MEASUREMENTS 189 



material ; their value consists in this ; that they give us an 

 exact arithmetical series which is valid for every one who 

 can count. With their assistance it for the first time 

 becomes possible to establish the corresponding series of 

 musical tones on a basis which is independent of individual 

 peculiarities. 



The same considerations apply to scales of colour. There are 

 many individuals whose colour sense is so keen as to enable 

 them to arrange a graduated series of colours with a close 

 approach to accuracy, but the gift is far from being universal, 

 and colours can only be measured by a reference to rhythm 

 in time or space. Intensity in colour is measured by 

 a spatial series ; what distinguishes a deep from a weak 

 shade of the same colour is the amplitude of the waves. 

 When the vibrations increase in rapidity, but remain the 

 same in amplitude, the colour itself changes through the 

 scale from red to violet, and the measurement is by time. 



The main advantages which measurements have over 

 mere comparisons are two. In the first place they detect 

 minute differences which would otherwise be overlooked; 

 secondly, where they are obtainable they are conclusive 

 on all questions of objective fact. To take a simple illus 

 tration from measurements in space. Few men, if shown 

 two rooms, one measuring 22 feet square and another 

 24 feet by 20, would be able to say with confidence whether 

 they differed in area, and, if so, which was the larger. 

 Measurement at once demonstrates that the area of the 

 first exceeds that of the other by four square feet ; and this 

 is a decision which leaves no opening for doubt or appeal. 

 Even when the unlikeness is much greater, the function 

 of measurement is usually the detection of small errors 

 of discrimination. A man judges that of two steeples 

 one is twice as high as the other, and finds by measurement 

 that one is 150 feet high and the other 320. 



Estimates of temporal duration vary much more widely 

 than estimates of space from the objective measurements, 

 and the differences between individual judgements are 

 sometimes very great. We will take the length of a sermon 



