1480 



VOICE. 



case varies as 



In the above table C 1 answers to 256 vibra- 

 tions. Miiller states that the numbers of vibra- 

 tions in these experiments are not exactly in the 

 direct ratio of the square roots of the stretch- 

 ing forces, and that the weights 4, 16, 64, did 

 not produce the octaves, but generally from a 

 semitone to two or three tones lower. Now 

 this result should have been anticipated ; but 

 it does not seem to have occurred to him that 

 whilst he increased the tension he at the 

 same time increased the length, and we know 

 (eq. 3.) that the number of vibrations in this 



v tension 



> and conse- 



^/length of cord 

 quently the numbers actually produced by the 

 weights above mentioned ought (agreeably to 

 Miiller's experiments) to be less than those 

 which correspond with octaves. We see by 

 the first experiment in the above table that 

 the tension sufficient to produce 818 musical 

 vibrations is 64 loths, or very nearly 33 ozs. 

 If, therefore, we take the mean length of the 

 vocal ligaments under the greatest tension at 

 '91 of an inch, and substitute in equation (3.) 

 their values for all known quantities, remem- 

 bering that P represents the tension of one 

 vocal cord, we shall find the weight of each 

 ligament, viz. 



* =^=1-144 grs. -(4.) 



In an adult male I found that the two vocal 

 ligaments, when divested of mucous mem- 

 brane, weigh one grain, which is scarcely one- 

 half their weight by theory; hence it appears 

 that a considerable portion of mucous mem- 

 brane is connected with the vocal cord in the 

 production of sound, which agrees with the 

 anatomy of these parts. 



It is now necessary to offer some explana- 

 tion respecting the vital state of the vocal 

 ligaments. The state of repose is the ordi- 

 nary condition of the vocal ligament in the 

 living subject, when the voice is not exercised ; 

 but we must not therefore conclude it to be 

 incapable of further contraction. In fact, the 

 state of repose during life is a state of tension, 

 for the ligaments being connected with the 

 thyro-arytenoid muscles, not in a few points, 

 but continuously throughout their whole 

 length, must obey the motion of these muscles, 

 which, like all other muscles, are in a state of 

 tension during repose. We also know by 

 experience that when we produce a sound 

 lower than the usual pitch of our voice, the 

 crico-thyroid chink is opened principally by 

 the contraction of the same muscles, and the 

 ligaments must therefore at the same time be 

 relaxed. It appears, then, both from the 

 anatomy and physiology of the human larynx, 

 that the ordinary state of the vocal cords is 

 one of considerable tension, which admits of 

 being lessened, and thereby produces the range 

 of lower notes. If we suppose the glottis 

 to be partially closed when we are talking, 

 that is, at the ordinary pitch of our voice, 

 and to be more opened as the tones become 

 graver, this of course will co-operate with 



the relaxation of the vocal cords. In the 

 production of the higher notes, the crico- 

 thyroid chink closes, and the thyro-arytenoid 

 muscles, and consequently the ligaments, are 

 elongated. Since, therefore, the vocal liga- 

 ments have been proved to extend and con- 

 tract for acute and grave tones respectively, 

 and after death vibrate in a great measure 

 like musical strings, we think it may be 

 fairly inferred that they likewise obey, to a 

 certain extent, during life, the laws of the 

 vibrations of such strings, and that the con- 

 clusions which we have derived from the 

 foregoing formulas are not far removed from 

 the truth. A further confirmation of these 

 views may be derived from the following con- 

 siderations. The length of a cord of invariable 

 weight varies directly as the tension, and in- 

 versely as the square of the number of vibra- 

 tions. Now, if we assume the length of the 

 vocal cord, which gave G 2 ^: under a tension 

 of 32 loths to be '91 inch, which is the mean 

 length of the male vocal cord in its greatest 

 tension, according to the first table, and which 

 gave the notes A 1 C 1 , under the tension 

 8 and 2 loths respectively, the corresponding 

 lengths of that cord, according to the formula, 

 will be '83 inch and *58 inch*; but '58 inch 

 is less than the least length in repose in the 

 table. This result is, however, quite consis- 

 tent with the theory here proposed ; because 

 after death the thyro-arytenoid muscle be- 

 comes of itself elongated, and consequently 

 the vocal ligament attached to it, and there- 

 fore the length of the ligament must be greater 

 in this state than when it is in that which we 

 have denned to be the state of repose before 

 it has lost its vitality. 



In experiments made on the larynx by 

 stretching the vocal ligaments with given 

 weights, and by forcing a current of air through 

 the glottis, care must be taken to keep the 

 organs moist, and of the same temperature 

 as they possess during life. The amount of 

 condensation of the air in the vocal tube has 

 been ascertained by Cagniard De la Tour, and 

 Miiller, the former in the living, and the latter 

 in the dead subject. In a person who had an 

 opening in the windpipe after the operation of 

 tracheotomy, Cagniard De la Tour found that 

 the tension of the air in the vocal tube, while 

 blowing the clarionet, was equal to a column of 

 water of thirty centimetresjn height, and that 

 to produce a simple vocal sound in the same 

 person a tension of sixteen centimetres was 

 necessary. Miiller found that he could pro- 

 duce sound in a larynx artificially by a tension 

 of 3'4 centimetres; but for very loud sounds 

 an increased tension was requisite. The dis- 

 crepancy between the experiments of Cag- 

 niard De la Tour and Miiller may be ascribed 

 to the circumstance that the one operated on 



A/P p 



* N varies as . - ; .'. I varies as _ , then -91 inch 

 <S I b* 



: length of cord for A* ; ; _||_ ; _|__, the length 



of the cord for A 1 = -83 inch ; and the length for 

 C 1 = -58 iuch. 



