The following elementary example will make this point clear. Consider a circle along which two bodies are moving in opposite directions. We shall assume that the two bodies leave a point at the same instant of time, hence in coincidence, and then meet again at a point halfway round the circle, hence diametrically opposite . There is no difficulty in ascertaining that the point is diametrically opposite , since we know how to measure space. All we have to do is to verify the fact that the length of the curve is equal to the length . Neither does the observation of a coincidence, that is, of the simultaneous presence of two objects at the same point of space, entail any knowledge of a measure of duration. Hence, although we know nothing of the measurement of time, we cannot escape the conclusion that the two bodies have taken the same time to pass from to by different routes. But these spatial routes are of equal length; hence we must assume that the speeds of the bodies along their respective paths have been the same. In all rigour, we may only claim that the mean speed has been the same, since one body may have slowed down, then spurted on again, making up for lost time. But if we repeat the experiment with circles of different sizes, and if in every case the bodies meet one another at the opposite point, we are justified in asserting that not only the mean speed, but also the instantaneous speed at every instant, is the same for either body. In short, thanks to spatial measurements coupled with the observation of coincidences, we have been able to establish the equality of two velocities, even though we knew nothing of time-measurement. A more elaborate presentation of the same problem would be given as follows: Waves of light leaving the centre of a sphere simultaneously are found to return to the centre also in coincidence, after having suffered a reflection against the highly polished inner surface of the sphere. As in the previous example, the light waves have thus covered equal distances in the same time; whence we conclude that [Pg 82] their speed is the same in all directions. Inasmuch as this experiment has been performed, yielding the results we have just described, even though the ether drift caused by the earth’s motion should have varied in direction and intensity, the isotropy of space to luminous propagations was thus established. (The experiment described constitutes but a schematic form of Michelson’s.) It is to be noted that in this experiment the observation of coincidences is alone appealed to (even spatial measurements can be eliminated).[25] When it is realised that coincidences constitute the most exact form of observation, we understand why it is that Einstein’s definition is justified.