SEVFFARTH ON THE THEORY OF THE MOON S MOTIONS. 4O3 



was obviously a gross mistake. For all events of Greek and Roman history 

 are at present, by infallible historical and mathematical certainties, so 

 accurately fixed that none of them can be referred to a date later or earlier 

 by one, or ten, or twenty years These evidences, finally, are confirmed 

 by an authority which every astronomer will respect. In 1857, Prof. Airy 

 was still fully convinced of the correctness of Hansen's theory of the lunar 

 motions; for in that year he determined, by means of the said Tables, the 

 dates of three total eclipses which he (but erroneously) referred to 309, 

 and 555, and 5S3 b.c. (See Transactions of the R. Astron. Soc. 1857, vol. 

 xviii. p. 92, and Month. Not. vol. xvii. p. 233.) Yet, a few months ago, 

 our newspapers report as follows : "In his last report Prof, ^iry devotes a 

 few words to the great work he has been engaged in, namely, the prepara- 

 tion for the formation of Lunar Tables, according to a new treatment of 

 the theory by which he hopes to be able to give greater accuracy to the 

 final results, by means of operations which are entirely numerical through- 

 out the work. Considerable progress has been made in these numerical 

 developments, and he expects, at least, to put his theory in such a state 

 that there will be no danger of its entire loss in the event of his death." — 

 This is, indeed, a gratifying confirmation of my iterated researches con- 

 cerning the secular accelerations of the moon's motions. First in 1846 I 

 essayed to harmonize the classic eclipses with the usual theory of the moon 

 based on the Almagest. (See the author's Chronologia Sacra, p. 2S1 to 

 358.) The same was done, but much more carefully, in Seebode, Jahn, 

 and Klotz's " Archiv fiir Philologie," 1848, p. 586; in Jahn's ''Astrono- 

 mische Unterhaltungen," 1853, p. 172; in''Gdttinger Gelehrte Anzeigen," 

 1855, No. 125; in my " Berichtigungen der alten Geschichte und Zeit- 

 rechnung," 1855, p. 92; in "Transactions of the St. Louis Academy of 

 Science," i860, p. 385. Twenty years ago I predicted, without being a 

 prophet, that Hansen's Lunar Tables would, after forty or fifty years, 

 prove as incorrect as Damoiseau's Tables did in 1851, on occasion of the 

 total eclipse of the sun in Germany; and from the publication of Han- 

 sen's Tables to 1875, less than twenty years having elapsed, the incor- 

 rectness of those Tables comes to light. 



These arguments will suffice for understanding that the theory of the 

 secular accelerations of the moon, her Nodes and Apsides, mainly depends 

 upon the classic eclipses, and not upon Ptolemy's computations in the Al- 

 magest; for the ancient eclipses which, according to reliable eye-witnesses, 

 coincided with sunrise, or sunset, or certain hours of the day, determine 

 the real longitude of the moon on the respective hours. To this class of 

 ancient eclipses refer, e.g., the solar eclipse in — 478, Feb. 27, i5h. 30m., 

 perceived, during sunrise, at Smyrna, and that in — 752, May 25, i6h., 

 which was seen in Rome 2 hours and about 30 minutes after sunrise. 

 Further, the eclipses which were total in certain localities determine the 

 real longitudes of the moon's Nodes on the respective days. From the 

 very small eclipses witnessed by ancient authorities we learn how far the 

 longitude of the moon's Nodes must be diminished in order to obtain a 



