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No. 18.]
TRUE LONGITUDE OF THE SUN IN HINDU ASTRONOMY.
260. The forward shift of the sun's apsis, while leaving the sun's mean longitude unaffected, causes a slight change every year in the sun's mean anomaly (his mean distance from the perigee-point), this becoming each year proportionally less as the perigee-point moves forward. And since the shift induces a corresponding, though very minute, change in the velocity of the sun (considered as a planet) at all times of the year, the sun's equation and true longitude are. each year a little different from what they were in the year previous.
The change in mean anomaly is stated in Table LI below.
243
The change caused by the shift of the apsis in the equation and true longitude of the sun at true Mesha-samkranti amounts to only 2" (actually 1"-9675) in the 300 years on either side of K. Y. 4500, which is the base-year of my main Table XLVIIIC,-the annual change being at the rate of about 0"-0066 per annum.1
The corresponding time-difference, or change in the sodhya-value, is about 0.16 per annum (actually 015975) by which amount the sodhya-value at true Mesha-samkranti increases every year. In 300 years this amounts to 47925 or about 48. (For particulars see Table LII.)
261. The length of the solar year from mean Mesha-samkranti to mean Mesha-samkranti according to this Siddhanta being 365d 6h 12m 9", it differs from that of the Arya-Siddhanta year of 365d 6h 12m 30s by 21 every year since K. Y. 0. The difference-Table given in Indian Chronography, p. 61, is here reprinted for ready reference (Table LIII). The difference is cumulative from K. Y. 0. In A.D. 1120, which is the very earliest date possible for the Siddhanta-Siromani to have come into use (it was probably 30 years later), the moment of mean Mesha-samkrānti by that authority was already 14 0 37m 21 earlier than the same according to the Arya-Siddhanta, and the difference between them increased with every subsequent year. Consequently both mean and true Mesha-samkranti by the Siddhanta-Siromani always fell respectively on the day previous to their occurrence by Arya-Siddhanta reckoning, the time of which is given in the "Indian Calendar," Table I, cols. 13 to 17.
When therefore we are examining a date and have worked in the ordinary way for settlement of details by the Arya-Siddhanta, using the Indian Calendar process for finding the values a, b, c, s and n, if we desire to find roughly the value of s according to the SiddhantaSiromani by use of the new Table XLVIIIC below for determination of the nakshatra by that authority, we must take the Table value of's (cols. 8-9) not for the Day-number given in the Table, but for the day next following. E.g., if we suppose that preliminary examination of a date by the Indian Calendar process proves the record-date to be Day 120 (as measured from 1st Jan.) and that Table I, cols. 13-17, shews that by the Arya-Siddhanta true Mesha-samkranti took place on Day 85, then in order to ascertain the equation and longitude of the sun by the Siddhanta-Siromani we must take the details given in Table XVIIIC not as given for (12085) Day 35, but for Day 36, that number of days having elapsed since true Mesha-sam kranti by the latter authority. For accuracy the difference between the times of true Meshasamkranti by the two authorities must be allowed for.
262. Since the Table-entries are for each twenty-four hour period from true Mesha-samkranti in any year it is necessary to know the number of hours and minntes since sunrise of the occurrence of true Mesha-samkranti in the year in question, and deduct the sun's movement during those hours and minutes, in order to arrive at his trae longitude at mean sunrise of the given day. For this purpose we may use Tables XLIX and L (in Vol. XIV above). The
1 Minus for years earlier, plus for years later, than the base-year.
2 These stand exact for the Arya-Siddhanta, but are close enough for general use. For absolute exactness see my last article (above, Vol. XIV, § 248).
2 K 2
