168 Lord Rayleigh on the Equilibrium of 



For the curvature in the perpendicular plane we have to 



Fig. 3. 



substitute PQ', measured along the normal, for PQ, whose 

 expression remains as before. Now 



JQ = ^EL^ =cos QPQ'-tan0sinQPQ' 

 r(j sin Q . . 



in which 



npn , CN J.,1 (dr\ 2 \-? , 1 /dry 



Approximately, 



Thus 



PQ' 



cos 6 



-f 



r cosO 

 sin 



a-\-r cos 



3 "i{i-p(»)*f- • « 



It will be found that it is unnecessary to retain (drjdd) 2 , 

 and thus the pressure equation becomes 



a/? 



cos 6 



T ~> 1 rdd*I + a + rcos0 



a sin ^ 1 </?' © 2 a 3 / 

 r 55 ~""2T\ 



1 + 



rcosfl X 2 



(29) 



a + r cos # 



It is proposed to satisfy this equation so far as terms of the 

 order r 2 /a 2 inclusive. 



As a function of 0, r may be taken to be 



r = r + Sr=r + r 1 cos# + r 2 cos 20 + ..., . (30) 



■ where r u r 2 , &c. are constants small relatively to r . It 



