The theories of Debye, Onsager, and Falkenhagen, stressing the connexion between the dielectric constant and the other properties of solutions of electrolytes, have focussed a considerable amount of attention on the problem of the accurate determination of the dielectric properties of conducting solutions. The results, however, of work published by various investigators during the past few years show wide discrepancies and, in fact, it can hardly be said that even the sign of the effect of electrolytes upon the dielectric constant of water has yet been established with any degree of certainty. That the results have been so unsatisfactory is not altogether surprising in view of the inherent difficulties of the problem; the system itself is a complicated one, consisting of simple water dipoles, the polymers dihydrol and trihydrol, and the solute molecules or ions dispersed throughout the liquid; furthermore, the experimental technique is frequently complicated by the requirement that the dielectric constants shall be determined at frequencies low enough to permit of computation of the maximum possible polarization of the system, including the rotational polarization of all polar molecules which may be present. Methods involving the direct determination of the capacity of a condenser containing the liquid, whether by capacity-bridge or by resonance, are rendered difficult or inaccurate through the poor capacity sensitivity of such systems in presence of an appreciable ohmic conductivity between the condenser plates. This difficulty is minimized by the use of very high frequencies, and a considerable amount of work has been carried out under these conditions by Wien, Röver, Falkenhagen, and others in connexion with the theory of strong electrolytes. The need has arisen, however, for the values of the dielectric constants of solutions of large polar molecules such as long-chained amino acids, polypeptides, and soluble proteins. Such substances have considerably enhanced periods of relaxation, and proportionately low frequencies of alternating current must be employed to avoid loss of the orientation polarization of the system. In the case of pure egg-albumin solution, dispersion of hertzian waves occurs at all frequencies above about 10
5
sec.
-1
. In view of this difficulty it seemed desirable that a thorough investigation should be made into the question as to whether precision results might be obtained from some general method which uses comparatively low frequencies of alternating current. The “force” method theoretically developed by Fürth, in 1924, seemed the most promising. Various modifications of this method have been used by many workers, unfortunately, however, with by no means concordant results, so far as conducting solutions are concerned. It consists broadly in the determination of the force exerted upon an ellipsoid, mounted to rotate about one of its minor axes, in a liquid dielectric across which an alternating field is applied in a direction at right angles to the axis of rotation of the ellipsoid. For such a system Fürth has shown that the torque on the ellipsoid may be expressed by εE
2
sin2θA, where ε represents the dielectric constant of the liquid, E the potential gradient, θ the angle between the major axis of the ellipsoid and the direction of the field, and A a constant involving the dimensions of the ellipsoid. This form of Fürth’s equation applies only so long as the resistance of the liquid dielectric is high relative to that of the ellipsoid itself.
Direct determination of amorphous number density from the reduced Pair Distribution Function
