CHAPTER III
The New Mechanics and Astronomy
I
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.
2º 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.