TIME AND MOTION 88 



way. As a matter of fact, the velocity observed 

 by Fizeau is simply that which is calculated 

 from the equation we have just set down. 



Next let us consider that mysterious shorten- 

 ing of a moving object which was assumed by 

 Fitzgerald and Lorentz and attributed to some 

 mechanical force. But by the principle of rela- 

 tivity we see that this shortening can be repro- 

 duced either by setting a body in motion or even 

 by thinking that it is in motion. Now a meter- 

 stick will trace in time and space a sort of rib- 

 bon. If we look back at Figure 8 of the last 

 chapter, the two parallel lines OA and QR may 

 represent the paths of the two ends of the stick, 

 and if we assume it to be at rest we draw our 

 time axis along one edge and our space axis 

 perpendicular to this, OQ, so that all the points 

 on the line OQ will represent positions of the 

 various particles of the meterstick at a given 

 instant. The distance OQ now represents the 

 length of the meterstick. Next let us assume 

 that the meterstick is in motion, and therefore 

 draw another time axis OB, the perpendicular 

 to which is OP. And now the length OP of the 

 meterstick has diminished, as we saw in the last 

 chapter, by the ratio VI — s^, which is the same 

 as VI — v^. This is precisely the well-kno\\Ti 



