Michell, Bennet, and Euler

Among the problems to which Maxwell applied his theory of stress in the medium was one which had engaged the attention of many generations of his predecessors.

The adherents of the corpuscular theory of light in the 18th century believed that their hypothesis would be decisively confirmed if it could be shown that rays of light possess momentum.

Several investigators directed powerful beams of light on delicately-suspended bodies. They looked for evidence of a pressure from the impulse of the corpuscles.

In 1708, Homberg did this experiment and [65] imagined that he actually achieved this.

But Mairan and Du Fay repeated his operations and failed to confirm his conclusion.[66]

The subject was afterwards taken up by Michell.

Priestley[67] in 1772 wrote that Michell tried “to ascertain the momentum of light much more accurately than how M. Homberg and M. Mairan had done.”

He exposed a very thin and delicately-suspended copper plate to the sun concentrated by a mirror, and observed a deflexion.

He was not satisfied that the effect of the heating of the air had been altogether excluded, but Priestley thinks that “the motion above mentioned is from the impulse of the rays of light.”

A similar experiment was made by A. Bennet[68]. He directed the light from the focus of a large lens on writing-paper delicately suspended in an exhausted receiver. But he “could not perceive any motion distinguishable from the effects of heat.”

Thus Bennet, and after him Young,[69] regarded the non-appearance of light-repulsion in this experiment as an argument in favour of the undulatory system of light.

Young writes: “For,” wrote , “the corpuscles of light have the utmost imaginable subtility. Their effects might naturally be expected to bear some proportion to the effects of the much less rapid notions of the electrical fluid, which are so very easily perceptible, even in their weakest states.”

Euler many years before had thought that light-pressure might be expected just as reasonably on the undulatory as on the corpuscular hypothesis.

Euler writes: “Just as [70] a vehement sound excites a vibratory motion in the air and a real movement of the dust in it. The vibratory motion set up by the light causes a similar effect.”

Euler believed:

• in the existence of light-pressure and
• that the tails of comets (adopting Kepler’s suggestion) were caused by the solar rays impinging on the comet’s atmosphere, driving off from it the more subtle of its particles.

Maxwell[71] examined this question from the point of view of the electromagnetic theory of light, which readily furnishes reasons for the existence of light-pressure.

Light falling on a metallic reflecting surface at perpendicular incidence may be regarded as constituted of a rapidly-alternating magnetic field. This must induce electric currents in the surface layers of the metal.

But. a metal carrying currents in a magnetic field is acted on by a ponderomotive force, which is at right angles to both the magnetic force and the direction of the current. It is therefore, in the present case, normal to the reflecting surface.

This ponderomotive force is the light-pressure. Thus, according to Maxwell’s theory, light-pressure is only an extended case of effects which may readily be produced in the laboratory.

The magnitude of the light-pressure was deduced by Maxwell from his theory of stresses in the medium. We have seen that the stress across a plane whose unit-normal is N is represented by the vector

Suppose that a plane wave is incident perpendicularly on a perfectly reflecting metallic sheet: this sheet must support the mechanical stress which exists at its boundary in the aether.

Owing to the presence of the reflected wave, D is zero at the surface; and B is perpendicular to N, so (B.N) vanishes.

Thus the stress is a pressure of magnitude (1/8π) (B.H) normal to the surface: that is, the light-pressure is equal to the density of the aethereal energy in the region immediately outside the metal. This was Maxwell’s result.

This conclusion has been reached on the assumption that the light is incident normally to the reflecting surface. If, on the other hand, the surface is placed in an enclosure completely surrounded by a radiating shell, so that radiation falls on it from all directions, it may be shown that the light-pressure is measured by one-third of the density of aethereal energy.