HARMONY IN MUSIC. 69 



concert-hall or ball-room traversed in every direction, and not 

 merely on the surface, by a variegated orowd of intersecting 

 wave-systems. From the mouths of the male singers proceed 

 waves of six to twelve feet in length ; from the lips of the song- 

 stresses dart shorter waves, from eighteen to thirty-six inches 

 long. The rustling of silken skirts excites little curls in the 

 air, each instrument in the orchestra emits its peculiar waves, 

 and all these systems expand spherically from their respective 

 centres, dart through each other, are reflected from the walls of 

 the room, and thus rush backwards and forwards, until they 

 succumb to the greater force of newly generated tones. 



Although this spectacle is veiled from the material eye, we 

 have another bodily organ, the ear, specially adapted to reveal 

 it to us. This analyses the interdigitation of the waves, which 

 in such cases would be far more confused than the intersection 

 of the water undulations, separates the several tones which 

 compose it, and distinguishes the voices of men and women 

 nay, even of individuals the peculiar qualities of tone given 

 out by each instrument, the rustling of the dresses, the footfalls 

 of the walkers, and so on. 



It is necessary to examine the circumstances with greater 

 minuteness. When a bird of prey dips into the sea, rings of 

 waves arise, which are propagated as slowly and regularly upon 

 the moving surface as upon a surface at rest. These rings are 

 cut into the curved surface of the waves in precisely the same 

 way as they would have been into the still surface of a lake. 

 The form of the external surface of the water is determined in 

 this, as in other more complicated cases, by taking the height 

 of each point to be the height of all the ridges of the waves 

 which coincide at this point at one time, after deducting the sum 

 of all similarly simultaneously coincident hollows. Such a sum of 

 positive magnitudes (the ridges) and negative magnitudes (the 

 hollows), where the latter have to be subtracted instead of being 

 added, is called an algebraical sum. Using this term, then, we 

 may say that the height of every point of the surface of the 

 water is equal to the algebraical sum of all the portions of tJie 

 waves ivhich at that moment there concur. 



