HAEMONY IN MUSIC. 85 



room to doubt that they are set into sympathetic vibra- 

 tion by the waves of sound which are conducted through 

 the ear. Now if we venture to conjecture — it is at 

 present only a conjecture, but after careful consideration 

 I am led to think it very probable — that every such 

 appendage is tuned to a certain tone like the strings 

 of a piano, then the recent experiment with a piano 

 shows you that when (and only when) that tone is 

 sounded the corresponding hair-like appendage may vibrate, 

 and the corresponding nerve-fibre experience a sensa- 

 tion, so that the presence of each single such tone in the 

 midst of a whole confusion of tones must be indicated 

 by the corresponding sensation. 



Experience then shows us that the ear really possesses 

 the power of analysing waves of air into their elementary 

 forms. 



By compound motions of the air, we have hitherto 

 meant such as have been caused by the simultaneous 

 vibration of several elastic bodies. Now, since the forms 

 of the waves of sound of dififerent musical instruments 

 are dififerent, there is room to suppose that the kind of 

 vibration excited in the passages of the ear by one such 

 tone will be exactly the same as the kind of vibration 

 which in another case is there excited by two or more 

 instruments sounded together. If the ear analyses the 

 motion into its elements in the latter case, it cannot well 

 avoid doing so in the former, where the tone is due to a 

 single source. And this is found to be really the case. 



I have previously mentioned the form of wave with 

 gently rounded crests and hollows, and termed it simple or 

 pure (p. 75). In reference to this form the French mathe- 

 matician Fourier has established a celebrated and impor- 

 tant theorem which may be translated from mathematical 

 into ordinary language thus : Any form of wave what- 

 ever can he compounded of a number of simple waves of 



