have moved in consequence of the motion; second, since B's clock is running slow, the time taken for light to traverse this too great distance is itself too great. Now if too great a distance is traversed in too great a time, then the velocity will Fig. 7. remain the same provided the factor which multiplies the distance is the same as that which multiplies the time. But unfortunately, or fortunately, a very little mathematics shows that this multiplier is not the same. A sees too short a distance being traversed by light in a second of time, and therefore B's yardstick is too short, and by an amount depending on the relative velocity of A and B. Thus we are led to the astonishing general conclusion of the relativity theory with reference to length: If two bodies are moving relative to each other, then to an observer on the one, the unit of length of the other, measured in the direction of this relative velocity, appears to be shortened by an amount depending on this relative velocity. This shortening must not be looked upon as due to the resistance of any medium, but, as Minkowski puts it, must be regarded as purely a gift of the gods, a necessary accompaniment of the condition of motion. The same objection might be raised here as in the case of the time unit. Perhaps the length of the yardstick appears to change, but does the real length change? But the answer is, there is no way of determining the real length, or more exactly, the words real length have no meaning. Neither A nor B can determine whether he is in motion or at rest absolutely, and if B compares his measure with another one traveling with him, he learns nothing, and if he compares it with one in motion relative to him, he finds the two of different length, just as A did.

This startling fact, that a railway train as it whizzes past us is shorter than the same train at rest, is at first a trifle disturbing, but how much of our amazement is due to our experience, or lack of it. A certain African king, on beholding white men for the first time, reasoned that as all men were black, these beings, being white, could not be men. Are we any more logical when we say that since in our experience no yardsticks have varied appreciably on account of their velocity, hence it is absurd to admit the possibility of such a thing.

Perhaps it might be well at this point to give some idea of the size of these apparent changes in the length of the time unit and the space unit, although the magnitude is a matter of secondary importance. The whole history of physics is a record of continual striving after more exact measurements, and a fitting of theory to meet new corrections, however small. So it need not occasion surprise to learn that these differences are exceedingly minute; the amazing thing, and the thing of scientific interest, is that they exist at all. If we consider the velocity of