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 which are 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 

 I of judging equality and of adding objects, 

 such that these rules are true. 



Lei lain what is meant by using as an example 



the able property, weight. 



Weight i measured by the balance. Two bodies 

 ed to have the same weight if, when they are pi 

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

 are added in respect of weight when they are both pi 

 on the same pan of the balance. Wiih these deiinit 

 of equality a it is found that the three i 



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



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



in OB tdoontin Ming it toothers, o> 



can be built up whieh \\ .re any other body placed 



inthot; ' (3) If the body A 1 the body B, 



i A and C in the same p.m will 

 1 I) in the G . 



yet clearer let us take r measurable property, 



1 See further, p. i 



