1914] on Fluid Motions 83 



tions, but the question remains : Is this motion stable ? Does a 

 small departure from the simple motion tend of itself to die out ? 

 In the case where the viscosity is relatively great, observation 

 suggests an affirmative answer ; and 0. Reynolds, whose illness and 

 comparatively early death were so great a loss to science, was able to 

 deduce the same conclusion from theory. Reynolds' method has 

 been improved, more especially by Professor Orr of Dublin. The 

 simple motion is thoroughly stable if the viscosity exceed a certain 

 specified value relative to the velocity of the moving plane and the 

 distance between the planes : while if the viscosity is less than this, 

 it is possible to propose a kind of departure from the original motion 

 which will increase /or a time. It is on this side of the question that 

 there is a deficiency. When the viscosity is very small, observation 

 appears to show that the simple motion is unstable, and we ought to 

 be able to derive this result from theory. But even if we omit 

 viscosity altogether, it does not appear possible to prove instability 

 a 2)riori, at least so long as we regard the walls as mathematically 

 plane. We must confess that at the present we are unable to 

 give a satisfactory account of skin-friction, in order to overcome 

 wldch millions of horse-power are expended in our ships. Even in 

 the older subjects there are plentv of problems left ! 



[R.] 



