OF THE HUMAN VOICE. 
561 
animal frame, the difficulty of finding a strictly mathematical solution is, in such a 
case, no objection to its truth, when the facts, so far as they have been observed, are 
decidedly favourable to its reality. Were the movements of the glottis independent of 
any tube or column of air, the study of the functions of the vocal organs would be 
much more simple, but we find it situated nearly in the centre of the vocal tube of 
which the trachea and bronchi are the inferior, and the upper part of the larynx, 
pharynx, nose and mouth, the superior portion; we have therefore to consider the 
influence of this tube, and of its inclosed column of air in the production of voice. 
In order to investigate the mutual relations between a reed and a pipe, two methods 
may be adopted: one of these is to vary the pitch of the reed while the length of 
the pipe remains constant, and the other, to vary the length of the pipe with a reed 
sounding one tone only, when detached from the tube. In the construction of 
reeded pipes for musical purposes, it is incumbent on the mechanician to adjust the 
length of the tube to the pitch of the reed. When a free reed is used on the prin- 
ciple of Kratzenstein or Grenie, it is found that, if the pipe be not in perfect unison 
with the reed, the purity of the tone decreases within certain limits, as the discord- 
ance between the reed and pipe increases. The researches of MM. Biot, Weber, 
Willis and Muller, have greatly enlarged our knowledge on this subject. We 
learn from their experiments how great an influence is mutually exerted between a 
pipe and its reed, when the pitch of the one is made to vary whilst the other remains 
constant, and we may conclude that analogous effects are produced between the vocal 
tube and the glottis. The slightest knowledge of acoustics is sufficient to inform us 
that the pitch of any pipe, such as the organ, the flute, the trumpet, in short of all 
musical tubes vibrating in a similar manner, depends on the velocity of an impulse 
propagated in the air within, and is determined by the length of the pipe. So long 
as the tubes of musical instruments remain rigid, the nature of the materials which 
compose them, does not affect the pitch of the sound, but merely influences the qua- 
lity of the tone, and it is indifferent whether we employ metal, wood, or paper in their 
construction ; each of these substances will yield a tone of a particular timbre, or 
quality, depending on the nature of the motions produced among its particles by the 
friction of the air on its surface ; but the pitch will be the same in each, if the lengths 
of the pipes be equal, proving that the air itself is the source of sound. When how- 
ever the sides of the tube are composed of flexible membranes, the inclosed air has 
a vibratory motion, conjointly with, and subordinate to that of the parietes of the 
tube, whereby the pitch of the sound is affected, as well as its quality. M. Savart 
found that by taking tubes composed of layers of paper of constant length, but vary- 
ing in thickness, graver sounds were produced as the parietes became thinner, and 
that the gravity of the sound was increased by moistening and relaxing the sides of 
the tubes. We shall presently see the application of these facts to the vocal apparatus. 
We find the flexibility of the trachea and bronchi capable of being varied by the 
operation of two forces, the one longitudinal or parallel to the axis of the tube, the 
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MDCCCXLVI. 
