CLASSICAL AND NEW MECHANICS 169 



ure time affect our ideas of time, but it also has an 

 important and unsuspected influence on our ideas of 

 the size and shape of a body. This may be shown by 

 an example. Suppose we wish to measure a rigid rod 

 of length, /, moving in the direction of its axis with 

 a velocity, v, then there are two methods of measuring 

 this length and they do not give concordant results. 



First an observer may move with the rod and meas- 

 ure its length by applying directly to it a measuring- 

 rod. He will evidently obtain the same result as if both 

 he and the rod were at rest. 



A second method is possible and is frequently em- 

 ployed. An observer remains at rest and notes the 

 positions of the two ends of the rod, at a certain time, 

 t, which he determines by means of clocks, also at rest 

 and tested for synchronism. These two points are 

 dependent on our ability to record simultaneous events ; 

 if the rod were at rest the problem would be the one 

 already discussed, but in this case the rod has a velocity, 

 v, and consequently the time used in signaling in one 

 direction involves, V v, and in the other, V + v. 

 So when he measures the distance between the two 

 points, which may also be called the length of the 

 rod, he will find it not equal to / as determined by the 

 first method, if he still regards his clocks as isochro- 

 nous; or if he determined two positions whose 

 measured distance is / then his clocks will no longer be 

 isochronous. 



