426 TRANS. ST. LOUIS ACAD. SCIENCE. 



numberless events of Roman, Greek, and Babylonian histories 

 are incontrovertibly fixed. 



Before, however, entering into a closer examination of the true 

 dates of ancient eclipses, it will be necessary to prove the incor- 

 rectness of the present theory of the moon's motions, and to 

 determine approximately the corrections of the principal statements 

 of the usual Lunar Tables. We confine ourselves to the secular 

 accelerations of the moon, her Nodes and Apsides, because the 

 solution of the whole of the problem belongs to professed astrono- 

 mers only. In all the following computations I shall apply 

 Lalande's Tables owing to their handiness, and because they suf- 

 ficiently agree with Damoiseau's and Hansen's Tables so far as 

 the old Babylonian, Greek, and Roman eclipses are concerned. 



Approximate Corrections of the present Theory of the Principal 

 Motions of the Moon. 



It is a well known fact that the total eclipse of the sun observed 

 in Germany a.d. 185 i, happened later than Damoiseau's Tables, 

 inclusive of Airy's correction, had predetermined, and that in that 

 year the longitude of the moon's Node was somewhat shorter. 

 The late Prof. Moebius, Director of the Leipzig Observatory, and 

 myself observed this eclipse, and we found that both the begin- 

 ning and ending of the obscuration happened 57 seconds later, 

 and that the obscuration of the sun amounted in Leipzig to less 

 than 10 inches, as was predicted by means of the said Tables. 

 Prof. D'Arrest, however, who observed the same eclipse in Dan- 

 zig, found that the obscuration of the sun commenced and finished 

 only 56 seconds later than Damoiseau's Tables, corrected by Airy, 

 had predetermined. Now, granting the mean motions of the moon, 

 her Nodes and Apsides, to depend, as all astronomers maintain, 

 on the law of gravitation, it follows that the difference of the com- 

 putation and the observation of the eclipse a.d. 1851 is to be put 

 on account of the secular accelerations of the moon's motions, 

 erroneously derived from the Babylonian eclipses in the Alma- 

 gest. The following compilations will, in the first place, de- 

 monstrate that on occasion of all ancient ecliptic new moons the 

 longitude of the nodes must have been somewhat shorter than 

 Damoiseau's Tables state. The total eclipse of the sun "u.c. 350, 

 Nonis Tunis," i.e. — 400, July 1st, 17I1. 57m. mean Roman time, 



