LAPLACE. 139 



prediction of the illustrious geometer was verified, in regard both to time 

 and space. Astronomy had just achieved a great and important' triumph, 

 and, as usual, had destroyed at one blow a disgraceful and inveterate pre- 

 judice. As soon as it was established that the returns of comets might 

 be calculated beforehand, those bodies lost forever their ancient prestige. 

 The most timid minds troubled themselves quite as little about them as 

 about eclipses of the sun and moon, which are equally subject to calcu- 

 lation. In fine, the labors of Clairaut had produced a deeper impres- 

 sion on the public mind than the learned, ingenious, and acute reasoning 

 of Bayle. The heavens offer to reflecting minds nothing more curious 

 or more strange than the equality which subsists between the movements 

 of rotation and revolution of our satellite. By reason of this perfect 

 equality the moon always presents the same side to the earth. The hem- 

 isphere which we see in the present day is precisely that which our an- 

 cestors saw in the most remote ages ; it is exactly the hemisphere which 

 future generations will perceive. 



The doctrine of final causes which certain philosoiihers have so abun- 

 dantly made use of in endeavoring to account for a great number of 

 natural phenomena was in this particular case totally inapplicable. In 

 fact, how could it be pretended that mankind could have any interest in 

 perceiving incessantly the same hemisphere of the moon, in never ob- 

 taining a glimpse of the opposite hemisphere ? On the other hand, the 

 existence of a perfect, mathematical equality between elements having 

 no necessary connection — such as the movements of translation and ro- 

 tation of a given celestial body — was not less repugnant to all ideas of 

 probability. There were, besides, two other numerical coincidences quite 

 as extraordinary : an identity of direction, relaMve to the stars, of the 

 equator and orbit of the moon ; exactly the same precessional movements 

 of these two planes. This group of singular phenomena, discovered by 

 J. D. Cassini, constituted the mathematical code of what is called the 

 libration of the moon. The libration of the moon formed a very imper- 

 fect part of physical astronomy when Lagrange made it depend on a cir- 

 cumstance connected with the figure of our satellite which was not 

 observable from the earth, and thereby connected it completely with the 

 principles of universal gravitation. 



At the time when the moon was converted into a solid body, the ac- 

 tion of the earth compelled it to assume a less regular figure than if no 

 attracting body had been situated in its vicinity. The action of our 

 globe rendered elliptical an equator which otherwise would have been 

 circular. This disturbing action did not prevent the lunar equator from 

 bulging out in every direction, but the prominence of the equatorial 

 diameter directed toward 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 ex- 

 amining it transversely, to be elongated toward the earth, to be a sort of 

 pendulum without a point of suspension. When a pendulum deviates 



