132 WHAT IS SCIENCE? 



substances to which the conception of density is applicable 

 at aU. 



Of course every one knows that this relation is actually 

 true ; it is so familiar that we are apt to forget that it is 

 an experimental truth that was discovered relatively 

 late in the history of civilization, which easily might not 

 be true. Perhaps it is difficult to-day to conceive that 

 when we take " more " of a substance (meaning thereby 

 a greater volume) the weight should not increase, but it 

 is quite easy to conceive that the weight should not 

 increase proportionally to the volume ; and yet it is upon 

 strict proportionality that the measurement of density 

 actually depends. If the weight had not been propor- 

 tional to the volume, it might still have been possible to 

 measure density, so long as there was some fixed numerical 

 relation between weight and volume. It is this idea 

 of a fixed numerical relation, or, as we shall call it 

 henceforward, a numerical law, that is the basis of the 

 " derived " process of measurement that we are consider- 

 ing ; and the process is of such importance to science 

 because it is so intimately connected with such numerical 

 laws. The recognition of such laws is the foundation of 

 modern physics. 



THE IMPORTANCE OF MEASUREMENT 



For why is the process of measurement of such vital 

 importance ; why are we so concerned to assign numerals 

 to represent properties. One reason doubtless is that 

 such assignment enables us to distinguish easily and 

 minutely between different but similar properties. It 

 enables us to distinguish between the density of lead and 

 iron far more simply and accurately than we could 

 do by saying that lead is rather denser than iron, but not 

 nearly so dense as gold and so on. But for that purpose 



