SKYFFARTH — ON THE THEORY OF THE MOON'S MOTIONS. 509 



16-19. Finally, we come to the four Alexandrian eclipses ob- 

 served by Ptolemy himself, provided the latter really lived at the 

 same time. These ecliptic full moons he referred to a.d. 125, 

 April 5th, 7h., ft 10° E., obscuration li inches; to 133, May 6th, 

 9h. 15m., y 5° E., obscuration 12J inches; to 134, Oct. 20th, 9h. 

 15m., ft 5° W., obscuration 10 inches; to 136, March 5th, I4h., 

 15 9° E., obscuration 5 inches. The times and magnitudes of 

 these four eclipses, however, disagree very much with Hansen's 

 Tables, as will be seen further on. Moi-eover, since Ptolemy 

 observed these eclipses with the naked eye, and without chro- 

 nometers and micrometers, it is evident that his statements 

 concerning the times and magnitudes of said eclipses are not suf- 

 ficiently accurate for establishing a correct theory of the secular 

 accelerations of our satellite, her Nodes and Apsides. According 

 to our Table, p. 429, the eclipses a.d. 125, 133, and 136, were 

 some inches greater than Ptolemy states. The eclipse of A.d. 

 134, ft 5° W., obscuration 10 inches, was smaller, because the ft 

 lay 3° 1 1 ' farther from the centre of the earth's shadow. Besides, 

 none of these eclipses took place, according to our corrections, 

 after sunrise. 



Corollaries. 



The following are, in short, the results of the preceding re- 

 searches : 



1. By means of new historical and astronomical methods, both 

 totally unknown to Petavius and his adherents down to Clinton 

 and Fischer, it came to light that all the dates of ancient historv 

 down to 80 A.D. are to be postdated, and the respective eclipses 

 mentioned by Roman, Greek, and Babylonian authorities have 

 been observed later, respectively, by one or two, and even three 

 years than was formerly believed correct. Some of them greatly 

 differ from those that have been determined by the instrumentality 

 of modern Lunar Tables. 



2. If we compute the hundred and some ancient eclipses, fixed 

 in the premises, by means of our Lunar Tables, the majority of 

 the forrrier remain irreconcilable with the reports of ancient eye- 

 witnesses ; for all total eclipses of the sun mentioned in Greek, 

 Roman, and other histories would have been partial, sometimes 

 even invisible ones. The same is the case with several total 



