range of wave-lengths over which we are able to make experiments will hold over very much greater ranges.

* These values of the square of the refractive index are for D-light.

It will be seen that in general the agreement is satisfactory. In some cases, such as water and alcohol, however, the values obtained for the specific inductive capacity are very much greater than Maxwell's theory would indicate. In the case of water, it has been found that the refractive index for electrical waves having a frequency of about 50 x 106 is 8.9. Hence for waves of this frequency the square of the refractive index, 79.2, is equal to the specific inductive capacity.

574. Transmission of Light and Conductivity.--Electrical waves can only be transmitted through a medium in which an electrical displacement calls forth an elastic resistance, for otherwise a vibratory motion is impossible. In a conductor of electricity, however, electrical displacement can take place, and no force will be called into play tending to oppose the displacement. Electrical waves cannot, therefore, be transmitted through a conducting medium, and since light waves are also electromagnetic waves, they also will not be transmitted through a conducting medium. Maxwell's theory thus explains why the metals are, without exception, opaque to light. Insulators or dielectrics, on the other hand, since they can transmit electrical waves, will also transmit light. It does not follow that if a body will not transmit light that it must be a conductor, for a medium may be opaque because its structure is not homogeneous. Thus glass in a block is transparent, but pounded glass is opaque, the opacity being due to the scattering of the light by the small particles of glass, since there will be a certain amount of reflection at every surface.

575. The Faraday Effect.-In 1845 Faraday discovered that when a beam of plane polarised light (§ 400) is passed through a magnetic field in the direction of the lines of force, the plane of polarisation of the light is rotated owing to its passage through the field. Thus if the light from the source L (Fig. 549) is passed through a polarising Nicol, P, then

through a tube T containing water, or better, carbon bisulphide, and finally through an analysing Nicol A, then, on rotating this analyser so that its principal plane is perpendicular to that of the polarising Nicol, no light will be transmitted. If, however, a current is passed through a coil c which surrounds the tube T,

с

T

so as to produce a magnetic field with the lines of force L parallel to the direction in ✡ which the light is travelling, the light will be found to pass through the analyser A. By turning the analyser it is, however, possible to again cut off all the light. This experiment, therefore, shows not only that the plane of polarisation of the light has been rotated, but also, since by rotating the analyser it is possible to cut off all the light, that the beam must remain plane polarised. If the direction of the current is reversed, the direction of the rotation is also reversed.

FIG. 549.

There is an important difference between the rotation of the plane of polarisation thus produced by matter when placed in a magnetic field and that produced when a ray of light is transmitted through a plate of an alotropic body such as quartz (§ 411). Suppose a ray of plane polarised light is transmitted through a tube containing water, T (Fig. 549), in the same direction as that in which the lines of force of the field proceed. Then, looking in the direction in which the lines of force run, the plane of polarisation will be rotated in the clockwise direction. If the direction of the light is reversed, the rotation will still take place in the clockwise direction, as seen by an observer looking along the direction of the lines of force, but will appear in the opposite direction to an observer looking in the direction in which the light is travelling. Hence, if the ray of light, after having once passed through the tube of water in the magnetic field, is reflected back along its course, it will be again rotated in the same direction, as far as the coil is concerned, as during its first passage, and the plane of polarisation will therefore be turned through twice the angle through which it was turned owing to the single passage. In the case, however, of a ray of plane polarised light transmitted through a plate of quartz, Q (Fig. 550), in a direction parallel to the axis of the crystal, the rotation will take place in one direction when the light passes one way, but will take place in the opposite direction, as far as the crystal is concerned, if the direction of the light is reversed. Hence, if a ray of plane polarised light is transmitted through such a plate of quartz, and is then reflected so as to again traverse the crystal in the reverse direction,

བའ་ཕྱིར་པར། །

FIG. 550.

the rotation during the second passage will be opposite to that during the first, and on the whole the plane of polarisation will not be rotated.

576. Verdet's Constant.--Verdet, who made a large number of measurements on the magnetic rotation of the plane of polarisation in different media, found that the rotation for any one medium obeyed the following law. If the length of the medium traversed by the light in the direction of the lines of force of a uniform magnetic field of strength H is L, the rotation & produced is given by

$=yLH,

where y is a constant dependent on the nature of the medium and the wave-length of the light employed, and is called Verdet's constant. The value of y is taken to be positive when the direction of rotation is the same as that of the current in the coil producing the magnetic field. If L and H are each unity, then the rotation produced is equal to the value of Verdet's constant, so that we may define y as the rotation produced by unit length of the given substance when placed in a magnetic field of unit strength. It is usual to measure the rotation in minutes of arc, so that in the following table the values given represent the rotations in minutes produced by 1 cm. of the substance in a field of which the strength is I c.g.s. unit. The light for which the values of y are given is yellow sodium light.

VERDET'S CONSTANT FOR D-LIGHT.

The value of Verdet's constant decreases with increase of temperature. The change in most cases is proportional to the change in temperature, water, however, being an exception.

In the case of water and carbon bisulphide, the value of Verdet's constant at a temperature is given by the following expressions :—

Carbon bisulphide.
Water.

.

.

Yt=0.04347 (1−0.0016967)

Yt=0.01311 (1 − 0.00003051 – 0.000003053).

In the case of solutions of ferric chloride in water, the rotation is in the negative direction.

When polarised light is transmitted through very thin films of the magnetic metals, iron, nickel, and cobalt, placed in a magnetic field, the plane of polarisation is rotated. In this case, however, the quotient

LH is not constant, but depends on the value of the magnetic field. H. du Bois has shown that although in the case of magnetic metals

Verdet's constant varies with the magnetic field, if the value is divided by the susceptibility, then the quotient is constant.

577. The Kerr Phenomenon. Another effect of magnetism on light has been discovered by Kerr, who found that if plane polarised light is reflected from the polished pole of a strong magnet the plane of polarisation is rotated. The direction of rotation when the light is reflected from a north pole is in the clockwise direction, that is, in the opposite direction to that in which a current would have to flow round a coil so as to produce the magnetisation of the magnet.

578. The Zeeman Effect. In 1897 Zeeman discovered another connection between magnetism and light. He found that if a flame coloured with common salt is placed between the poles of a powerful electro-magnet, and the light given by the flame is examined with a spectroscope of great dispersive power, the appearance of the D-lines is greatly altered. If the source of light is viewed at right angles to the lines of force of the field, then recent examination with very powerful magnetic fields and great dispersion has shown that D, becomes converted into four lines, while D1⁄2 becomes a sextet. In each case the two central lines are plane polarised, the vibrations taking place at right angles to the length of the line. The outer lines are also plane polarised, but the vibrations are in a direction parallel to the length of the lines. A more usual type of line is one in which a single line becomes, when viewed at right angles to the magnetic field, transformed into a triplet, in which the vibrations in the central line take place at right angles to the length, and in the side lines parallel to the length of the line.

If the source of light is viewed in the direction of the lines of force, the outer components of the triplet obtained are circularly polarised in opposite directions, while the central line is plane polarised.

Lorentz and Larmor have shown that the Zeeman effect can be accounted for if we assume that in all bodies there are present small electrically charged particles which have a definite mass, and that all electrical phenomena are due to the configuration and motion of these charged particles or electrons, while light is produced by the vibration of these electrons. When these electrons move in a magnetic field their natural periods will be subjected to perturbations, owing to the action of the field, and these perturbations will be such as would account for the differences in period indicated by the duplicated lines obtained. From the amount of the change in period produced by a given field, it is possible to calculate the ratio of the charge on each electron to its mass. In 563 we have mentioned that Professor J. J. Thomson had calculated the mass of the electric carriers in the kathode rays, and it is interesting to note that, if we suppose that these carriers are simply electrons, then the masses, as calculated from the Zeeman effect and the kathode rays, agree. On this hypothesis the molecule of a gas would consist of about 1000 electrons.

CHAPTER XX

ELECTRICAL OSCILLATIONS

579. Oscillatory Discharge of a Leyden Jar.— When a condenser, such as a Leyden jar, is charged, say the inside coating being at the higher potential, there will be a displacement in the dielectric separating the coatings. When the jar is discharged by connecting its coatings by a conducting wire, the displacement decreases till it becomes zero, but when this point is reached under certain circumstances, which we shall consider later, the inertia of the electrical displacement carries it through its position of equilibrium, and a displacement in the opposite direction to the original one occurs. This displacement corresponds to the charging of the jar in the opposite direction, that is, the inside coating becomes negatively charged. As this charging in the reverse direction proceeds, that is, as the negative displacement increases, an opposing elastic force will be called into play which will diminish the electrical kinetic energy till, when the whole of this energy is converted into potential energy in the form of dielectric strain, the jar will start discharging in the opposite direction. The negative displacement will then decrease, becoming zero, and then a displacement will occur in the positive direction, the inside coating again becoming positively charged. Thus the discharge of the jar does not consist of a simple passage of a current in one direction, but the charge surges backwards and forwards, each coating becoming charged alternately positively and negatively, so that an alternating or oscillating current is set up both in the wire connecting the coatings, where the current is a conduction current, and also in the dielectric, where it is a displacement current. The magnitude of the charge decreases with each oscillation, for the passage of the current through the wire is accompanied by the development of heat, according to Joule's law, and this energy has to be supplied by the electrical energy which was originally stored up by the strain of the dielectric. The phenomenon of the oscillatory discharge of a condenser is exactly the same as that of the vibration of a flexible rod clamped at one end. When the free end of the rod is at the extremity of its swing its energy is entirely potential, due to the strain set up. The condition of the rod now corresponds to that of the jar when it has its maximum charge, and possesses energy due to the strain of the dielectric. As the rod swings towards its position of rest, the potential energy becomes gradually con