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In very dilute solutions the relationship between solvent and solute is such as to admit of simple and exact mathematical treatment, and it is in this field that the theory of' electrolytic dissociation has been applied with the greatest success. Until recently it was generally believed that the formulae deduced from a consideration of the properties of very dilute solutions could be applied without any serious loss of accuracy to solutions of moderate concentration. This hope has, however, not been realised. A careful comparative study, especially by Whetham and by Griffiths, of the electrical and osmotic properties of dilute solutions has shown that even at concentrations as low as 0‐01 gram-molecule per litre there is a discrepancy between the values for the coefficient of ionisation deduced by the two methods. It appears, in fact, that the formulae in which Arrhenius’s hypothesis has usually found expression, can only be regarded as accurate when applied to solutions containing more than 100 litres of water for each gram-molecule of dissolved salt. As a qualitative expression, however, the theory is applicable to electrolytes of all kinds, and the development of exact numerical relationships is only hindered by the difficulty of procuring the necessary experimental data, a difficulty that in many cases can only be overcome by the discovery of new methods of investigation. The essential postulate of Arrhenius’ theory is that a salt may exist both in an active and in an inactive form as regards conductive power, so that when brought into an electrical circuit, only part of the total weight of electrolyte is as a rule directly operative in carrying the current. This conception finds expression in the co-efficient of ionisation,α , which represents the proportion of the salt which is thus active in electrolytic conduction. Independently of any particular theory as to the exact nature of the difference between the ionised and un-ionised part of the salt, the formulaK =mα (u +v ) is universally applicable as expressing the fact that the specific conductivityk of any binary compound is dependent on the massm of the compound contained in unit volume, the proportion that is able to take part in the transport of the current, and the velocitiesu andv with which the oppositely charged ions move through the solution under the action of the electrical forces. In the case of dilute aqueous solutions the numerical values of α,u , andv are accurately known. In the case of less dilute solutions they are approximately known. In the case of concentrated solutions and in the case of fused salts they are altogether unknown.

VII. The electrical conductivity and other properties of sodium hydroxide in aqueous solution as elucidating the mechanism of conduction