310 



Mr Harrison, The pressure in. a viscous liquid 



real. It clearly indicates that when a is small the critical value of 

 Uq/2v may be somewhat large. 



If a > 7r/4, the lateral pressure increases for all values of Uq. 



(2) It is a simple matter to discuss the variation of the pressure 

 when Uq/2i> is large. We have, approximately 



uJ2v 



sn' 



1 + k^ 

 3F = 



m" = 



a = 



1 + P' 



(1 + F)3 ' 



k will be real provided F > |, and, corresponding to real 

 values of k, a will be small. 



In the absence of viscosity, so that u = Uq for all values of d, 



1^69 = 



2r2 



C. 



1 + k^ 

 Thus the lateral pressure increases at a rate which is ■ ,^3 



of the rate for a non- viscous liquid. 



The following table will indicate the character of the results 

 when k is real. 



m 



For larger values of a than those given above, and for the corre- 

 sponding values of uJ2v, k is unreal. 



When a is small there is apparently an approximation which 

 JefEery gives, viz. 



u= — 2v {1 — m^ — m^k^) — Qvk^m'^d^, 



1 



