SEYFFARTH ON THE THEORY OF THE MOONS MOTIONS. 429 



Add to these the following eclipses: -360, May 12, 3h. 15m., 

 at Thebes, Boeotia ; -306, June 13th, 22h. 45m., a little east of 

 Syracuse ; _ 201, Oct. iS, 23!!. 30m., near Carthage, and so forth, 

 which were likewise, according to ancient authorities, total, but, 

 according to our Tables, annular ones. 



These examples will be sufficient for understanding that the 

 present theory of the moon's motions principally fails concerning 

 the secular accelerations* of the moon, her Nodes and Apsides. 



Now, remembering, on the one hand, that the present theory 

 of the moon relies on the Babylonian eclipses in Ptolemy's Alma- 

 gest, and that the times and magnitudes of those eclipses, speci- 

 fied in the Almagest, are the results of Ptolemy's computations ; 

 that, on the other hand, the dates of the classic eclipses are 

 mathematically fixed, — the problem remains to bring our Lunar 

 Tables into harmony with the reports of the classic authors. For 

 this purpose we proceed in the following way. 



Since the total eclipse in a.d. 1851 commenced and ended, at 

 Danzig, 56 seconds later than our Tables had predetermined, we 

 presume the real longitude of the moon on that day to have been 

 shorter by 13 seconds, which gives a retardation of 24 seconds. 

 The longitude of the Perigeum may be diminished by 17 seconds, 

 which effected the conjunction to come later by 32 seconds. 

 These corrections would explain that the said eclipse commenced 

 and finished later by 56 seconds than it was expected. Moreover, 

 since the central shadow of the moon then traversed unexpectedly 

 higher degrees of latitude of our globe, we presume the longitude 

 of the moon's Nodes to have been, during the conjunction, shorter 

 by 37 seconds. These quantities increase, of course, proportion- 

 ally to the squares of times ; and hence we obtain the following 



TABLE OF APPROXIMATE CORRECTIONS. 



Epochs. 



[800 

 [700 

 1600 

 [500 

 ■- I4OO 

 [300 

 [2CO 

 [IOO 



Long. Nodes. 



-p- oh. om. 24.S 

 o 1 36 

 o 3 36 

 o 6 24 



