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284
THE INDIAN ANTIQUARY
(SEPTEMBER, 1890.
MISCELLANEA THE ROMAKA SIDDHANTAS.
the equinoxes by one-fourth of the value assigned I have just received the May part of the Indian by Hipparkhos, he had introduced a sensible aug. Antiquary, and read with interest Mr. Shankar mentation in the length of the tropical year as Balkrishna Dikshit's paper on the Romaka Bid. determined by his predecessor. The coincid dantas. In doing so, my attention was at once here is remarkable, and at once reminds one of arrested by the elements given at p. 139, and Dr. Bhau Daji's remark (Jour. R. As. Soc. N. S. first by "the length of the solar year, -365 days,
Vol. I. p. 409) that he considered "that the 14 ghatis, 48 palas," these being exactly the Romaka-Siddhanta was composed in accordanon figures given by Ptolemy (Math. Synt. lib. III. with the work of some Roman or Greek author." cap. i.), vix. 3050 14' 48", - for he uses the sexa. A comparison of the other elements given in gesimal division of the day, as well as of the the Table with those of Ptolemy may be interest. circlo; and owing to his reducing the precession of 'ing: thus we have - Moon's synodic revolution ............ ....................... 10409531 - 35250r = 298 31gh 50-09p Ptolemy's value (Math. Syn. lib. IV. cap. ii.) is ............
............... 290 31 50-14" Moon's tropical revolution .......................................... 1040953d 3 81001 270 19g 17.776
Ptolemy's value ............................................................. ................ 27d 19. 1780" Moon's dail, anomalistic motion.......... (38100 -- 322 031) 360°-1040953 - 13° 3' 53-98" Ptolemy's value
................ 13° 3' 53-94" Moon's daily motion from the node ... (38100 + 153 ) * 360° +1040953 == 13° 13' 45-69" Ptolemy's value
............... 13° 13' 45-66 Moon's daily angular elongation
....
35250 x 360°
1040958 = 12° 11' 26.708" Ptolemy's value ........
........ 12° 11' 26.689 The agreement in all these is very close, but failed to explain the double inequality of the the values do not materially differ from those of planets, and pointed out that the only way to do so the other Siddhantas. The use of Ptolemy's value was by a combination of the two hypotheses of the of the length of the tropical year,-much as Utpala excentrio and the epicycle.' Eie could only have says, “what with us is civil time (sávana), is done this in the course of a pretty full discussion of with Pulisaâchârya solar (saura) time" (Kern, their motions. His works, however, may not have Bri.-Samh. int. p. 49), - is the peculiarity. been published; they are not cited by any writer
It is much to be desired that the texts of the except Ptolemy, who may have found the only Punchasiddhantika and Brahma Siddhanta were mannscript of them in the Alexandrian Library. published, with a faithful collation of varice In speaking of the lunar motions, Ptolemy says lectiones, and perhaps a careful analysis, if not Jib. iv. cap. 2), that Hipparkhos has showed. a translation.
from the observations he has recorded on this With reference to Mr. Dikshit's assumption that matter, that the least number of days after which Hipparkhos did not treat of planetary astronomy eclipses recur in the same number of months and (ante, p. 142), I would remark that, beyond the the like other revolutions, is 126007 days and one information on stellar astronomy in his extant hour equinoxial; in this he finds 4267 oomplete commentary on the Phenomena of Aratus and months, 4573 returns of anomaly, 4612 revolutions Eudoxus, we know nothing of the extent and in the zodiac, and 7% degrees nearly yyora) contents of his astronomical works except from wanting of 345 entire sidereul revolutions of the the Syntaxis of Ptolemy. And the latter was 80 sun.' Again he says, 'after having determined indebted to the former, that he is sometimes cited the anomalistic period. Hipparkhos compare as if his data were almost entirely borrowed from intervnls in months between two remote eclipses Hipperkhos. Statements taken at second hand perfectly alike in quantity and duration, and must, therefore, be used with caution. That shewed that in 5458 months there were 5923 Hipparkhos devoted attention to planetary revolutions with reference to the nodes. Ptolemy astronomy also is clear from the recorded fact that then adds that Hipparkhos has given the length he' showed that the hypotheses of his predecessors of the synodical month correctly enough, but that
.
I Hipparkhoa's value is 29d. 31' 508" 91v 20v 11 vr, and Ptoleroy's 29d. 31' 506 8. 201v; the difference is only 0.07 of a second; but Ptolemy's periods of tbe anomalistic
tropical revolutions are 2.588. and 4-378.. respectively greater than those deducible from the above data.
