LEWIS AND JACKSON. — POLARIZATION ON MERCURY CATHODE. 409 



while the velocity J 7 of the reaction is given by the equation, V — k c 1 m l 



where m x is the " order " of the reaction. The current can flow only as 



the reaction proceeds, and is therefore proportional to V, We may write 



i 

 therefore, 1 = h' c^ whence In c L = In I v h + constant. Substituting 



in equation (3) we have, 



RT , _ 



Mi = =,Jn / + constant, 



nil fix r 



.0002 T 



or E=- lo gl0 I+B. (4) 



mi % 



Attempting to obtain a similar equation for the more general case, 

 that two or more of the products are accumulated, we find that this is 

 only possible when certain simple relations exist between the several 

 values of m and n. 



One might consider from the development of equation (4) given by 

 Haber (1. c.) that for all cases of polarization our accepted theories, 

 without the aid of further hypotheses, would lead directly to an equation 

 of the same logarithmic form. We see, however, that this is not the 

 case. If the polarization be due to the exhaustion of one or more of the 

 substances used up in the electrolytic reaction, the equation will take an 

 entirely different form. We shall return to this point presently. But 

 even assuming, as we did above, that the polarization is due to the accu- 

 mulation of a single one of the products, we must introduce an important 

 assumption in order to obtain equation (4), namely, that the substance is 

 removed according to the simple law of Guldberg and Waage. This as- 

 sumption includes two others, namely, that the process in question is a 

 homogeneous chemical reaction, that is, that it includes no processes such 

 as those of diffusion ; and secondly, that the reverse reaction takes place 

 to a negligible extent. The latter assumption is undoubtedly justified in 

 most cases of the sort that we are considering, but whether the former 

 assumption is justified can only be decided by experiment. 



Equation (4) is more special and more definite than equation (1), for 

 the former attempts to tell us more about the quantity A than that it is a 

 constant at a given temperature. Now, as a matter of fact, several 

 investigators have shown that in a number of cases equation (1) holds 

 with considerable accuracy, but that on the other hand, the values of A 

 not only cannot be calculated from equation (4), but are altogether in- 

 consistent with it, A proving in most cases to be greater than .0002 T, 

 while the equation demands that it be either equal to this number or 



