420 Dr. S. R. Miiner on the 



when it may be transferred to A without the expenditure of 

 further work. The work required for this compression is 



Q 



2 

 ne 



CP2 



I pdv. 

 Jpi 



Finally, the transference of the Q/we gram ions of solid silver 

 deposited at the A electrode, back to that in B where an equal 

 amount was dissolved, can be accomplished without work, 

 and the ceil is by these means brought back to its initial con- 

 dition. By equating the efficiency of this isothermal cycle to 

 zero we have (reckoning work done by the cell as positive) 



EQ+ — {-p^+^2- 2 pdv\=0, 



or 



2 f p i 

 E= — I vdp 



independently of the special form of the relation between p 

 and v. The electrode in the concentration c x is also the 

 positive pole of the cell. 



This value of the E.M.F. of course includes the potential 

 step set up at the partition Z. The amount of this may be 

 calculated simply, from the consideration that in the region 

 of the partition where the concentration of the N0 3 ions is 

 varying from c x to f 2 , there must be no resultant motion of 



these in either direction. Hence the force, ~hx. due to the 



dx 



osmotic pressure on the JN0 3 ions in a layer of unit area and 



thickness Bx, must be equal and opposite to the electrostatic 



pull upon the same. The value of this last is the product of 



the potential slope dcf)/dx, and the total charge on the N0 3 



ions in the layer; that is, it is necBoc . d<fi/dx, and acts in the 



opposite direction. Equating these, and integrating, we have 



nej ft c nej p2 



the potential of A being above that of B by this amount. The 

 difference in the potential steps at the two electrodes, there- 

 fore, is E — cf>, or 



— I v dp. 



ne t 



ne , 



From this the value of the potential step at the single elec- 

 trode in A may at once be obtained by making the concen- 

 tration of the ions in B such that there is no difference of 

 potential between the solution and the electrode in this com- 



