Epigraphia Indica Vol 16

SR No.: 032570
Original Sutra Author: N/A
Author: F W Thomas, H Krishna Sastri
Publisher: Archaeological Survey of India
Publication Year: 1921
Total Pages: 474
Language: English
Classification: Book_English
File Size: 22 MB

Page 139

104
EPIGRAPHIA INDICA.
[VOL. XVI.
CONSTRUCTION OF THE TABLES.
291. No special remarks are necessary except with reference to Tables LXIII B (lengths of solar months), LXVI A and LXVII A(Detailed "Equation b" and "Equation c"), LXVIII (Indices of tithis, etc.), and the three Tables LXXII, LXXIII, LXIV. 'The remainder are only duplicates of the similar Tables in the " Indian Calendar." (See "Arrangement of Tables," above, $ 288.)
Table LXIII B.--Lengths of the true solar months. 292. M. Louis de Ries has been repeatedly quoted in these pages as a most careful calculator. Several years ago he kindly worked out for me an estimate of the lengths of the true solar months according to the First Arya-Siddhānta, but did not inform me of the process by which he obtained his results. An entirely independent calculation has now been carried out, based on my own Table of the sun's true longitude for each 24-hour period of the solar year (abore, Vol. XIV, Table XLVIII A-a Table, let it be understood, prepared some years subsequent to M. de Ries' communication and to which he has never had access. Comparison of results proves the accuracy of M. de Ries' figures, and these have been adopted without alteration in my Table. The complete agreement of our respective fixtures is really remarkable.
For example, M. de Ries found that the true gun, according to Aryabhata as corrected by Lalla, reaches 180° of celestial long., the moment of the Tulā-samkranti, 1864 216 21m 37682 after the moment of true Mosha-samkrānti, the astronomical beginning of the true solar year.
My cwn work for solution of this problem is as follows:-It will be seen from Table XLVIII A (above, Vol. XIV) that on that 186th day, i.e. after 186 periods of 24 hours each from the moment of true Mesha-samkrānti, the true sun has to travel (180°-179' 6' 55"-21=) 53' 4":79 before reaching the Tula-samkrānti point, 180°. Calculating by his actual velocity on day 186 (Table XLIX, Vol. XIV), the time required for him to accomplish this journey (using his true, not mean, velocity in minutes and seconds as well as in hours) is found to be 21h 21m 37.-82,-precisely M. de Ries' fixture. All the details given by M. de Ries have been similarly examined, and found correct.
Dewan Bahadur L. D. Swamikannu Pillai's estimate of the lengths of these months (Indian Chronology, Table II) differs somewhat from ours, the sun according to him arriving at each sankranti always a little later than it does by our determination. The greatest difference between us is at the Tulá-samkrānti, which his Table shews to occur 3m 34"-18 later than the time yielded by our Table. Adding together the lengths of the twelve solar months ag given by him, the length of the Arya-Siddhanta year appears to be 3654 6h 12m 37, or 7 seconds longer than its accepted length.
Tables LXVI A, LXVII A.-" Equation 6 " and " Equation c." 293. In order to obtain the correct working equations of ( and from their respective mean anomalies it is only necessary in ordinary cases to use Tables LXVI, LXVII, which give the values of "eqn.b" and "eqn.c" roughly in whole numbers. For very close calculation, however, Tables LXVI A and LXVII A are provided, which give the exact
1 It was published during the war.
That is to my, dividing op the velocity per hour (Table XLIX) on that day into minutes and seconds, and not using Table L-which only states the sun's mean velocity.