Laws of Irreversible Phenomena. 395 



w x and w 2 being, however, quite different, the elements will, 

 of course, separate after a time infinitely short ; likewise 6^ 

 and Bx 2 , $y x and By 2 , & z i an( l Bz 2 must be understood to be 

 quite independent variations. Let us write 



P<fc{5T-8V + 2P t .8fc + 8'Q}=0, . . . (1) 



and let us adopt, as a definition of the terms, the following 

 equations : — 



8T = ST 1 + 8T 2 , (2) 



(3) 

 (5) 



(6) 

 (7) 



6V = SV 1 + oT 2 , .... 



Tl = 2 JJT dx i tyi dz \ Pi( u i 2 + v i 2 + w i) > 

 T 2 = i JJJ dx 2 dy 2 dz 2 p 2 {u 2 2 + v 2 2 + w 2 2 ) , 



SP ^ = IST^'i ^1 ^ pi ( x i ^1 + Y i 5 ^i + z i ^1) 



+ j]J dx 2 dy 2 dz 2 p 2 (X 2 8x 2 + Y 2 &/ 2 + Z 2 &zr 2 ) 



+ f(TdS 1 p 1 {cos (n^) S^i + cos [n^y) hy x + cos (n^) o^} 



+ JJT ^^2^2 { cos ( n 2 x ) ^2 + cos (n^y) 8y 2 + cos (w^) 6> 2 } . (8) 



The quantity of heat generated in time dt by diffusion may 

 be written 



JJJ <&e <fy ^ Ap x p 2 { (w 2 — u x ) (d# g — d^i) + (w 2 — i'i) (d?/ 2 — dy x ) 



+ (i0 3 — 1^) (dz 2 —dz x ) }, (9) 



the expression cfa <iy dz being understood to mean indifferently 

 dx x dy } dz x or dx 2 dy 2 dz 2 , and A being a constant coefficient 

 intimately connected with the " coefficient of diffusion " of 

 the gases. If the temperature is to remain constant, the 

 quantity (9) must be taken away ; hence 



S'Q,= —^)dx dy dz Ap x p 2 { (u 2 — u x ) (Bx 2 — Bx 1 ) 



+ {v 2 -v 1 )(Sy 2 -8y l )+{w 2 -w 1 )(8z 2 -8z 1 )}. (10) 



