Revolving Liquid under Capillary Force. 167 



OC=a, PCX = 0. Then, r being supposed constant, the 

 principal radii of curvature are r and a sec6 + r, so that the 

 equation of equilibrium is 



Po 1 cos# to 2 , >..„ /oox 



£? = -+ — ^ - ^(a + rcos^) 2 , . (23) 



1 r a + r cos 6 21 v 7 v 7 



in which p should be constant as 6 varies. In this 



cos0 If r A 3r\ ' r 0/1 r 2 ozl \ 



S+F^T* = «t -ra + V 1 + ^- 2 ) COS ^^ COs2 ^^ 2COS ^N 



(l + >s^ = l-£ + Jco S ^£ 2 cos2^. 



Thus approximately 

 a»o « r o. 2 a 3 /, r 2 \ „/, 3r 2 <u 2 a 3 .2rl 



+«"{-£-£»} +'•»»•»• (24) 



The term in cos 6 will vanish if we take co so that 



^-K 1 -?) <» 



The coefficient of cos 26 then becomes 



- ^ + cubes of - (26) 



If we are content to neglect r/a in comparison with unity, 

 the condition of equilibrium is satisfied by the circular form; 

 otherwise there is an inequality of pressure of this order in 

 the term proportional to cos 20. From (25) it is seen that if 

 a and T be given, the necessary angular velocity increases 

 as the radius of the section decreases. 



In order to secure a better fulfilment of the pressure 

 equation it is necessary to suppose r variable, and this of 

 course complicates the expressions for the curvatures. For 

 that in the meridianal plane we have 



i ' r dff i + i \do) 



or with sufficient approximation 



1 If, ld*r , 1 /dr\*\ 



