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more than 30,000 times as great as that produced by glass of equal thickness; that produced by cobalt is nearly the same; whilst that produced by nickel is decidedly weaker, being only about 14,000 times greater than that produced by glass.

466. All these metals exhibited rotatory dispersion. The dispersion produced by cobalt and nickel was feeble, whilst that produced by iron was much more powerful, and was anomalous; for iron was found to rotate red light to a greater extent than blue.

467. Kundt also made the following experiments upon magnetized glass, which are of some importance, inasmuch as they afford an experimental test of the theory, which will afterwards be proposed.

The poles of a large electromagnet were adjusted at a distance of about 3 cms. apart. A glass plate, the sides of which were not quite accurately parallel, so that the rays reflected from the posterior surface were well separated from those reflected at the anterior surface, was laid upon the poles of an electromagnet. The lines of magnetic force were accordingly parallel to the reflecting surface; also the plane of incidence was parallel to the lines of magnetic force, and the polarizing angle of the glass was 56°4'.

The light which had been twice refracted at the anterior surface and once reflected at the posterior surface, was examined on emergence; and it was found, that when the incident light was polarized in the plane of incidence, the plane of polarization of the emergent light was always rotated in the positive direction; but that when the light was polarized perpendicularly to the plane of incidence, the rotation was negative from normal incidence up to the polarizing angle, and positive from the polarizing angle to grazing incidence.

When the glass plate was magnetized perpendicularly to the reflecting surface, it was found that when the incident light was polarized in the plane of incidence, the rotation was always positive; but that when it was polarized perpendicularly to the plane of incidence, the rotation was positive from normal incidence to the polarizing angle, and negative from the polarizing angle to grazing incidence.

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It thus appears, that with regard to the reflected light, the glass plate behaves in an opposite manner to that of iron, nickel and cobalt. With respect however to the transmitted light, glass behaves in the same manner as these metals.

468. Kundt sums up the facts connected with the electromagnetic rotation of the plane of polarization of light as follows.

(i) Most isotropic solid bodies, fluids and those gases, which have been examined, rotate the plane of polarization of the transmitted light in the positive direction.

(ii) A concentrated solution of perchloride of iron produces a negative rotation.

(iii) Oxygen, which is comparatively powerfully magnetic, produces positive rotation.

(iv) When light is transmitted through a thin film of iron, cobalt or nickel, the rotation is positive.

(v) When light is reflected at normal incidence from a magnetic pole of iron, cobalt or nickel, the rotation is negative.

(vi) Upon passing through, as well as upon reflection from, iron, the rotatory dispersion of the light is anomalous; the red rays being rotated more powerfully than the blue.

Hall's Effect.

469. Before we proceed to the theoretical explanation of these phenomena, we must refer to a very important experimental fact, which was discovered by Dr E. H. Hall1 of Baltimore. He found that, when an electric current passes through a conductor, which is placed in a strong field of magnetic force, an electromotive force is produced, whose intensity is proportional to the product of the current and the magnetic force, and whose direction is at right angles to the plane containing the current and the magnetic force.

Hence if a, B, y be the components of the external magnetic force, u, v, w those of the current, and P', Q, R', those of the additional electromotive force, we shall have

P' = − C (yv — ẞw), Q' = — C' (aw — yu), R' = — C' (Bu — av).....(1).

1 Phil. Mag. March, 1880.

470. The constant C is a quantity, which depends upon the physical constitution of the medium through which the current is flowing. We shall refer to it as Hall's constant, and to the additional electromotive force as Hall's effect.

471. Let the conductor consist of a plane plate, which will be chosen as the plane of xy; let the magnetic force be in the positive direction of the axis of z, and let the primary current flow along the positive direction of the axis of y. Then

P' - C Q'=0, R' = 0.

The additional electromotive force will therefore act in the positive or negative direction of the axis of x, according as C is negative or positive. We may express this by saying, that Hall's effect is positive, when Hall's constant is negative.

472. Various experiments have been made for the purpose of determining the magnitude and sign of Hall's effect, the description of which more properly belongs to a treatise on Electromagnetism than to one on Optics'. It will however be desirable to call attention to the experiments of Von Ettinghausen and Nernst, who found the following values for Hall's effect, its value for tin being taken as unity.

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They found in addition, that the effect was positive in steel, lead, zinc, and cadmium; but negative in all the other metals which they examined.

1 Phil. Mag. Sept. 1881, p. 157; Ibid. (5) XVII. pp. 80, 249, 400.

2 Amer. Journ. of Science, (3rd Series), xxxiv. p. 151; and Nature, 1887, p. 185.

THEORY OF MAGNETIC ACTION ON LIGHT.

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Theory of Magnetic Action on Light.

473. In the experiments of Kerr and Kundt, on reflection from magnets, and transmission through thin magnetized films, the substance experimented upon was a metal. It is therefore hopeless to attempt to construct a theory, which will furnish a complete explanation of these phenomena, until a satisfactory theory of metallic reflection has been obtained. The theory of magnetic action on light, which we shall now consider', only applies to transparent media, and depends upon the experimental result discovered by Hall, which has been discussed in the preceding sections.

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Now Professor Rowland has assumed, that this result holds good in a dielectric, which is under the action of a strong magnetic force; if, therefore, we adopt this hypothesis, we must substitute the time variations of the electric displacement for the current, and the equations of electromotive force become

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where a, B, y are the components of the total magnetic force.

When the magnetic field is disturbed by the passage of a wave of light, a, B, y may be supposed to have the same values as before disturbance, since their variations when multiplied by f, g, h are terms of the second order, which may be neglected. Since we shall confine our attention to the propagation of light in a uniform magnetic field, a, B, y may be regarded as constant quantities.

We shall therefore assume, that when light is transmitted through a medium, which, when under the action of a strong magnetic force, is capable of magnetically affecting light, the

1 Phil. Trans. 1891, p. 371. For other theories, see Maxwell, Electricity and Magnetism, vol. II. ch. xxi.; Fitzgerald, Phil. Trans. 1880, p. 691.

2 Phil. Mag., April, 1881, p. 254.

equations of electromotive force are represented by (1), where C is Hall's constant. Since we shall require to use the letters a, B, y to denote that portion of the magnetic force which is due to optical causes, we shall write these equations in the form

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All the other equations of the field are the same as Maxwell's, with the exception that we do not suppose that

dF/dx + dG/dy+dH/dz,

is zero.

474. In order to obtain the equations of electric displacement, let us consider a medium which is magnetically isotropic but electrostatically æolotropic. Let k be the magnetic permeability; K1, K,, K, the three principal electrostatic capacities; also let

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Substituting the values of P, Q, R from the equations

P = 4πf|K1, &c., and recollecting that

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