236 REPORT— 1897. 



If U is different from V a difference of potential is set up, the effect 

 of which, when a steady state is reached, is to make the ions travel to- 



dP 



gather. If the potential gradient is the numbers of the two ions which 



ax 



would cross, under the action of this force alone, are 



—JJqc — - dt and+ Yqc -,- dt. 

 ax ax 



Under the influence of both the osmotic and the electric forces the 

 number of gram-equivalents which diffuse in a given time must be equal, 

 so that we get 



or eliminating dVjdx, 



,^ 2UV dp ., 



For dilute solutions we may assume that the gaseous laws hold good, so 

 that 



jp=cRT, 



c, the concentration, being the reciprocal of the volume in which one 

 gram-molecule is dissolved. 



U + V ^ dx 



We shall need the intermediate steps of this investigation when we 

 consider Nernst's account of contact diflerences of potential ; but it has 

 been pointed out to the writer by Professor Fitzgerald that, when the 

 electrostatic forces make the opposite ions diffuse at equal rates, this last 

 equation merely expresses the fact that the resistance offered by the liquid 

 to the passage of an electrolyte is the sum of the resistances offered to the 

 passage of its ions— a result which we should naturally have expected from 

 the general properties of electrolytic solutions. 



Thus, on the osmotic pressure analogy, the force acting on one gram- 



molecule of hydrochloric acid is / ; so that, if we call k the resistance 



c dx 



offered when the velocity is unity, the average velocity will be ^ 



ck dx* 

 and the number of gram-molecules crossing a section of the cylinder in one 

 second will be 



dN=-14P.cqdt=.-lqf-dL 

 ck dx k dx 



Now the osmotic pressure of an electrolyte with two ions is double the 

 normal value, so that 



^=2cIlT, 

 and we get 



,T.-r 2RT dc ,, 



d2\ = — —-— q -=- dt. 

 k ax 



The resistances to hydrogen and chlorine moving with unit velocity are 

 1/U and 1/V respectively, so that the resistance to hydrochloric acid is 



7,-1 I 1_U+V 

 U + V~ UV ' 



