Continuity 25 



for this would mean infinite accuracy. 

 We proceed to as many places of decimals 

 as correspond to the order of accuracy 

 aimed at. 



Whenever, then, a commensurable number 

 is really associated with any natural phe- 

 nomenon, there is necessarily a noteworthy 

 circumstance involved in the fact, and it 

 means something quite definite and ulti- 

 mately ascertainable. Every discontinuity 

 that can be detected and counted is an 

 addition to knowledge. It not only means 

 the discovery of natural units instead of 

 being dependent on artificial ones, but it 

 throws light also on the nature of phe- 

 nomena themselves. 



For instance: 



The ratio between the velocity of light 

 and the inverted square root of the pro- 

 duct of the electric and magnetic con- 

 stants was discovered by Clerk Maxwell 

 to be i ; and a new volume of physics was 

 by that discovery opened. 



Dalton found that chemical combina- 

 tion occurred between quantities of dif- 

 ferent substances specified by certain 



