Hertz' Experiments

Hertz’s deduction is ingenious and interesting will readily be admitted.

That it is conclusive may scarcely be claimed: for the argument of Helmholtz regarding the induction of currents is not altogether satisfactory; and Hertz, in following his master, is on no surer ground.

In the course of a discussion[48] on the validity of Hertz’s assumptions, which followed the publication of his paper, E. Aulinger[49] brought to light a contradiction between the principles of the unity of electric and of magnetic force and the electrodynamics of Weber. Consider an electrostatically charged hollow sphere, in the interior of which is a wire carrying a variable current.

According to Weber’s theory, the sphere would exert a turning couple on the wire; but according to Hertz’s principles, no action would be exerted, since charging the sphere makes no difference to either the electric or the magnetic force in its interior.

The experiment thus suggested would be a crucial test of the correctness of Weber’s theory; it has the advantage of requiring nothing but closed currents and electrostatic charges at rest; but the quantities to be observed would be on the limits of observational accuracy.

After his attempt to justify the Maxwellian equations on theoretical grounds, Hertz turned his attention to the possibility of verifying them by direct experiment.

His interest in the matter had first been aroused some years previously, when the Berlin Academy proposed as a prize subject “To establish experimentally a relation between electromagnetic actions and the polarization of dielectrics.”

Helmholtz suggested to Hertz that he should attempt the solution; but at the time he saw no way of bringing phenomena of this kind within the limits of observation. From this time forward, however, the idea of electric oscillations was continually present to his mind; and in the spring of 1886 he noticed an effect[50] which formed the starting-point of his later researches.

When an open circuit was formed of a piece of copper wire, bent into the form of a rectangle, so that the ends of the wire were separated only by a short air-gap, and when this open circuit was connected by a wire with any point of a circuit through which the spark-discharge of an induction-coil was taking place, it was found that a spark passed in the air-gap of the open circuit.

This was explained by supposing that the change of potential, which is propagated along the connecting wire from the induction-coil, reaches one end of the open circuit before it reaches the other, so that a spark passes between them; and the phenomenon therefore was regarded as indicating a finite velocity of propagation of electric potential along wires.[51]

Continuing his experiments, Hertz[52] found that a spark could be induced in the open or secondary circuit oven when it was not in metallic connexion with the primary circuit in which the electric oscillations were generated.

He rightly interpreted the phenomenon by showing that the secondary circuit was of such dimensions as to make the free period of electric oscillations in it nearly equal to the period of the oscillations in the primary circuit; the disturbance which passed from one circuit to the other by induction would consequently be greatly intensified in the secondary circuit by resonance.

The discovery that sparks may be produced in the air-gap of a secondary circuit, provided it has the dimensions proper for resonance, was of great importance: for it supplied a method of detecting electrical effects in air at a distance from the primary disturbance; a suitable detector was in fact all that was needed in order to observe the propagation of electric waves in free space, and thereby decisively test the Maxwellian theory. To this work Hertz now addressed himself.[53]

The radiator or primary source of the disturbances studied by Hertz may be constructed of two sheets of metal in the same plane, each sheet carrying a stiff wire which projects towards the other sheet and terminates in a knob; the sheets are to be excited by connecting them to the terminals of an induction coil.

The sheets may be regarded as the two coatings of a modified Leyden jar, with air as the dielectric between thein; the electric field is extended throughout the air, instead of being confined to the narrow space between the coatings, as in the ordinary Leyden jar. Such a disposition ensures that the system shall lose a large part of its energy by radiation at each oscillation.

As in the jar discharge,[54] the electricity surges from one sheet to the other, with a period proportional to (CL)

…

where C denotes the electrostatic capacity of the system formed by the two sheets, and L denotes the self-induction of the connexion. The capacity and induction should be made as small as possible in order to make the period small.

The detector used by Hertz was that already described, namely, a wire bent into an incompletely closed curve, and of such dimensions that its free period of oscillation was the same as that of the primary oscillation, so that resonance might take place.

Towards the end of the year 1887, when studying the sparks induced in the resonating circuit by the primary disturbance, Hertz noticed[55] that the phenomena were distinctly modified when a large mass of an insulating substance was brought into the neighbourhood of the apparatus.

Thus, confirming the principle that the changing electric polarization which is produced when an alternating electric force acts on a dielectric is capable of displaying electromagnetic effects.

Early in the following year (1888) Hertz determined to verify Maxwell’s theory directly by showing that electromagnetic actions are propagated in air with a finite velocity.[56]

For this purpose he transmitted the disturbance from the primary oscillator by two different paths, viz., through the air and along a wire; and having exposed the detector to the joint influence of the two partial disturbances, he observed interference between them. In this way he found the ratio of the velocity of electric waves in air to their velocity when conducted by wires.

The latter velocity he determined by observing the distance between the nodes of stationary waves in the wire, and calculating the period of the primary oscillation. The velocity of propagation of electric disturbances in air was in this way shown to be finite and of the same order as the velocity of light.[57]

Later in 1888 Hertz[58] showed that electric waves in air are reflected at the surface of a wall; stationary waves may thus be produced, and interference may be obtained between direct and reflected beams travelling in the same direction.

The theoretical analysis of the disturbance emitted by a Hertzian radiator according to Maxwell’s theory was given by Hertz in the following year.[59]

The effects of the radiator are chiefly determined by the free electric charges which, alternately appearing at the two sides, generate an electric field by their presence and a etic field by their motion. In each oscillation, as the charges on the poles of the radiator increase from zero, lines of electric force, having their ends on these poles, move outwards into the surrounding space.

When the charges on the poles attain their greatest values, the lines cease to issue outwards, and the existing lines begin to retreat inwards towards the poles; but the outer lines of force contract in such a way that their upper and lower parts touch each other at some distance from the radiator, and the remoter portion of each of these lines thus takes the form of a loop; and when the rest of the line of force retreats inwards towards the radiator, this loop becomes detached and is propagated outwards as radiation.

In this way the radiator emits a series of whirl-rings, which as they move grow thinner and wider; at a distance, the disturbance is approximately a plane wave, the opposite sides of the ring representing the two phases of the wave. When one of these rings has become detached from the radiator, the energy contained may subsequently be regarded as travelling outwards with it.

To discuss the problem analytically[60] we take the axis of the radiator as axis of z, and the centre of the spark-gap as origin. The field may be regarded as due to an electric doublet formed of a positive and an equal negative charge, displaced from each other along the axis of the vibrator, and of moment

…

the factor

…

The simplest method of proceeding, which was suggested by FitzGerald,[61] is to form the retarded potentials φ and a of L. Lorenz.[62] These are determined in terms of the charges and their velocities by the equations

…

whence it is readily shown that in the present case

…

where

…

The electric and magnetic forces are then determined by the equations

…

It is found that the electric force may be regarded as compounded of a force φ2, parallel to the axis of the vibrator and depending at any instant only on the distance from the vibrator, together with a force φ1 sin θ acting in the meridian plane perpendicular to the radius from the centre, where di depends at any instant only on the distance from the vibrator, and 0 denotes the angle which the radius makes with the axis of the oscillator.

At points on the axis, and in the equatorial plane, the electric force is parallel to the axis.

At a great distance from the oscillator, φ2 is small compared with φ1, so the wave is purely transverse. The magnetic force is directed along circles whose centres are on the axis of the radiator; and its magnitude may be represented in the form φ3 sin θ, where φ3 depends only on r and t; at great distances from the radiator, cφ3 is approximately equal to φ1.

If the activity of the oscillator be supposed to be continually maintained, so that there is no damping, we may replace p1, by zero, and may proceed as in the case of the magnetic oscillator[63] to determine the amount of energy radiated. The mean outward flow of energy per unit time is found to be c3A2(2π/λ)4; from which it is seen that the rate of loss of energy by radiation increases greatly as the wave-length decreases.

The action of an electrical vibrator may be studied by the aid of mechanical models. In one of these, devised by Larmor,[64] the aether is represented by an incompressible elastic solid, in which are two cavities, corresponding to the conductors of the vibrator, filled with incompressible fluid of negligible inertia,

The electric force is represented by the displacement of the solid.

For such rapid alternations as are here considered, the metallic poles behave as perfect conductors; and the tangential components of electric force at their surfaces are zero, This condition may be satisfied in the model by supposing the lining of each cavity to be of flexible sheet-metal, so as to be incapable of tangential displacement; the normal displacement of the lining then corresponds to the surface-density of electric charge on the conductor.

In order to obtain oscillations in the solid resembling those of an electric vibrator, we may suppose that the two cavities have the form of semicircular tubes forming the two halves of a complete circle. Each tube is enlarged at each of its ends, so as to present a front of considerable area to the corresponding front at the end of the other tube.

Thus at each end of one diameter of the circle there is a pair of opposing fronts, which are separated from each other by a thin sheet of the elastic solid.

The disturbance may be originated by forcing an excess of liquid into one of the enlarged ends of one of the cavities. This involves displacing the thin sheet of clastic solid, which separates it from the opposing front of the other cavity, and thus causing a corresponding deficiency of liquid in the enlarged end behind this front. The liquid will then surge backwards and forwards in each cavity between its enlarged ends; and, the motion being communicated to the elastic solid, vibrations will be generated resembling those which are produced in the aether by a Hertzian oscillator.

In the latter part of 1888, the researches of Hertz[65] yielded more complete evidence of the similarity of electric waves to light.

It was shown that the part of the radiation from an oscillator which was transmitted through an opening in a screen was propagated in a straight line, with diffraction effects.

Of the other properties of light, polarization existed in the original radiation, as was evident from the manner in which it was produced; and polarization in other directions was obtained by passing the waves through a grating of parallel metallic wires; the component of the electric force parallel to the wires was absorbed, so that in the transmitted beam the electric vibration was at right angles to the wires.

This effect obviously resembled the polarization of ordinary light by a plate of tourmaline. Refraction was obtained by passing the radiation through prisms of hard pitch.[66]

The old question as to whether the light-vector is in, or at right angles to, the plane of polarization[67] now presented itself in a new aspect.

The wave-front of an electric wave contains two vectors, the electric and magnetic, which are at right angles to each other. Which of these is in the plane of polarization?

The answer was furnished by FitzGerald and Trouton,[68] who found on reflecting Hertzian waves from a wall of masonry that no reflexion was obtained at the polarizing angle when the vibrator was in the plane of reflexion.

The inference from this is that the magnetic vector is in the plane of polarization of the electric wave, and the electric vector is at right angles to the plane of polarization.

An interesting development followed in 1890, when O. Wiener[69] succeeded in photographing stationary waves of light. The stationary waves were obtained by the composition of a beam incident on a mirror with the reflected beam, and were photographed on a thin film of transparent collodion, placed close to the mirror and slightly inclined to it.

If the beam used in such an experiment is plane-polarized, and is incident at an angle of 45°, the stationary vector is evidently that perpendicular to the plane of incidence; but Wiener found that under these conditions the effect was obtained only when the light was polarized in the plane of incidence; so that the chemical activity must be associated with the vector perpendicular to the plane of polarization—i.e., the electric vector.