330 
Proceedings of the Royal Society 
Having thus stated what takes place in the cell, the question next 
to be decided is, Whether the heat given out by these reactions cor- 
respond exactly with the electromotive force of the cell ? 
Sir William Thomson, in publishing his formula connecting the 
electromotive force of a cell with the heat set free by the reactions 
taking place, assumed that this correspondence existed. Recent 
experiments have shown, however, that this is not a true assumption 
in many cases, and Helmholtz has recently treated the subject from 
a new point of view.* 
The following is, as I understand it, the outcome of his work on 
chemical combination, in so far as it applies to finding the connec- 
tion between the heats of combination and the electromotive force of 
the cell. 
In general, when an infinitely small current de passes through a 
cell at a given absolute temperature 0, a certain amount of heat, cZQ, 
must be supplied to or removed from the cell to keep its temperature 
constant, apart from the heat developed by the electric resistance of 
the liquid. 
If the electromotive force of the cell corresponds exactly to the 
heat given out by the reaction taking place in the cell, then no heat 
need be added or removed. 
How the measurement of this cooling or heating of the cell would 
be difficult in practice, but, applying the second law of thermo- 
dynamics, Helmholtz obtains the following formula, showing that a 
measure of dQ can be obtained from the variations in electromotive 
force due to temperature — 
8^de = JdQ, 
d0 
where dp is the variation in electromotive force due to temperature. 
It is necessary, then, in practice to measure the electromotive 
force of the cell experimented upon at different temperatures and 
find the variation, if any, of the electromotive force. 
In a cell of one volt, electromotive force at 300° ab. temp., a 
variation of - 0001 volt per deg. cent, would mean a correction of 
•03 volt, or 3 per cent, to be applied before determining the heat of 
combination from the electromotive force. 
* Die Therm odynamik Chemischer Vorganger. Wissenschaftliche Abhand- 
lungen , Yon Hermann Helmholtz, Zweiter Band. 
