MEASUREMENT 111 



and costs 5 shillings. But I may also ask of what variety 

 the potatoes are, and whether they are good cookers ; 

 to those questions I shall not expect a number in answer. 

 The dealer may possibly call the variety " n .No. 11 " in 

 somebody's catalogue ; but even if he does, T shall feel 

 that such use of a number is not real measurement, and 

 is not of the same kind as the use in connexion with 

 weight or cost. What is the difference ? Why are 

 some properties measurable and others not ? Those 

 are the questions I want to discuss. And I will outline 

 the answer immediately in order that the reader may 

 see at what the subsequent discussion is aiming. The 

 difference is this. LSuppose I have two sacks of potatoes 

 which are identical in weight, cost, variety, and cooking 

 qualities ; and that I pour the two sacks into one so that 

 there is now only one sack of potatoes. This sack will 

 differ from the two original sacks in weight and cost 

 (the measurable properties), but will not differ from them 

 in variety and cooking qualities (the properties that 

 are not measurable). TRe measurable properties of a 

 body are those which are changed by the combination 

 of similar bodies ; the non-measurable properties are 

 those that are not changed?? We shall see that this 

 definition is rather too crude, but it will serve for the 

 present. 



NUMBERS 



In order to see why this difference is so important 

 we must inquire more closely into the meaning of 

 " number." And at the outset we must note that 

 confusion is apt to arise because that word is used to 

 denote two perfectly different things. It sometimes 

 means a mere name or word or symbol, and it sometimes 

 means a property of an object. Thus, besides the 

 properties which have been mentioned, the sack of 



