In 1881 A. A. Michelson undertook an experiment, originally suggested by Maxwell, to determine the relative motion of our earth to the ether ocean and six years later he repeated it with the assistance of E. W. Morley. The experiment is now known as the Michelson-Morley experiment and since it is the great physical fact upon which the theory of relativity rests, it will be well for us to examine it in detail. Since we can scarcely think that our earth is privileged in the universe and that it is at rest with respect to this great ether ocean that fills space, we propose to discover how fast we are actually moving. But the startling fact is that the experiment devised for this purpose failed to detect any motion whatever of the earth relative to the ether. [3] The explanation of this very curious fact was given by both H. A. Lorentz and G. F. Fitzgerald in what is now widely known under the name of the "contraction hypothesis." It is nothing more nor less than this: Every solid body undergoes a slight change in dimensions, of the order of ($v^2/c^2$), when it moves with a velocity $v$ through the ether. The reason why the experiment failed, then, was not because the earth was not moving through the ether, but because the instruments with which the experiment was being conducted had shrunk just enough to negative the effect that was being looked for. [4] THE LORENTZ TRANSFORMATION We can not at this point forebear introducing a little mathematics to further emphasize the theory and the very logical nature of this contraction hypothesis. Let us suppose that we were on a world that was absolutely motionless with respect to the ether and were looking at a ray of light. The magnetic and electric fields which form the ray can be described by means of four mathematical expressions which have come to bear the name of "Maxwell's field equations." Now suppose that we ask ourselves the question: How must these equations be changed so that they will apply to a ray of light which is being observed by people on a world that is moving with a velocity v through the ether? The answer is immediate. From the Michelson-Morley experiment we know that we can not tell how fast or how slowly we are moving with respect to the ether. This means that no matter what world we may be upon, the form of the Maxwell field equations will always be the same, even though the second set of axes (or frame of reference) may be moving with high velocity with respect to the first. Starting from this hypothesis (called in technical language the covariance of the equations with respect to a transformation of coordinates), Lorentz found that the transformation which leaves the field equations unchanged in form was the following: $$x' = k(x - vt), y' = y, z' = z, t' = k(t - vx/c)$$ where $k$ is as on page 92.