96 DIFFUSION OF GASES 257 



learnt from the observations on viscosity. We shall there- 

 fore not be justified, when considering the encounters 

 between particles of different kinds, in taking the value of 

 the radius that is proper to either the one or the other kind 

 of gas, but we must introduce a third value of this radius, 

 which we shall denote by the letter <r, to distinguish it from 

 the symbol $ which we have before employed for a homo- 

 geneous gas. In the formula for the collision-frequency and 

 for the free path we have therefore to replace the section Try* 



by 7TCT 2 . 



According to a suggestion made by Stefan, 1 which 

 seems to be confirmed by experiment, the magnitude a- 

 stands in a simple relation to the two magnitudes s l and $ 2 , 

 the values that hold for the two simple gases ; this relation 

 being probably 



<* = i(*i + %) 



The meaning of this equation is directly intelligible if we 

 do not look upon the molecules as massive points, but 

 ascribe to them the property of extension in space, and take 

 ^s l and ^ as the mean radii of the two kinds of' molecules. 

 The interpretation of the formula is, however, not bound up 

 with this material conception, but it admits of a dynamical 

 explanation ; we may consider the molecules to be centres 

 of force surrounded by spheres of force of radius J$, if we 

 ascribe to the spheres of force the property of not suffering 

 the one to penetrate into the other. 2 



The free path of a molecule of one gas in another gas will, 

 in the second place, depend on the speeds of both kinds of 

 molecules. To determine the character of this dependence, 

 let us first for simplicity consider a gaseous medium whose 

 molecules do not move to and fro in all possible directions 

 of space, but only in directions which are perpendicular to 

 those of the entering particle. These to-and-fro motions 

 make the probability of a collision greater than it would be 

 if the particle moved into a medium at rest ; for a particle 

 moving hither and thither will require a greater space for 



1 Wien. Sitzungsber. 1872, Ixv. Abth. 2, p. 323. 

 - Compare 44, 63, 113. 



