[51] Owing to an error of calculation the actual value obtained by Maxwell from these observations for the coefficient of viscosity is too great. More recent observers have found lower values than those given by him; the difference is thus explained. [52] Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten Sitz d. k. Akad Wien, Band LVIII., 1868. [53] Another supposition which might be made, and which is necessary in order to explain various actions observed in a compound gas under electric force, is that the parts of which a molecule is composed are continually changing. Thus a molecule of steam consists of two parts of hydrogen, one of oxygen, but a given molecule of oxygen is not always combined with the same two molecules of hydrogen; the particles are continually changed. In Maxwell’s paper an hypothesis of this kind is not dealt with. [54] _Nature_, vol. 1., p. 152 (December 13th, 1894). [55] See papers by Mr. Capstick, _Phil. Trans._, vols. 185–186. [56] _Nature_, vol. x. [57] An historical account of the development of the science of electricity will be found in the article “Electricity” in the _Encyclopædia Britannica_, ninth edition, by Professor Chrystal. [58] Thomson (Lord Kelvin), “Papers on Electrostatics and Magnetism,” p. 15. [59] J. J. Thomson, B.A., Report, 1885, pp. 109, 113, Report on Electrical Theories. [60] Papers on “Electrostatics,” etc., p. 26. [61] It is difficult to explain without analysis exactly what is measured by Maxwell’s Vector Potential. Its rate of change at any point of space measures the electromotive force at that point, so far as it is due to variations of the electric current in neighbouring conductors; the magnetic induction depends on the first differential coefficients of the components of the electro-tonic state; the electric current is related to their second differential coefficients in the same manner as the density of attracting matter is related to the potential it produces. In language which is now frequently used in mathematical physics, the electromotive force at a point due to magnetic induction is proportioned to the rate of change of the Vector Potential, the magnetic induction depends on the “curl” of the Vector Potential, while the electric current is measured by the “concentration” of the Vector Potential. From a knowledge of the Vector Potential these other quantities can be obtained by processes of differentiation. [62] The 4 π is introduced because of the system of units usually employed to measure electrical quantities. If we adopted Mr. Oliver Heaviside’s “rational units,” it would disappear, as it does in (B).