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(b, iii.) Or, lastly, we may, saving much trouble, work entirely by decimals as given in Table XX.A. Here the sum to be done is— 0.9772̇59̇ × 8.67. This = 8.492838, and =, as before, 8 d. 11 h. 50 m. 15 s.

[It must be remembered that, whereas in years later than the base-year of the Siddhānta the days intervening between the tropical and sidereal saṁkrāntis belong to the sidereal month preceding the sidereal saṁkrānti, in years earlier than the base-year those days belong Note to Examples 9, 10, 18a, 18b. to the month bearing the same name as, or to a month later than, the sidereal saṁkrānti. The base-year, for instance, of the Ārya Siddhānta for tropical calculations is Śaka 445 current, A.D. 522–23, when by that authority the sidereal and tropical signs coincided. After that year the tropical saṁkrāntis preceded the sidereal, or were earlier in time than they, and the intervening period belonged to the sidereal months preceding the given one. On the other hand, in years earlier than Śaka 445 current the tropical saṁkrāntis were later in time than the sidereal one, and the intervening days fell in the same, or, in case of much earlier years, a later sidereal month. It is not possible to simplify by tabulation the process of work for tropical saṁkrāntis, for we cannot, as in the case of sidereal saṁkrāntis, ascertain and tabulate the exact lengths of the months. These vary in every year in consequence of the change of position of the equinoctial point. Calculation for the moment of occurrence of every tropical saṁkrānti must therefore be specially made according to the rules given.]

Example 19.—To find the European civil day corresponding to a given Hindu solar day by either Siddhānta.

Rule. Find, from Table I. or by Examples 1, 3, or 4, the moment of true sidereal Mēsha samkrānti according to the authority used. Add to the time so found the collective duration of intervening solar months, by the same authority, to the end of the month preceding the given month (Table III. of the Indian Calendar, or Tables XVIII.A or XVIII.B). This gives the moment of saṁkrānti at the beginning of the given month. Decide by the rules given under "Days of a civil month," § 43, above, and from the moment of the saṁkrānti last found, which European day was the first civil day of the solar month. Add the number of intervening days, remembering that the Hindū civil day begins at sunrise.

Wanted the European day corresponding to Tuesday, the 24th day of Karka in K.Y. 4372 expired.

This is an actual date of an inscription. The year A.D. 1271–72. Work by the Ārya Siddhānta first—

We examine the rules for the first civil day of Karka:—

Add 23 days in each case, the given day being the 24th, and we have for result (Rules i., iii., iv.) Tuesday, July 21st, or (Rule ii.) Monday, July 20th. The inscription itself quotes Tuesday as the