Page:Eddington A. Space Time and Gravitation. 1920.djvu/162

is at least approximately correct. The experiment was originally performed by Kaufmann; but much greater accuracy has been obtained by recent modified methods.

Unless the velocity is very great the mass $M$ may be written $m/{\sqrt {(1-2^{2})}}=m+{\tfrac {1}{2}}mu^{2}$. Thus it consists of two parts, the mass when at rest, together with the second term which is simply the energy of the motion. If we can say that the term $m$ represents a kind of potential energy concealed in the matter, mass can be identified with energy. The increase of mass with velocity simply means that the energy of motion has been added on. We are emboldened to do this because in the case of an electrical charge the electrical mass is simply the energy of the static field. Similarly the mass of light is simply the electromagnetic energy of the light.

In our ordinary units the velocity of light is not unity, and a rather artificial distinction between mass and energy is introduced. They are measured by different units, and energy $E$ has a mass $E/C^{2}$ where $C$ is the velocity of light in the units used. But it seems very probable that mass and energy are two ways of measuring what is essentially the same thing, in the same sense that the parallax and distance of a star are two ways of expressing the same property of location. If it is objected that they ought not to be confused inasmuch as they are distinct properties, it must be pointed out that they are not sense-properties, but mathematical terms expressing the dividend and product of more immediately apprehensible properties, viz. momentum and velocity. They are essentially mathematical compositions, and are at the disposal of the mathematician.

This proof of the variation of mass with velocity is much more general than that based on the electrical theory of inertia. It applies immediately to matter in bulk. The masses $m_{1}$ and $m_{2}$ need not be particles; they can be bodies of any size or composition. On the electrical theory alone, there is no means of deducing the variation of mass of a planet from that of an electron.

It has to be remarked that, although the inertial mass of a particle only comes under physical measurement in connection with a change of its motion, it is just when the motion is changing that the conception of its mass is least definite; because it is at