208 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 

 The equation (118) may now be written 



+ *>* 1 (V + «.* + < + ft (&* + vf + & 2 )) 



(d.pu d.pv d.pw\ 

 dx dy dz . /' 



(119) 



The whole increase of energy is therefore that due to the 

 action of the external forces minus the cooling due to the ex- 

 pansion of the mixed gases. If the diffusion takes place without 

 alteration of the volume of the mixture, the heat due to the 

 mutual action of the gases in diffusion will be exactly neutra- 

 lized by the cooling of each gas as it expands in passing from 

 places where it is dense to places where it is rare. 



Determination of the Inequality of Pressure in different directions 



due to the Motion of the Medium. 

 Let us put 



(120) 



Then, by equation (52), 



<|l = -pk^q 1 _ 1J -A_ (2M 1 A 1 + 3M 2 ! A 8 V a y 1 



M 



M, 



-*(3A 2 -2A 1 ) M - f: ! i - ^-^^—^ 



2 2 2 2 



— -A ] )(2m 1 — u 2 — v x — v 2 — w 1 —w 2 ) } . . , 



(121) 



the last term depending on diffusion ; and if we omit in equa- 

 tion (75) terms of three dimensions in f, tj, f, which relate to 

 conduction of heat, and neglect quantities of the form %r)p and 

 p£ 2 ~P when not multiplied by the large coefficients k, k v and 

 k 2 , we get 



~dq , n du 2 /du , dv , dw\ Bq ^ n n\ 



tt+SP.S 



If the motion is not subject to any very rapid changes, as in 

 all cases except that of the propagation of sound, we may neglect 



~. In a single system of molecules, 

 ot 



JL^-MAjq, . 



(123) 



