Evolution of the Earth-Moon System. 337 



<V7> - 5" (,) 



where 7/ = distance between centers of earth and moon. 

 t = time -1 epoch. 



_ p(n-.Q) (2) 



^-i+p«(n-ri)« (2) 



w = angular velocity of earth's rotation. 



il = angular velocity of moon's orbital revolution. 



p = quantity varying inversely as the viscosity of the planet. 

 The extreme interest of equation (1) consists in the appearance 

 of the inverse sixth power of the distance. 



As the function W varies very slowly, we find by integration, 

 for any portion of time during which W may be regarded as 



(3) 



mind turned to a 

 retardation of the 

 3 exerted upon the 







1-ArV + B, 



a most 



uncxp 



ected and remarkable result. 



Upor 



i ro:idi 



ng Mr. Darwin's papers, my 



problen 



1 with 



which I was familiar, viz: the 



earth's i 





i produced bv the lunisolar tid 



ocean supposed collected in an equatorial cj 





.•ing n 



o declination, and 1 readily to 



express 



the e 



volution of the earth-moon sy 





ypothe 





This 



equation is the following : 







a W7 ) « &* 



where 









• : 



v (n-n) 





f- 



- coefficient of friction suppos 





V 





This 



leads." 



as in Mr. Darwin's hypothesis . 



ar, therefore, tha 



t the remar 



kabh 



; expression (1) 







" \V" 



3ial hypothesis 



h. but cai 



i be c 



I educed eq 





well from the 



on^fa't 



of an 



juido, 



absolutely 



rigid 



earth retarded 



