as the Almagest says, by Babylonian astronomers; and they contradict, 

 apparently, Greek and Roman history. The classic eclipses, on the con- 

 trary, are chronologically fixed by mathematical certainties, and the classic 

 authors were, in nearly all instances, eye-witnesses; they were able and 

 willing to tell the truth ; they had nothing to gain or to lose by imposing 

 on their contemporary or future readers. 



The principal difterences of the theory of the moon, derived from the 

 Almagest, and that based on the classic eclipses, will be seen in the fol- 

 lowing table : 



]) Long. m. Anom. m. ^ 



I. i« i8° 42/ 21" 10^20° 47' 28" 9=11° 30' 20" 

 II. I 16 3 54 10 17 4 13 9 4 O 46 



No. I. is, in the first place, the mean longitude of the moon, apart from 

 the secular equation, for the epoch — 800, Jan. 0.0., determined by Lalande 

 and by his predecessors and followers, trifling deviations not being noted. 

 The following figures represent the mean longitude of the apsides, and, 

 after them, that of the moon's node for the same epoch, according to 

 Lalande, etc. It is true, by applying these principal elements of the 

 theory of the moon's motions, the eclipses in the Almagest come out iah'- 

 ter qualiter; but the whole Roman, Greek, and Egyptian histories concur 

 in proving that Ptolemy referred all his older eclipses to wrong years, and, 

 moreover, it is absolutely impossible to harmonize this theory with the 

 classic eclipses, of which the times and magnitudes are reported. (See 

 Trans, iii. 525, 1. 9.) In order to represent Ptolemy's eclipse in — 720, 

 March 19th, 6h. 49m., the longitude of the moon was presumed to have 

 been 11^ 19° 52' ; but in this case the eclipse during the founding of Rome, 

 as well as that near Smyrna in — 478, Feb. 17, i5h., and the like, would 

 have been illusions. For the purpose of obtaining a total eclipse in — 380. 

 Dec. 12, 9h., it was necessary to place the IS 2° 31' east of the sun, but in 

 this case it turned out that none of the "total" Greek and Roman eclipses 

 were total. The following two facts will suffice to convince every unpre- 

 judiced man. Aristophanes, a reliable eye-witness, testified in the face of 

 all the Athenians, being present whilst his "Nubes" were enacted, that in 

 the preceding spring of the year in which Cleon was lawfully elected stra- 

 tegus, both a total eclipse of the moon and a partial one of the sun took 

 place within fifteen days. The scholiast specifies even the day of the latter, 

 namely, the i6th day of Anthesterion, i.e. Jan. iSth, — 420 (1. 14, p. 475). 

 Such an eclipse only once coinciding with Jan. i8th during a period of 19 

 years, the date of this eclipse is fixed with mathematical certainty. But, 

 alas, on the said day, confii-med by the total eclipse of the moon during the 

 spring of the same year, viz. that is, — 420, Feb. 2d, no eclipse of the sun 

 was possible on our globe. For on the said day the IS lay 17° east of the 

 sun, and in this case, as every astronomer knows, the eclipse was visible 

 only beyond the north pole; and this is ratified by Pingre's computations 

 of all eclipses visible on our globe. In order to obtain, on the aforesaid 



