458 Mr Harrison, On the stability of the steady motion of viscous 



>a>a^/fji fo 



The calculated values of pcoa^/fM for series of values of bja and A 

 are shown below. 



The values marked * give the critical values of ^ for the corre- 

 sponding values of b/a. 



Write b — a = D, then we have 



bja^ M 2 10 



Dla= -119 



Critical value of pcoa^/fx = 423 137 17 



Critical value of pcoZ)2//^ - 4-23 137 1380 



The critical values of pcoD^/fji may be compared with Orr's 

 result BpD^jjx = 177 for the shearing motion between parallel 

 planes, showing that the shearing motion between circular cylinders 

 is relatively more stable than the shearing motion between parallel 

 planes if 6/a is small, and relatively less stable if bja is large. 



There are some approximations which are of interest. 



(a) A large. 



Since s^ is positive, it follows that p^ is greater than the positive 

 root of 



3^4 + 2(1+ A2) ^2 _ (1 _ A2)2 =. 0, 



considered as a quadratic equation in 'p^. The same result follows 

 by considering the reality of tan sn. Hence 



^2>i{2(A4^A2+l)i-(l+A2)}. 



