A. M. Mayer—Researches in Acoustics. 85 
mathematical fiction, admirable because it renders computation 
facile, but not corresponding necessarily to anything in reality ? 
Why consider the pendulum-vibration as the irreducible ele- 
ment of all vibratory motion? We can imagine a whole, 
divided in a multitude of different ways; in a calculation we 
may find it convenient to replace the number 12 by 8+4, in 
order to bring 8 into view; but it does not necessarily follow that 
12 should always and necessarily be considered as the sum o 
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 decomposi- 
tion, 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 advan- 
tageous than any other in mathematical researches. For the 
methods of demonstration which comport with the intimate na- 
ture 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 
no 
dy- 
namics would read as follows : “ Hvery periodic vibratory moti 
has the proper velocity, will cause the sensation of a musical 
note, a i 
s 
sponding to the elementary sounds of the given musical note. 
Heretofore we have called in the aid of the sensations,— 
assumed to be received through the motions of the co-vibrating 
* Professor Donkin, in his Acoustics, Oxford, 1870, p. 11, advises the use of tone 
to to distin; a sound 
designate a si d the word note guish % 
gry ping (Gr. ) real tension, and the effect of ten- 
Sion is to determine the pitch of the sound of a string ;” while a musical note is gen- 
Fang, & composite sound. Pro : i ; ~~ “ oe 
words klang and ton to signify compound and simple musical so ' 
followed him in adopting the la’ oo a sound as that of the human 
voice could hardly in English be a clang, ing too 
~ . 
