Hendrik Lorentz

“ If the mechanism of gravitation consisted in vibrations which cross the aether with the velocity of light, the attraction ought to be modified by the motion of the celestial bodies to a much larger extent than astronomical observations make it possible to admit.
§ 5. Though the states of the aether, the existence and the laws of which have been deduced from electromagnetic phenomena, are found insufficient to account for universal attraction, yet one may try to establish a theory which is not wholly different from that of electricity, but has some features in common with it. ”

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

“ We shall also omit all terms containing such factors as or (k a moderate number) . These reverse their signs by a very small change in r; they will therefore disappear from the resultant force, as soon as, instead of single particles P and Q, we come to consider systems of particles with dimensions many times greater than the wave-length.
From what has been said, we may deduce in the first place that, in applying the above formulae to the ion P, it is sufficient, to take for and the vectors that would exist if P were removed from the field. ”

“ According to these physicists, every particle of ponderable matter consists of two oppositely electrified particles. Th us, between two particles of matter, there will be four electric forces, two attractions between the charges of different, and two repulsions between those of equal signs. Mossotti supposes the attractions to be somewhat greater than the repulsions, the difference between the two being precisely what we call gravitation. It is easily seen that such a difference might exist in cases where an action of a specific electric nature is not exerted. ”

“ In the second place, in consequence of the velocity of vibration, there will be an electromagnetic force with the components
If, as we shall suppose, the displacement of the ion be 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. ”

“ Then, in what follows, 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. Now, as soon as the ion has shifted from its position of equilibrium, new forces come into play. ”

“ If, in differentiating such expressions, we wish to avoid in the denominator powers of r, higher than the first — and this is necessary, in order that (7) may remain free from powers higher than the second — and have to be treated as constants. Moreover, the factors are such, that the vibrations are perpendicular to the line QA. If, now, A coincides with P, and QA with the axis of x, in the expression for bx we shall have , and since this factor is not to be differentiated, all terms in (7) will vanish. ”

“ Next, let the aether be traversed by electromagnetic vibrations, the dielectric displacement being denoted by , and the magnetic force by , then the ion will be acted on by a force
,
whose direction changes continually, and whose components are
In these formulae 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. ”