46 
of the metallic elements of the pile or voltaic arrangement, 
the chemical action of the fluids being merely accessory, - 
and merely affecting the resistance, R. According to the 
chemical theory, the electro- motive force is developed by the 
chemical action of the electrolyte, the contact of the metals 
being only necessary to complete the circuit. The contact 
theory, I think myself justified in saying, has been mainly 
upheld on the continent on account of its appearing to be so 
fully borne out by Ohm's theory. The chemical theory has 
its results perfectly expressed by Ohm's law, and is supported 
by the strict correlation of the amount of chemical action 
taking place in the cells of the battery and the force of the 
current developed. According to the contact theory and 
Ohm's law, the effect produced is quite independent of the 
size of the elements, being the electro-motive force divided 
by the resistance, and expressed thus, F = ^ ; but, on 
examining the resistance of the liquid portion of the circuit, 
we find that the resistance bears a strict ratio to the surface 
of the elements exposed to chemical action. The argument 
is, therefore, so far, equal and inconclusive on both sides. 
I now propose to present the principal equation of Ohm's 
law in a more expanded form : — F = -, in which R is 
the resistance of the electrolyte, and r that of the metallic 
or other resistances closing the circuit. It may easily be 
shown that the resistance of all conductors to the passage of 
the voltaic current is directly as the length, and inversely as 
the thickness or section, of the conductor. This holds good 
as regards the liquid, as well as the solid, portions of the 
circuit; therefore, instead of R we may substitute R', the 
specific resistance of the electrolyte multiplied into D, the 
distance of the plates, and divided by S, the exposed sec- 
E 
tional area. The formula, therefore, becomes F = - . 
S 
but when the number of elements is increased, so as to form 
