HAEMONY IN MUSIC. 79 



skirts excites little curls in the air, each instrument in 

 the orchestra emits its peculiar waves, and all these sys- 

 tems 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 regu- 

 larly 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 sur- 

 face 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 coin- 

 cide 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 alge- 

 braical 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 jportions of the 

 waves which at that moment there concur. 



