Diffusion Cells in Ionized Gases. 501 



electric field is just sufficient to cause the positive and 

 negative ions to drift at equal average rates toward the 

 negative plate, numbers of: them recombining as they drift. 



Such an explanation of the electromotive force of con- 

 centration-cells in ionized gases accounts for the sign of 

 the electromotive force observed by Mr. Jenkinson without 

 introducing any hypothesis regarding the phenomena at the 

 surface of the metal. That it is the correct explanation is 

 indicated by the following experiments. 



The process just described may be put in a form for quan- 

 titative experimental test by applying Prof. J. J. Thomson's 

 well-known equations for the time rate of increase of the 

 number n of ions per unit volume at any point in the gas : 



dn l j. d 2 n x d 



dn 2 -p. d 2 n. 2 d 



It =</-*»i»^ D ^ +«^( x »s); 



where subscripts 1 and 2 refer to the positive and negative 

 ions, respectively, q represents the rate of: production of 

 ions by the ionizing agent ; a and D are the coefficients of 

 recombination and diffusion, respectively ; u is the ionic 

 velocity in afield of unit intensity; X is the electric intensity, 

 and x is the coordinate normal to the plates. 



We may eliminate the terms involving q and a by sub- 

 traction and integrate the resulting equation. The inte- 

 gration constant vanishes, since the current through the gas 

 vanishes in the final steady state. By Poisson's equation it 

 follows that in the steady state n x -=n 2 at any point in the gas. 

 Making this substitution and integrating again, we find 



VJ D x — D 2l n a 

 \d=: —±- — log -, 



"l + u 2 n 



where d is the distance between the plates and n and n a are 

 the ionic concentrations in the immediate vicinities of the 

 plates. Xd = E, where E is the electromotive force, and 

 B = UTu/e*. Thus we have 



E= gj>l-M 2 ^ fjg (2) 



e Mi + W2 n v J 



This equation is given in Winkelmann's Handbuch der 

 Pliysik, 2 ed. vol. iv. p. 616, being there derived by a con- 

 sideration of partial pressures as in the case of an electrolyte. 



* J. J. Thomson, 'Conduction of Electricity through Gases/ p. 43. 



