98 THE WORLD-ENERGY 



of comparison. The rending force of gunpowder would 

 be regarded as intensive compared with that of freezing 

 water, while on the other hand, it would rather bear the 

 character of extensive quantity, when compared with 

 dynamite. In other words, any given quantity of energy 

 is not merely extensive or intensive; it is both extensive 

 and intensive. The distinction between these phases can 

 never be suppressed, while, at the same time, their unity 

 is inseparable. 



And yet all measure proves to be relative, even abso- 

 lutely relative. So that, as it seems to turn out, we know 

 absolutely that all our knowledge, especially our exact 

 knowledge, is relative. It is a hopeful-discouraging out- 

 come. Assuredly, if we are anywhere to obtain knowledge 

 that may be called absolute, it must be in the realm of 

 measure, which is pre-eminently the realm of the exact 

 sciences. There is, at least, one science universally ac- 

 knowledged to be exact the science of pure quantity, or 

 mathematics. And yet, even here, there have been skep- 

 tical murmurings, not to say loud protests. The very 

 axioms of mathematics have been called in question.* 

 And not only so, but here and there, especially in the 

 applications of mathematics, there is full confession of the 

 necessity of approximation, as will be seen more fully 

 when we come to consider the subject of motion. So that 

 a momentary shadow of suspicion arises lest the very sci- 

 ence in which men have so long confided with absolute 

 serenity may prove to be, after all, only the exact science of 

 approximation. And so much the more as those sciences 

 which have come to be called " exact/" through the 



* See, for example, Helmholz's criticism cm The Axioms of Mathematics, 

 in his Popular Scientific Lectures (Second Series). 



