of charged Ions through a Gas. 377 



without modification to the case when the forces are attractive. 

 Maxwell gives an expression for the coefficient of diffusion of one 

 gas A into another B of the form 



^''~ ^hV m.^1 



where mj, 'm^ are the masses of the molecules of A and B, v^, v^. 



the number of these molecules in unit volume, K the force at 



unit distance and h = N/2p, where p is the pressure exerted by 



a gas in which there are N molecules per cubic centimetre, 



k 

 A = 2 , where A; is a constant and 6 the absolute temperature of 



the gas. A I is a, numerical constant, having when the forces are 

 repulsive the value 2"659. Suppose now nii is the mass of a 

 charged ion the preceding equation will give us the coefficient 

 of diffusion of the ion through the gas, if we change the value 

 of Ai to allow for the force being attractive, and put K = 2e^a^, 

 where a is the radius of a molecule of the gas B. We can eliminate 

 a by means of the relation 



fi^-l^N'-^a^ 



where /X2 is the index of refraction of the gas B when there are 

 N of its molecules per cubic centimetre. In the case of an ion 

 diffusing through a gas, Vi may be neglected in comparison with V2 

 so that 



^ _ 1 /rth+m^ / 



SttN 



e^{fji2— 1) AiV2 



The mass of the charged particle only enters this expression 

 through the term w — ? , thus when the mass of the charged 



particle is small compared with the mass of a molecule of a gas 

 through which it is diffusing, the coefficient of diffusion varies 

 inversely as the square root of the mass of the ion ; if however 

 the mass of the ion is large compared with that of the molecule 

 the coefficient of diffusion varies exceedingly slowly with the 

 mass of the charged ion. Hence it seems to me that we can 

 attach but little value to the determinations of the atomic weight 

 of the emanations made by measuring their rate of diffusion 

 through air or hydrogen, for if these were positively charged 

 heavy particles the rate would be practically the same whether 

 the atomic weight of the emanation were 200 or 2000, though 

 this objection would not apply to methods based on the diffusion 

 through porous plugs. 



