1910-11.] Temperature Coefficient of Concentration Cells. 3 77 
Let Cj, Cu be the solution pressure of M in the two solvents, m, nu the 
transfer numbers of the kations in I. and II., K k , K A the specific partition 
coefficients of the ions between the two phases, then 
RT, C n RT 7 k K c z n * RT 7 
E = - In — t + x .hi — ^-1 + (1 - x) In 
m Cj m c n m 
In =0. 
k A Cj m C n 
If now k be taken as the partition coefficient between the undissociated 
solvents, and K] K n the ionisation constant for each solvent, then 
xr _ x • 
lV n — IVj— — , 
therefore 
K r 
and therefore 
K n * 
E = — In - r + 
fe) 2 ; 
(%) 2 
RT 7 C x RT K k Cj ^ 3vT 7 c n 
m 
consequently the relation follows, 
iz - + n 
m Kc n m C n 
^■^ = 1 orC n = CA, 
Ml 
Having thus established the general conditions for a cell in which 
the concentrations are in partition equilibrium, Abel proceeds to consider 
the case where the concentrations in the two solvents are not in such 
equilibrium and there is consequently an actual E.M.F. developed. 
It is evident that when the two solutions are brought into contact the 
partition equilibrium will be at once established at the surface of contact, 
and that therefore each cell can be supposed to be divided into four parts, 
namely a concentration Cj and c u round the two electrodes, and a concen- 
tration Cj and c u on each side of the boundary between the two liquids, 
and the E.M.F. therefore is made up of two parts due to the concentration 
slope in each liquid, from Cj to Cj and from Cn to Cn, and therefore if Vj U\ 
and Vu ^ii be the ionic velocities in the two solvents respectively, the 
E.M.F. is given by the equation 
E= - — 1 KT In - 1 _ 2b " RT i n '^1 . 
u Y + v 1 m c Y u n + v n m c n 
The experimental testing of this equation involves, unfortunately, an 
amount of knowledge as to the conditions pertaining in organic solutions, 
which is seldom available, and then usually for such solvents like ethyl and 
methyl alcohol, which are mixable with water. 
The above equations are in complete agreement with what has already 
been stated as to the conditions pertaining to such cells. 
When the two solvents can be mixed a fresh factor is introduced owing 
