HARMONY IN MUSIC. 71 



by throwing in a stone the motion thus caused is pro- 

 pagated in the form of waves, which spread in rings over 

 the surface of the water. The circles of waves continue 

 to increase even after rest has been restored at the point 

 first affected. At the same time the waves become con- 

 tinually lower, the further they are. removed from the 

 centre of motion, and gradually disappear. On each 

 wave-ring we distinguish ridges or crests, and hollows or 

 troughs. 



Crest and trough together form a wave, and we measure 

 its length from one crest to the next. 



While the wave passes over the surface of the fluid, the 

 particles of the water which form it do not move on with 

 it. This is easily seen, by floating a chip of straw on the 

 water. When the waves reach the chip, they raise or 

 depress it, but when they have passed over it, the position 

 of the chip is not perceptibly changed. 



Now a light floating chip has no motion different from 

 that of the adjacent particles of water. Hence we con- 

 clude that these particles do not follow the wave, but, 

 after some pitching up and down, remain in their original 

 position. That which really advances as a wave is, con- 

 sequently, not the particles of water themselves, but only 

 a superficial form, which continues to be built up by fresh 

 particles of water. The paths of the separate particles of 

 water are more nearly vertical circles, in which they re- 

 vive with a tolerably uniform velocity, as long as the 

 pass over them. 



In Fig. 2 the dark wave-line, ABC, represents a section of 

 surface of the water, over which waves are running in the 

 direction of the arrows above a and c. The three circles, a, b, 

 and c, represent the paths of particular particles of water at the 

 surface of the wave. The particle which revolves in the circle b, 

 is supposed at the time that the surface of the water presents the 

 form A B C, to be at its highest point B, and the particles re- 



