256 PHENOMENA DEPENDENT ON MOLECULAR PATHS 95 



There exists, however, an important difference between 

 the two formulae for the coefficients of viscosity and diffusion, 

 which lies in the different significations of the molecular 

 free paths. While in our discussions on viscosity we had 

 to deal with only those paths which a molecule passes over 

 in a crowd of molecules of the same kind, the question in 

 the theory of diffusion concerns the lengths of the paths of a 

 particle which moves among other particles not only of its 

 own kind but also of another kind, and which collides with 

 particles of both kinds. To calculate these free paths, 

 therefore, we have to find the number of collisions of both 

 kinds in unit of time. 



Since we have already learnt how to determine the 

 number of collisions of a particle by others of its own kind, 

 it is now only necessary to calculate how often a particle 

 collides with the particles which are present of another 

 kind. We attain thereby at once the possibility of cal- 

 culating the mean length of the paths which a single 

 particle can traverse in a crowd of gaseous molecules of 

 another kind. 



96. Free Path, of a Gaseous Molecule in a Gas of 

 Different Kind 



This calculation may be carried out in exactly the same 

 manner as it is in Chapter VI. for the value of the free path 

 of a molecule of a simple gas ; and the calculation is so 

 fully analogous to that simpler one that a complete repeti- 

 tion of it seems unnecessary ; it will be sufficient to bring 

 forward the distinguishing points of importance which have 

 reference to the molecular sphere of action and the molecular 

 speed. 



The probability of a collision, or the frequency of the colli- 

 sions, is proportional to the section of the sphere of action or 

 to the area of the circle whose radius is equal to the distance 

 between the centres of the two colliding molecules at the 

 first moment of the encounter. This radius and this area 

 must have different values for every different kind of gas, 

 since the free path differs for different gases, as we have 



