MEASUREMENT i;;:3 



the " arbitrary " measurement of density, depending 

 simply on the arrangements of the substances in their 

 order (p. 127), would serve equally well. The true 

 answer to our question is seen by remembering the con- 

 clusion, at which we arrived in Chapter III, that the terms 

 between which laws express relationships are themselves 

 based on laws and represent collections of other terms 

 related by laws. When we measure a property, either 

 by the fundamental process or by the derived process, 

 the numeral which we assign to represent it is assigned as 

 the result of experimental laws ; the assignment implies 

 laws. And therefore, in accordance with our principle, 

 we should expect to find that other laws could be dis- 

 covered relating the numerals so assigned to each other 

 or to something else ; while if we assigned numerals 

 arbitrarily without reference to laws and implying no 

 , then we should not find other laws involving these 

 numerals. This expectation is abundantly fulfilled, and 

 nowhere is there a clearer example of the fact that the 

 terms involved in laws themselves imply laws. When we 

 a property truly, as we can volume (by the 

 fundamental process) or density (by the derived process) 

 then we are always able to find laws in which these pro- 

 ivolved ; we find, e.g., the law that volume is 

 proportional to weight or that density determines, in a 

 n, the sinking or floating of bodies. 

 But when w. measure it truly, then we do not find 



a law. An : \amplr is provided by the property " hard- 

 ness " (p. 128); the diliirnlties met with in arranging 

 bodies in order of hardness have been overcome ; but 

 we still do not know of any way of measuring, by the 

 derived process, the property hardiu >s ; we know of n<> 

 numerical law which leads to a numeral whieh always 

 follows the order of hardness. And so, as we expect 

 do not ki accurate and gem -nil laws n latmg hard- 



ness to other proj 



