Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/36

varies every day of the year. And at any given place, and on any given day of the year, it is not the same for all years. The calculation, therefore, of the exact moment of true sunrise at any place is very complicated—too complicated to be given in this work,^[1] the aim of which is extreme simplicity and readiness of calculation, and therefore mean time at the meridian of Ujjain^[2] or Lanka is used throughout what follows.

All ending moments of tithis calculated by our method C (Arts. 139 to 160) are in Ujjain mean time; and to convert Ujjain mean time into that of any other given place the difference of longitude in time— 4 minutes (10 palas) to a degree—should be added or subtracted according as the place is east or west of Ujjain. Table XI. gives the differences of longitude in time for some of the most important places of India.

The difference between the mean and apparent (true) time of any place in India at the present day varies from nil (in March and October) to 26 minutes (in January and June) in the extreme southern parts of the peninsular. It is nowhere more than 65 minutes.

37. Basis of calculation for the Tables. All calculations made in this work in accordance with luni-solar reckoning are based on the Sûrya-Siddhânta, and those for solar reckoning on the Sûrya and Ârya Siddhântas. The elements of the other authorities being somewhat different, the ending moments of tithis etc., or the times of sankrantis as calculated by them may sometimes differ from results obtained by this work; and it must never be forgotten that, when checking the date of a document or record which lays down, for instance, that on a certain week-day there fell a certain tithi, nakshatra, or yoga, we can only be sure of accuracy in our results if we can ascertain the actual Siddhânta or other authority used by the author of the calendar which the drafter of the document consulted. Prof. Jacobi has given Tables for several of the principal Siddhântas in the Epigraphica Indica (Vol. II., pp. 403 et seq.), and these may be used whenever a doubt exists on the point.

Although all possible precautions have been taken, there, must also be a slight element of uncertainty in the results of a calculation made by our Tables owing to the difference between mean and apparent time, independently of that arising from the use of different authorities. Owing to these two defects it is necessary sometimes to be cautious. If by any calculation it is found that a certain tithi, nakshatra, yoga, or karaṇa ended nearly at the close of a solar day—as, for example, 55 ghaṭikâs after mean sunrise on a Sunday, i.e., 5 ghaṭikâs before sunrise on the Monday—it is possible that it really ended shortly after true sunrise on the Monday. And, similarly, if the results shew that a certain tithi ended shortly after the commencement of a solar day,—for instance, 5 ghaṭikâs after mean sunrise on a Sunday,—it is possible that it really ended shortly before the true termination of the preceding day, Saturday.