86 RESEARCH COMMITTEES. 
For gas-batteries, putting V=volume at one atmosphere pressure 
of one electrochemical equivalent of gas, we obtain 
EB, :2+ B, =sV. dog: sy, eae Wea a CRS) 
Gilbault submitted equations (H) and (K) to the test of 
experiment for a large number of cells, and over a range of 
pressure from | to 500 atmospheres; and found a very satisfactory 
agreement between the calculated and observed changes of e. m. f. 
The change produced in the e. m. f. of a Daniell’s cell by applying 
a pressure of 100 atmospheres is about the hundreth part of that 
produced in Grove’s gas-battery ; it is, however, quite measurable, 
and the results agree with theory equally well in both cases. 
Small outstanding differences are ascribed by Gilbault, in the 
case of solids and liquids, to secondary chemical actions, which— 
though not fully investigated—were definitely shown to occur at 
high pressures ; similar discrepancies in the case of gases are 
ascribed partly to the cause abovementioned, partly to the failure 
of Boyle’s Law.* 
APPENDIX. 
Ir seems only fair to point out that several of the results here exhibited as 
deductions from the laws of thermodynamics can be obtained by totally 
different methods, some of which may fairly claim a degree of generality 
little, if at all, inferior to that possessed by the methods of thermo- 
dynamics. 
Thus the relation between thee. m. f. of a gas-cell and the external pressure 
has been deduced by J. J. Thomson+ directly from the Lagrangian function 
without subsidiary assumptions, thus proving it to be amenable to strictly 
dynamical reasoning. Again, by combining with the principle of least 
action the assumption—which has much to recommend it—that ‘‘the portion 
of the energy of a system which contains the temperature as a factor is 
essentially kinetic,’ Thomson has deducedt an expression practically 
identical with equation (C), 2.e., with Helmholtz’s law. It must, however, 
be admitted that, in view of the assumption which it contains, this part of 
his investigation cannot Jay claim to the same strictly dynamical character 
as the other. 
Finally it may be mentioned that Nernst’s theory of electromotive force 
leads directly to Helmholtz’s law§ ; but Nernst’s theory lacks the generality 
possessed by those founded either on dynamical or thermodynamical 
considerations. 
* The e. m. f. of a gas-cell is equal and opposite to the counter-electromotive force of 
polarisation in a water-voltameter at the same pressure; hence the relation between the 
e. m. f. needed to decompose water and the pressure is given by equation (K). Substituting 
the known value of V this becomes 
dy 
E, — E, = 0°018868 loge G y 
0 
which is identical with the result obtained by Helmholtz’s calculations. Gilbault verified 
this expression over a tolerably wide range of pressures. 
} ‘‘ Applications of Dynamics to Physics and Chemistry,” p. 86. 
t ‘‘ Applications of Dynamics to Physics and Chemistry,” p. 98. 
§ See Ostwald, ‘‘ Lehrbuch der allgemeinen Chemie,” vol. ii, pt. i, p. 859. 
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