Revolving Liquid under Capillary Force. 169 



will appear that to our order of approximation (Sr/r ) 2 may 

 be neglected and that it is unnecessary to include the r's 

 beyond r 3 inclusive. We have 



a a j Br ( Sr\ 2 \ 

 r-^U-^ + W *' 



. a + r cos 2a 4a I 4er 4a 4a J 



-co S 2<?{£ + £} + cob3* /£_£*} 

 I 2a T 2a J I 4a 2 4a 2a J • 



\ + a / a 2 + 2a 2+ 2a 2 



+ „.*{£• +&+$£ + «£) 



la a 2a 2 2a 2 J 



a d 2 r a j 1 



- ~2 Jqi = ~2 { r i cos 6 + 4r a cos 29 + 9r 3 cos 3(9 j , 



a sin fl 1 oV _ rj r 9 J I*! r 2 3r 3 1 



a + r cos r </0 ~ 2r Q + 2i +cos \ ia ~ r + 4a~ J 



+ cos2^{A_^} + cos3 W^_nl 

 L2r 2?' J Uo 4a J 



Thus altogether for the coefficient of cos 6 on the right of 

 (29) we get 



l -u -A. HI* °^l j 2r o . !!? 1 

 4a 2 2a r 2T l'i + a J * 



This will be made to vanish if we take co such that 



co 2 a 2 r 3r 2 r, 3r 2 . . 



1 4a- 2a 2r v 7 



The coefficient of cos 26 is 



3ar 2 r r x 3r 3 o> 2 a 3 f )\ r% r 2 1 

 "V ~2a"*~2r~ ~2T ~ ~2T 1 a~ + a + 2a 2 J ' 

 or when we introduce the value of oy from (31) 



3ju_,_P_2r 3 



»'o 4a r v y 



