LIBRATION OF THE MOON. 821 
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 all 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 
14* 
