184 DYNAMICAL THEORY OF SOUND 



differs, in a moving gas, from p, as thus fixed ; but from 

 considerations based on the kinetic theory of gases Maxwell* 

 inferred (1866) that the two things are identical, and that 

 accordingly 



V }/*' W 



As we are interested chiefly in the order of magnitude of 

 the effects, the precise determination of X' is not of much 

 consequence to us; accordingly Maxwell's view is adopted for 

 simplicity in what follows. 



The dimensions of // are those of a stress multiplied by 

 a time, or [ML~ 1 T~ 1 ]. It is found that /*' is independent of 

 the density, but (in gases) increases with rise of temperature. 

 Its value for air at C. is about '000170 in absolute c.G.s. 

 units. It will appear however immediately that the effect of 

 viscosity in modifying motion depends not so much on the 

 value of fA as on its ratio to the inertia of the fluid. This 

 ratio 



v = p/po (5) 



is therefore called by Maxwell the " kinematic " coefficient of 

 viscosity; its dimensions are [L 2 T~~ 1 ]. For air at C. its value 

 is about '132 c.G.s. 



The rate at which the stresses on the faces of a unit cube 

 are doing work in changing its size and shape is given by 



X'A 2 + 2fl' (tf + 6 2 2 + 6 3 2 ) 

 ' {( 2 - 6 3 ) 2 + (63 - <0 2 + (^ - 6 2 ) 2 }. . . .(6) 



The term p& represents the rate at which the intrinsic 

 energy is increasing. The remaining terms, which are essenti- 

 ally positive, indicate a dissipation of energy at the rate 



f/{fe-*s) 2 + (- *0 2 + (, -<U 2 } (7) 



per unit volume. The mechanical energy thus lost is converted 

 into heat. It will be noticed that (7) vanishes in the case of 

 uniform expansion (e t = e 2 = 6 3 ) ; this is a necessary consequence 

 of our previous assumption as to the value of the constant X'. 



* James Clerk Maxwell (1831 79), professor of experimental physics at 

 Cambridge (187179) ; author of the electromagnetic theory of light. 



