16 THE PHILOSOPHY OF BIOLOGY 



our different perceptions were those of heat of different 

 degrees of intensity, so transferring to the perceptions 

 themselves the notions of space-magnitudes acquired 

 by a study of the expansion of the mercury in the 

 thermometer, or by the adoption of the physical 

 theory of the kinetic structure of the water. Yet it is 

 quite certain that what we experienced were quite 

 different things or conditions, cold, warmth, heat, 

 and pain, and indeed, in this series of perceptions 

 different receptor organs are involved. 



Suppose we listen to the note emitted by a syren 

 which is sounding with slowly increasing loudness but 

 with a pitch which remains constant. We do not 

 notice at first that the sound is becoming louder, but 

 after a little time we do notice a difference. Let us 

 call the amplitude of vibration of the air when the syren 

 first sounds E, and then, when we notice a difference, 

 let us call the amplitude ^E + E, AE being the in- 

 crement of amplitude. Let us call our sensation when 

 the syren first sounds S, and our sensations when 

 the sound has become louder S + AS, AS being the 

 " increment of sensation." Then the relation holds : — 



aE 



P^ = constant. 



That is to say, the louder is the sound the greater must 

 be the increase of loudness before we notice a difference. 

 Let us assume now that the successive sensations of 

 loudness that we receive as the syren blows louder and 

 louder are, each of them, just the same amount louder 

 than the preceding sound ; that is to say, let us assume 

 that what we experience are " minimal perceptible 

 differences " of sensation — that they are " elements 

 of loudness " — thus we construct a series of sounds 

 each of which differs from that preceding it by an 

 elemental increment of loudness. Now things that 



