Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/308

(b) When the year of the given era is both Meshâdi and non-Meshâdi, three possible cases; (a) Meshadi year current, (b) Meshâdi year expired = non-Meshâdi year current, (c) non-Meshadi year expired.

(II.) With reference to the civil beginning of the month, all the cases in Art. 28.

C. When the era of a date is not known, all known possible eras should be tried.

D. (a) According to Hindu Astronomy a tithi of a bright or dark fortnight of a month never stands at sunrise on the same week-day more than once in three consecutive years. For instance, if Chaitra śukla pratipadâ stands at sunrise on a Sunday in one year, it cannot stand at sunrise on Sunday in the year next preceding or next following.

(b) It can only, in one very rare case, end on the same week-day in two consecutive years, and that is when there are thirteen lunar months between the first and second. There are only seven instances^[1] of it in the 1600 years from A.D. 300 to 1900.

(c) It cannot end on the same week-day more than twice in three consecutive years.

(d) But a tithi can be connected with the same week-day for two consecutive years if there is a confusion of systems in the naming of the civil day, naming, that is, not only by the tithi current at sunrise, but also by the tithi current during any time of that day. Even this, however, can only take place when there are thirteen lunar months between the two. If, for instance, Chaitra śukla 1st be current during, though not at sunrise on, a Sunday in one year; next year, if an added month intervenes, it may stand at sunrise on a Sunday, and consequently it may be connected with a Sunday in both these (consecutive) years.

(e) A tithi of an amânta month of one year may end on the same week-day as it did in the pûrṇimânta month of the same name during the preceding year.

(f) The interval between the weekdays connected with a tithi in two consecutive years, when there are 12 months between them, is generally four, and sometimes five; but when thirteen lunar months intervene, the interval is generally one of six weekdays. For instance, if Chaitra śukla 1st ends on Sunday (= 1) in one year, it ends next year generally on (1 + 4 = 5 =) Thursday. and sometimes on (1 + 5 = 6 =) Friday, provided there is no added month between the two. If there is an added month it will probably end on (1 + 6 = 0 =) Saturday.

(g) According to Hindu Astronomy the minimum length of a lunar month is 29 days, 20 ghaṭikâs, and the maximum 29 days and 43 ghaṭikâs. Hence the interval between the weekdays of a tithi in two consecutive months is generally one or two. If, for instance, Chaitra śukla pratipadâ falls on a Sunday, then Vaiśâkha sukla pratipada may end on Monday or Tuesday. But by the existence of the two systems of naming a civil day from the tithi current at its sunrise, as well as by that current at any time in the day, this interval may sometimes be increased to three, and we may find Vaiśâkha śukla pratipadâ, in the above example, connected with a Wednesday.

E. (a) A saṅkrânti cannot occur on the same week-day for at least the four years preceding and four following.

(b) See Art. 119, par. 3.

160 (c) To find the apparent longitude of Jupiter. (See Art. 63, p. 37, and Table XII.)

I. To find, first, the mean longitude of Jupiter and the sun.

(i.) Find the mean longitude of Jupiter at the time of the Mesha sankranti by the following Table W. That of the sun is 0° at that moment.

(ii.) Add the śodhya (Art. 26, p. n, Art. 90, p. 52) given in the following Table Y to