( 1 ) √(1 ——————————— ). ( 100,000,000 ) The difference between these two numbers is ¹/₂₀₀,₀₀₀,₀₀₀, and the two hundred millionth part of the earth’s diameter is equal to 6½ centimetres. It is the figure we had already found. This formula, which gives the value of the contraction in all cases, is elementary. Even the inexpert can easily see the meaning of it. It enables us to calculate the extent of contraction for every rate of velocity. We can easily deduce from it that if the earth’s orbital motion were, not 30 kilometres, but 260,000 kilometres a second, it would be shortened by one-half its diameter in the plane of its motion (without any change in its dimensions in the perpendicular). At that speed a sphere becomes a flattened ellipsoid, of which the small axis is only half the length of the larger axis; a square becomes a rectangle, of which the side parallel to the motion is twice as small as the other. These deformations would be visible to a stationary spectator, but they would be imperceptible to an observer who shares the movement, for the reason already given. The measuring rods and instruments, and even the eye of the observer, would be equally and simultaneously altered. Think of the distorting mirrors which one sees at times in places of amusement. Some show you a greatly elongated picture of yourself, without altering your breadth. Others show you of your normal height, but grotesquely enlarged in width. Try, now, to measure your height and breadth with a rule, as they are given in these deformed reflections in the mirror. If your real height is 5 feet 6 inches, and your real width 2 feet, the rule will, when you apply it to the strange reflection of yourself in the glass, merely tell you that this figure is 5 feet 6 inches in height and 2 feet in breadth. The rule as seen in the mirror undergoes the same distortion as yourself. Hence it is that, even if the globe of the earth had the fantastic speed which we suggested above, its inhabitants would have no means of discovering that they and it were shortened by one-half in the plane east to west. A man 5 feet 6 inches in height, lying in a large square bed in the direction north-south, then changing his position to east-west, would, quite unknown to himself, have his length reduced to 2 feet 9 inches. At the same time he would become twice as stout as before, because previously his breadth was orientated from east to west. But the earth travels at the rate of only thirty kilometres a second, and its entire contraction is only a matter of a few centimetres.