On the other hand, the Maxwell-Lorentz equations have proved their validity in the treatment of optical problems in moving bodies. No other theory has satisfactorily explained the facts of aberration, the propagation of light in moving bodies (Fizeau), and phenomena observed in double stars (De Sitter). The consequence of the Maxwell-Lorentz equations that in a vacuum light is propagated with the velocity , at least with respect to a definite inertial system , must therefore be regarded as proved. According to the principle of special relativity, we must also assume the truth of this principle for every other inertial system. Before we draw any conclusions from these two principles we must first review the physical significance of the concepts "time" and "velocity." It follows from what has gone before, that co-ordinates with respect to an inertial system are physically defined by means of measurements and constructions with the aid of rigid bodies. In order to measure time, we have supposed a clock, , present somewhere, at rest relatively to . But we cannot fix the time, by means of this clock, of an event whose distance from the clock is not negligible; for there are no "instantaneous signals" that we can use in order to compare the time of the event with that of the clock. In order to complete the definition of time we may employ the principle of the constancy of the velocity of light in a vacuum. Let us suppose that we place similar clocks at points of the system , at rest relatively [Pg 28] to it, and regulated according to the following scheme. A ray of light is sent out from one of the clocks, , at the instant when it indicates the time , and travels through a vacuum a distance , to the clock ; at the instant when this ray meets the clock the latter is set to indicate the time = + .[7] The principle of the constancy of the velocity of light then states that this adjustment of the clocks will not lead to contradictions. With clocks so adjusted, we can assign the time to events which take place near any one of them. It is essential to note that this definition of time relates only to the inertial system , since we have used a system of clocks at rest relatively to . The assumption which was made in the pre-relativity physics of the absolute character of time (i.e. the independence of time of the choice of the inertial system) does not follow at all from this definition. [7]Strictly speaking, it would be more correct to define simultaneity first, somewhat as follows: two events taking place at the points and of the system are simultaneous if they appear at the same instant when observed from the middle point, , of the interval . Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to , which register the same simultaneously.