PLANE WAVES OF SOUND 183 



much less, owing to the diminution of amplitude by spherical 

 divergence. 



64. Viscosity. 



The essence of viscosity is that in a moving fluid the stresses 

 differ from a state of pressure uniform in all directions about a 

 point, by quantities depending on the rates of deformation. It 

 is usually assumed that these quantities are linear functions of 

 the rates of strain ; from our present standpoint this is 

 sufficiently justified by the fact that the strain- velocities are 

 regarded as infinitely small. As in 40 there will at any 

 instant, and at any given point, be three principal axes of the 

 deformation which is taking place, and these will naturally be 

 the principal axes of the corresponding stress. We therefore 

 write, by analogy with 42 (1), 



............... (1) 



where lt e 2 > *s are the principal strain- velocities, and 



A = 1 + 2 + 3 ...................... (2) 



By the same kind of proof as in 41, // is recognized as the 

 coefficient of viscous resistance to a shearing motion in parallel 

 planes; viz. if TJ denote the rate of shear, and TS the corre- 

 sponding stress, we have 



r = //i) ......................... (3) 



The value of // has been determined with considerable accuracy 

 for a number of fluids, gaseous as well as liquid. 



It will be noticed that the meaning of the symbol p, and 

 consequently the value of V, is so far indeterminate, since 

 nothing is altered in the shape of the formulae (1) if we 

 incorporate in p any constant multiple of A. In the case of 

 liquids it is in fact usual so to incorporate the second terms in 

 (1). In the application to gases it is convenient to regard p as 

 defined by the gaseous laws (p = DpO). There is at present no 

 experimental evidence as to how far the mean stress about a 

 point, viz. 



i (Pi +p* +p,) = -P + (*' + I A*') A, 



