THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 27 



disagreeableness of the notes they are quantities. In all cases 

 the distances between terms of the series (if they possess distance) 

 have magnitude, while the whole composed of a stretch is also 

 a quantity. The correlating of magnitudes whether of terms 

 or of distances with the number series will present no new 

 feature except in the remarkable cases in which it is possible 

 to say that one magnitude is double of another. 



It is not difficult to see that such a statement applies in 

 the first instance only to numbers, and contains a reference to 

 the process of logical addition. The books on the top two 

 shelves in front of me as I write form similar classes : I could 

 " tell off " a book from the top shelf against one from the 

 second until the whole of the books were simultaneously 

 exhausted. Both classes of books possess, then, the same 

 number which happens to be 18. By logical addition I can 

 regard both sets of books as constituting one class, " the books. 

 on the top two shelves." The number of this class, which is 

 the logical sum of the original similar classes, is 36. This 

 number is called the "double" of 18. This simple case 

 illustrates the property of numbers which, besides their ready 

 accessibility to all, and the ease with which they lend them- 

 selves to correlation, is the most important which they possess 

 for the purposes alike of practical life and of science. The 

 essence of this property is that when correlation has been 

 effected between any" terms of series and appropriate members 

 of the number series, it is possible to predict the effect of 

 carrying out a given operation on these numbered objects by 

 mere consideration of the properties of the terms of the 

 number series the result of the operation in question being 

 always indicated in an interpretable way by its correlation 

 with the single number which is the result of the operations 

 that have been performed on the numerical data. Thus we 

 can predict without actual trial the number of pieces of paper, 

 each 1 foot square, which it is possible to place on a rectangular 

 area measuring 4 feet long and 3 feet wide. 



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