LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 717 



We thus see that a meter-stick, which, when held perpendicular to 

 its line of motion, has the same length as ? meter-stick at rest, will 

 be shortened when turned parallel to the line of motion in the ratio 



y~ •—, and indeed any moving body must be shortened in the direc- 

 tion of its motion in the same ratio. 9 



Let us emphasize once more, that these changes in the units of time 

 and length, as well as the changes in the units of mass, force, and 

 energy which we are about to discuss, possess in a certain sense a 

 purely factitious significance ; although, as we shall show, this is 

 equally true of other universally accepted physical conceptions. We 

 are only justified in speaking of a body in motion when we have in 

 mind some definite though arbitrarily chosen point as a point of rest. 

 The distortion of a moving body is not a physical change in the body 

 itself, but is a scientific fiction. 



When Lorentz first advanced the idea that an electron, or in fact any 

 moving body, is shortened in the line of its motion, he pictured a real 



9 Certain of Einstein's other deductions from the principle of relativity 

 will not be needed in the development of this paper, but may be directly 

 obtained by the methods here employed. For example, the principle of rela- 

 tivity leads to certain curious conclusions as to the comparative readings of 

 clocks in a system assumed to be in motion. 



Consider two systems in relative motion. An observer on system a places 

 two carefully compared clocks, unit distance apart, in the line of motion, and 

 has the time on each clock read when a given point on the other system 

 passes it. An observer on system b performs a similar experiment. The 

 difference between the readings of the two clocks in one system must be the 

 same as the difference in the other system, for by the principle of relativity 

 the relative velocity v of the systems must appear the same to an observer in 

 either. However, the observer A, considering himself at rest, and familiar 

 with the change in the units of length and time in the moving system which 

 we have already deduced, expects that the velocity determined by B will be 



greater than that which he himself observes in the ratio — 2 , since he has 



concluded that B's unit of time is longer, and his unit of length in this direc- 

 tion is shorter, each by a factor involving ^/l — (3 2 . The only possible way in 

 which A can explain this discrepancy is to assume that the clocks which B 

 claims to have set together are not so in reality. In other words he has to 

 conclude that clocks, which in a moving system appear to be set together, really 

 read differently at any instant (in stationary time), and that a given clock is 

 "slower" than one immediately to the rear of it by an amount proportional to 

 the distance. From what has preceded it can be readily shown that if in a 

 moving system two clocks are situated, one in front of the other by a distanee 



Iv . • 



I, in units of this system, the difference in setting will be — . From this point 



Einstein's equations concerning the addition of velocities also follow directly. 



