_Gravitation_
Mass may be defined in two ways:
1º By the quotient of the force by the acceleration; this is the true definition of the mass, which measures the inertia of the body.
2° By the attraction the body exercises upon an exterior body, in virtue of Newton's law. We should therefore distinguish the mass coefficient of inertia and the mass coefficient of attraction. According to Newton's law, there is rigorous proportionality between these two coefficients. But that is demonstrated only for velocities to which the general principles of dynamics are applicable. Now, we have seen that the mass coefficient of inertia increases with the velocity; should we conclude that the mass coefficient of attraction increases likewise with the velocity and remains proportional to the coefficient of inertia, or, on the contrary, that this coefficient of attraction remains constant? This is a question we have no means of deciding.
On the other hand, if the coefficient of attraction depends upon the velocity, since the velocities of two bodies which mutually attract are not in general the same, how will this coefficient depend upon these two velocities?
Upon this subject we can only make hypotheses, but we are naturally led to investigate which of these hypotheses would be compatible with the principle of relativity. There are a great number of them; the only one of which I shall here speak is that of Lorentz, which I shall briefly expound.
Consider first electrons at rest. Two electrons of the same sign repel each other and two electrons of contrary sign attract each other; in the ordinary theory, their mutual actions are proportional to their electric charges; if therefore we have four electrons, two positive _A_ and _A'_, and two negative _B_ and _B'_, the charges of these four being the same in absolute value, the repulsion of _A_ for _A'_ will be, at the same distance, equal to the repulsion of _B_ for _B'_ and equal also to the attraction of _A_ for _B'_, or of _A'_ for _B_. If therefore _A_ and _B_ are very near each other, as also _A'_ and _B'_, and we examine the action of the system _A_ + _B_ upon the system _A'_ + _B'_, we shall have two repulsions and two attractions which will exactly compensate each other and the resulting action will be null.
Now, material molecules should just be regarded as species of solar systems where circulate the electrons, some positive, some negative, and _in such a way that the algebraic sum of all the charges is null_. A material molecule is therefore wholly analogous to the system _A_ + _B_ of which we have spoken, so that the total electric action of two molecules one upon the other should be null.
But experiment shows us that these molecules attract each other in consequence of Newtonian gravitation; and then we may make two hypotheses: we may suppose gravitation has no relation to the electrostatic attractions, that it is due to a cause entirely different, and is simply something additional; or else we may suppose the attractions are not proportional to the charges and that the attraction exercised by a charge +1 upon a charge -1 is greater than the mutual repulsion of two +1 charges, or two -1 charges.
In other words, the electric field produced by the positive electrons and that which the negative electrons produce might be superposed and yet remain distinct. The positive electrons would be more sensitive to the field produced by the negative electrons than to the field produced by the positive electrons; the contrary would be the case for the negative electrons. It is clear that this hypothesis somewhat complicates electrostatics, but that it brings back into it gravitation. This was, in sum, Franklin's hypothesis.
What happens now if the electrons are in motion? The positive electrons will cause a perturbation in the ether and produce there an electric and magnetic field. The same will be the case for the negative electrons. The electrons, positive as well as negative, undergo then a mechanical impulsion by the action of these different fields. In the ordinary theory, the electromagnetic field, due to the motion of the positive electrons, exercises, upon two electrons of contrary sign and of the same absolute charge, equal actions with contrary sign. We may then without inconvenience not distinguish the field due to the motion of the positive electrons and the field due to the motion of the negative electrons and consider only the algebraic sum of these two fields, that is to say the resulting field.
In the new theory, on the contrary, the action upon the positive electrons of the electromagnetic field due to the positive electrons follows the ordinary laws; it is the same with the action upon the negative electrons of the field due to the negative electrons. Let us now consider the action of the field due to the positive electrons upon the negative electrons (or inversely); it will still follow the same laws, but _with a different coefficient_. Each electron is more sensitive to the field created by the electrons of contrary name than to the field created by the electrons of the same name.
Such is the hypothesis of Lorentz, which reduces to Franklin's hypothesis for slight velocities; it will therefore explain, for these small velocities, Newton's law. Moreover, as gravitation goes back to forces of electrodynamic origin, the general theory of Lorentz will apply, and consequently the principle of relativity will not be violated.
We see that Newton's law is no longer applicable to great velocities and that it must be modified, for bodies in motion, precisely in the same way as the laws of electrostatics for electricity in motion.
We know that electromagnetic perturbations spread with the velocity of light. We may therefore be tempted to reject the preceding theory upon remembering that gravitation spreads, according to the calculations of Laplace, at least ten million times more quickly than light, and that consequently it can not be of electromagnetic origin. The result of Laplace is well known, but one is generally ignorant of its signification. Laplace supposed that, if the propagation of gravitation is not instantaneous, its velocity of spread combines with that of the body attracted, as happens for light in the phenomenon of astronomic aberration, so that the effective force is not directed along the straight joining the two bodies, but makes with this straight a small angle. This is a very special hypothesis, not well justified, and, in any case, entirely different from that of Lorentz. Laplace's result proves nothing against the theory of Lorentz.
