LECT. XIX. PROPAGATION OF SOUND. 359 



by the two sounds, coincide upon the acoustic nerve ; and, 

 if these coincidences be sufficiently near and regularly re- 

 peated, we have the sensations of a very grave sound. 

 When these coincidences are very rare, which happens 

 with sounds almost in unison with each other, we have no 

 other sensation than that of the well-known phenomenon of 

 beats, observed for the first time by Tartini. 



Not being able to speak of all that relates to the act of 

 conscience, awakened through the excitation of the acoustic 

 nerve, I cannot stop at the theories of music. If the sounds 

 that we hear simultaneously are, by the relative number of 

 their vibrations, in simple ratio to each other, we then ex- 

 perience those most agreeable sensations which we call 

 harmonics ; and the contrary effect takes place when these 

 relations do not exist. Experiment teaches us, that har- 

 monic sounds are obtained simultaneously by touching a 

 thick cord, extended so as to make it render the funda- 

 mental sound due to the vibration of its entire length. We 

 therefore conclude, that the cord divides itself into a certain 

 number of parts, which vibrate separately and at the same 

 time. We also know, that by having several cords to- 

 gether, if their lengths are in simple ratios, it is sufficient to 

 cause one to vibrate, in order that the others should render 

 the sound proper to their lengths. We may therefore as- 

 sume, that the membrane of the tympanum, the membrane 

 of the fenestra ovalis, and perhaps, also, the extremities of 

 the acoustic nerve, may be the seat of harmonic sounds ; 

 and, that the elasticity of these parts is not opposed to these 

 movements. The contrary should hold good for sounds 

 which we call discords. 



