154 THE LIMITATIONS OF SCIENCE 



the square root of a length times a mass. Now it is 

 quite certain that a quantity of electricity has nothing 

 in common with length. Taking a step further, we 

 find that the resistance of a conductor to an electrical 

 current may be expressed as a velocity. Yet it would 

 be absurd to attach any concrete relation between elec- 

 trical resistance and mechanical velocity. 



These three examples of velocity illustrate quite 

 clearly the difference between the abstractive and hypo- 

 thetical methods. From the definite and clear idea of 

 the mechanical velocity of a concrete body, we pass to 

 an indefinite idea of the velocity of light in empty 

 space and in order to link this idea to mechanical 

 notions, we assign to light a hypothetical material 

 existence. But our mathematical equations lead us a 

 step further and we can derive a purely f ormular rela- 

 tion between mechanical velocity and electrical resist- 

 ance; in this case analogy between physics and mathe- 

 matics entirely fails and no idea, even hypothetical, 

 has been attached to the result. 



The principles of the science of mechanics, on which 

 the theories of the other branches have been built, 

 date from the time of Galileo and Newton. As they 

 had withstood the searching criticism of the masters 

 of the science for centuries without having been shown 

 to be either false or inadequate, the belief grew that 

 however other theories of physics might change, the 

 laws of mechanics as stated by Newton were prob- 



