MEASUREMENT 117 



WHAT PROPERTIES ARE MEASURABLE ? 



And now, after this discussion of number, we can return 

 to the other measurable properties of objects which, like 

 number, can be represented by numerals.} We can now 

 say more definitely what is the characteristic of these 

 properties which makes them measurable. It is that 

 there are rules true of these properties, closely analogous 

 to the rules on which the use of number depends. If a 

 property is to be measurable it must be such that (i) 

 two objects whicLare the same in respect of that property 

 as some third object are the same as each other ; (2) by 

 adding objects successively we must be able to make a 

 standard series one member of which will be the same in 

 respect of the property as any other object we want to 

 measure ; (3) equals added to equals produce equal sums. 

 In order to make a property measurable we must find 

 some method of judging equality and of adding objects, 

 such that these rules are true. 



Let me explain what is meant by using as an example 

 the measurable property, weight. 



Weight is measured by the balance. Two bodies are 

 judged to have the same weight if, when they are placed 

 in opposite pans, neither tends to sink ; and two bodies 

 are added in respect of weight when they are both placed 

 on the same pan of the balance. With these definitions 

 of equality and addition, it is found that the three rules 

 are obeyed, (i) If the body A balances the body B, and 

 B balances C, then A balances C. (2) By placing a body 

 in one pan and continually adding it to others, collections 

 can be built up which will balance any other body placed 

 in the other pan. 1 (3) If the body A balances the body B, 

 and C balances D, then A and C in the same pan will 

 balance B and D in the other pan. To make the matter 

 yet clearer let us take another measurable property, 



1 See further, p. 122, 



