140 LAPLACE. 



from the vertical, the action of gravity brings it back ; when tbe princi- 

 pal axis of tbe moon recedes from its usual direction, tbe eartb in 

 like manner compels it to return. 



We bave bere, tben, a complete explanation of a singular phenome- 

 non, without tbe necessity of having recourse to the existence of an al- 

 most miraculous equality between two movements of translation and 

 rotation, entirely independent of each other. Mankind will never see 

 but one face of the moon. Observation bad informed us of this fiict; 

 now we know further that this is due to a physical cause which may be 

 calculated, and which is visible only to tbe mind's eye ; that it is attrib- 

 utable to tbe elongation which tbe diameter of the moon experienced 

 when it passed from the liquid to tbe solid state under the attractive 

 influence of tbe earth. 



If there bad existed origiimlly a slight difference between tbe move- 

 ments of rotation and revolution of the moon, tbe attraction of tbe earth 

 would bave reduced tbese movements to a rigorous equality. This at- 

 traction would bave even sufficed to cause the disappearance of a slight 

 want of coincidence in tbe intersections of the equator and orbit of tbe 

 moon with the plane of tbe ecliptic. 



The memoir in whicb Lagrange has so successfully connected tbe laws 

 of libration with the principles of gravitation, is no less remarkable for 

 intrinsic excellence than style of execution. After baving perused tbis 

 production, tbe reader will bave no difficulty in admitting that tbe word 

 "elegance" may be ai)propriatel3' applied to mathematical researches. 



In this analysis we bave merely glanced at tbe astronomical discov- 

 eries of Clairaut, D'Alembert, and Lagrange. We sball be somewhat 

 less concise in noticing tbe labors of Laplace. 



After bavihg enumerated tbe various forces wbicb must result from 

 the mutual action of tbe planets and satellites of our system, even tbe 

 great Newton did not venture to investigate tbe general nature of tbe 

 effects produced by them. In the midst of tbe labyrinth formed by in- 

 creases and diminutions of velocity, variations in the forms of the 

 orbits, changes of distances and inclinations, wbicb tbese forces must 

 evidently produce, tbe most learned geometer would fail to discover a 

 trustworthy guide. Tbis extreme complication gave birtb to a dis- 

 couraging reflection. Forces so numerous, so variable in position, so 

 different in intensity, seemed to be incapable of maintaining a condition 

 of e(iiiilll)rium except by a sort of miracle. Newton even went so far as 

 to suppose that the planetary system did not contain within itself tbe 

 elements of indeflnite stability ; be was of opinion that a powerful band 

 must intervene from time to time to repair the derangements occasioned 

 by tbe mutual action of the various bodies. Euler, although farther 

 advanced than Newton in a knowledge of tbe planetary perturbations, 

 refused also to admit that tbe solar system was constituted so as to 

 endure forever. Never did a greater philosophical question offer itself 

 to the inquiries of mankind. Laplace attacked it with boldness, perse- 



