340 LAPLACE. 



The admirable memoir of Lagrange upon the libra- 

 tion of the moon seemed to have exhausted the subject. 

 This, however, was not the case. 



The motion of revolution of our satellite around the 

 earth is subject to perturbations, technically termed secu- 

 lar, which were either unknown to Lagrange or which 

 he neglected. These inequalities eventually place the 

 body, not to speak of entire circumferences, at angular 

 distances of a semi-circle, a circle and a half, &c., from 

 the position which it would otherwise occupy. If the 

 movement of rotation did not participate in such pertur- 

 bations,* the moon in the lapse of ages would present in 

 succession all the parts of its surface to the earth. 



This event will not occur. The hemisphere of the 

 moon which is actually invisible, will remain invisible 

 for ever. Laplace, in fact, has shown that the attraction 

 of the earth introduces into the rotatory motion of the 

 lunar spheroid the secular inequalities which exist in the 

 movement of revolution. 



Researches of this nature exhibit in full relief the 

 power of mathematical analysis. It would have been 

 very difficult to have discovered by synthesis truths so 

 profoundly enveloped in the complex action of a multi- 

 tude of forces. 



We should be inexcusable if we omitted to notice the 

 high importance of the labours of Laplace on the im- 

 provement of the lunar tables. The immediate object of 

 this improvement was, in effect, the promotion of mari- 

 time intercourse between distant countries, and, what 

 was indeed far superior to all considerations of mercan- 

 tile interest, the preservation of the lives of mariners. 



Thanks to a sagacity without parallel, to a perse- 

 verance which knew no limits, to an ardour always 





