If the accelerations are null, the frameworks are at rest or in uniform motion relatively to one another. This special case is the "restricted" principle of relativity, which asserts that it is impossible experimentally to detect a uniform motion through the ether. Being thus superfluous for descriptions of natural phenomena, the ether may be abandoned, at least temporarily. The older physics sought this absolute ether framework to which all motions could be unambiguously referred, and failed to find it. The most exacting experiments, notably that of Michelson-Morley, revealed no trace of the earth's supposed motion through the ether. Fitzgerald accounted for the failure by assuming that such motion would remain undetected if every moving body contracted by an amount depending upon its velocity in the direction of motion. The contraction for ordinary velocities is imperceptible. Only when as in the case of the beta particles, the velocity is an appreciable fraction of the velocity of light, is the contraction revealed. This contraction follows immediately from Einstein's generalization constructed upon the equivalence hypothesis and the restricted relativity principle. We shall see that the contraction inevitably follows from the actual geometry of the universe. [2] Let us return for a moment to the moving ball. Four measures, three of distances and one of time, are required in specifying its position with reference to some framework at each point and at each instant. All of these measures can be summed up in one compendious statement--the equations of motion showed how in changing from our room to his accelerated auto we found a new summary, "transformed equations," which seemed to indicate that the ball had traversed a strong, variable field of force. Is there then in the chaos of observational disagreements anything which is independent of all observers? There is, but it is hidden at the very heart of nature. PATHS THROUGH THE WORLD OF FOUR DIMENSIONS