5IO TRANS. ST. LOUIS ACAD. SCIENCE. 



eclipses of the moon witnessed by ancient authors. Moreover, all 

 the eclipses which, according to history, coincided with sunrise, 

 or with fixed hours of the civil day, preceded sunrise and the 

 attested hours according to the usual Lunar Tables. Finally, a 

 number of very small eclipses of the sun and the moon, witnessed 

 by coeval authors, would have been fictitious ones if our Lunar 

 Tables were right. 



3. If we, on the other hand, compute the hundred and some 

 ancient eclipses by applying the approximate corrections specified 

 on pp. 429-30, none of the ancient eclipses drop out of existence ; 

 all total eclipses were total ones, all partial ones agree with the 

 statements of the Tables, and the alleged hours of ancient eclipses 

 prove more or less true. 



4. The secular accelerations of the moon, her Nodes, her Apsi- 

 des, and probably other elements of the moon's motions, are to be 

 determined by means of the classic eclipses, and not by those in 

 Ptolemy's Almagest. It is impossible to bring both classes of 

 eclipses into harmony ; either the former or the latter must be 

 given up. Tertium non datur. 



Objections concerning the New Theory of the Moon's secular accel- 

 erations. 



The proposition that the principal motions of the moon are to 

 be fixed by means of the classic eclipses, arid not by those in the 

 Almagest, is so paradoxical that there is no doubt all kinds of 

 objections will be raised, which deserve to be canvassed in 

 advance. 



1. The nineteen eclipses of the moon, of which the times and 

 magnitudes are so nicely specified in the Almagest, it will be 

 objected, agree with all Lunar Tables constructed since Ptole- 

 my ; consequently, it will be said, the eclipses cited in the 

 Almagest must have been the same which the ancients ob- 

 served, and hence any other theory of the moon's motions 

 differing from the Almagest is nonsense. But, alas and alack ! 

 this logical deduction is a gross conclnsio in circulo, a vicious 

 circle, and I cannot altogether conceive how it came to pass 

 that so many learned astronomers and historians were blinded 

 by the chimera. To state the case clearly : the Babylonian 

 eclipses in the Almagest are the principal basis, the ter?ninns a 



