It was very nearly true; and that makes all the difference between true and false. To say that 999,990 + 9 = 1,000,000, is to say something that is very nearly true, and is therefore false. When it was discovered that the earth was round no change was made in their procedure by architects. They continued to build as if the direction indicated by the plumb-line was always parallel to itself. In the same way those who make our locomotives and aeroplanes will not have to consider the forms of the machines as dependent on their velocities. What does it matter? The practical point of view is not, and cannot be, that of science except indirectly. So much the worse if there is no indirect influence, or if it is slow in coming. Some years ago, however, we discovered things which move at speeds, relatively to us, of tens or hundreds of thousands of kilometres a second; the projectiles of the cathode rays and of radium. In this case the Relativist contraction is very considerable. We shall see how it has been observed. But let us first recapitulate what we have seen. Objects seem to alter their shape in the direction of their movement and not in the direction perpendicular to this. Therefore their forms, even if they be composed of an ideal and perfectly rigid material, depend on their velocity relatively to the observer. This is the essentially new point of view which Einstein’s “Special Relativity” superimposes upon the Relativity of classical mechanics and philosophers. For these the absolute dimensions of a rigid object or a geometrical figure were not absolute; it was only the _relations_ of these dimensions which were real. The new point of view is that these relations are themselves relative, because they are a function of the velocity of the observer. It is a sort of Relativity in the second degree, of which neither the philosophers nor the classic physicists had dreamed. Spatial relations themselves are relative, in a space which is already relative. In the case of our Pullman car and the two pegs which mark its length when it is stationary, an observer situated in the carriage would find the distance between the two pegs shortened as he passes them. The coach would seem to him longer than the distance between the pegs. I who remain beside the pegs observe the contrary. Yet I have no means of proving to the passenger that he is wrong. I see quite plainly that the ray of light which comes from the back peg runs behind the coach, and has therefore, relatively to it, a speed of less than 186,000 miles a second. I know that this is the reason for the passenger’s error, but I have no means of convincing him that he is wrong. He will always say, and rightly: “I have measured the speed at which this ray reaches me, and I have found it 186,000 miles a second.” Each of us is really right.