HARMONY IN MUSIC. 63 



and c). The positions of the crests are marked with figures. The 

 same figures in the three circles show where the respective revolving 

 particle would be, at the moment the wave assumed the corresponding 

 form. It will be noticed that the particles advance by equal arcs of 

 the circles, as the crest of the wave advances by equal distances 

 parallel to the water level. 



In the circle b it will be further seen that the particle of water in 

 its positions 1, 2, 3 hastens to meet the approaching wave-crests, 

 ] , 2, 3, rises on its left-hand side, is then carried on by the crest from 

 4 to 7 in the direction of its advance, afterwards halts behind it, 

 sinks down again on the right side, and finally reaches its original 

 position at 13. (In the 'Lecture itself, Fig. 2 was replaced by a 

 working model, in which the movable particles, connected by threads, 

 really revolved in circles, while connecting elastic threads represented 

 the surface of the water.) 





All particles at the surface of the water, as you see by this draw- 

 ing, describe equal circles. The particles of water at different depths 

 move in the same way, but as the depths increase, the diameters of 

 their circles of revolution rapidly diminish. 



In this way, then, arises the appearance of a progressive motion 

 along the surface of the water, while in reality the moving particles 

 of water do not advance with the wave, but perpetually revolve in 

 their small circular orbits. 



To return from waves of water to waves of sound. Ima- 

 gine an elastic fluid like air to replace the water, and the 

 waves of this replaced water to be compressed by an inflexible 

 plate laid on their surface, the fluid being prevented from escap- 

 ing laterally from the pressure. Then on the waves being thus 

 flattened out, the ridges where the fluid had been heaped up 



