o22 LAPLA* 1. 



the earth became four times greater than that of the 

 diameter which we see perpendicularly. 



The moon would appear then, to an observer situate 

 in space and examining it transversely, to be elongated 

 towards the earth, to be a sort of pendulum without a 

 point of suspension. Whrn a pendulum deviates from 

 the vertical, the action of gravity brings it back ; when 

 the principal axis of the moon recedes from its usual 

 direction, the earth in like manner compels it to return. 



We have here, then, a complete explanation of a singu- 

 lar phenomenon, without the necessity of having recourse 

 to the existence of an almost miraculous equality be- 

 tween two movements of translation and rotation, entirely 

 independent of each other. Mankind will never see but 

 one face of the moon. Observation had informed us of 

 this fact ; now we know further that this is due to a 

 physical cause which may be calculated, and which is 

 visible onlv to the mind's eve, that it is attributable to 



* . 



the elongation which the diameter of the moon experi- 

 enced when it passed from the liquid to the solid state 

 under the attractive influence of the earth. 



If there had existed 01 iu'inallv a slight difference be- 



/ * - 



tween the movements of rotation and revolution of the 

 moon, the attraction of the earth would have reduced 

 these movements to a rigorous equality. This attraction 

 would have even sutliced to cause the disappearance of 

 a slight want of coincidence in the intersections of the 

 equator and orbit of the moon with the plane of the 

 ecliptic. 



The memoir in which Lagrange has so successfully 

 connected the laws of libration with the principles of 

 gravitation, is no less remarkable for intrinsic excellence 

 than style of execution. After having perused this pro- 



