122 WHAT IS SCIENCE? 



it is mentioned in order to impress the reader with the 

 fact that measurement does depend upon experimental 

 laws ; that it does depend upon the facts of the external 

 world ; and that it is not wholly within our power to 

 determine whether we will or will not measure a certain 

 property. That is the feature of measurement which it 

 is really important to grasp for a proper understanding of 

 science. 



MULTIPLICATION 



Before we pass to another kind of measurement refer- 

 ence must be made to a matter which space does not 

 allow to be discussed completely. In stating the rules 

 that were necessary in order that weight should be measur- 

 able (p. 117), it was said that a collection having the same 

 weight as any given body could be made by adding other 

 bodies to that first selected. Now this statement is 

 not strictly true ; it is only true if the body first selected 

 has a smaller weight than any other body it is desired to 

 weigh ; and even if this condition is fulfilled, it is not true 

 if the bodies added successively to the collection are oi 

 the same weight as that first selected. Thus if my first 

 body weighs i lb., I cannot by adding to it make a collec- 

 tion which weighs less than i lb., and by adding bodies 

 which each weigh i lb., I cannot make a collection which 

 has the same weight as a body weighing (say) 2 J lb. 



These facts, to which there is no true analogy in con- 

 nexion with number, force us to recognize " fractions." 

 A considerable complication is thereby introduced, and 

 the reader must accept my assurance that they can all 

 be solved by simple developments of the process of 

 measurement that has been sketched. But for a future 

 purpose it is necessary to notice very briefly the processes 

 of the multiplication and division of magnitudes on which 

 the significance of fractions depends. 



