88 ON THE PHYSIOLOGICAL CAUSES OF 



effected, and, in point of fact, any given form of wave could be 

 reproduced. 1 



When various simple waves concur on the surface of 

 water, the compound wave-form has only a momentary 

 existence, because the longer waves move faster than the 

 shorter, and consequently the two kinds of wave imme- 

 diately separate, giving the eye an opportunity of recog- 

 nising the presence of several systems of waves. But 

 when waves of sound are similarly compounded, they 

 never separate again, because long and short waves traverse 

 air with the same velocity. Hence the compound wave 

 is permanent, and continues its course unchanged, so that 

 when it strikes the ear, there is nothing to indicate 

 whether it originally left a musical instrument in this 

 form, or whether it had been compounded on the way, 

 out of two or more undulations. 



Now what doe's the ear do? Does it analyse this 

 compound wave? Or does it grasp it as a whole? The 

 answer to these questions depends upon the sense in 

 which we take them. We must distinguish two different 

 points the audible sensation, as it is developed with- 

 out any intellectual interference, and the conception, 

 which we form in consequence of that sensation. We 

 have, as it were, to distinguish between the material ear 

 of the body and the spiritual ear of the mind. The 

 material ear does precisely what the mathematician 

 effects by means of Fourier's theorem, and what the 

 pianoforte accomplishes when a confused mass of tones is 

 presented to it. It analyses those wave-forms which were 

 not originally due to simple undulations, such as those 

 furnished by tuning forks, into a sum of simple tones, and 



1 Of course the waves could not overhang, but waves of such a form 

 would have no possible analogue in waves of sound [which the reader will 

 recollect are not actually in the forms here drawn, but have only condensa- 

 tions and rarefactions, conveniently replaced by these forms, p. 73]. 



