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128
EPIGRAPHIA INDICA.
VOL. XVII.
Now this value stands for mean sunrise of Sunday, 22 March, A.D. 599, i.e. for the sunrise succeeding the moment of occurrence of mean M5sha-sankranti in K.Y. 3700; but in all my Tables tire calculation is for mean sunrise on the actual day of that occurrence, and we have therefore to deduct one day's value of a (riz. 338-631985412–Table LIVA above) from the above estimate. This done, we have, for mean sunrise on Saturday, a=6028 192932094.
(ii) The value of b (moon's mean anom.) at the same moment. At the epoch of the Kaliyuga the moon's mean anom. was, as stated above ( 313 x), in 1,000ths of a circle, 151-399691358. Using the century figures of b in the heading of Table LIVA, and multiplying for 32 common and 5 defective centuries, it is found that, excluding whole revolutions of 1,000 each, the result is 604 144838202. Adding the value of b at K.Y. O, as above, we have at beginning of K.Y. 3700, for the value of b, 755-544529560. But this (see above, 1) was its value at mean sunrise on Sunday, 22 March, A.D. 599. Deducting one day's value of b (36 291649786) the fixture for mean sunrise on Saturday, 21 March, amounts to 719-252879774.
(iii) The value of c (the sun's mean anom.) at the same moment. The correct increase of c by the Brahma-Siddhānta in centuries of 36525 and 36526 days has been given abovy in the latter part of $ 316. Multiplying those quantities for 32 common and 5 defective centuries, and discarding whole revolutions of 1,000 each, we arrive at the increase, after 37 centuries, of 1.728389014. To this has to be added the value of at K.Y. O (abore, 313, 1x), ris. 284.0. The value of c, therefore, at mean sunrise of Sunday, 22 March, A.D. 599, was 285.728589044. Deducting the c for one day (2737787543) we have finally, for mean sunrise on Saturday. 21 March, c=282.990601501.
The entries, therefore, for the aforesaid Saturday of K.Y. 3700 in Table LXXXVI below are
a = 6028-1929 b = 719.2529
c= 282-9906. The rest of that Table follows by addition of the proper century values.
Duration of true solar months. 318. It hrs been mentioned above ($ 313,xi) that, while the length of the mean solar month must be the same both by the Brahma-Siddhinta and the Siddhinta-Siromani, the lengths of the true solar months according to the two anthorities differ because of their different estimate of the shift of the sun's apsis. Thus in K.Y. 4000, the middle year of my general Table LXXXII below, the sun's perigee-point according to the Siddhanta-Siromami was at long. 258° 55' 12". while by the Brahma-Siddhanta it was at long. 257' 55' 12". Hence the velocity of the true sun (he is alwnys considered as a planet) at the several true solar sankrantis, when the true sun's centre enters the several signs, is not the enme by the two authorities quoted. And this has necessitated the preparation of a new Table (LXXXIIIA below), giving the lengths of the true solar months and increase of a, b, c therein individually and collectively according to the Brahma-Siddhinta.
There being in K.Y. 4000 a difference of only +' 49" between the positions of the sun's perigee, as estimated by the Brahma-Siddhānta and by the First Arya-Siddhanta, the former placing it at 257° 55' 12' and the latter at 258°, it was considered sufficiently safe to use Table XLIX (above, Vol. XIV) for the trae sun's velocity at different points of his orbit in hours and minutes, and Table L-A for seconds. His true long. at each sankranti was computed from his known mern longitude + the equation of the centre, which was calculated in each case.
1 Professor Jacobi's figure for this is 758:1, in my notation, against my 756-5. * This grocs with Professor Jacobi's Axtare, whieh, menadred from perige and in my notation, is 2857
