440 Mr. J. Prescott on the Precise Effect of Radial 



we may put/ y (7 , 1 ) = Kr 1 . Thus the term which has to be 

 added to the potential of the non-radial force is 



W=K n 26„Q n+1 . 



We have now to find particular integrals of the equations 

 of equilibrium due to the term W, and to determine its con- 

 tribution to the boundary conditions. 



The equations of equilibrium are three such equations as 



?>a aw 



(X + ^ + ^u + p°^=0, .... (4) 



the symbols used having the same meaning as in Love's 

 book. 



We shall obtain particular integrals by assuming that 



o4> d<t> ~d4> 



ox dy o~ 



Then equation (4) gives 



o+w£+^«o, ••• (5) 



whence 



(X + 2 /i )v fi </)=-/)W (6) 



Now if W»+i denotes a solid harmonic of order (n + 1) we 

 know that 



vVW»+i)=K^+JP + 3)^ 2 W M+1 . . . (7) 



By putting p = 3 in equation (7) we see that the solution 

 of (6) is 



This gives 



A + 2/x o# o(w-r-o) 



and two similar expressions for v and iv. 

 Also 



A = v 2 <£ 



— £Sp&»» • • • < 10 > 



