By developing the quantitative relations between osmotic forces and the electrical potential, Nernst[3] was able to show that, at room temperature[529] (17°–18°), the following logarithmic relation [p261] holds for the ‹potential difference› between a ‹metal›[530] and a solution of its ‹ion›, which bathes it: ε_{Me, Me-salt} = (0.0575 / ‹v›) log(C / K). In this equation ε_{Me, Me-salt} is the electrical potential, in volts, existing between the metal Me and the solution of its salt, Me-salt; ‹v› is the number of electrical charges transferred from the metal to its ion, and ‹vice versa›, in the action Me ⇄ Me_{ion}; in the present case, it is identical with the ‹valence› of the metal ion, which the metal forms. C is the concentration of this ion in any given case, and K is the concentration represented by the solution-tension constant, ‹i.e.› by the equilibrium constant. The logarithm is the common one. In place of the concentrations, K and C, the corresponding ‹osmotic pressures› of the metal ion (P and ‹p›, as used by Nernst) may be used in the equation, and for solutions in which osmotic pressure and concentration are not strictly proportional, the osmotic pressure should be used by preference (see footnote 4, p. 258). The ‹sign›[531] given to [p262] ε_{Me, Me-salt}, in any given case, shows the ‹sign› of the ‹electric charge› on the «first component named in the subscript», which is the ‹metal›, in the present instance. For the relation between copper and cupric-ion we would have: ε_{Cu, Cu-salt} = (0.0575/2) log(C / K). When the concentration of cupric-ion is equal to the constant, C = K, the logarithm has the value 0 and the potential difference is 0. When the concentration of cupric-ion is smaller than the constant, C < K, the potential ε_{Cu, Cu-salt} is ‹negative›, ‹i.e.› the ‹metal› receives a negative charge. This ‹negative› charge is the greater, the smaller C is. When C > K, ε_{Cu, Cu-salt} is positive, the copper plate receives a positive charge, and this ‹positive› charge is the greater, the larger the value of C is. «Applications.»—It should be clear, from these considerations, ‹that an electric current will result, if copper plates are introduced into solutions containing different concentrations of cupric-ion› and the solutions and electrodes are connected in such a way as to allow the flow of a current. If we call Cu′ the copper plate dipping into a solution containing cupric-ion at a concentration C′, and Cu″ the plate in a solution containing [Cu^{2+}] = C″, we have[532]: [p263] ε_{Cu′, Cu″} = ε_{Cu′, CuX} − ε_{Cu″, CuX} = (0.0575 / 2) [log(C′ / K) − log(C″ / K)] and[533] ε_{Cu′, Cu″} = (0.0575 / 2) log(C′ / C″). It is also clear, from this equation, that the greater the difference in concentration of the cupric-ion in the two solutions, the greater should be the potential difference produced. The following series of experiments illustrates these relations and confirms the conclusions reached. [p264]