84 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



truth demonstrated anew in the field of Biology, where Pro- 

 fessor Karl Pearson* has so brilliantly illustrated old Eoger 

 Bacon's dictum that Mathematics is the " gateway and key 

 to all other Sciences " ; while, doubtless, even before Egyptian 

 priests began to survey the lands left dry after the inundations 

 of the Nile, men felt the application of number and measure to 

 the spatial world to be natural and obvious. 



But as Mr. Kussell has shown, if A is 12 inches and B 

 24 inches from 0, there is really an element of convention in 

 the familiar assertion that B's distance from is twice as great 

 as A's.f Those distances are definite relations which cannot 

 strictly be identified with the relation of one number to 

 another. The fuller truth is that it is possible, since the 

 numbers form a " continuous series," to correlate every position 

 on the straight line B with a single number, while there is a 

 practical convenience in arranging the " one-one correlation " 

 in such a way that if the distance (i.e., the spatial relation 

 itself before the advent of measurement) between and A is 

 equal to that between A and B, the difference between the 

 numbers assigned to and B is twice the difference between 

 those assigned to A and 0. 



By the simple device of measuring with the foot rule, we 

 are able to overcome the difficulty that different perceived 

 distances between A and B have yet the same " representative 

 value,"t that is, refer to the same real distance. Much the 

 same holds good of such conceptions as temperature .and 

 weight. The same body at the same time may be pronounced 

 by two different persons to be hot and cold, a result which is 

 taken to mean not that the thing is both hot and cold, but that 

 the felt hotness and coldness are simply different representatives 

 of the same objective value. If a thermometer is placed in 



* Pearson, Phil. Trans., vol. 185 et seq., also The 'Grammar of 

 Science, 2nd fed. 



t Op. cit., p. 180 ; also supra, p. 29. 

 J Stout, Proc. Arist. Soc., 1903, loc. cit. 



