332-336] Maxwell's Equations of Transfer 281 



335. We shall require to give other values to Q in equation (654), but 

 in calculating these it will, for reasons which will be seen afterwards, be 

 sufficient to neglect deviations from Maxwell's Law of distribution of velocities. 

 We accordingly take 



IP = V* = W2 = q, 



Uv = vw = wu = 0, 

 and equation (654) becomes 





Dt du Dt dv Dt dw Dt 



9 , - 



Dw A 

 Dt \ 



II. Q = u\ 



336. We first use this equation by putting 



Q = u* = U J + 2w U + U 2 , 

 so that Q u 2 + q, 



-- 



_ - <*>()) ^. - ^ 



3w dv dw 



uQ=2u q, vQ 

 Then the equation becomes 



(657). 



There are two similar equations for v* and vf. If we add the system 

 of three together, we obtain 



8, = - fry + + + A' + A, + AW ..... (658). 



D a \dac dy cz ) 



We have, however, 



Aw 2 + Av 2 + Aw 2 = A(w 2 + fl 2 + w 2 )=0 ............... (659), 



since, as already explained, 2 (v? + v 2 + w 2 ) remains unchanged by collisions. 

 Hence equation (657) becomes 



. + ..................... (660 ). 



dz J 

 -p. 



This equation may be regarded as giving r=g . Substituting this value 



JJt 



in equation (657), we obtain 



2, 2 " = Atf ...... . ........ (661). 



a 



