330 Lord Rayleigh on Stability of Simple Shearing 



been made which it may be desirable to record, especially as- 

 the preliminary results may have other applications. 



If we take a real rj such that 



p + kfy=-(yvk 2 l3 2 )> V , .... (4) 

 we obtain d 2 S r . a /tr . 



;v=- 9m > s < 5 > 



This is the equation discussed by Stokes in several papers*,, 

 if we take x in his equation (18) to be the pure imaginary 



irj ' 



The boundary equation (3) retains the same Form with; 



e Kl> drj for e ky dy, where 



X 3 = 9i/P//3 (6) 



In (5), (6) 7) and X are non-dimensional. 



Stokes exhibits the general solution of the equation 



S- 9 * s =° • w 



in two forms. In ascending series which are always con- 

 vergent, 



L 2.3 + 2. 3. 5. 6 + 2. 3. 5. 6. 8. 9 * "'J 



„ f 9a>* 9V 9¥° l 



+ B r + 3jr + 3"T4^7 + 3.4.6.7.9.10 + "'J' {S) ' 



The alternative semi-convergent form, suitable for calcula- 

 tion when x is large, is 



. 2x s/2 ; _ 1.5 1.5.7.11 



1.144*^ + 1.2 



1.5.7.11.13.17 



[_ 1.144^+ 1.2.144V 



1.2. 3. 144^ 9 / 2 



•■■} 



X \_ 1.144^/2 + 1.2.144 2 ^ 



1.5.7.11.13.17 



.-.}, • 0) 



1.2.3.144A^ 2 

 in which, however, the constants C and D are liable to a 



* Especially Camb. Phil. Trans, vol. x. p. 106 (1857) ; Collected 

 Papers, vol. iv. p. 77. 



