C8 OX THE PHYSIOLOGICAL CAUSES OP 



period of vibration the pressure increases uniformly, and at the 

 end falls back suddenly to its minimum. 



It is to such differences in the forms of the waves of sound 

 that the variety of quality in musical tones is due. "We may 

 even carry the analogy farther. The more uniformly rounded the 

 form of wave, the softer and milder is the quality of tone. The 

 more jerking and angular the wave-form, the more piercing the 

 quality. Tuning-forks, with their rounded forms of wave (Fig. 

 3), have an extraordinarily soft quality; and the qualities of 

 tone generated by the zither and violin resemble in harshness 

 the angularity of their wave-forms. (Figs. 5 and 6.) 



Finally, I would direct your attention to an instructive 

 spectacle, which I have never been able to view without a cer- 

 tain degree of physico-scientific delight, because it displays to 

 the bodily eye, on the surface of water, what otherwise could 

 only be recognised by the mind's eye of the mathematical thinker 

 in a mass of air traversed in all directions by waves of sound. 

 I allude to the composition of many different systems of waves, 

 as they pass over one another, each undisturbedly pursuing its 

 own path. We can watch it from the parapet of any bridge 

 spanning a river, but it is most complete and sublime when 

 viewed from a cliff beside the sea. It is then rare not to see 

 innumerable systems of waves, of various length, propagated in 

 various directions. The longest come from the deep sea and dash 

 against the shore. Where the boiling breakers burst shorter 

 waves arise, and run back again towards the sea. Perhaps 

 a bird of prey darting after a fish gives rise to a system of 

 circular waves, which, rocking over the undulating surface, are 

 propagated with the same regularity as on the mirror of an in- 

 land lake. And thus, from the distant horizon, where white 

 lines of foam on the steel blue surface betray the coming trains 

 of wave, down to the sand beneath our feet, where the impres- 

 sion of their arcs remains, there is unfolded before our eyes a 

 sublime image of immeasurable power and unceasing variety, 

 which, as the eye at once recognises its pervading order and law, 

 enchains and exalts without confusing the mind. 



Now, just in the same way you must conceive the air of a 



