610 Lord Rayleigh on the 



answer, though suggested by common experience and the 

 special investigations of 0. Reynolds *, seemed difficult to 

 reconcile with the undoubted fact that great viscosity makes 

 for stability. 



It was under these circumstances that " the Criterion of 

 the Stability and Instability of the Motion of a Viscous 

 Fluid," with special reference to cases (i.) and (ii.) above, 

 was proposed as the subject of an Adams Prize essay f , and 

 shortly afterwards the matter was taken up by Kelvin t in 

 papers which form the foundation of much that has since 

 been written upon the subject. His conclusion was that in 

 both cases the steady motion is wholly stable for infinitesimal 

 disturbances, whatever may be the value of the viscosity (fi); 

 but that when the disturbances are finite, the limits of 

 stability become narrower and narrower as fi diminishes. 

 Two methods are employed : the first a special method 

 applicable only to case (i.) of a simple shear, the second (ii.) 

 more general and applicable to both cases. In 1892 (I. c.) 

 I had occasion to take exception to the proof of stability by 

 the second method, and Orr § has since shown that the same 

 objection applies to the special method. Accordingly Kelvin's 

 proof of stability cannot be considered sufficient, even in 

 case (i.). That Kelvin himself (partially) recognized this is 

 shown by the following interesting and characteristic letter, 

 which I venture to give in full. 



July 10, (? 1895) 



" On Saturday I saw a splendid illustration by Arnulf 

 Mallock of our ideas regarding instability of water between 

 two parallel planes, one kept moving and the other fixed. 

 (Fig. 1) Coaxal cylinders, nearly enough planes for our 

 illustration. The rotation of the outer can was kept very 

 accurately uniform at whatever speed the governor was set 

 for, when left to itself. At one of the speeds he shewed me, 

 the water came to regular regime, quite smooth. I dipped a 

 disturbing rod an inch or two down into the water and 

 immediately the torque increased largely. Smooth regime 

 could only be re-established by slowing down and bringing 

 up to speed again, gradually enough. 



" Without the disturbing rod at all, I found that by resisting 

 the outer can by hand somewhat suddenly, but not very 



* Phil. Trans. 1883, Part III. p. 935. 



t Phil. Mag. xxiv. p. 142 (1887). The suggestion came from me, but 

 the notice was (I think) drawn up bv Stokes. 



J Phil. Mag. xxiv. pp. 188, 272 (1887); Collected Papers, iv. p. 321. 

 § Orr, Proc. Roy. Irish Acad. vol. xxvii. 1907. 



