of Viscous Liquid under Capillary Force. 151 



by (26). In like manner, 



ar 

 Thus 



T(1 ~3 V) - [A J '(jka) + B J '(Wa) ] 



= ^ v [B k ^ k ' 2 ^ k2 h Q (ik'a)+2k 2 AJ '\ika) + 2kk'BJ '\ik'a)l 



+ ^ [ A iha J {ika) + B ih'a J (i£'a)] .... (29) 



fca ~ 



Between (28) and (29) we now eliminate the ratio A/B, and 

 thus obtain as the equation by which [in conjunction with 

 (17)] the value of wis to be determined 



pa" nW+k^ o{lka) 



Je'(k'*-k*)J '(ika) T rjl 1 

 -*(** + **) Jo'li^a) ol J J 



-< z'&a J (z&a) — , , g , g T °, , ., , ik'a J (ik'a) >. (30) 



We shall now apply this result to the particular case where 

 the viscosity is very great in comparison w T ith the inertia. 

 The third part of (30) may then be omitted, and we have to 

 seek the limiting form of the remainder when k! is nearly 

 equal to k, as we see must happen by (17). In the first part, 



k /2 -k 2 _ Sk 

 k'* + k 2 ~ k' 

 In the second, 



and 



U{1P-U) J '(ika) _ JoBk 



kyp+k*) j '{ik'ay o[l/ca) - k • 



Thus the limiting form is 



T(l— k 2 a 2 ) 2ka . ika f T „ 2 T , T ,„ <J Jo' \ 



ka 



