is so feeble that the proper resistance of the electrolyte makes no sensible difference between these potentials.
The electromotive force p at any instant is numerically equal to the mechanical equivalent of the electrolytic process going on at that instant which corresponds to one electrochemical equivalent of the electrolyte. This electrolytic process, it must be remembered, consists in the deposit of the ions on the electrodes, and the state in which they are deposited depends on the actual state of the surface of the electrodes, which may be modified by previous deposits.
Hence the electromotive force at any instant depends on the previous history of the electrode. It is, speaking very roughly, a function of σ, the density of the deposit, such that p = 0 when σ = 0, but p approaches a limiting value much sooner than σ does. The statement, however, that p is a function of σ cannot be considered accurate. It would be more correct to say that p is a function of the chemical state of the superficial layer of the deposit, and that this state depends on the density of the deposit according to some law involving the time.
269.] (3) The third thing we must take into account is the dissipation of the polarization. The polarization when left to itself diminishes at a rate depending partly on the intensity of the polarization or the density of the deposit, and partly on the nature of the surrounding medium, and the chemical, mechanical, or thermal action to which the surface of the electrode is exposed.
If we determine a time T such that at the rate at which the deposit is dissipated, the whole deposit would be removed in a time T, we may call T the modulus of the time of dissipation. When the density of the deposit is very small, T is very large, and may be reckoned by days or months. When the density of the deposit approaches its limiting value T diminishes very rapidly, and is probably a minute fraction of a second. In fact, the rate of dissipation increases so rapidly that when the strength of the current is maintained constant, the separated gas, instead of contributing to increase the density of the deposit, escapes in bubbles as fast as it is formed.
270.] There is therefore a great difference between the state of polarization of the electrodes of an electrolytic cell when the polarization is feeble, and when it is at its maximum value. For instance, if a number of electrolytic cells of dilute sulphuric acid with platinum electrodes are arranged in series, and if a small electro-
