202 Tlieory of the Small Ion in Gases. 



Langevin*, by treating a limiting case of Maxwell's inverse 

 fifth power law for the mutual attractions of the molecules, 

 has obtained expressions for F identical with those of 

 Stefan. The method which I adopted is based on Lan gevin's 

 earlier formula f for the mobility, which takes account of 

 the acceleration in the direction of the field imparted to the 

 ions between collisions. In the general case when the ion 

 and molecule are of different mass, it leads to an expression 

 for F of a different form ; but when they are of the same 

 mass, which was the case I considered, the two expressions 

 for F take the same form, the coefficient in my case being 

 1*63 times that of Stefan's second expression. 



(2) Jf the ion be regarded as a molecule instead of an 

 atom (all Mr. Sutherland's arguments with regard to the 

 structure of the ion applying apparently just as much to the 

 molecule as to the atom) the coefficient in his expression (10) 

 for F will have to be multiplied by 1*52. 



(3) In order to obtain the numerical value of the factor re- 

 sulting from the increased collision frequency, Mr. Sutherland 

 makes use of the experimental results for the variation of 

 the ionic mobilities with temperature. It is important to 

 notice that this procedure supposes the mass of the ion not to 

 vary with temperature ; we know from the experiments of 

 H. A. Wilson and Moreau in connexion with ionic mobilities 

 in flames, that at temperatures above 1000° C. the mass of 

 the negative ion is certainly less than that of an atom, and it 

 is not unreasonable to suppose that the mean ionic mass alters 

 continuously with any temperature variations. Mr. Suther- 

 land's deduction from his line of argument (p. 345) that at 

 high temperatures the mobilities of the positive and negative 

 ions tend to become equal is surely not supported by experi- 

 mental observations. The method which I employed in order 

 to estimate the value of the factor arising from the fields of 

 force of the ions depended upon an estimation of the force 

 between ion and molecule at collision by the introduction of 

 the experimental values for the dielectric constants of gases. 

 For air at 0° C. my factor thus determined is 1*0 times that 

 of Mr. Sutherland. 



The above considerations all tend in the one direction, 

 viz. to increase the value which has been assigned by 

 Mr. Sutherland to F, the viscous resistance to the moving- 

 ion, and simultaneously to diminish the need for introducing 

 such a quantity as 6; and, inasmuch as has been arbitrarily 



* Ann. de Chim. et tie Phys. vol. v. p. 2GG (1905). Vide also Nabl, Phys. 

 Zeits. vii. p. 240 (190G). 



t Ann. de Chim. et de Phys. [7] vol. xxviii. p. 335 (1903). 



