IONIC VELOCITIES. 375 



current through this same area, and if we take Ohm's law 

 we can find another measure for it, vis., the electromotive 

 force between the sides of a centimetre cube divided by its 

 electrical resistance. If we call these E and r respectively, 



we get — 



E = NV 



r 0*0001035 



.-. V = 0-0001035 x ^- • 



Now since the length of the side of our little cube is 1 

 centimetre, E represents the fall of potential (i.e., the elec- 

 tromotive force) per unit length. If we put E = 1 we shall 

 get a value for V corresponding to what we may call unit 

 potential gradient — 



XT 0*0001035 /• X 



V ' " N,— M 



r, the resistance of our little cube is the specific resistance 

 of the solution, and can be measured by a modification of 

 the ordinary Wheatstone's bridge method. We can, there- 

 fore, at once deduce the value of V 1} the velocity with 

 which the ions are sheared past each other by a potential 

 gradient equal to unity. Thus in the case of a solution of 

 hydrochloric acid whose strength is one-tenth of a gram-equiv- 

 alent (3*64 grams) per litre (i.e., a decinormal solution), the 

 specific resistance was found by Kohlrausch to be 2*90 x io 10 

 in C.G.S. units. N the number of gram-equivalents per cubic 

 centimetre is io~ 4 , hence — 



v 0*00010352 _ n 



Vl " 10- 4 x 2-90 x io 10 - 3 57 x 10 



centimetres per second. 



This is calculated for unit potential gradient on the 

 C.G.S. system. For a gradient of one volt per centimetre 

 we get V = 3*57 x io -3 or '00357 centimetres per second. 



In order to find the absolute velocity of either hydrogen 

 or chlorine, we must consider whether the opposite ions 

 travel with equal velocity. If that were so the absolute 

 velocity of each would obviously be half their relative 



