In a medium such as this waves of periodic displacement could be set up, and would travel with a velocity depending on its electric properties. The value for this velocity can be obtained from electrical observations, and Maxwell showed that this velocity, so found, was, within the limits of experimental error, the same as that of light. Moreover, the electrical oscillations take place, like those of light, in the front of the wave. Hence, he concludes, “the elasticity of the magnetic medium in air is the same as that of the luminiferous medium, if these two coexistent, coextensive, and equally elastic media are not rather one medium.” The paper thus contains the first germs of the electro-magnetic theory of light. Moreover, it is shown that the attraction between two small bodies charged with given quantities of electricity depends on the medium in which they are placed, while the specific inductive capacity is found to be proportional to the square of the refractive index. The fourth and final part of the paper investigates the propagation of light in a magnetic field. Faraday had shown that the direction of vibration in a wave of polarised light travelling parallel to the lines of force in a magnetic field is rotated by its passage through the field. The numerical laws of this relation had been investigated by Verdet, and Maxwell showed how his hypothesis of molecular vortices led to laws which agree in the main with those found by Verdet. He points out that the connection between magnetism and electricity has the same mathematical form as that between certain other pairs of phenomena, one of which has a _linear_ and the other a _rotatory_ character; and, further, that an analogy may be worked out assuming either the linear character for magnetism and the rotatory character for electricity, or the reverse. He alludes to Prof. Challis’ theory, according to which magnetism is to consist in currents in a fluid whose directions correspond with the lines of magnetic force, while electric currents are supposed to be accompanied by, if not dependent upon, a rotatory motion of the fluid about the axis of the current; and to Von Helmholtz’s theory of a somewhat similar character. He then gives his own reasons--agreeing with those of Sir W. Thomson (Lord Kelvin)--for supposing that there must be a real rotation going on in a magnetic field in order to account for the rotation of the plane of polarisation, and, accepting these reasons as valid, he develops the consequences of his theory with the results stated above. His own verdict on the theory is given in the “Electricity and Magnetism” (vol. ii., § 831, first edition, p. 416):-- “A theory of molecular vortices, which I worked out at considerable length, was published in the _Phil. Mag._ for March, April, and May, 1861; Jan. and Feb., 1862.