Единая теория электоромагнетизма и гравитации
Оливера Хевисайда
This reproduction of Heaviside's article is an unedited copy of the original, except that some formulas and all vector equations have been converted to modern notation.

From the book "Causality, Electromagnetic Induction, and Gravitation" by Oleg D. Jefimenko (pp. 189-202)

[Part II, The Electrician, 31, 359 (1893)]

In my first article on this subject (The Electrician, July 14, 1893, р. 281), I partly assumed a knowledge on the part of the reader of my theory of convective currents of electrification ("Electrical Papers," Vol. II., p. 495 and after), and only very briefly mentioned the modified law of the inverse squares which is involved, viz., with a lateral concentration of the lines of force. The remarks of the Editor , and of Prof. Lodge on gravitational aberration, lead me to point out now some of the consequences of the modified law which arises when we assume that the ether is the working agent in gravitational effects, and that it propagates disturbances at speed v in the manner supposed in my former article. There is, so far as I can see at present, no aberrations effect, but only a slight alteration in the intensity of force in different directions round a moving body considered as an attractor.

The Electrician, July 14, p. 277, and July 23, p. 340

The Electrician, July 28, p. 347

Thus, take the case of a big Sun and small Earth, of masses and , at distance apart. Let be the unmodified force of on , thus

,                                    (1)

using rational units in order to harmonise with the electromagnetic laws when rationally expressed. Also, let be the modified force when the Sun is in motion at speed through the ether. Then 

This is the case of steady motion. There is no simple formula

when the motion is unsteady

,                                 (2)

where is the small quantity , and is the angle between and the line of motion. ("Electrical Papers," Vol. II., pp. 495, 499).

Therefore, if the Sun is at rest, there is no disturbance of the Newtonian law, because its "field of force" is stationary. But if it has a motion through space, there is a slight weakening of the force in the line of motion, and a slight strengthening equatorially. The direction is still radial.

To show the size of the effect, let


This value of is not very different from the speed attributed to fast stars, and the value of is the speed of light itself.

So we have

,                                       (4)

i.e., one millionth. All perturbing forces of the first order are, therefore, of the order of magnitude of only one-millionth of the full force, even when the speed of propagation is as small as that of light.

The simplest case is when the common motion of the Sun and Earth is perpendicular to the plane of the orbit. Then , all round the orbit, and

,                                  (5)

showing increase in the force of attraction of on of one two-millionth part, without alteration of direction or variation in tile orbit.

4 But Prof. Lodge tells me that our own particular Sun it considered to move only miles per second. This 11 stupendously slow. The size of is reduced to about 1/360 part of that in the text, and the same applies to the corrections depending upon it.

But when the common motion of the Sun and Earth is in their plane, в varies from 0 to in a revolution, so that the attraction on , whilst towards the Sun's centre, always undergoes a periodic variation from


when , to


when . The extreme variation is, therefore, , according to the data used. The result is a slight change in the shape of the orbit.

But, to be consistent, having made v finite by certain suppositions, we should carry out the consequences more fully, and allow not merely for the change in the Newtonian law, as above, but for the force brought in by the finiteness of v which is analogous to the "electromagnetic force." This is very small truly, but so is the above change in the Newtonian law, and since they are of the same order of magnitude, we should also count the auxiliary force. Call it . Then

,                                 (8)

where is as before, in (2) above, is the actual speed of the Earth (not the same as u), and in the third vectorial factorand , are unit vectors drawn parallel to the direction of the Earth's motion, of the Sun's motion, and from the Sun to the Earth. We see at once that the order of magnitude cannot be greater than that of the departure of from before considered, because and will be of the same order, at least when is big. As for , it is simply a numerical factor, which cannot exceed 1, and is probably 2/3

The simplest case is when the motion 'of the Sun is perpendicular to the orbit of the Earth. Then


gives the tensor5 or size of the auxiliary force. It is radial, but

5 Heaviside uses the word "tensor" fur the magnitude of the force vector (0. D. J.).
outwards, so that the result is merely to reduce the size of the previous correction, viz., the difference of from in the same motional circumstances.

But when the line of motion of Sun is in the plane of the orbit, the case is much more complicated. The force is neither constant (for the same distance) nor radial, except in four positions, viz., two in the line of motion of the Sun, when the auxiliary force vanishes, and two when , when it is greatest. But this force is still in the plane of the orbit, which is an important thing, and is, moreover, periodic, so that the tangential component is as much one way as the other in a period.

All we need expect, then, so far as I can see from the above considerations, are small perturbations due to the variation of the force of gravity in different directions, and to the auxiliary force. Of course, there will be numerous minor perturbations

If variations of the force of the size considered above are too small to lead to observable perturbations of motion, then the striking conclusion is that the speed of gravity may even be the same as that of light. If they are observable, then, if existent, they should turn up, but if non-existent then the speed of gravity should be greater. Furthermore, it is to be observed that there may be other ways of expressing the propagation of gravity.

But I am mindful of the good old adage about the shoemaker and his last, and am, therefore, reluctant to make any more remarks about perturbations. The question of the ether in its gravitational aspect must be faced, however, and solved sooner or later, if it be possible. Perhaps, therefore, my suggestions may not be wholly useless.


Web-публикация: guts@univer.omsk.su, Omsk, December 15, 2001.


Russia, Omsk - 2002