118 WHAT IS SCIENCE? 



length. Two straight rods are judged equal in length, if 

 they can be placed so that both ends of one are contiguous 

 to both ends of the other ; they are added in respect of 

 length, when they are placed with one end of one con- 

 tiguous with one end of the other, while the two form 

 a single straight rod. Here again we find the three rules 

 fulfilled. Bodies which are equal in length to the same 

 body are equal in length to each other. By adding 

 successively rods to each other, a rod can be built up 

 which is equal to any other rod. And equal rods added to 

 equal rods produce equal rods. Length is therefore a 

 measurable property. 



It is because these rules are true that measurement of 

 these properties is useful and possible ; it is these rules 

 that make the measurable properties so similar to 

 numbers, that it is possible and useful to represent them 

 by numerals the primary purpose of which is to repre- 

 sent numbers. It is because of them that it is possible 

 to find one, and only one numeral, which will fitly repre- 

 sent each property ; and it is because of them, that these 

 numerals, when they are found, tell us something useful 

 about the properties. One such use arises in the combina- 

 tion of bodies possessing the properties. We may want 

 to know how the property varies when bodies possessing 

 it are added in the way characteristic of measurement. 

 When we have assigned numerals to represent the 

 property we shall know that the body with the property 

 2 added to that with the property 3 will have the same 

 property as that with the property 5, or as the combina- 

 tion of the bodies with properties 4 and i. This is not 

 the place to examine exactly how these conclusions are 

 shown to be universally valid ; but they are valid only 

 because the three rules are true. 



