produced by Vibrating Bodies. 39 



supplementary sounds become so feeble, that the perception 

 of these sounds might be attributed to a preconceived illusion 

 of the mind, although analogy then lends its aid to the con- 

 clusions. Nevertheless, if any doubt still remained, it would 

 be easy to remove it by the following observations. 



When the bow causes a string to sound, its hairs execute 

 transversal vibrations. To prove this, it suffices to pass a 

 simple wire ring around the hairs: whilst the bow moves 

 on the sonorous string, the wire ring, by its movements, ren- 

 ders the vibrations of the hairs evident. 



The vibrations rendered perceptible by the wire ring are 

 very remarkable when the bow is reduced to a single hair, and 

 especially when the place of the hairs is supplied by a sono- 

 rous cord, rubbed with resin. 



Ordinarily the tension given to the hairs of the bow is such, 

 that the sound rendered by each hair, vibrating separately, is 

 very grave with reference to the sound which the bow should 

 draw from a string ; whatever tension is given to the hairs of 

 the bow or to the bodies which supply their place, the trans- 

 versal vibrations are always established and are constantly 

 rendered evident by the experiment, so that the shocks of the 

 vibrating string against the hairs, and consequently the shocks 

 of the hairs against the string, are incontestable. 



It would be difficult to say a priori what influence the vi- 

 brations of the bow have on the clearness of the vibrations of 

 the string, and consequently on the purity of the sounds pro- 

 duced. This influence is probably not to be neglected. It is 

 known that a double-base, a tenor, or a violin bow can- 

 not be employed indifferently for an instrument; it is also 

 known that artists bestow great care in the choice which they 

 make among bows of the same kind, and that they adopt cer- 

 tain tensions for the hairs. It would be interesting to sub- 

 mit the properties of bows to experimental analysis, and per- 

 haps some result useful to practical music might be found. 

 When the tension of the bow is such, that the sound of each 

 hair has for octave of higher or lower order the sound of the 

 vibrating string, or one of its consonances, would the sound 

 produced be finer than under other conditions? 



The analytical solution of the problem of vibrating strings 

 is remarkably beautiful, and yet it is incomplete. To explain 

 the effects produced, it is not enough, in practice, to recur, 

 as is done in analysis, to very various primitive states. Ordi- 

 narily the initial state is the state of equilibrium under the 

 influence of the tension of the string, and yet what variety of 

 effects does the bow produce ! 



Ordinary analysis does not even suffice in the very simple 



