Laws of Irreversible Phenomena. 405 



D f Dt being the rate of variation of the kinetic energy arising 

 from the dissipative forces, we see that, in this case, 



DF/D*=-2F/t and DT/D*=-2T/t. . (3) 



Cf. Lord Rayleigh, • The Theory of Sound/ vol. i. p. 78. 



§ 19. Dissipation Function of Conduction. — In the Philo- 

 sophical Magazine for June 1895, p. 506, it was shown that 

 in conduction of heat the dissipation function is of the form 



m=-§$***v<i*{ pr *Tz +pr M +pr '¥z}> 



(i) 



the symbol being employed to denote 3(Z 2 + v 2 + i 2 )' From 

 (12) and (39) in the paper referred to, we have 



"D*^' uf- bp ^y> T5T~ 5i ^" (2) 



P^ = -^ ; P^=- 5 A^;^ = -^/>r;(3) 



Bt k P x Vt k P * Bt k H 2 ' K } 



equations (2) are the " kinematical/' and equations (3) the 

 " coercive " equations of the problem. They must be fulfilled 

 in order to make the equations hold : 



pr '~ k ^x' pr >~ k -dy' pr ~ V' " ' {) 



and, therefore, to secure applicability for Fourier's equation. 

 The time of relaxation we define as 



r=k/5p, ....... (5) 



neglecting differences p—p^, &c. From (1) and (4) we 

 obtain 



»-iJ^**i{CpO , +&»»v) , + (prJ , }> • (6) 



and from (1) and (2) we have : 



whence, by (5), we find again 



DF 2F 



w=-v ( 8 > 



§ 20. Connexion between the periods t. — Let r p be the 



