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



gives stationary relative kinetic energy for this mode of disturbance^ 

 the steady motion is bound to be stable whatever the nature of the 

 disturbance. 



These equations are (compare with (9) in the previous paper) 



/, du du dv\ dp 



^ ^ \ ox oy oy J oy 



Writing ^=-|' " = i' 



jT/ _ _ iZ F — _ 



^ ~ dy'^~dx' 



eliminating jo, and transforming to polar coordinates (r, 9), noticing: 

 that T" is a function of r only, we find 





r dd dr \ dr^ r dr J 

 Now T = ^ log r + ^Br\ 



Hence V^^ - ^^^ f ^''A _ 1 9'A\ _ q 



Assume that ijj varies as e'^^, where A can take integral values, and 

 we have equation (17). 



Let the notation be changed by writing 



k = 2^Ap//x, 



SO that (21) becomes 



m* + 2 (1 + A2) m2 + ^m + (1 - \^f = 0. 

 Write logg {hja) = n, then equation (25) becomes 

 2cts cos an cos sn — (4^9^ — a^ — s'^) sin an sin sn — 2as cos 2pn =0 



(1). 



This equation is identical with equation (15) on page 125 of 

 Orr's paper in the Proceedings of the Royal Irish Society, vol. xxvii,. 

 Section A. He shows that either s or cr must be imaginary. 

 Write a = La', and (1) becomes 



2a's cosh a'n cos sn — (4^^ + a'^ — s^) sinh a'n sin sn 



-2a'sco&2pn^0 (2). 



