490 



REPORT — 1894. 



larger than those through the acid. If we compare the number of mole- 

 cules of the gas with the number of molecules of sulphuric acid in the same 

 volume, we tind that the ' molecular conductivity ' of the gas must be many- 

 million times that of the sulphuric acid (see J. J. Thomson, ' Recent 

 Researches on Electricity and Magnetism,' p. 101). A calculation of the 

 intensity of the current tlirough the gas shows that some hundreds of 

 amperes must be passing through a square centimetre of the gas, a greater 

 current than is allowed l)y the Board of Trade rules to pass through the 

 best conducting electric light leads. 



The presence of a very small number of charged ions in a gas will impart 

 to it a conductivity large enough to bedetected bythe method just described. 

 As this method of detecting the existence of free ions may perhaps be of 

 some service to Chemistry, it may be worth while to calculate from the 

 principles of the Kinetic Theory of Gases the conductivity of a mixture of 

 free ions and undissociated gas. For the sake of simplicity I will take 

 the case when the ions form but a small fraction of the undissociated s;as. 

 Let e be the charge of electricity on the positive atom, -ni^ the mass of 

 this ion, —e the charge on a negative ion, ui.j its mass, N the number of 

 positive or of negative ions per unit volume, X the electric intensity 

 parallel to the axis of x, it,, it, ^^^^ mean translatory velocity pai'allel to 



Fig. 2. 



the axis of x of the positive and negative ions respectively. We shall 

 suppose that the undissociated gas has no mean movement. Thus (Art. 

 Diffusion, ' Encyclopfedia Britannica,' or Maxwell's ' Collected Papers,' 

 vol. ii. p. 629) we have, if p is the density of the undissociated gas, 



di Nnii ax in 



where G2, G3 are constants depending on the size of the molecules and 

 the temperature, p, is the pressure due to the positive ions. 



