126 WHAT IS SCIENCE? 



But the feature of density, from which it derives its 

 importance, makes it totally impossible to measure 

 density by the fundamental process discussed earlier in 

 the chapter. How then do we measure it ? Before we 

 answer that question, it will be well to put another. As 

 was insisted before, if measurement is really to mean 

 anything, there must be some important resemblance 

 between the property measured, on the one hand, and 

 the numerals assigned to represent it, on the other. 

 In fundamental measurement, this resemblance (or the 

 most important part of it) arises from the fact that the 

 property is susceptible to addition following the same 

 rules as that of number, with which numerals are so 

 closely associated. That resemblance fails here. What 

 resemblance is left ? 



MEASUREMENT AND ORDER 



There is left a resemblance in respect of " order." 

 The numerals are characterized, in virtue of their use 

 to represent numbers, by a definite order ; they are 

 conventionally arranged in a series in which the sequence 

 is determined : " 2 " follows " i " and is before " 3 " ; 

 " 3 " follows " 2 " and is before " 4 " and so on. This 

 characteristic order of numerals is applied usefully 

 for many purposes in modern life ; we " number " 

 the pages of a book or the houses of a street, not in 

 order to know the number of pages in the book or of 

 houses in the street nobody but the printer or the 

 rate-surveyor cares about that but in order to be able 

 to find any given page or house easily. If we want p. 201 

 and the book opens casually at p. 153 we know in which 

 direction to turn the pages. 1 Order then is characteristic 



1 Numerals are also used to represent objects, such as soldiers or 

 telephones, which have no natural order. They are used here because 

 they provide an inexhaustible series of names, in virtue of the ingenious 

 device by which new numerals can always be invented when the old 

 ones have been used up. 



