202 PHENOMENA DEPENDENT ON MOLECULAR PATHS 80 



mixture of two gases whose molecular weights are m } and 

 m 2 contain N l and N 2 molecules of them respectively in 

 unit volume, the mean value of the molecular weight is 

 m = (m l N l + m 2 N 2 ) / N 



where N = N l + N 2 . 



By means of this mean value m the mean value of the speed 

 O is at once obtainable from the two magnitudes fl^ O 2 

 which denote the mean speeds of the two kinds of particles ; 

 for there must be equilibrium of temperature, and therefore 



whence for the factor wO in the numerator of the expression 

 for 97 we may put 



mil = m l Q, l ^(mlm l ) = m l fl l ^/(N l IN-t N 2 m 2 /N7n l ). 



Similarly we may alter the denominator. If we put s l 

 and s 2 for the radius of the sphere of action of the two 

 kinds of molecules, the mean volume of the spheres of 

 action is 



NJ IN, 



and therefore the mean central section of the sphere of 

 action is 



Replacing the ratio of s 2 to s { in terms of the viscosity 

 coefficients from the formulae 



77! = 0-30967 ra^/TjWS, ^ 2 = 0-30967 m 2 O 2 /7r? 2 V2, 

 whence we obtain 



we have for the mean section 



. 



\7j 2 m l 

 If we put these two mean values in the numerator and 



