398 Dr. G. von Hevesy on the 



per cm., and K a constant) is analogous to equation (3) given 

 above, namely, 



ii 



D = 0-02232 -. 



n 



The older measurements of the valency of gas ions invariably 

 gave a value of 1. According to more recent experiments 

 by Townsend* and by Frank and Westphalj*, however, some 

 bivalent ions are produced when air is ionized by X-rays. 

 By allowing the ions to diffuse partially, the last named 

 authors were able to separate the bivalent ions partially from 

 the monovalent. This affords a proof, of great importance 

 to the theory given here, that the mobility of the ions is 

 independent of the charge of the ion. Since, however, the 

 velocity of diffusion is inversely proportional to the charge, 

 it is at once apparent that by comparing the two quantities, 

 the charge, and therefore the valency, can be obtained. 



Gaseous ions of higher valency than two have not been 

 isolated. Consequently it is not possible to test the equation 

 for higher values of n. 



§ 6. Determination of the Diffusion Constants of 

 the Radioelements. 



The method employed in these experiments was that of 

 Graham and Stephan. This method consists in placing the 

 solution, the diffusion of which is under investigation, under 

 a vertical column of water, and after a certain time has 

 elapsed and diffusion has taken place, removing different 

 layers and analysing them. From the ratio of the concen- 

 tration of the layer which initially contained all the substance 

 to that of another layer, and from the height of this layer, 

 the diffusion constant in sq. cm. per day is calculated from 

 the equation 



d=(§) 2 /tk, 



where h is the height of the layer in cm., T the time in days, 

 and K a function of the ratio of the concentrations, obtained 

 from Stephanas table. 



As is well known, this method assumes only the validity 

 of Fick's differential equation of diffusion, that is to say, it 

 assumes that the velocity of diffusion is independent of the 

 absolute concentration, and depends only on the fall of con- 

 centration. This condition has always been fulfilled strictly 



* Proc. Roy. Soc. vol. lxxx. p. 207 (1908). 

 t Ber. deut. phys. Ges. vol. xi. p. 152 (1909). 



