Can we ascribe gravity to a certain state of the aether?

A theory of universal attraction, founded on the state of the aether, would take the simplest form.

It is believed that only electrically charged particles or ions, are directly acted on by the aether.

This leads to the idea that every particle of ponderable matter might consist of 2 ions with equal opposite charges. Or at least:

• they might contain 2 such ions
• gravity might be the result of the forces experienced by these ions.

So many phenomena have been explained by a theory of ions. This idea seems to be more admissible than before.

Electromagnetic disturbances in the aether might possibly be the cause of gravitation. This is possible if they could penetrate all bodies without diminishing in intensity.

Electric vibrations of extremely small wavelength possess this property.

But what action there would be between 2 ions, if the aether were traversed in all directions by trains of electric waves of small wavelength?

The above ideas are not new.

Every physicist knows Le Sage’s theory in which innumerable small corpuscula are supposed to move with great velocities. This produces gravitation by their impact against the coarser particles of ordinary ponderable matter.

This theory is not in harmony with modern physical views.

But it was found that a pressure against a body may be produced as well by trains of electric waves and by rays of light (e.g. as by moving projectiles).

When penetrating x-rays were discovered, it was natural to replace Le Sage’s corpuscula by vibratory motions.

There could be radiations, far more penetrating than even the X-rays. This would account for gravity which is independent of all intervening matter.

But this theory of rapid vibrations as a cause of gravitation cannot be accepted.

Part 2

Let an ion carrying a charge e1 and a mass be at the point P(x,y,z). It may be subject or not to an elastic force, proportional to the displacement and driving it back to P, as soon as it has left this position.

Let the aether be traversed by electromagnetic vibrations, the dielectric displacement being denoted by d , and the magnetic force by H. Then the ion will be acted on by a force.

4 π V 2 e d

whose direction changes continually, and whose components are X = 4 π V 2 e d x , Y = 4 π V 2 e d y , Z = 4 π V 2 e d z (1)

V means the velocity of light.

By the action of the force (1) the ion will be made to vibrate about its original position P, the displacement (x, y,z) being determined by well known differential equations.

We shall confine ourselves to simple harmonic vibrations with frequency n.

All our formulae will then contain the factor cos ⁡ n t or sin ⁡ n t, and the forced vibrations of the ion may be represented by expressions of the form

x = a e d x − b e d ˙ x , y = a e d y − b e d ˙ y , z = a e d z − b e d ˙ z (2)

with certain constant coefficients a and b.

The terms with d ˙ x , d ˙ y have been introduced in order to indicate that the phase of the forced vibration differs from that of the force (X,Y,Z); this will be the case as soon as there is a resistance, proportional to the velocity, and the coefficient b may then be shown to be positive.

One cause of a resistance lies in the reaction of the aether, called forth by the radiation of which the vibrating ion itself becomes the centre.

At the same time, this reaction determines an apparent increase of the mass of the particle.

We have kept in view this reaction in establishing the equations of motion, and in assigning their values to the coefficients a and b.

So we need only consider the forces due to the state of the aether, in so far as it not directly produced by the ion itself.

Since the formulae (2) contain e as a factor, the coefficients a and b will be independent of the charge.

Their sign will be the same for a negative ion and for a positive one.

As soon as the ion has shifted from its position of equilibrium, new forces come into play.

In the first place, the force 4 π V 2 e d {\displaystyle 4\pi V^{2}e{\mathfrak {d}}} {\displaystyle 4\pi V^{2}e{\mathfrak {d}}} will have changed a little, because, for the new position, d {\displaystyle {\mathfrak {d}}} {\displaystyle {\mathfrak {d}}} will be somewhat different from what it was at the point P. We may express this by saying that, in addition to the force (1), there will be a new one with the components, 4 π V 2 e ( x ∂ d x ∂ x + y ∂ d x ∂ y + z ∂ d x ∂ z ) etc. (3)

In the second place, in consequence of the velocity of vibration, there will be an electromagnetic force with the components e ( y ˙ H z − z ˙ H y ) , etc. (4)

If the displacement of the ion is very small, compared with the wave-length, the forces (3) and (4) are much smaller than the force (1); since they are periodic — with the frequency 2n, — they will give rise to new vibrations of the particle.

We shall however omit the consideration of these slight vibrations, and examine only the mean values of the forces (3) and (4), calculated for a rather long lapse of time, or, what amounts to the same thing, for a full period 2 π n {\displaystyle {\tfrac {2\pi }{n}}} {\displaystyle {\tfrac {2\pi }{n}}}.