A ae) 
: 
322 LAPLACE. i 
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. When 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 only to the mind’s eye,—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 originally 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 sufficed 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- 
