MEASUREMENT 119 



THE LAWS OF MEASUREMENT 



But what is the nature of these rules ? They are laws 

 established by definite experiment. The word " rule" 

 has been used hitherto, because it is not quite certain 

 whether they are truly laws in their application to 

 number ; but they certainly are laws in their application 

 to other measurable properties, such as weight or length. 

 Xhe fact that the rules-are true can be, and must be, deter- 

 mined by experiment in the same way as the fact that 

 any other laws are true. Perhaps it may have appeared 

 to the reader that the rules must be true ; that it requires 

 no experiment to determine that bodies which balance 

 the same body will balance each other ; and that it 

 is inconceivable that this rule should not be true. But I 

 think he will change his opinion, if it is pointed out that 

 the rule is actually true only in certain conditions ; for 

 instance, it is only true if the balance is a good one, and 

 has arms of equal length and pans of equal weight. If 

 the arms were unequal, the rule would not be found to 

 be true unless it were carefully prescribed in which pan 

 the bodies were placed during the judgment of equality. 

 Again, the rules would not be true of the property length, 

 unless the rods were straight and were rigid. In implying 

 that the balance is good, and the rods straight and rigid, 

 we have implied definite laws which must be true if the 

 properties are to be measurable, namely that it is possible 

 to make a perfect balance, and that there are rods which 

 are straight and rigid. These are experimental laws ; 

 they could not be known apart from definite experiment 

 and observation of the external world ; they are not self- 

 t evident. 



Accordingly the process of discovering that a property 



is measurable in the way that has been described, and 



/ setting up a process for measuring it, is one that rests 



entirely upon experimental inquiry. It is a part, and a 



