Solid Sphere in contact with a Liquid Surface. 151 

 (i.) becomes 

 M I -M = 2^ { 2a?d-~ + M _ ^_ | (21W_«P) } (ii.) 



Equation (viii.) of the previous paper *, modified to suit 

 the present circumstances, becomes 



2a 2 1 , 8a 3 



vf =^ = (;/ - di y- 1 L { M-(y-d 1 )*}i-2a* + W , • (m.) 



which, inserting the condition thatp= tan fa when ?/ = d, gives 



(rf-^) 2 = 2« 2 a+cos^)+^^a 2 -(^-^) 2 R- 8 £ 



=2a 2 (l + cos^x) approximately. 

 Whence, more exactly, and remembering that cos fa = ~" , 

 1 J jv 02/0 d\2s/2a'/d\l 8a 3 , 



= 4a 2 approximately. 

 Putting the approximate values 



r 2 = r' 2 = 2Rd = 2R(2a + d 1 ) 

 in the small terms we readily obtain 



*-*-*(l-iB- &- 3 ^ 2B y8a + J • • (T - } 

 = 2a approximately. 



Reverting now to equation (ii.), and substituting therein 

 the value of d given by (v.) we obtain, after a few reductions. 



-g (2a + <*,)•]. 

 The last term is in most cases negligible, giving finally 



* i. c. p. 927. 



