198 PHENOMENA DEPENDENT ON MOLECULAK PATHS 79 



tables, however, for diatomic and triatomic molecules the 

 numbers determined for argon fit in much less well. 



For gases which have more than three atoms in the 

 molecule the foregoing numbers permit of just as little 

 certainty with respect to a regular dependence on the mole- 

 cular weight. A difficulty which specially arises is that, as 

 the following table shows, the differences between the values 

 of the viscosity-coefficient and of the magnitudes deduced 

 from it become the smaller the higher the number of atoms 

 in the molecule. 



The explanation of the relations described is, on the 

 whole, not difficult to give from the theoretical formula for 

 the free path, 



L = X 3 /7r*V2, 



according to which it appears as a magnitude which is not 

 directly dependent on the mass m of the molecule, but only 

 on the occupation of space by a molecule. It is therefore 

 variable with the molecular weight only in so far as the 

 space-occupation depends upon it. But this enters into the 

 formula in two ways, both in the numerator and in the 

 denominator. The volume X 3 of the elemental cube, i.e. 

 of that part of space which contains just one molecule 

 (63), occurs in the numerator; but this, according to 

 Avogadro's law ( 31), is the same for all gases when they 

 are at the same pressure and temperature. Only the de- 

 nominator, therefore, in the formula for the free path, that 

 is, only the area Trs 2 of the central section of the sphere of 

 action, is variable with the molecular weight. With respect 

 to this section we may in general suppose that it increases 



