Preface 



becomes apparent by the interpenetration of 

 the sciences which, separate at first, unify 

 progressively their experimental procedure, 

 their methods and their principles. But this 

 evolution is not haphazard. Mathematics form 

 a primary connection between all our scientific 

 knowledge, since it is woven by our mind and 

 reveals the organic conditions of its activity. 

 We cannot imagine a triangle the sum of whose 

 angles shall not be two right angles, nor an 

 equation of the second degree with three roots. 

 But there is also a necessary logic of things 

 existing outside our mind. It is impossible to 

 heat a bar of iron without it expanding. That 

 is a condition imposed upon the external world. 

 We can recognise it without knowing what heat 

 is, just as we can reason correctly without know- 

 ing the nature of thought. 



Physics in its present-day broadened state 

 teaches the necessary relations between external 

 things, as mathematics reveals the rules of 

 thought. From this point of view all experi- 

 mental sciences are subordinate to it, just as 

 our reasoning is subject to mathematical logic. 

 Mechanics has its origin in experiments upon the 



XI 



