74 0<* THE PHYSIOLOGICAL CAUSES OF 



in their hollows for the keel of a ship of the line, and 

 their ridges can scarcely be overlooked from the mast- 

 head. The waves of sound present similar differences. 

 The little curls of water with short lengths of wave corre- 

 spond to high tones, the giant ocean billows to deep tones. 

 Thus the contrabass C has a wave thirty-five feet long, its 

 higher octave a wave of half the length, while the highest 

 tones of a piano have waves of only three inches in length. 1 

 You perceive that the pitch of the tone corresponds 

 to the length of the wave. To this we should add that 

 the height of the ridges, or, transferred to air, the degree 

 of alternate condensation and rarefaction, corresponds to 

 the loudness and intensity of the tone. But waves of the 

 same height may have different forms. The crest of 

 the ridge, for example, may be rounded off or pointed. 

 Corresponding varieties also occur in waves of sound of 

 the same pitch and loudness. The so-called timbre or 

 quality of tone is what corresponds to the form of the 

 waves of water. The conception of form is transferred 

 from waves of water to waves of sound. Supposing waves 

 of water of different forms to be pressed flat as before, the 

 surface, having been levelled, will of course display no 

 differences of form, but, in the interior of the mass of 

 water, we shall have different distributions of pressure, 

 and hence of density, which exactly correspond to the 

 differences of form in the still uncompressed surface. In 

 this sense then we can continue to speak of the form of 

 waves of sound, and can represent it geometrically. We 

 make the curve rise where the pressure, and hence density, 

 increases, and fall where it diminishes just as if we had 



1 The exact lengths of waves corresponding to certain notes, or symbols 

 af .tone, depend upon the standard pitch assigned to one particular note, 

 and this differs in different countries. Hence the figures of the author 

 have been left unreduced. They are sufficiently near to those usually 

 adopted in England, to occasion no difficulty to the reader in these general 

 remarks. TE. 



