270 Prof. A. M. Mayer's Researches in Acoustics. 



into view; but it does not necessarily follow that 12 should al- 

 ways and necessarily be considered as the sum of 8 + 4. In 

 other cases it may be more advantageous to consider the number 

 as the sum of 7 + 5. 



" The mathematical possibility, established by Fourier, of de- 

 composing any sonorous motion into simple vibrations, cannot 

 authorize us to conclude that this is the only admissible mode 

 of decomposition, if we cannot prove that it has a signification 

 essentially real. The fact that the ear effects that decomposition, 

 induces one, nevertheless, to believe that this analysis has a 

 signification, independent of all hypothesis, in the exterior 

 world. This opinion is also confirmed precisely by the fact 

 stated above, that this mode of decomposition is more advanta- 

 geous than any other in mathematical researches ; for the me- 

 thods of demonstration which comport with the intimate nature 

 of things are naturally those which lead to theoretic results the 

 most convenient and the most clear/'' 



The theorem of Fourier, translated into the language of dy- 

 namics, would read as follows : — " Every periodic vibratory motion 

 can always, and always in one manner, be regarded as the sum of 

 a certain number of pendulum-vibrations/ 3 



Now we have seen that any periodic vibratory motion, which 

 has the proper velocity, will cause the sensation of a musical note, 

 and that a pendulum-vibration gives the sensation of a simple 

 sound*; therefore, if Fourier's theorem is applicable to the 

 composition and decomposition of a composite sonorous wave, it 

 will be thus related to the phenomena of sound: — "Every vi- 

 bratory motion in the auditory canal, corresponding to a musical 

 sound, can always, and always in one manner, be considered as 

 the sum of a certain number of pendulum-vibrations, corresponding 

 to the elementary sounds of the given musical note J 3 



Heretofore we have called in the aid of the sensations (as- 

 sumed to be received through the motions of the covibrating 

 parts of the ear) to help us in our determination of the simple 

 or composite character of a given vibratory motion ; but Fou- 

 rier's theorem does not refer to the subjective effects on the 

 organ of hearing, the dynamic function of whose parts are yet 



* Professor Donkin, in Lis 'Acoustics/ Oxford, 18/0, p. 11, advises the 

 use of tone to designate a simple sound, and the word note to distinguish 

 a composite sound. His reasons are " that tone (Gr. rovos) really means 

 tension, and the effect of tension is to determine the pitch of the sound of a 

 string;" while a musical note is generally a composite sound. Professor 

 Donkin further states, "Helmholtz uses the words Klany and Ton to signify 

 compound and simple musical sounds. We have followed him in adopting 

 the latter term ; but such a sound as that of the human voice could hardly 

 in English be called a citing, without doing too much violence to established 

 usage." 



