MEASUREMENT 131 



other sciences are measured in this way that physics, 

 the science to which this process belongs, is so largely 

 the basis of other sciences. But it may appear exceed- 

 ingly obvious to the reader, and he may wonder why the 

 invention was delayed so long. He may say that the 

 notion of density, in the sense that a given volume of the 

 denser substance weighs more than the same volume of 

 the less dense, is the fundamental notion ; it is what we 

 mean when we speak of one substance being denser (or 

 in popular language " heavier ") than another ; and that 

 all that has been discovered in this instance is that the 

 denser body, in this sense, is also denser in the sense of 

 p. 127. This in itself would be a very noteworthy dis- 

 covery, but the reader who raises such an objection has 

 overlooked a yet more noteworthy discovery that is 

 involved. 



For we have observed that it is one of the most charac- 

 teristic features of density that it is the same for all 

 bodies, large and small, made of the same substance. It 

 is this feature which makes it impossible to measure it 

 by the fundamental process. The new process will be 

 satisfactory only if it preserves this feature. If we are 

 going to represent density by the weight divided by the 

 volume, the density of all bodies made of the same sub- 

 stance will be the same, as it should be, only if for all of 

 them the weight divided by the density is the same, that 

 is to say, in rather more technical language, if the weight 

 is proportional to the density. In adopting the new pro- 

 cess for measuring density and assigning numerals to 

 represent it in a significant manner, we are, in fact, assum- 

 ing that, for portions of the same substance, whether they 

 are large or small, the weight is proportional to the 

 volume. If we take a larger portion of the same sub- 

 stance and thereby double the weight, we must find, if 

 the process of measurement is to be a success, that we also 

 double the volume]; and this law must be true for 'all 



