Laws of Irreversible Plienomena. 401 



in an important case it received the name of the modulus of 

 the time of relaxation* and may, without inconvenience, be 

 called so in other similar cases. 



Equation (V.) may be verified in various cases, which we 

 shall take in order. 



§ 15. Irreversible Hydrodynamics. — From § 10 we have 



Writing p xxy p jy for the usual components, we have 



and four other equations of the same form. These equations, 

 it is well known, must be fulfilled if the dynamical equations 

 of Navier, Poisson, Stokes, and Maxwell are to be true ; they 

 may be described, therefore, as being in agreement with ex- 

 perience, and so also may be equation (1). Hence 



»-jff*** ±\ ^-^y^-^^n (3) 



JJJ ^ */*( +2/4 + 2^+2^4. J 



Again, if the disturbance is not a very violent one, we have 

 the equations f 



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

 it may be well to point out that they are " kinematical " 

 equations, therefore independent of any particular molecular 

 hypothesis. Now, if we put 



^- . 



p^, (5) 



we obtain from (2) and (4) 



~D(p xx —p) _ p xx —p Djy _ pjz , 



Vt ~ T ' D* " T > ' ' • {b) 



* Philosophical Transactions, 1867, p. 82. See also 'Treatise on 

 Electricity and Magnetism,' third edition, vol. i. p. 451. 

 t Philosophical Transactions, 1867, p. 81. 



Phil. Mag. S. 5. Yol. 41. No. 252. May 1896. 2 F 



