OF THE HUMAN VOICE. 
555 
laminated figure. The vocal ligaments, with their lining membrane, are stretched 
by the thyro-cricoid muscles, not all round like a drum, but in one direction only, 
namely, in that of their length, being attached on three sides, leaving one only free 
to vibrate. The vocal cords are, as has been seen, rectangular-shaped membranes, 
and from experiments made on the larynx after death by Ferrien, Muller, and 
others (which the author has repeatedly verified), are found to vibrate like cylindrical 
cords ; we will therefore apply to the former, the well-known formulas which regulate 
the vibrations of the latter. 
In cords composed of the same material, and of uniform thickness, the time of a 
complete musical vibration, or double oscillation, is 
t = 2 
lp_ 
2gV 
( 1 .) 
where l is the length of the cord, p its weight, P the force with which it is 
stretched, and ^=16^ feet. 
In order to apply this formula to the vocal ligaments, let a be their depth, b their 
breadth, and & their specific gravity ; then p will be equal to abll, and equation (1.) 
becomes 
( 2 .) 
and the number of such vibrations ini" will be 
N= . (3.) 
2 1 V abt 
We observe in the first place, that if all other things remain the same, the number 
of vibrations varies inversely as the length of the cord ; hence, if the vocal ligaments 
were divided by nodes into n ventral segments, each segment might be considered a 
separate vibrating ligament, whose length would be -th of the vocal cord*, and con- 
sequently the number of its vibrations in a given time would be n times as many as 
that of the whole cord. 
Owing to the elasticity of the thyro-arytenoid ligaments, their lengths, when in a 
state of repose, differ considerably from those which they present under the greatest 
tension. They differ also in the two sexes. In a series of experiments by Muller, 
the differences of length were observed to be as represented in the following table, the 
figures of which are in inches and decimals of an inch. From these experiments it 
appears that the lengths of the male and female vocal cords in repose are nearly as 
7 to 5, and in tension as 3 to 2. In boys at the age of fourteen, the length is to that 
of females after puberty as 6‘25 to 7, so that the pitch of the voice is nearly the same. 
These experiments afford an idea, although an imperfect one, of the elasticity of the 
vocal ligaments. It has always been a subject of surprise, if the thyro-arytenoid 
ligaments obey the laws of strings, how such short and narrow laminas should pro- 
duce such very grave tones as many bass singers are capable of uttering ; and this 
4 c 2 
