Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/95

exact mean time for other places is required, apply the correction given in Table XI., according to the rule given under that Table. If after this correction the ending time of a tithi is found to fall on the previous or following day the (${\displaystyle d}$) and (${\displaystyle w}$) should be altered accordingly.

Mean time is used throughout the parts of the Tables used for these rules, and it may sometimes differ from the true, used, at least in theory, in Hindu paṅchâṅgs or almanacks.

The ending time of a tithi arrived at by these Tables may also somewhat differ from the ending time as arrived at from authorities other than the Sûrya Siddhânta which is used by us. The results, however, arrived at by the present Tables, may be safely relied on for all ordinary purposes.^[1]

147. N.B. i. Up to 1100 A.D. both mean and true intercalary months are given in Table I. (see Art. 47 above). When it is not certain whether the given year is an expired or current year, whether it is a Chaitrâdi year or one of another kind, whether the given month is amânta or pûrṇimânta, and whether the intercalary month, if any, was taken true or mean, the only course is to try all possible years and months.

N.B. ii. The results are all Old Style dates up to, and New Style dates from, 1753 A.D The New Style was introduced with effect from after 2nd September, 1752. Since only the initial dates of 1752 and 1753 are given, remember to apply the correction (+ 11 days) to any date between 2nd September, 1752, and 9th April, 1753, in calculating by the Hindu solar year, and between 2nd September, 1752, and 4th April, 1753, in calculating by the Hindu luni-solar year, so as to bring out the result in New Style dates A.D. The day of the week requires no alteration.

N.B. iii. If the date A.D. found above falls after February 28th in a leap-year, it must be reduced by 1.

N.B. iv. The Hindus generally use expired (gata) years, while current years are given throughout the Tables. For example, for Śaka year 1702 "expired" 1703 current is given.

148. Example 1. Required the week-day and the A.D. year, month, and day corresponding to Jyeshṭha śukla paṅchâmî (5th), year Śârvari, Śaka year 1702 expired (1703 current), and the ending and beginning time of that tithi.

The given year is Chaitrâdi (see N.B. ii., Table II., Part iii.). It does not matter whether the month is amânta or pûrṇimânta, because the fortnight belongs to Jyeshṭha by both systems (see Table II., Part i.). Looking to Table I. along the given current Śaka year 1703, we find that its initial day falls in A.D. 1780 (see note 1 to Art. 139), a leap-year, on the 5th April, Wednesday; and that ${\displaystyle d}$ (col. 19), ${\displaystyle w}$ (col. 20), ${\displaystyle a}$ (col. 23), ${\displaystyle b}$ (col. 24) and ${\displaystyle c}$ (col. 25) are 96, 4, 1, 657 and 267 respectively. We write them in a horizontal line (see the working of the example below). From Table I., col. 8, we find that there is no added month in the year. The number therefore of tithis between Chaitra ś. 1 and Jyeshṭha ś. 5 was 64, viz., 60 up to the end of Vaiśâkha (see Table III., col. 3), the month preceding the given one, and 4 in Jyeshṭha. The sixtieth part of 64 (neglecting the fraction ⁠4/60⁠ because it is not more than half) is 1. Reduce 64 by one and we have 63 as the approximate number of days between Chaitra ś. 1 and Jyeshtha ś. 5. We write this number under (${\displaystyle d}$). Turning to Table IV. with the argument 63 we find under (${\displaystyle w}$) (${\displaystyle a}$) (${\displaystyle b}$) (${\displaystyle c}$) the numbers 0, 1334, 286, 172, respectively, and we write them under their respective heads, and add together the two quantities under each head. With the argument (${\displaystyle b}$) (943) we turn to Table VI. for the equation. We do not find exactly the number 943 given, but we have 940 and 950 and must see the difference between the corresponding equation figures and fix the appropriate figure for 943. The auxiliary table given will fix this, but in practice it can be easily calculated in the head. (The