278 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
is now the gas-constant belonging to an electrical equivalent per unit volume, which 
is 8580 in c.g.s. units : this may he expressed in the form RT log P/y), where P 
depends on the metal of the electrode and on the solvent employed in the cell and 
on the temperature, but not on the concentration of the solution. This quantity P 
has been called by Nernst, on grounds of analogy, the solution pressure of the 
metal electrode in the solvent.* When the electrode is 2 :)olarizable so that the 
processes are not reversible, the difference of potential must be less than this formula 
would give. If now we are dealing with a two-fluid cell, in which the fluids are 
separated by an osmotic partition and passage of the solvent is prevented by balancing 
the osmotic tendency by hydrostatic pressure, the processes are still reversible and 
the electromotive force of the cell will be PvT (log Pj/pi — log Pg/p.j), while passage 
of a current will gradua.lly polarize the faces of the partition. If however the ions 
could pass through the partition into the solution of different concentration without 
diffusion of the fluids in bulk, the part of this electromotive force depending on 
concentration would be cancelled, and there would remain PtT log Pi/Pj due solely to 
the afiinity of the solvent for the materials of the electrodes. But if we are dealing 
with a cell, in which the fluids are in direct contact along an interface of finite 
dimensions so that steady diffusion at a finite rate is going on, or in which they are 
even allowed to diffuse steadily across an osmotic partition, there will be loss of 
availability owing to that diffusion, so that the back electromotive force arising at the 
junction of the fluids is less than the maximum value — RT log In the 
absence of knowledge of the rate at which the diffusive degradation of energy is 
proceeding and is affected by electric transfer, the principle of availability cannot 
supply a formula for this diminution of the back electromotive force, which will 
depend on the nature of the layer of transition : but a theory of the process of steady 
interdiffusion of two ionized fluids has been formulated by Nernst and Planck which 
involves an expression for its magnitude.t Thus, considering diffusion of a simple 
* There appears a clifBculty in imagining, in accordance with the view here taken, that the value of P 
can be dependent on a layer of the metallic ions extending into the solution, especially as the potential 
difference between dielectrics could not be so explained. Cf. § 56 supra. 
t I find that applications similar to the above, but on a more extensive scale and with considerable 
differences in the argument, especially a more prominent use of entropy, are made in Planck’s later 
important exposition “ Ueber das Princip der Vermehrung der Entropie,” ‘ Wied. Ann.,’ 44, 1891, pp. 
385-428. The general formula for the potential difference between two diffusing solutions is there 
obtained from the variation of an analytical function, w'hich is really the available energy, on the 
hypothesis that the solutions are in a permanent state of diffusion, determined by Nernst’s principles, 
in which the concentration varies from point to point so slowly that the diffusive dissipation other 
than electric may be neglected. Cj. also on the history of the subject Negbace, ‘ Wied. Ann.,’ 44, 
p. 737. In the text above the statements are confined to the case of binary electrolytes. 
The development of the laws of chemical equilibrium given in § 60 has also been largely anticipated 
as to form by Planck, ‘Wied. Ann.,’ 32, 1887 : his postulates are however different from those that 
enter here, where the analysis occurs as an outcome of a general view of the relations of molecules in bulk 
to the mther and taeach other, §§ 11-12. [_Cf. Planck, “ Yorlesungen fiber Thermodynamik,” 1897.] 
