﻿Physical Constitution of the Moon. 33 



the nearest centre will be behind the other. This apparent oscil- 

 lation of the two centres is indeed an immediate effect of the 

 moon's libration in longitude. 



Now the inequalities in the moon's motion, computed from 

 the theory of gravitation, are those of a supposed centre of gra- 

 vity. But the inequalities given by observation are those of the 

 centre of figure. Hence, in the case supposed, the inequalities 

 of observation will be greater than those of theory. Also their 

 ratio will be inversely as that of the distances of the centres 

 which they represent. 



Professor Hansen, in comparing his theory with observations, 

 found that the theoretical inequalities would agree better with 

 observation when multiplied by the constant factor 1*0001544. 

 Supposing that this result could be accounted for on the hypo- 

 thesis of a separation of the centres of gravity and figure, he 

 thence inferred that the hypothesis was true. But the result 

 cannot be entirely accounted for in this way, because the largest 

 inequality of theory (evection) has a factor (excentricity) which 

 can only be determined from observation ; and therefore even 

 the theoretical evection is that of the centre of figure, and not of 

 the centre of gravity. It must not be forgotten that the excen- 

 tricity, which is not given by theory, is subject to be multiplied 

 by the same factor that multiplies the other inequalities. To be 

 more explicit, — 



Let e be the true excentricity of the orbit described by the 

 moon's centre of gravity. Then the true evection in the same 

 orbit will be 



ex A, 



A being a factor depending principally on the mean motions of 

 the sun and moon. And on Hansen's hypothesis, the apparent 

 evection, or that of the centre of figure, will be 



ex Ax 1-0001544. 



On the same hypothesis, the excentricity derived from observa- 

 tion, being half the coefficient of the principal term of the equa- 

 tion of the centre, will be 



ex 1-0001544, 



and the theoretical evection computed with this excentricity 

 will be 



ex 1-0001544 x A, 



which is the same with that derived from observation. Hence 



The theoretical evection will agree with that of observation 3 not- 

 withstanding a separation of the centres of gravity and figure of the 

 moon. 



Phil Mag. S. 4. Vol. 37. No. 246. Jan. 1869. D 



