328 DIEECT PROPERTIES OF MOLECULES 118 



distance apart of the molecules, and therefore on the same 

 elements which regulate the molecular free path. This 

 explanation makes the connection of the two magnitudes to 

 appear no longer surprising. 



Clausius 1 has developed the theory of these relations 

 after the method of Maxwell and Helmholtz. His 

 theory, with the assumption that the molecules are spherical 

 in shape and are perfect conductors of electricity, gives the 

 dielectric capacity K in the form 



where g denotes the fraction of the volume containing the 

 gas which its molecules actually occupy. By transformation 

 then we obtain the value of g expressed in terms of the 

 dielectric capacity K, viz. 



We see at once that this magnitude g is closely allied in 

 its meaning to the coefficient of condensation t> introduced 

 byLoschmidt; for both ratios represent exactly the same 

 thing if the molecules come into actual contact in their 

 utmost state of compression. But it is possible, and even 

 probable, that the spherical surfaces on which the electric 

 charges of the molecules reside, do not come into actual 

 contact with each other, even when the molecules are on the 

 point of entering within the range of their spheres of action. 

 The fraction denoted by g may therefore be less than that 

 denoted by \>, and can at most be equal to it. 



If, therefore, we replace \> in Loschmidt's formula 



by g, we shall probably obtain a smaller value for the mole- 

 cular diameter s- than is given by either Loschmidt's or 

 van der Waals's formula. Dorn 2 is the first who has 

 carried out this calculation of s by the formula 



s = 6^2 gL = 6V2 L(K - 1) / (K + 2), 



and he combined the values of the dielectric capacity K 



1 Mechanische Warmetheorie, 1879, 2. Aufl. ii. p. 94. 



2 Wied. Ann. 1881, xiii. p. 378. 



