L1BRATION OF THE MOON. 321 



have so abundantly made use of in endeavouring to ac- 

 count 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 obtaining a glimpse of the opposite hemisphere ? 

 On the other hand, the existence of a perfect, mathe- 

 matical equality between elements having no necessary 

 connection such as the movements of translation and 

 rotation of a given celestial body was not less repug- 

 nant to ah 1 ideas of probability. There were besides two 

 other numerical coincidences quite as extraordinary ; an 

 identity of direction, relative 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 imperfect 

 part of physical astronomy when Lagrange made it de- 

 pend on a circumstance 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 action of the earth compelled it to assume a 

 less regular figure than if no attracting body had been 

 situate 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 lu- 

 nar equator from bulging out in every direction, but the 

 prominence of the equatorial diameter directed towards 



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