394 



Prof. L. Xatanson on the 



so that from (8), (10), (12), and again from (3), (4), (5) we 

 obtain 



*p 





>] + &[® + £>] 



+§§dxdydzp { 





+ 



a* 



= -8V + yQ+jydS(p,^+p f ^+^&) (13) 



Further, we see that 



-fc*S$*.4,* l @.l. + %* + $«.)-£*«. (Ml 



because d# <iy <%) does not vary ; and collecting our results 

 we see that (11) reduces to 



Jtr 



dt{Vr-$V + l,l? i 8q i + 8'Q}=:0, . . . (14) 

 (6), (10) to define the terms within 



with equations (7), (8), 

 brackets. 



§ 11. Difusion. — We next take two gases which are 

 diffusing into one another. Let the masses of the portions 



considered be JJJ dx l dy x dz 1 p x and j jj dx 2 dy 2 dz 2 p 2 ', and Si 



and S 2 their respective boundaries. When the motion of the 

 gases is going on, three irreversible phenomena will occur, viz., 

 internal friction in the first gas, internal friction in the second, 

 and mutual interdiffusion of both ; in the following both the 

 first and the second are neglected. Let again u u i\, w u 

 u 2 , v 2j w 2 denote the velocity components, X 1? Y,, Z ls X 2 , Y 2 , Z 2 

 those of extraneous acceleration,^,^ the mean pressure, at 

 the time t and a given point of space, where at that time both 

 the elements dx 1 dy x dz 1 and dx 2 dy 2 dz 2 of the gases happen to 

 be momentarily situated. The quantities u x and w 2 , i^ and v 2 , 



