RELATIVITY — RUSSELL. 203 



He will now say, " If these mirrors were really on a circle the light 

 would take longer to reach me from those which were in the direction 

 of my path than from those at right angles. Since the light returns 

 simultaneously from all, the mirrors are not arranged on a circle but 

 on an ellipse, which is longer at right angles to the direction of my 

 motion than it is the other way. " 



If, as in the case previously discussed, he supposes himself to be 

 moving with half the speed of light, he will conclude that the longer 

 diameter of this ellipse is about fifteen per cent greater than the 

 shorter diameter. If he estimates his own velocity higher, he will 

 regard it as differing still more from a circle. 



But although the mirrors in this case are not all at equal distances 

 from him, he cannot find this out by measuring the distance with a 

 measuring rod. In fact, if he does so, their distances will all appear 

 to be exactly the same, if the principle of relativity is true. For, 

 otherwise, by combining an optical experiment and a direct measure- 

 ment he would have a method by which he could distinguish between 

 rest and uniform motion; and this is, by the very hypothesis, im- 

 possible. 



Hence nature must be so constituted that his measuring rod would 

 automatically change in length when turned from a position parallel 

 to his motion to one at right angles to it. 



This sounds strange enough, but something of the sort is entirely 

 necessary in order to explain the Michelson-Morley experiment. The 

 assumption that material bodies, when moving through space, con- 

 tract slightly in the direction of motion was made by Lorentz in 

 order to explain this experiment before the more general theory had 

 been developed. At such speeds as are actually reached by the plan- 

 ets in their orbits, the contraction is less than one part in one hundred 

 million and beyond detection by anything except the most refined 

 investigations. 



We have now seen that, according to the principle of relativity, 

 the answer to the question whether two material rods laid on the table 

 at right angles to one another are of the same length or of different 

 lengths depends on whether we choose to think that we and the room 

 in which the apparatus is situated and the rest of the world, are at rest 

 in space or are moving in different directions with high uniform 

 speeds. 



The fact that when the two rods are laid side by side they are ob- 

 viously exactly equal does not prove that they are the same length 

 when we turn them so that they make an angle with one another. 



So much for the measuring of distances and the measuring of the 

 lengths of things. 



