368 Mr. A. Frumkin on the 



In consequence we may assume that the potential of the 

 electrode remains constant when the potential of the mercury 

 or its surface area is varied. Between the mercury and the 

 electrode an electromotive force is inserted. 



Let c be the concentration of mercury in the solution in 

 gram-equivalents per c.cm., s the surface area of the mercury, 

 yfr the potential difference between the electrode and the 

 mercury, and E the quantity of electricity which has passed 

 through the solution from the electrode to the mercury since 

 a certain moment. Independently of the original com- 

 position of the solution the state of the system is wholly 

 determined by the quantities s and yjr. If we increase s by 

 ds and E by ^E, the work performed will be 



dA=yds + ydE = L+f~\ds + ^^d^ 



o^ 

 5^, 



whence / 3E\ . / £E\ 



ot 



and ?)<v T^E 



|^ + ^=0 (2) 



of os v 



Let us now consider the change in potential of an insulated 

 mercury mass by surface increase. 

 Since now dF> is z3i*o, 



BE dE 



ds oy 



and 





BE y 



oy 



ds B^ 



-ds~ 



BE "SB' 



0-yjr of 



^-r- is the quantity of electricity which must pass through 



the solution to increase f by unity. This quantity is partly 

 spent in changing the concentration of the solution, partly in 

 charging the double layer 



BE_/dE\ J f < d 2 E „Bc CVyj 



whence ^7 



F # + l#* 



being the volume of the solution. 



