Maxwell’s theory reduced itself to certain equations, known as “Maxwell’s equations.” Through all the revolutions which physics has undergone in the last fifty years, these equations have remained standing; indeed they have continually grown in importance as well as in certainty—for Maxwell’s arguments in their favor were so shaky that the correctness of his results must almost be ascribed to intuition. Now these equations were, of course, obtained from experiments in terrestrial laboratories, but there was a tacit assumption that the motion of the earth through the ether could be ignored. In certain cases, such as the Michelson-Morley experiment, this ought not to have been possible without measurable error; but it turned out to be always possible. Physicists were faced with the odd difficulty that Maxwell’s equations were more accurate than they should be. A very similar difficulty was explained by Galileo at the very beginning of modern physics. Most people think that if you let a weight drop it will fall vertically. But if you try the experiment in the cabin of a moving ship, the weight falls, in relation to the cabin, just as if the ship were at rest; for instance, if it starts from the middle of the ceiling it will drop onto the middle of the floor. That is to say, from the point of view of an observer on the shore it does not fall vertically, since it shares the motion of the ship. So long as the ship’s motion is steady, everything goes on inside the ship as if the ship were not moving. Galileo explained how this happens, to the great indignation of the disciples of Aristotle. In orthodox physics, which is derived from Galileo, a uniform motion in a straight line has no discoverable effects. This was, in its day, as astonishing a form of relativity as that of Einstein is to us. Einstein, in the special theory of relativity, set to work to show how electromagnetic phenomena could be unaffected by uniform motion through the ether if there be an ether. This was a more difficult problem, which could not be solved by merely adhering to the principles of Galileo. The really difficult effort required for solving this problem was in regard to time. It was necessary to introduce the notion of “proper” time which we have already considered, and to abandon the old belief in one universal time. The quantitative laws of electromagnetic phenomena are expressed in Maxwell’s equations, and these equations are found to be true for any observer, however he may be moving.[3] It is a straight-forward mathematical problem to find out what differences there must be between the measures applied by one observer and the measures applied by another, if, in spite of their relative motion, they are to find the same equations verified. The answer is contained in the “Lorentz transformation,” found as a formula by Lorentz, but interpreted and made intelligible by Einstein.