560 
MR. BISHOP ON THE PHYSIOLOGY 
edge of the ligament attached to the thyro-arytenoid muscle ; the vibrations take 
place in a plane perpendicular to the axis of that muscle, and the length of the tongue 
is the breadth of the ligament. The author has observed in repeated experiments on 
the larynx after death, that the chink of the glottis was partially opened and closed 
in the production of sound, and Muller found that by decreasing the breadth of the 
ligament he rendered the note more acute ; but as this breadth is so small, being in 
its ordinary state in an adult generally less than one-tenth of an inch, it is extremely 
difficult to measure the variations corresponding with different notes ; and the author 
cannot learn that any one has yet succeeded in determining these varying lengths with 
sufficient accuracy to form data for the application of the mathematical formulas of 
elastic vibrating tongues*. We know that the number of vibrations made by the 
same tongue in a given time varies inversely as the square of its length. If, there- 
fore, a tongue whose length is only *1 inch give any note, the length necessary to 
produce the octave will be '07 inch, that is, the variation will be only '03 inch ; we 
see then how minute must be the changes answering to the intermediate notes, and 
consequently how much more difficult it is to determine them in the vocal ligament 
when considered as a tongue, than as a stretched membrane or cord. It is moreover 
observable that the extension and relaxation of the vocal cord, which, as we have 
seen, are analogous to those of a musical string, produce a corresponding shortening 
and elongation of its axis, regarded as a tongue ; and lastly, since one tone only is 
produced at a time, the vibrations resulting from the double action which appears to 
exist in the vocal apparatus must be synchronous. 
We have seen how nearly, when we take into account the delicacy and difficulty of 
the experiments, their results agree with the theory that the vocal cords are subject 
to the same laws as other stretched laminas, and it would be highly interesting to 
compare these results with the simultaneous variations which they undergo trans- 
versely, and thus discover how far the laws of vibrating elastic tongues may be ap- 
plied to them. It might possibly be objected to the idea of this twofold action, that 
the production of sound by the vocal cords is sufficiently accounted for by supposing 
them to vibrate merely as elastic tongues, but then it is found by experiment, that by 
artificially dividing their length into two ventral segments, there results the octave 
of the fundamental note, which proves that at all events they vibrate as cords. In 
conclusion, we must ever bear in mind the vast difference between natural and arti- 
ficial mechanism, and however complicated a problem it may be to determine that 
constitution of the vocal apparatus, by which the thyro-arytenoid ligaments may 
simultaneously obey the laws of cords and tongues, yet to a physiologist who is ac- 
customed to meet with the most admirable contrivances and combinations in the 
* The formula of Giordano Riccati is . / ^5, where N is the number of vibrations, D the thick- 
L- 'y G 
ness, and L the length of the tongue or rod, R its rigidity, G its specific gravity, g the space through which a body 
falls by gravity in 1", and n a number constant, for each mode of vibration, depending on the number of nodes. 
