552 
MR. BISHOP ON THE PHYSIOLOGY 
Euler, Bernoulli, Riccati, Biot, Poisson, Sir John Herschel and others. It is a 
subject requiring the most profound analysis, and the solution of problems of much 
greater complexity than those either of strings or bars, but in order to bring the 
theory of vibrating membranes within the reach of computation, the membranes are 
supposed to be homogeneous and of equal thickness and elasticity. Now these 
hypotheses will not satisfy the conditions of the vibratory movements of the vocal 
organs, such as the windpipe for example, which is composed of tissues of variable 
thickness, density, and elasticity ; it would therefore be futile in the present state 
of the science of acoustics, to attempt any mathematical solution of the laws of the 
equilibrium and movements of the heterogeneous masses of the vocal tube. When, 
however, a membrane is stretched in one direction only, it obeys the same laws as 
a string. 
Having adapted two laminas of India rubber to a pipe connected with the bellows 
of an organ, M. Biot caused a current of air to pass over their free edges, by which 
means he obtained sounds of different pitch with facility. The Rev. Mr. Willis 
made similar experiments with leather and caoutchouc, but with these substances 
could not produce so great a range of tones as the glottis will yield, and therefore 
concluded that the vocal ligaments possess greater elasticity. Mr. Willis has also 
investigated the position in which it is necessary that membranous laminas should 
be placed, in order that they may be excited and sustained in a state of vibration. 
He has likewise given a satisfactory explanation of the mode of action of the air on 
reeds, such as those of the organ pipe, which applies also to free reeds, and every 
other case where a vibratory motion is maintained by a current of air. 
The experiments and theory of Mr. Willis are exceedingly important, for he has 
shown that in ordinary breathing the vocal cords remain inclined to each other, 
at an angle which prevents any vibratory motion ; whereas when their surfaces lie in 
the same plane the breath immediately excites them into a state of vibration; the 
natural position of the vocal cords in these two states is seen in Plate XXX. figs. 1 
and 2. Muller also made some experiments on stretched membranous bands, both 
isolated, and in connection with a tube, from which he concludes that the force ot 
the current of air influences the pitch of the note produced, so that a strong current 
will produce a more acute tone than a weak one, and vice versa-, but the author has 
not found this to be the case in any of the experiments which he has made. To obtain 
a pure quality of tone when two membranous bands are stretched across a tube, it is 
necessary that they should be of equal weight and length, and subjected to equal 
tension, otherwise they cannot vibrate freely in equal periods of time. According to 
Cagniard la Tour, if two membranous laminas of equal length and weight be stretched 
by unequal forces, so that there is an interval of a fifth between the notes they yield 
separately, the note resulting from their combined action is the intervening third. 
Muller is disposed to doubt the accuracy of La Tour, but his own views do not 
differ materially from those of the latter, as he says that when one tongue is most 
