THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 29 



an element of convention is still present (for the magnitude of 

 the whole can hardly be regarded as the sum of the magnitudes 

 of the parts), we judge one magnitude to be double another if 

 the quantity which has the former magnitude can be divided 

 into two quantities whose magnitude is the same as that of the 

 latter. N 



In the cases considered, then, we can, by the aid of certain 

 more or less easy conventions, solve the problem of measure- 

 ment. That is, we can so correlate the members of the 

 number series with the members of the series ill question that 

 whenever the numbers are twice, thrice, four times one another, 

 and so on, the corresponding quantities or stretches or 

 distances will be in the senses indicated, twice, thrice, four 

 times one another, and so on. In every such case we may 

 make use of the correlated numbers for the purposes of 

 practice or theory in the manner already indicated.* It is 

 clear, moreover, that by conventions which contain the familiar 

 rules for the manipulation of decimal " fractions " we may 

 apply to this purpose the whole of the extended " compact " 

 series of numbers that was reached in the last section. 



It is a commonplace that the series of Time and Space play 

 an all-important part in Science ; it will be desirable, therefore, 

 to consider briefly certain special characteristics and special 

 difficulties which they present. "We can dismiss in a few 

 words the property possessed by the spatial series of having 

 more than one " dimension." From the critical standpoint it is 

 chiefly important to note that this is not a unique property. 

 The notes played by a performer on the pianoforte may be 



* It should be noted that measurement of "magnitudes of divisi- 

 bility" such as Space and Time and (conventionally) Weight require a 

 unit a part which is repeatedly applied in order to measure the whole. 

 Such measurement involves the assumption that during the successive 

 applications of the unit its magnitude remains unchanged. 



