29* MOLECULAR FREE PATHS 415 



and on introducing polar coordinates as given by 



it = <*> cos s, tt = o> sin s cos ij/, tt) = o> sin s sin ^ 

 Q takes the simple form 



s sn 

 Jo Jo o 



which leads to the value 



Hence, finally, we find for the average number of collisions 

 which a particle undergoes in unit time 



F 



or, if the mean velocity O of the molecular motion as calculated 

 in 19* is introduced, 



T = 



This formula, first given by Maxwell, 1 differs from that of 

 Clausius, which was deduced in 28*, only in the slightly 

 different factor V2 = 1-41 instead of $ = 1*33. The assumption, 

 therefore, which is not quite correct, that a single mean velocity 

 may be ascribed to all the particles instead of velocities that are 

 constantly changing, leads in this problem, too, to tolerably correct 

 conclusions. 



30*. Collision-freqiiency in Mixed Gases 



This procedure may be also extended to the case of two 

 different gases mixed together, as of nitrogen and oxygen in 

 atmospheric air. If we wish to determine the collision-frequency 

 of a particle of gas in such a mixture, we have only to note that 

 this is made up of two parts, viz. the collision-frequency with 

 particles of its own kind and the collision-frequency with particles 

 of the other sort. The former number is given by the calculation 

 just made ; the latter can be obtained by repeating that calcula- 

 tion, and remembering that the molecules of the two kinds of gas 

 differ not only in mass, but also in the magnitude of their sphere 

 of action, so that unit volume of the mixture may contain unequal 

 numbers of them. We must therefore distinguish the different 

 values of m, 9, and N ; on the contrary the value of the constant 



1 Phil. Mag. [4] xix. 1860, p. 28 ; Scientific Papers (Cambridge 1890), i. 

 p. 387. 



