of the Dissipation Function. 459 



if the disturbance is not very violent, we shall find 



g(f»-pP)=-8/>(«-W) (23) 



|fa?)=/>A, (24) 



and other equations which may be written down from 

 symmetry. Hence 



+ 2(ptfy+2( P ftf + 2( P f)y\. . (25) 



From this it appears that the direction of that transformation 

 of energy the rate of which is F depends on the nature of the 

 mutual action between molecules. Molar energy will become 

 converted into molecular energy if molecular interaction is 

 such as to tend to diminish the absolute values of the terms 

 P~~p£ 2 i PvK an( i similar terms ; i. e. such as to tend gradually 

 to calm the disturbance existing : F is then always a positive 

 quantity and the opposite transformation of molecular energy 

 into molar energy is impossible. That this is precisely what 

 is realised in all fluids in Nature, as attested by the phe- 

 nomenon of viscosity, cannot, however, be deduced from 

 Kinematical Theory. We have ascertained, as it were, the 

 path of change of the molar energy, but we are unable to say 

 why one of the two possible directions of change is always 

 selected. 



If now we suppose the following equations to be given : — 



p-pf*=2v(a-id), (26) 



pr)£=—fiA, ... ... (27) 



(the symbol /jl denoting a constant, the coefficient of viscosity), 

 and four other equations, to be written down from symmetry, 

 we shall find it possible to complete our solution. Maxwell 

 deduced these equations from his well-known assumption as 

 to the law of force between molecules ; Foisson, Sir Gr. G. 

 Stokes, and others have given them in the ordinary Theory of 

 Viscosity. It follows, then, that 



p= - {Kp-piy+i(p-p?y + Kp-pfr+(pv^+(pm°-+ &&)% 



= - {i(fiV % -p?Y + i(P^-pf^ + Upe-p^ + (p^+(p^f + (pflf} 

 =p{|(6- (! ) 2 +f(c-a) 2 + f(a-?') 2 + A 2 + B 2 + 2 }, 



