450 ME. S. CHAPMAN ON THE KINETIC THEORY OF A GAS 



Thus we have 



A .,3 -1/2 i mm ' 2 / hmm'\ 3/2 \'^ 2 - D , 3 km" p/ , 1 



A 12 M = 4ir ' vv 7 rr, - ; , " 12+ g - , lv i2fOfii 

 (m+m') 3 \m + m7 LI m + m' J 



7 rr 

 (m+m') 



f_ w , 1 



, 



If we write 



(37) ^ \* _../-" 12 11**- 13 > 



arid substitute for P' 12 in terms of the coefficient of diffusion D 12 , the equation for 

 A 12 M 2 is simplified to 



""' 



2 1 "" 



jX s *- 



* 



- - -- - - 



v + v h 2 mm' (m + m') D 12 (\ m 



Again, by means of the expression obtained for /*, the equation (27) for A u w 2 

 reduces to 



We get similar equations for A u w' 2 and A 12 w' 2 , writing p.' for the coefficient oi 

 viscosity of a gas composed only of the second kind of molecules. Hence, 

 remembering that AQ = A U Q + A 12 Q, we have 



E = Aa u + Ba' n , E = C u + Da' n , 

 where 



1 (i\k m '\ - " 

 ' ' 





1 __ \_l\_V\ 

 '- ( 



D = - - __ __ _ l+k _ _*_ 



- ' ' 2V' 



We next substitute for a n and a' u their values p iz , ^p' xx respectively in the 



V V 



above equations, and solve so as to obtain p zz +p' zz (the total normal pressure parallel 

 to Ox) in terms of E. After a little reduction we find that 



_/ A'+B'+C'+D' 



A'D'-B'C' 

 where 



^ 



