of Recombination of the Ions of Gases. 439 



where /a is the coefficient of viscosity of the gas and p its 

 density. 



e • 



For hydrogen D = 1'7 and the value of — = 10 4 approxi- 

 mately. m 



Therefore — =10~ 6 , 



mic 



and ^=10 8 for 1 volt per cm. 



therefore w = 340cm. 



The velocity of a molecule of hydrogen through hydrogen 

 and carrying an atomic charge is thus 340 cms. per second, 

 while the experimentally determined value is only 104 cms. 

 per second. The disagreement of theory and experiment 

 seems to point to the conclusion that either the charge is 

 less than the charge carried by an ion in ordinary electro- 

 lytes, or that the carrier is larger than the molecule. We 

 have not sufficient experimental evidence to decide between 

 the two suppositions, but some experiments on the velocity 

 of the ions in gases like hydrochloric acid and sulphuretted 

 hydrogen seem to point to the conclusion that the carrier is 

 larger than the molecule. We may suppose that when an 

 ion is liberated it becomes a centre of an aggregation of 

 molecules. This cluster of molecules is in stable equilibrium 

 under the attractive force due to the charge on the ion, and 

 the size of the cluster is determined by the intensity of the 

 bombardment of the molecules of the gas on its surface. 

 Such an hypothesis would explain the observed fact that the 

 positive and negative ions of gases like hydrochloric acid and 

 sulphuretted hydrogen have equal velocities ; for the size of 

 the aggregation is dependent only on the charge on the ion 

 for the same gas, and is therefore the same for the positive 

 and negative ions. In the electrolysis of hydrochloric acid 

 we know that the velocity of the hydrogen ion is much 

 greater than that of the chlorine ion, so that there is an 

 essential difference between the carriers in the two cases. 



Proceeding on this assumption of the formation of clusters 

 round a central nucleus, we may readily determine the dia- 

 meter of the clusters to give the observed velocity of the 

 carrier. If D is the coefficient of interdiffusion of a molecule 

 of diameter a x , the coefficient of interdiffusion of the carrier 

 of diameter a 2 through the gas is given by 



02 



