117 DIRECT PROPERTIES OF MOLECULES 327 



from which we get for the determination of s the formula 

 *== (24/5^/2) bL. 



The factor, according to these theories, becomes 24/ 5\/2=3'39, 

 and attains therefore a value by which a satisfactory agree- 

 ment is established. 



118. Calculation of the Size of the Molecules from 

 the Dielectric Capacity 



Stefan, 1 in his memoir on the theory of the diffusion of 

 gases, drew attention to a simple relation in which the 

 values of the mean free paths of the gaseous molecules 

 stand to the refractivities of the gases. He remarked that 

 the refractive index n of a gas is the smaller the greater the 

 free path L of its molecules, the simple law, indeed, that the 

 product 



(n - 



has a nearly constant value, holding for many gases, especially 

 for those whose properties have been investigated with the 

 greatest exactness. 



Now Maxwell's electromagnetic theory of light re- 

 quires the refractive index of a substance to be equal to the 

 square root of its dielectric capacity ; and this law has been 

 shown by Boltzmann's 2 experiments on seven gases to be 

 very exactly correct. Therefore also the dielectric capacity 

 of a gas must stand in as simple a relation to the mean free 

 path of its molecules as its refractive power. 



The surprising fact that a simple connection exists 

 between two such different magnitudes as the dielectric 

 capacity and the molecular free path finds its explanation 

 in an assumption regarding the molecular qualities of 

 dielectric bodies made by Faraday and by Mossotti. 

 The molecules of such substances are assumed to be good 

 conductors of electricity, while the interspaces between 

 them are taken to be insulating. According to this assump- 

 tion the dielectric polarisation must depend on the size and 



1 Wien. Sitzungsber. 1872, Ixv. Abth. 2, p. 341. Compare also Kubenson, 

 Oefv. Kgl. Vetensk.-AUad. Forhandl. Stockholm, 1884, xli. No. 10, p. 3. 



2 Pogg. Ann. 1875, civ. p. 421. 



