S8 M. J. Antoine on the Multiple Sounds 



The bow acts thus by a series of slight impulses which it im- 

 parts to the string. These shocks, being continually renewed, 

 keep up the movement which tends to become weaker ; be- 

 coming slighter or more energetic, they change the ampli- 

 tude of the vibrations, and consequently the strength of the 

 sounds; by being applied to the different parts of the string, 

 in suitable conditions, they are able to determine various 

 modes of vibrations which give rise to the separate or simul- 

 taneous harmonics. 



The impulses which the bow can impart are renewed with 

 such great rapidity, that we cannot be assured of their existence 

 when looking at the string. However, if the pressure of the 

 bow is considerable and the velocity very moderate, the sounds 

 produced present the same characters as if they were attri- 

 butable to a series of shocks. Moreover a series of jerks 

 may then be seen, which render manifest to the eye the dif- 

 ferent shocks of the bow. The experiment takes a nev/ cha- 

 racter of evidence when the tension of the string is very weak 

 or the vibrations are slow. 



When the experiment is performed which has just been 

 indicated, and the jerks of the string are very perceptible, in- 

 dependent of the fundamental tone of the string, two supple- 

 mentary sounds are heard which are the fundamental tones of 

 the two portions of the string separated by the bow. 



If the pressure of the bow be gradually diminished and its 

 velocity increased, the jerks become more rapid, more dif- 

 ficult to observe, at the same time that the two supplementary 

 sounds are weakened ; as long as the supplementary sounds 

 continue, they are as it were proofs of the shocks produced by 

 the bow. Lastly, the jerks cease to be perceptible, and yet 

 the two supplementary sounds are still heard, feebly it is true, 

 but still perceptible enough to be distinguished, with a little 

 attention. Thus the friction of the bow produces a succession 

 of shocks, the origin of all the effects of this instrument. 



It is not necessary to imagine that these shocks must be re- 

 newed in a regular manner in order to sustain the sound, for 

 the sound of a string may be sustained by striking it gently 

 with the finger and rapidly renewing the shocks almost in an 

 arbitrary manner. The only difference that is remarked in 

 the sounds sustained by the bow or by a rapid succession of 

 shocks effected by pinching the string with the finger, is refer- 

 able only to the delicacy and the lightness of the shocks of 

 the bow. 



The existence of the supplementary sounds, incontestable 

 proofs of the shocks of the bow, is very clear and very decided, 

 when the rapidity of the bow does not exceed certain limits. 

 In the case where the bow moves in the ordinary way, the 



