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believe in the transmigration of souls. (13) On the doctrines of the Suanis. (14) On the doctrines of the Maleki and Shâfa'i sects. (15) On the sect founded by Ibn Kalâb. (16) On Sufis. (17) On the doctrines of the Qushairi. (18) Tenets of the Sunnis with regard to the anbiyd. (19) Doctrines of the Shi'ahs. (20) On the discrimination of the true from the spurious. (21) On the Imâmiyeh. (22) On the story of the Bâgh-iFadek. (23) On certain Hadis. (24) On the wrong doings of the Beni Umayyeh. (25) Anecdotes regarding the followers of justice and predestination. (26) On some of the tenets of the Imâmiyeh.
S. J. A. C.
THE INDIAN ANTIQUARY.
A TABLE FOR THE ABDAPA, TITHI-SUDDHI, AND TITHI-KENDRA.
In using Prof. K. L. Chhatre's Tables for calculating the week-days, ending-times, and English dates, of Hindu tithis,' some inconvenience is entailed by the number of the quantities that have to be taken, at starting, from his Table I. For instance, in calculating a date with the basis of Saka-Samvat 1134 expired, we have to take out, under the three columns of the Abdapa, the Tithi-buddhi, and the Tithi-kendra, the quantities for the years 0, 1000, 100, 30, and 4,-or altogether fifteen sets of figures, and also to work out from Table II., by proportion, the correction in the Tithi-buddhi and the Tithikendra, before the operation is started by addition, in their respective columns, of all the quantities thus obtained.
The object of the accompanying Table for the Abdapa, Tithi-suddhi, and Tithi-kendra, is to simplify this part of the work. The quantities given in it are all complete, including the kahépaka or additive quantities for Saka-Samvat O expired. And, in working, for instance, with the expired year quoted above, all that is necessary is to take out, from the body of the Table, the quantities for the year 1130, with the corrections for the same year (21-1 p., and 1 gh. 19 p.) as being a sufficiently close approximation, and to add the difference for 4 years from the subsidiary Table at the bottom of the page.
One revolution of the moon's kendra is completed in 27 tithis, 59 ghatts, and 33-36 palas. But, to save trouble on the part of the calculator, it is taken to contain 28 tithis, in adding the quanti. ties of the Tithi-kéndra for the several component parts of a given Saka year; no sensible error being
[SEPTEMBER, 1888.
introduced thereby in the ultimate results. In preparing the Tables, however, one revolution of the kendra is taken to contain, not 28, but the correct number, viz. 27 ti. 59 gh. 33 36 p. Thus, for example, the variation in the Tithi-kéndra for 4 years is given (7 ti. 9 gh. 421 p. x 427 ti. 59 gh. 333 p.) 0 ti. 39 gh. 15 p. (see Kâlasâdhana Table I. p. 10, last column) and, in preparing the accompanying Table, I have thought it desirable to follow the correct way. Thus, the Tithi-kendra for Suka-Samvat 1150 expired is 2 ti. 57 gh. 16 p. in my Table; while, by adding the quan. tities for the Saka years 0, 1000, 100 and 50, and taking the remainder over the multiple of 28, it would have been 2 ti. 55 gh. 56 p. Accordingly, the figures of the Tithi-kéndra in my Table will differ a little from those that would be obtained from Prof. Chhatre's Tables; but the change is, it must have been seen, on the correct side. And the ultimate results worked out from my Table will sometimes be more correct than those obtained from Prof. Chhatre's Tables by about seven palas.
There is another point of difference. The correction in the Tithi-buddhi and Tithi-kendra given in Prof. Chhatre's Kalasadhana Table II. p. 12, is too vague, being for the interval of each thousand years. This Table II. is based on the correction in the moon's mean longitude and mean anomaly given in Table IV. p. 89, in which that correction is given for the interval of each hundred years. It is evident, therefore, that the correction in the Tithi-buddhi and Tithi-kendra, calculated from the figures in Table IV. p. 89, will be more accurate. I calculated it accordingly, and have given it in the accompanying Table. This correction becomes nil in Saka-Samvat 1622 expired; and in other years from Saka-Samvat 1500 to 1700 expired, it is less than one pala with respect to the Tithi-buddhi, and less than five palas in the Tithi-kendra; the latter causing a difference of half a pala at the utmost in the ultimate results. The correction for these years, therefore, is neglected in the accompanying Table.
in Prof. K. L. Chhatre's Table I., with the modiThe present Table, thus prepared from the details fications explained above, extends from SakaSamvat 0 to 1690, both expired. Table VII. in his book gives the required quantities for every year from Saka-Samvat 1700 to 1800, both expired. And the two Tables together will render it quick work to calculate any date in the first eighteen centuries of the Saka era.
1 Grahasadhanachih Koshtakém, pp. 10 to 30, KAlasadhana Tables I. to XI.
SH. B. DIKSHIT.
See ante, Vol. XVI. p. 115, col. 2 and p. 116, col. 2. See ante, Vol. XVI. p. 116, col. 2.
