356 Mr. G. G. Stokes on a difficulty in the Theory of Sound. 



Saint- Venant and Wantzel, in the 27th Cahier of the Journal 

 de VEcole Poly technique. 



The strange results at which I have arrived appear to be 

 fairly deducible from the two hypotheses already mentioned. 

 It does not follow that the discontinuous motion considered 

 can ever take place in nature, for we have all along been rea- 

 soning on an ideal elastic fluid which does not exist in nature. 

 In the first place, it is not true that the pressure varies as the 

 density, in consequence of the heat and cold produced by con- 

 densation and rarefaction respectively. But it will be easily 

 seen that the discontinuous motion remains possible when we 

 take account of the variation of temperature due to condensa- 

 tion and rarefaction, neglecting, however, the communication 

 of heat from one part of the fluid to another. Indeed, so far 

 as the possibility of discontinuity is Concerned, it is immaterial 

 according to what law the pressure may increase with the 

 density. 



Of course the communication of heat from one particle of 

 the fluid to another would affect the result, though whether 

 to the extent of preventing the possibility of discontinuity I 

 am unable to say. But there is another supposition that we 

 have made which is at variance with the actual state of elastic 

 fluids. It is not true that one portion of an elastic fluid is 

 incapable of exerting any tangential force on another portion 

 on which it slides, even though the variation of velocity from 

 the one portion to the other be not abrupt but continuous. 

 In consequence of this tangential force, analogous in some 

 respects to friction in the case of solids, the mutual pressure 

 of two adjacent elements of a fluid is not accurately normal to 

 the surface of separation, nor equal in all directions about the 

 same point. In many cases the influence of this internal fric- 

 tion is insensible, while in other cases it is very important. 

 Its general effect is to check the relative motion of the parts 

 of a fluid. Suppose now that a surface of discontinuity is very 

 nearly formed, that is to say, that in the neighbourhood of a 

 certain surface there is a very rapid change of density and 

 velocity. It may be easily shown, that in such a case the 

 rapid condensation or rarefaction implies a rapid sliding mo- 

 tion of the fluid ; and this rapid sliding motion would call into 

 play a considerable tangential force, the effect of which would 

 be to check the relative motion of the parts of the fluid. It 

 appears, then, almost certain that the internal friction would 

 effectually prevent the formation of a surface of discontinuity, 

 and even render the motion continuous again if it were for an 

 instant discontinuous. 



