138 
PROFESSOR DANIELL ON VOLTAIC COMBINATIONS. 
unfortunately) the contact theory of the electromotive force ; and although his for- 
mula is easily adapted to either of the two rival views, it is perhaps necessary, in 
selecting the chemical theory, that I should define the exact meaning which I attach 
to his symbols, and explain the expansions which I think it necessary to introduce. 
The formula, you will remember, is 
A 
R + r~ A > 
where E represents the electromotive force (so called) in the cell : R the resistances 
in the cell : r the amount of exterior resistances : A the effective force, measured by 
the work performed. Now according to the chemical view, E must be the balance of 
several active forces in the cell. 
1st. The superior affinity of the generating plate for the anion, of the electrolyte, 
which we will designate by B. 
2nd. The inferior affinity of the conducting plate for the same anion, which we will 
call b. 
3rd. The affinity of the cation, disengaged from the electrolyte and accumulated 
upon the conducting plate for the anion, this we will call e ' : these two last tend to 
produce polarization, as it is not very appropriately called, and a current in the op- 
posite direction to B ; therefore 
E = B — (b -f d), or 
E = B — b — d. 
R, the resistance in the cell, varies directly as the thickness of the electrolyte (or the 
distance between the generating and conducting plates), D, and inversely as the 
area of the section of the electrolyte, S ; therefore 
r represents all the exterior resistances, whether metallic or electrolytic. In the 
metallic parts of the circuit, it will be inversely as the area of the section (i. e. the 
square of the diameter) of the wire s, and directly as the length l, or distance through 
which the current passes. In electrolytic work this metallic resistance may gene- 
rally be disregarded ; the lengths of the connecting wires being insignificant with 
regard to the resistance of the electrolyte. This latter will be inversely as the area 
of the section of the electrolyte, s', and directly as the distance d between the elec- 
trodes : therefore 
But we must now inquire particularly what it is we mean by the section of the elec- 
trolyte. The limits of the section of the metallic conductor are strict and easily 
* The resistance of each liquid is specific, and depends upon the nature of the liquid, the degree of saturation 
(if a solution), and the temperature ; these circumstances remaining constant, it also is constant, and is so 
considered in this review of the formula. 
