MEASUREMENT 113 



some way to distinguish it from the rest (e.g. by putting 

 it into a box), and then perform a similar operation on 

 a potato from the other sack. I then repeat this double 

 operation continually until I have exhausted the potatoes 

 from one sack. If the operation which exhausts the 

 potatoes from one sack exhausts also the potatoes from 

 the other, then I know that the sacks had the same 

 number of potatoes ; if not, then the sack which is not 

 exhausted had a larger number of potatoes than the 

 other. 



THE RULES FOR COUNTING 



This process could be applied equally well if the objects 

 counted against each other were not of the same nature. 

 The potatoes in a sack can be counted, not only against 

 another collection of potatoes, but also against the men 

 in a regiment or against the days in the year. The 

 " mark/' which is used for distinguishing the objects 

 in the process of counting, may have to be altered to suit 

 the objects counted, but some other suitable mark could 

 be found which would enable the process to be carried 

 out. If, having never heard of counting before, we applied 

 the process to all kinds of different objects, we should 

 soon discover certain rules which would enable us to 

 abbreviate and simplify the process considerably. These 

 rules appear to us to-day so obvious as to be hardly 

 worth stating, but as they are undoubtedly employed 

 in modern methods of counting, we must notice them 

 here. The first is that if two sets of objects, when counted 

 against a third set, are found *to have the same number 

 as that third set, then, when counted against each other 

 they will be found to have the same number. This rule 

 enables us to determine whether two sets of objects 

 have the same number without bringing them together ; 

 if I want to find out whether the number of potatoes 



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