63 MOLECULAE FREE PATHS 155 



of probabilities allows us to take for this distance the mean 

 diameter of a molecule. But it is very conceivable that two 

 molecules cannot come so near each other as to actually 

 touch, but that they are repelled from each other, without 

 actual contact occurring, by forces that come into play at 

 certain, though very small, distances. On account of this 

 possibility it is better that, as already suggested in 44, we 

 should not put the smallest distance apart of two molecules 

 during a collision as absolutely equal to their diameter. With 

 Clausius, we suppose each molecule to be surrounded by 

 a spherical envelope which is called the sphere of action, 

 meaning thereby that the mean point or centre of gravity 

 of another molecule cannot penetrate into it. The radius of 

 this sphere is thus equal to the smallest distance apart 

 of the centres of the particles at the moment of a collision. 



By introducing this conception we allow the possibility 

 of the molecules exerting forces upon each other of sufficient 

 strength to prevent actual contact and to cause mutual 

 rebound from each other ; we do not, however, thereby, on 

 the other hand, bring in this hypothesis as necessary, as it 

 still remains open to us to assume actual contact on col- 

 lision ; in the latter case we should have to define the sphere 

 of action as eight times the volume of a molecule, and we 

 might call the actual space occupied by a molecule its 

 molecular sphere. 



Denoting the radius of the sphere of action by s, and, 

 therefore, the area of its central section by TT^, we find that 

 if the moving particle considered advances by the mean 

 distance X between neighbouring molecules, its anterior 

 convex surface traverses a cylindrical space bounded by 

 hemispherical ends, the anterior convex and the posterior 

 concave, of volume equal to TTS^X. Since there is on the 

 average only a single molecule in a volume equal to X 3 , the 

 probability that there is a molecule in the cylinder TTS*\ 

 described is as much smaller than 1 as 7ry 2 X is less than X 3 . 

 The probability, therefore, that the particle moved strikes 

 another as it passes over a path of length X is determined 

 by the ratio 



