MEASUREMENT 125 



The property which we shall take as an example of this 

 dependent or, as it will be termed, derived measurement, 

 is density. Every one has some idea of what density 

 means and realizes, vaguely at least, why we say that 

 iron is denser than wood or mercury than water ; and 

 most people probably know how density is measured, 

 and what is meant when it is said that the density of 

 iron is 8 times that of wood, and the density of mercury 

 13! times that of water. But they will feel also that there 

 is something more scientific and less purely common- 

 sense about the measurement of density than about the 

 measurement of weight ; as a matter of fact the discovery 

 of the measurement of density certainly falls within the 

 historic period and probably may be attributed to 

 Archimedes (about 250 B.C.). And a little reflection will 

 convince them that there is something essentially different 

 in the two processes. 



For what we mean when we say a body has a weight 2 

 is that a body of the same weight can be made by com- 

 bining 2 bodies of the weight i ; that is the fundamental 

 meaning of weight ; it is what makes weight physically 

 important and, as we have just seen, makes it measurable. 

 But when we say that mercury has a density 13 J we do 

 not mean that a body of the same density can be prepared 

 by combining 13 J bodies of the density i (water). For, 

 if we did mean that, the statement would not be true. 

 However many pieces of water we take, all of the same 

 density, we cannot produce a body with any different 

 density. Combine water with water as we will, the result- 

 ing body has the density of water. And this, a little 

 reflection will show, is part of the fundamental meaning 

 of density ; density is something that is characteristic 

 of all pieces of water, large and small. The density of 

 water, a " quality " of it, is something fundamentally 

 independent of and in contrast with the weight of water, 

 the " quantity " of it. 



