CHAPTER VI 

 MEASUREMENT 



WE have now examined the chief types of scientific 

 proposition and discussed what are the prin- 

 ciples and the facts on which all science rests. 

 Already we have had occasion to notice differences 

 between the various branches of science, and when we 

 leave such very fundamental questions the differences 

 are bound to become more prominent. It does not seem 

 to me that there is much left to say (except in amplifica- 

 tion of what has been said already) that would be applic- 

 able to the whole of science. But there is one further 

 matter which may fitly receive some attention ; for 

 though it affects only part of science, that part is con- 

 stantly growing both in volume and in importance. 

 Moreover, the sciences into which it enters are generally 

 held to be particularly difficult to popularize, and to be 

 beyond the reach of the untrained reader. Accordingly, 

 we shall scarcely diverge from the main purpose of our 

 discussion if in the next two chapters we give it some 

 consideration. 



This matter is measurement and all the structure of 

 mathematical science which rests upon measurement. 

 Every one knows that measurement is a very important 

 part of many sciences ; they know too, that many sciences 

 are " mathematical " and can only be apprehended 

 completely by those versed in mathematics. But very 

 few people could explain exactly how measurement enters 

 into science, why it enters into some and not in others, 

 why it is so important, what mathematics is and why it 

 is so intimately connected with measurement and with 

 the sciences in which measurement is involved. In the 



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