emy, it was natural that he referred the Babylonian eclipses, linked only 

 to certain years of certain kings, to wrong years, and that he discovered 

 invisible eclipses and committed errors of one hour and fifteen minutes. 

 Thus it is apparent how it came to pass that all Lunar Tables from Al- 

 phonsus down to Hansen were useless a few years after their construction, 

 and that none of them corresponded with the classic eclipses. 



My assertion that Ptolemy erroneously referred, e.g., the Babylonian 

 eclipse of — 717, Jan. i6th, 4h., to — 720, Mar. 19th, 8h., is confirmed bv 

 the following fact. As soon as I learned that Hansen's new Lunar Tables 

 were to agree with the eclipses in the Almagest, I communicated to him 

 my researches concerning the true epochs of the eclipses in the Almagest. 

 Some time after I myself went over to Gotha for the purpose of discussing 

 with him orally the fallacy of the Almagest, but Hansen insisted upon it 

 that his new Lunar Tables were the result often years of toil. As soon as 

 Hansen's Tables were published I publich' prophesied, without being a 

 prophet, that the work, after twenty or thirty years, would disappoint the 

 astronomers as much as Damoiseau's Tables (inclusive of Airy's correc- 

 tions) did in 1S51. And lo ! two years ago it came to light that the longi- 

 tude of the moon was a good deal shorter than Hansen had presumed, 

 and, consequently, that Ptolemy had antedated the Babylonian eclipses. 

 I am sorry, indeed, that Prof. Newcomb relies on the Almagest. 



Furthermore, the same lays great stress upon Zech's computations of 

 some classic eclipses, of which the origin is as follows. Having since 1846 

 (Chronologia Sacra) and much more correctly in 1848 (Archiv. fiir Philol. 

 p. 586) fixed the real dates of the classic eclipses, I convinced the Director, 

 of the Leipzig Observatory, the late Prof. Moebius, by my computations, 

 that in all instances the longitudes of the moon and her nodes must have 

 been shorter than the usual Lunar Tables state. My harmonious correc- 

 tions of the latter surprised Prof. Moebius so much that he resolved to 

 decide the question by the help of the Tablonowskian Society at Leipzig, 

 and by two prize theses. The first of these, published in 1851, concerned 

 the eclipses in the Almagest, which were computed by the instrumentality 

 of Damoiseau's Tables, based on the Almagest. The result, of course, was 

 that Zech's computations agreed with the Almagest in consequence of a' 

 demons ir a tio ht circulo. In the same year, the same Society elicited the 

 second prize thesis, viz., to decide whether some classic eclipses corre- 

 spond with Airy's corrections of Damoiseau's Tables or not. Having de- 

 monstrated myself, three years earlier, that Petavius had all events and 

 all eclipses of the Greeks and Romans referred to wrong years, I expected 

 indeed that the aforesaid Society would select a number of eclipses, really 

 observed by the Greeks and Romans, to be taken into account. But the 

 late Prof. D'Arrest, then Adjunct at the Leipzig Observatory, being a very 

 young man, made only a small number of classic eclipses, viz., the same 

 which Petavius had computed by means of La Hire's Tables, relying on 

 the Almagest, the object of the prize thesis. Since, then, both La Hire's 



