540 The Rev. S. Haughton on Physical Geology. [Dec. 20, 



Suppose 



then 



or 



^=A' = ^, 



log e (A') = ny, 



log e A' 



y 



(12) 



This equation determines n, the number of wabbles necessary to reduce 

 p to p n , where 



to be a given quantity. 

 Let us now proceed to calculate the coefficient of friction from the 

 retardation of the earth's angular velocity produced by the friction of the 

 Tidal Eesidual Current. 



This retardation amounts to one second in the length of the day in 

 100,000 years* 



The accompanying figure shows Newton's construction for the dis- 

 turbing force of the moon upon the ocean. The moon lies in the direc- 



tion AO, and the distance of the moon from the earth (=60 AB) repre- 

 sents the attraction of the earth at the distance of the moon. The dis- 

 turbing force is BC, if AC = BAD. Let AB=r, then the tangential 

 component of the disturbing force is 



BC sin 0=3r sin^> cos tf>, 



Tangential force = sin 2(j>. ..... . (13) 



The relative velocity of the tide is thus found, 



dv— — ^ sin 2(f) dt, 



* Delaunay, ' Sur le>alentissement du mouyement de rotation de la Terre ' (Paris, 

 1866). 



