of Viscous Liquid under Capillary Force, 149 



and i|r 2j of which ^ satisfies 



and i/r 2 satisfies 



^-^-^=4(^ S )-^=0 ; . (16) 



where 



k'* = JP + in/v (17) 



At the surface we have to consider the normal stress P, and 

 the tangential stresses. Of the latter one vanishes in virtue 

 of the symmetry, and the other is to he made to vanish in con- 

 formity with the condition that there is to be no impressed 

 tangential force *. Thus 



or in terms of yfr by (13) 



dr 2 rdr ^~ ^ ' 



Introducing yjr h ^ 2 , and having regard to (15), (16), we 

 may express this condition in the form 



2k 2 f 1 +(k / ' 2 + k 2 )ylr 2 = i .... (20) 



which is to be satisfied when r = a. 

 Again, for the normal stress, 



P = — p + 2/x du/dr 



(u v „ 9 \ , ~ du 



\ik \rdr ) dr\r J J kr dr ' * ' 



Herein 



2 /l^|r\_lj^ ^(l^±\_^^± 



\r dr J rdr dr\r dr / r dr' 

 For yfr lt 



1 d / dldyjr x \ £ 2 <tyi =Q 



r dr\ drr dr / r dr ' 



* It is here assumed that there is no " superficial viscosity." 



