378 Proceedings of the Royal Society of Edinburgh. [Sess. 
to the fact that a series of layers will be formed containing various propor- 
tions of the two solvents. Professor Abel investigated these conditions and 
arrived at the following equation : — 
E = 2 (1 - «„)?! In On + 2 (1 - %)??*„ ^ + 2 ET ["' In * . dn, 
m m Ci m J n ii c 
where the expression within the integral sign is the summation of the 
effects due to the interdiffusion of the two solvents, and x is the ionic 
partition coefficient. 
Abel comes to the conclusion that in such cells the E.M.F. will not be 
constant for a given concentration, owing to the uncertain element intro- 
duced by the diffusion layers of the two electrolytes into each other. He 
therefore proceeds to investigate the case when a third liquid is introduced 
between the other two and mixes with neither but contains the salt in 
solution. 
It is unnecessary to state here the steps of this investigation. 
His equation is then further simplified by defining the unit of electric 
current as the current which will transfer a gramme molecule of salt, thus 
avoiding the factors, for the time being, depending on the ionic velocities in 
the various solvents, and defining x 11 1 as the ionic partition coefficient 
simplifies the equation to 
A = 2 ?i?te£L x II-L 
m c n 
This is in a slightly different form from the equation I have used in this 
paper for pot. iodide cells, namely : — 
E = RT (log c x x - log c), 
when a: is a constant for high dilutions, depending on the partition 
coefficient and capable of expression as a definite experimentally determined 
ratio of concentration. 
I shall also throughout the paper take the above definition of unit 
quantity of electricity in order to lighten the equations. 
The equations which I shall give in developing the theory of the change 
of E.M.F. with temperature will all be capable of expanding into the form 
of Abel’s equation if required. 
Abel takes in his equations the ionic partition coefficient, while I have 
taken throughout the partition coefficient for the salt as a whole, which 
includes the partition for the unionised solvents and for the ions, and is the 
experimental value with which we meet in practice. Evidently, if this is 
known and the ionisations in both solutions, Abel’s partition coefficient can 
be calculated. When the solutions are in mechanical equilibrium they are 
