TIME AND MOTION 71 



a yardstick, distance along any other line repre- 

 sents readings of a clock, while the relative slope 

 between two lines such as QA and QB represents 

 a relative velocity. Thus we see that the theorem 

 in the shear geometry which we mentioned in 

 the last chapter, namely, that the slope between 

 lines QA and QC is equal to the sum of the 

 slopes QA to QB and QB to QC, or s^ = s^ -\- 

 $2, is identical with the law of the addition of 

 velocities which is characteristic of the New- 

 tonian kinematics. 



If it had been kno^n earlier that the kine- 

 matics of Ne\\i:on could be reduced to a geome- 

 try, indeed to one of the simplest of all geome- 

 tries, might not some Minkowski of an earlier 

 day have used mth equal justice the words that 

 I quoted at the beginning of this chapter.^ In 

 any case, the discovery of this coincidence would 

 have increased confidence in the correctness of 

 the kinematics and aroused interest in the study 

 of that geometry; for when a certain kind of 

 mathematics fits a large group of experimental 

 facts we feel sure that it will also agree with the 

 next fact to be discovered. We say that nature 

 would not play us so scurvy a trick as to make 

 our mathematics fit at so many points and fail 



