180 WHAT IS SCIENCE? 



the case of density, I find that if I measure the weight 

 and the volume of a body (both measurable by the funda- 

 mental process and therefore definitely fixed), and I divide 

 the weight by the volume, then the numerals thus 

 obtained for different bodies lie in the order of their den- 

 sities, as density was defined on p. 127. Thus I find that 

 I gallon of water weighs 10 lb., but I gallon of mercury 

 weighs 135 lb. ; the weight divided by the volume for 

 water is 10, for mercury is 135 ; 135 is greater than 10 ; 

 accordingly, if the method is correct, mercury should be 

 denser than water and any body which sinks in mercury 

 should sink in water. And that is actually found to be 

 true. If therefore I take as the measure of the density 

 of a substance, its weight divided by its volume, then I 

 get a number which is definitely fixed, 1 and the order of 

 which represents the order of density. I have arrived 

 at a method of measurement which is as definitely fixed 

 as the fundamental process and yet conveys adequately 

 the physically significant facts about order. 



The invention of this process of measurement for 

 properties not suited for fundamental measurement is a 

 very notable achievement of deliberate scientific investi- 

 gation. The process was not invented by common 

 sense ; it was certainly invented in the historic period, 

 but it was not until the middle of the eighteenth century 

 that its use became widespread. 2 To-day it is one of the 

 most powerful weapons of scientific investigation ; and 

 it is because so many of the properties of importance to 



1 Except in so far as I may change the units in which I measure 

 weights and volume. I should get a different number if I measured 

 the volume in pints and the weight in tons. But this latitude in the 

 choice of units introduces a complication which it will be better to 

 leave out of account here. There is no reason why we should not 

 agree once and for all to use the same units ; and if we did that the 

 complication would not arise. 



2 I think that until the eighteenth century only two properties were 

 measured in this way which were not measurable by the fundamental 

 process, namely density and constant acceleration. 



