324 DIEECT PROPERTIES OF MOLECULES 117 



the cohesion of the gases and partly in the space occupied 

 by their molecules. On the basis of this theory the values 

 of two constants a and b, the latter of which represents a 

 measure of the size of the molecules, could be calculated 

 from Kegnault's observations on the compressibility of 

 gases and on their expansibility under the action of heat. 



This magnitude b is directly connected with the coeffi- 

 cient of condensation u described in the last paragraph, and 

 to recognise this more clearly we will seek with van der 

 Waals to push Clausius' theory of the molecular free 

 path a step further. The correction, which is calculated 

 in fuller detail in 34* of the Mathematical Appendices, 

 results from regard being paid to the fact that a particle 

 cannot pass over paths between other particles which are 

 equal to the distances apart of these other particles, or, more 

 strictly, of their centroids ; for the paths cannot be greater 

 than the length left free between the spheres of action of the 

 particles. For this reason the estimated molecular free path, 



L = X 3 /7rA/2, 



has to be diminished by an amount which depends on the 

 radius s of the sphere of action. This correction attains 

 its greatest value when the collision is direct and central, 

 in which case the paths of both colliding molecules are 

 together shortened by the radius s. On the average its 

 value is smaller, and equal to 



(V'2/3) ,, 



so that the free path would, strictly speaking, be represented 

 by the formula 



L = (X 3 -f7rs 3 )/7rA/2. 



From this we see that the so-called elemental cube X 3 , in 

 which a single molecule is contained, is diminished in the 

 corrected formula by 



|7r* 3 = 447r* 3 , 



that is, by four times the volume of the molecular sphere. 



From this remark we at once obtain the meaning of the 

 constant b which comes into vanderWaals's theory, since 

 on this theory a similar correction was introduced by putting 



