produced hy Vibrating Bodies. 37 



M. Duhamel does not consider directly the shocks as they 

 take place in reality, but he substitutes for them an equivalen- 

 system; instead of the string affected by the compound niovet 

 ment, he substitutes two identical strings placed close to each 

 other, each executing simple vibrations which are an octave 

 from each other. It is certain that the movement imparted to 

 the air, whether by the single string, or by the two equivalent 

 strings united, is very perceptibly the same, and our organ 

 must be affected in the same manner in the two cases ; now, 

 it is known that two adjacent strings, one of which vibrates 

 the octave of the other, cause the two sounds to be heard 

 simultaneously; they must therefore be thus heard by virtue 

 of the equivalent vibrations of the single string. 



If I have rightly seized the point of view which M. Duhamel 

 has taken, it appears from the preceding developments, that 

 M. Duhamel, with all the physicists of the present day, finds 

 the origin of multiple sounds in the manner in which the vi- 

 bratory movement of bodies is composed. To establish this 

 dependence, physicists consider directly the different shocks 

 really imparted to the air, whilst M. Duhamel substitutes for 

 the body vibrating with a compound movement, an equivalent 

 system of simple movements, the impression of which on our 

 organs is well known. 



The common theory of multiple sounds is more direct than 

 that of M. Duhamel, since in it we regard phaenomena as they 

 are really produced ; it is also more elementary, and conse- 

 quently more simple, as it does not require us to have recourse 

 to propositions, one of which at least is not within the reach 

 of every one. For these two reasons, the ordinary theory ap- 

 pears to us preferable in general; nevertheless, in certain 

 complicated cases, we think that the mode of demonstration 

 proposed by M. Duhamel may have the advantage. 



Whichever of the two theories be adopted, one difficulty 

 relative to the multiple sounds of bodies remains entirely to 

 be solved. This difficulty arises from our not having as yet 

 been able to submit to analysis the true theory of the bow. 



The bow produces four principal effects. It sustains the 

 equality of the sounds as long as is wished ; it sustains also 

 those feeble sounds which appear to die away under the 

 fingers of the artist, whilst the sounds given by the strings, 

 when pinched, are at first powerful, then soon become weak- 

 ened, and are very quickly lost. The bow admits of giving 

 to sounds different degrees of strength ; it serves to impart 

 to them particular qualities by appropriately awakening the 

 harmonics ; and lastly, it can bring out separately the different 

 harmonics from a string. By these effects, the bow i» the 

 supreme master of sounds. 



