Superphysics
Chapter 4

# The Luminiferous Medium, From Bradley To Fresnel

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Newton refrained from committing to any doctrine regarding the ultimate nature of light.

The next generation writers interpreted his criticism of the wave-theory as an acceptance of the corpuscular hypothesis.

The chief optical discovery of this period tended to support the corpuscular hypothesis.

In 1728, James Bradley (b. 1692, d. 1762) was then a Savilian Professor of Astronomy at Oxford. He sent an “Account of a new discovered motion of the Fix’d Stars to the Astronomer Royal (Halley)."[1]

In observing the star `γ` in the head of the Dragon, he had found that during the winter of 1725–6, the transit across the meridian was continually more southerly, while during the following summer its original position was restored by a motion northwards.

Such an effect could not be explained by parallax. Bradley guessed it to be due to the gradual propagation of light.[2]

`CA` is a ray of light falling on the line `BA`.

• If the observer is travelling along BA, with a velocity which is to the velocity of light as BA is to CA.
• The corpuscle of light, by which the object is discernible to the observer at A, would have been at C when the eye was at B.
• The tube of a telescope must therefore be pointed in the direction BC, in order to receive the rays from an object whose light is really propagated in the direction CA.
• The angle BCA measures the difference between the real and apparent positions of the object.

It is evident from the figure that the sine of this angle is to the sine of the visible inclination of the object to the line in which the eye is moving, as the velocity of the eye is to the velocity of light.

Observations such as Bradley’s will therefore enable us to deduce the ratio of the mean orbital velocity of the earth to the velocity of light. This is called “the constant of aberration”.

From its value, Bradley calculated that light is propagated from the sun to the earth in 8 minutes 12 seconds.

With the exception of Bradley’s discovery, which was primarily astronomical rather than optical, the 18th century was barren in terms of the experimental and theoretical investigation of light. This is in contrast to the brilliance of electrical researches.

In 1736, the younger John Bernoulli (b. 1710, d. 1790) was awarded the prize of the French Academy for the suggestive study[4] of the aether.

In 1701, his father, the elder John Bernoulli (b. 1667, d. 1748) tried to connect the law of refraction with the mechanical principle of the composition of forces.

If 2 opposed forces whose ratio is `μ` maintain in equilibrium a particle which is free to move only in a given plane, it follows from the triangle of forces that the directions of the forces must obey the relation:

where `i` and `r` denote the angles made by these directions with the normals to the plane.

This is the same equation as that which expresses the law of refraction, and the elder Bernoulli conjectured that a theory of light might be based on it; but he gave no satisfactory physical reason for the existence of forces along the incident and refracted rays. This defect his son now proceeded to remove.

According to Bernoulli Jr, all space is permeated by a fluid aether containing an immense number of excessively small whirlpools.

The aether appears to have elasticity that lets it transmit vibrations. This is really due to the presence of these whirlpools.

Each whirlpool is continually striving to dilate due to the centrifugal force. This presses it against the neighbouring whirlpools.

Bernoulli is a thorough Cartesian in spirit.

He rejects action at a distance. He insists that even the elasticity of his aether* shall be explicable in terms of matter and motion.

*Superphysics Note: In actual Cartesian Physics, the vortices manifest as the spacetime vortices which are different from the aether.

This aggregate of small vortices, or “fine-grained turbulent motion,” as it came to be called a century and a half later,[6] is intenspersed with solid corpuscles, whose dimensions are small compared with their distances apart.

These are pushed about by the whirlpools whenever the aether is disturbed, but never travel far from their original positions.

A source of light communicates to its surroundings a disturbance which condenses the nearest whirlpools.

These by their condensation displace the contiguous corpuscles from their equilibrium position. These in turn produce condensations in the whirlpools next beyond them, so that vibrations are propagated in every direction from the luminous point.

Bernoulli speaks of these vibrations as longitudinal. He actually contrasts them with those of & stretched cord, which, “when it is slightly displaced from its rectilinear form, and then let go, performs transverse vibrations in a direction at right angles to the direction of the cord.”

Newton objected to longitudinal vibrations on the score of polarization.

Bernoulli’s aether closely resembles that which Maxwell invented in 1861-2 for the express purpose of securing transversality of vibration.

Bernoulli explained refraction by combining these ideas with those of his father.

Within the pores of ponderable bodies the whirlpools are compressed, so the centrifugal force must vary in intensity from one medium to another.

Thus, a corpuscle situated in the interface between two media is acted on by a greater elastic force from one medium than from the other. By applying the triangle of forces to find the conditions of its equilibrium, the law of Snell and Descartes may be obtained.

Not long after this, the echoes of the old controversy (between Descartes and Format about the law of refraction were awakened[7] by Pierre Louis Moreau de Maupertuis (b. 1698, d. 1759).

• According to Descartes, the speed of light is fastest in dense media.
• According to Fermat, the speed of light is fastest in free aether.

The arguments of the corpuscular theory convinced Maupertuis that on this particular, Descartes was correct.

But nevertheless, he wished to retain for science the beautiful method by which Fermat had derived his result.

This he now proposed to do by modifying Fermat’s principle so as to make it agree with the corpuscular theory.

Instead of assuming that light follows the quickest path, he supposed that “the path described is that by which the quantity of action is the least”.

He defined this action to be proportional to the sum of the spaces described, each multiplied by the velocity with which it is traversed. Thus instead of Fermat’s expression:

(where t denotes time, v velocity, and ds an element of the path) Maupertuis introduced:

as the quantity which is to assume its minimum value when the path of integration is the actual path of the light.

Since Maupertuis’ v, which denotes the velocity according to the corpuscular theory, is proportional to the reciprocal of Fermat’s v, which denotes the velocity according to the wave-theory, the two expressions are really equivalent, and lead to the same law of refraction.

Maupertuis’ memoir is, however, of great interest from the point of view of dynamics ; for his suggestion was subsequently developed by himself and by Euler and Lagrange into a general principle which covers the whole range of Nature, so far as Nature is a dynamical system.

The natural philosophers of the 18th century for the most part, like Maupertuis, accepted the corpuscular hypothesis.