252 The Rev. Samuel Haughton on the 



I. — On the Physical Cause of the Equality of the Mean Angular Movement of 

 Revolution and Rotation of the Moon and other Satellites. 



The exact equality which exists between the mean angular motion of revo- 

 lution and rotation of the moon has given rise to many investigations and specu- 

 lations as to its physical cause. The French Academy of Sciences proposed as 

 the subject for a prize essay, in 1764, the theory of the Libration of the 

 Moon. This prize was obtained by Lagrange, who showed, that if there 

 were in the beginning a veiy small difference between the movements of revolu- 

 tion and rotation of the moon, the attraction of the earth would be sufficient to 

 establish a rigorous equality between these motions. Laplace, in his Systeme 

 du Monde, p. 472,* has made some remarks on the physical cause of this re- 

 markable phenomenon, which is not peculiar to the moon, but has been proved to 

 exist in the case of the four satelHtes of Jupiter, and the eighth satellite of Saturn; 

 according to him, there must have been some physical cause which first brought 

 the difference between the angular motions of revolution and rotation of the 

 satellites within the narrow limits, in which the attraction of the planet could 

 establish their perfect equality ; and subsequently the libration caused by the 

 establishment of this exact equality must have been destroyed by the operation 

 of the same cause, at least in the case of the moon, since the observations of 

 Mayer, Bouvard, and Nicollet have proved that no such libration now ex- 

 ists in that satelhte. A physical cause capable of producing both these effects, 

 Laplace believed might be found in the nebular hypothesis proposed by him- 

 self to account for other remarkable phenomena of the planetary system, such 

 as the movement of the planets in the same direction, and nearly in the same 

 plane; the movement of the satellites in the same direction as that of the 

 planets ; the movement of rotation of these different bodies, and of the sun, 

 in the same direction as their movement of revolution, and in planes nearly 

 the same ; and the small eccentricity of the orbits of the planets and satellites. 

 According to this hypothesis, the moon, when existing in a gaseous condition, 



* Vid. note. 



