Stability of Viscous Fluid Motion, 611 



much so, the torque increased suddenly and the motion 

 became visibly turbulent at the lower speed and remained so. 



Fig. 1. 



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U I have no doubt we should find with higher and higher 

 speeds, very gradually reached, stability of laminar or non- 

 turbulent motion, but with narrower and narrower limits as 

 to magnitude of disturbance ; and so find through a large 

 range of velocity, a confirmation of Phil. Mag. 1887, 2, 

 pp. 191-19G. The experiment would, at high velocities, 

 fail to prove the stability which the mathematical investi- 

 gation proves for every velocity however high. 



"As to Phil. Mag. 1887, 2, pp. 272-278, I admit that the 

 mathematical proof is not complete, and withdraw [tempo- 

 rarily ?] the words 'virtually inclusive ' (p. 273, line 3). 

 I still think it probable that the laminar motion is stable for 

 this case also. In your (Phil. Mag. July 1892, pp. 67, 6S) 

 refusal to admit that stability is proved you do'nt distinguish 

 the case in which my proof was complete from the case in 

 which it seems, and therefore is, not complete. 



" Your equation (24) of p. 68 is only valid for infinitely 

 small motion, in which the squares of the total velocities are 

 everywhere negligible ; and in this ease the motion is mani- 

 festly periodic, for any stated periodic conditions of the 

 boundary, and comes to rest according to the logarithmic 

 law, if the boundary is brought to rest at any time. 



" In your p. &2, lines 11 and 12 are ' inaccurate.' Stokes 



2R2 



