78 Proceedings of the Royal Irish Academy. 



Couette found that when a cylmder of radius 14'6395 cm. was rotated 

 in water at 16'7° C. outside a concentric one of radius 14'3930 cm., the 

 motion ceased to be thoroughly stable when the speed exceeded about 

 56 revolutions per minute ; taking ^ to be "Oil, this corresponds to a value 

 of BpD''jfx = 1940 for liquid shearing at the same rate as that in contact 

 with the fixed cylinder. In Mallock's experiments, when a cylinder of 

 radius 9'943 cm. was rotated outside one of 7"632 cm., it appears from a 

 diagram that, at the temperature 0° C, the motion was not thoroughly stable 

 when the speed exceeded about 75 revolutions per minute ; this corresponds 

 to a value of BpD' = 204, or, taking fx = -018, BpD'jfx = 11300. When 

 another outer cylinder of 8*687 cm. radius was substituted, the corresponding 

 number of revolutions was about 78, giving BpD'Jn = 4500. (Up to these 

 speeds the resistance varied as the velocity.) Moreover, Mallock states that 

 the critical velocity he found at different temperatures was not proportional 

 to the viscosity. " At a temperature of 50° C. the viscosity of water is only 

 about a third of what it is at 0° C, but, at the former temperature, instability 

 begins at a speed only of 11 or 12 per cent, less than at the latter." (His 

 diagrams seem to indicate 15 to 20 per cent, less.) 



In the experiments with different cylinders, the conditions of dynamical 

 similarity are not satisfied ; but they would appear to be practically satisfied 

 with the same cylinders at different temperatures; (apparently conditions 

 concerning pressure and gravity may be disregarded). Unless Mallock's 

 results are rejected altogether, Eeynolds' conclusion that in similar systems 

 eddies appear when ULpJix exceeds some definite limit depending on the 

 form of the apparatus {L denoting the linear dimensions), would seem to be 

 open to doubt, despite the strong confirmation it receives from Couette's 

 experiments. 



Mallock attempted experiments in which the outer cylinder was fixed 

 and the inner one rotated, and states that, in these circumstances, the motion 

 seemed essentially unstable at all speeds. I have great difficulty in accepting 

 this conclusion ; and apparently the fact may just as well have been that it 

 was found impossible to establish the steady motion starting from rest. 



It seems remarkable too that the values of the coefficient of viscosity 

 which Mallock deduced from his two sets of experiments differ from one 

 another, and exceed the usually accepted values, one set being, throughout 

 the whole range of temperatures, not much less than twice that given by 

 Poiseuille. 



In earlier experiments of a similar type by Mallock,' it was found that at 



> " Determination of the Viscosity of Water," Proc. lioy. Soc. xlv., 1888, p. 126. 



