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 to consider them not as mutually exclusive "forms" of thought but as parts of a larger matrix, a sort of four-dimensional continuum, which at once includes both of them and binds them into a unity higher than that of either of them.

2. The theorem which we stated in section III. concerning units of length in the line of relative motion of two systems of reference not at rest relative to each other leads to the conclusion that when a material body is set in motion it undergoes a shortening in the direction of the line of motion and that this deformation takes place as it were automatically without the expenditure of work. This brings to light a very peculiar connection between material bodies and the "empty space" in which they lie or through which they move. Compare the discussion of mass in section VIII.

3. In the classical mechanics the mass of a body is an invariable quantity. In particular, it is independent of the velocity with which the body moves. Its measure is the same in whatever direction it is measured. In section III. we have already seen that none of these statements are true in the theory of relativity. The mass of a body is intimately connected with the absolute value of the velocity with which it moves relative to a system of reference and also (what is stranger still) with the direction in which the mass is measured relative to the direction of motion of the body.

4. It may also be shown that the measure of gravitation depends in a similar way on the motion of the system on which it is measured.

5. Again, the total amount of energy which a body possesses is a simple linear function of its transverse mass, so that energy and mass are connected in a most intimate manner. In fact, changes in energy and changes in transverse mass are proportional, the factor of proportionality being the square of the velocity of light.

Thus we have enumerated several important and striking connections, brought to light by the theory of relativity, where we have heretofore supposed that there were no connections whatever. If we look at these a little more closely we shall be able to perceive a still more profound connection underlying those which we have already mentioned. A material body in motion has kinetic energy. The connections which we treated depend on relative motion. It is then not far to the conclusion that these connections depend essentially on the energy which is involved in this relative motion. Thus all the interlocking relations mentioned might be thought of as due to the energy states involved in the several cases.