78 ON THE PHYSIOLOGICAL CAUSES OF 



Finally, I would direct your attention to an instructive 

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

 certain degree of physico-scientific delight, because it dis- 

 plays 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, propa- 

 gated 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 inland 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 im- 

 pression 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 concert-hall or ballroom traversed in every direction, 

 and not merely on the surface, by a variegated crowd 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 songstresses dart shorter waves, from 

 eighteen to thirty-six inches long. The rustling of silken 



