30 M. J. Antoine on the Multiple Sounds 



perceptible vibrations; and further, it causes beats to be 

 heard. This experiment shows the imperfection of one of 

 the processes which are indicated for tuning instruments. 



In order to produce from a string the series of its har- 

 monics in succession, Sauveur afterwards devised a second 

 method, more convenient, and more effective than the first. 

 As in the old process the string was not touched, the har- 

 monic which it was desired to excite was sounded by the side, 

 but he produced this first generating sound by vibrating the 

 prolongation itself of the cord. The harmonics obtained in 

 this manner are in some degree indefinite ; the higher ones 

 are not, it is true, so well characterized as the lower. Never- 

 theless, with a string one metre in length, Sauveur distin- 

 guished clearly thirty-two harmonics, and could hear more 

 than a hundred and twenty-eight. Sauveur's method is, in 

 this respect, much superior to the old process. 



Sauveur did not seek whether it is possible to establish the 

 subdivisions of the string, by vibrating it directly with the 

 bow. This may however be attained, although the execution 

 presents difficulties. If the bow is moved on the middle of the 

 string, avoiding to impart the movement of totality which gives 

 rise to the fundamental tone, we have at first only a harsh and 

 very disagreeable grating sound. This fact, related by Wallis 

 as known before him, is produced, as Wallis has remarked, 

 when the bow is drawn on one of the points of the string 

 which correspond to its division into aliquot parts, with this 

 circumstance however, that the sound becomes less and less 

 disagreeable, in proportion as the divisions are more nu- 

 merous. 



It must not however be imagined that the phaenomenon 

 mentioned by Wallis is constantly verified. For, on passing 

 the bow on the middle of the string and modifying its ve- 

 locity and its pressure, a sharp sound of great purity is in the 

 end obtained, after some essays. When this sound is full, it is 

 easy to sustain it as long as is desired, even whilst increasing 

 considerably the pressure of the bow. By this means the un- 

 even harmonics may be drawn from a string. 



It is easy to distinguish in these experiments the formation 

 of the nodes and their position. If the string gives, for ex- 

 ample, the nineteenth harmonic, when observing it in broad 

 daylight, it looks as if formed of nineteen equal spindles, placed 

 one after another. The points where these spindles unite 

 appear immoveable ; if they are lightly touched with the fin- 

 ger, the sound which the bow maintains is not changed, and 

 the string is not felt to tremble. If, on the contrary, one of the 

 spindles is touched at a proper distance from their extremities, 



