Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/94

one (or two) to, both (${\displaystyle d}$) and (${\displaystyle w}$);^[1] subtract from, or add to, the (${\displaystyle a}$) (${\displaystyle b}$) (${\displaystyle c}$) already found, their value for one (or two) days (Table IV.); add to (${\displaystyle a}$) the equations for (${\displaystyle b}$) and (${\displaystyle c}$) (Tables VI. and VII.) and the sum (${\displaystyle t}$) will then indicate the tithi. If this is the same as given (if not, proceed again as before till it corresponds), the (${\displaystyle w}$) is its week-day, and the date shewn in the top line and side columns of Table IX. corresponding with the ascertained (${\displaystyle d}$) is its equivalent date A.D. The year A.D. is found on the line of the given Chaitrâdi year in col. 5, Table I. Double figures are given in that column; if (${\displaystyle d}$) is not greater than 365 in a common year, or 366 in a leap-year, the first, otherwise the second, of the double figures shows the proper A.D. year.

140. For all practical purposes and for some ordinary religious purposes a tithi is connected with that week-day at whose sunrise it is current. For some religious purposes, however, and sometimes even for practical purposes also, a tithi which is current at any particular moment of a week-day is connected with that week-day. (See Art. 31 above.)

141. In the case of an expunged tithi, the day on which it begins and ends is its weekday and equivalent. In the case of a repeated tithi, both the civil days at whose sunrise it is current,^[2] are its week-days and equivalents.

142. A clue for finding when a tithi is probably repeated or expunged. When the tithi-index corresponding to a sunrise is greater or less, within 40, than the ending index of a tithi, and when the equation for (${\displaystyle b}$) (Table VI.) is decreasing, a repetition of the same or another tithi takes place shortly after or before that sunrise; and when the equation for (${\displaystyle b}$) is increasing an expunction of a tithi (different from the one in question) takes place shortly before or after it.

143. The identification of the date A.D. with the week-day arrived at by the above method, may be verified by Table XIII. The verification, however, is not in itself proof of the correctness of our results.

144. To find the moment of the ending of a tithi. Find the difference between the (${\displaystyle t}$) on the given day at sunrise and the (${\displaystyle t}$) of the tithi-index which shews the ending point of that tithi (Table VIII.). With this difference as argument find the corresponding time either in ghaṭikâs and palas, or hours and minutes, according to choice, from Table X. The given tithi ends after the given sunrise by the interval of time so found. But this interval is not always absolutely accurate. (See Art. 82). If accuracy is desired add the (${\displaystyle a}$) (${\displaystyle b}$) (${\displaystyle c}$) for this interval of time (Table V.) to the (${\displaystyle a}$) (${\displaystyle b}$) (${\displaystyle c}$) already obtained for sunrise. Add as before to (${\displaystyle a}$) the equations for (${\displaystyle b}$) and (${\displaystyle c}$) from Tables VI. and VII., and find the difference between the (${\displaystyle t}$) thus arrived at and the (${\displaystyle t}$) of the ending point of the tithi (Table VIII.). The time corresponding to that difference, found from Table X., will show the ending of the tithi before or after the first found time. If still greater accuracy is desired, proceed until (${\displaystyle t}$) amounts exactly to the (${\displaystyle t}$) of the ending point (Table VIII.) For ordinary purposes, however, the first found time, or at least that arrived at after one more process, is sufficiently accurate.

145. The moment of the beginning of a tithi is the same as the moment of ending of the tithi next preceding it; and this can be found either by calculating backwards from the (${\displaystyle t}$) of the same tithi, or independently from the (${\displaystyle t}$) of the preceding tithi.

146. The moment of beginning or ending of tithis thus found is in mean time, and is applicable to all places on the meridian of Ujjain, which is the same as that of Laṅkâ. If the