116 PROCEEDINGS OF THE AMERICAN ACADEMY. 



quantities for the positive and negative ions respectively. Now let us 

 subject a solution of this salt to the action of gravity. If the positive 

 ion C"*" is denser than the iodide ion, it will tend to move downward 

 through the solution more rapidly and will produce a potential gradient 

 in the solution —dEJdh. As this potential gradient is produced, 

 however, it tends to decrease the downward velocity of the positive ion 

 and increase the velocity of the negative ion so that under the final 

 potential gradient produced they will move downward through the 

 solution with equal velocities. We may now proceed to derive 

 expressions for these equal velocities. 



The total downward force acting on one mol of positive ions is the 

 weight (gMc), minus the buoyant force exerted by the solution 

 {gMcVccI), minus the electrical repulsion {10~ FdEi/dh) correspond- 

 ing to the potential gradient. If u and v are the velocities with which 

 the positive and negative ions move under unit force, the velocity 

 with which they will move under the actual forces can now be calcu- 

 lated by simple multiplication, since the validity of Ohms law in solu- 

 tions shows us that the velocity with which the ions move is propor- 

 tional to the force acting on them. 



Equating the velocities of the negative and positive ions, we have ^ 



n(^g3I, (1 - v^d) - 10' F^^ = v {^g M, (1 - v,d) + 10' i^^) . 



Solving for dEJdh and integrating between the limits o and h, 

 where h is the difference in height between the electrodes, we have 



10' E.P- k9 [-r/r- (1 --'^ - ( 1 - ,7^,) 'r. d - <■.<*)] 



(3) 



In order to obtain the actual electromotive force between the elec- 

 trodes, we must consider not only the potential gradient in the solution, 

 but also the potential drops which occur directly at the electrodes due 

 to the electrode reaction I h + e= /. Since this reaction is accom- 

 panied by the change in volume Mi {vj — v,„) and takes place under the 

 difference in pressure between the upper and lower electrodes which is 



3 It should bo noted that when the concentration of the salt in the lower 

 portion of the tube has appreciably increased, the concentration gradient adds 

 new forces tending to slacken the downward motion of the ions. When the 

 final equilibrium is reached the concentration gradient will be such that no 

 l)oten(ial gradient exists. We arc interested, however, in the original condition 

 before appreciable concentration changes have taken place. 



