns 19, 20 of Table I. of the Indian Calendar
- ↑ This month by regular rule was Māgha.
- ↑ The above is the easiest method of work, but if care be used in noting the correspondence of months the figures given in the Ind. Cal. (cols. 19 to 25 of Table I.) may be equally used under the mean system. Thus if we have to find, in a date of an inscription, the week-day and other particulars for a tithi in amānta Chaitra and in amānta Jyéshṭha of K.Y. 3412 current, as calculated by the mean system, we can either work as directed in the text, or we can make the months correspond with those found by the Indian Calendar, Table I. In the latter case all we have to do is to remember that the month called "Chaitra," K.Y. 3412 current, under the mean system, was, under the true system, called "adhika Vaiśākha," since Māgha was intercalated in the previous year under the mean system and Vaiśākha was intercalated in K.Y. 3412 under the true system. "Chaitra" of the mean system was the second month, adhika Vaiśākha, of the true system. Similarly "Jyéshṭha" of the mean system was the fourth month of the true system; and, because of the intercalation of Vaiśākha under the true system, it was the same month, Jyéshṭha, both in place and name as the Jyéshṭha of the true system found from Table I., cols. 19 to 25, of the Ind. Cal. Working therefore as in the text by Table XXIV., by the mean system, the months to be calculated are Chaitra (1st) and Jyéshṭha (3rd); but equally correctly the same months can be calculated by the "true" system, using Table I. as it stands, but working for adhika Vaiśākha (2nd month) and Jyéshṭha (4th).
