OHAPTEE IX. 



MEASUEE AND THE MEASUEELESS. 



WE have thus seen that the extended world is first 

 known to us through the qualitative differences 

 of attraction and repulsion; that these in turn, through 

 their necessary interactions, develop, or rather are seen to 

 involve, an unlimited complex of quantitative relations; 

 and again, that these quantitative relations reciprocally 

 serve to render completely explicit a whole world of qual- 

 itative characteristics. It is also evident that these 

 mutually inclusive qualitative and quantitative relations 

 constitute the reality of the extended world. 



Let us noAV inquire further of this extended world and 

 obtain, as far as we may, a more adequate knowledge of 

 its fundamental character and modes of existence. 



In the first place, it is evident that whatever knowledge 

 we possess of the quantitative relations of this extended 

 world must involve comparison of one phase with another. 

 But these comparisons also imply a fixed standard. And 

 comparison with a fixed standard constitutes measure. 



At the same time, we must soon become aware that all 

 standards of measurement in the extended world must be 

 arbitrary, and hence the measure must be purely relative. 

 Hence, it may be remarked by the way, there can be no 

 absolute distinction between extensive and intensive quan- 

 tity. On the contrary, a given quantity may be regarded 

 as either extensive or intensive, according to the standard 



A^ /"! Trt-TT * 



