[v] The advantages and defects of the optical structure of our human eyes have been carefully estimated by Helmholtz. He has also discussed the difficulties attending eyesight considered as a sensation and perception. Extracts from his clear yet popular Lectures are given in Additional Note B. [93] _Proceedings of the Royal Institution._ V. 456. [94] All theories of light require these immense numbers. Sir J. Herschel says there is no "mode of conceiving the subject which does not call upon us to admit the exertion of mechanical forces which may well be termed infinite." The numeration in the text is a rough and ready shape of statement at once intelligible. But it is interesting to view the subject more exactly.--Light travels in one second 192,000 miles. Each mile contains 63,360 inches, and in each inch are 39,000 waves of red light, calculated at their _mean_ length. Now, multiply these three sets of figures together, and we get a rate of 474,439,680,000,000 red waves per second. The mean length of a violet wave is the 1/57500th part of an inch; and by a like multiplication we find a product of 699,494,400,000,000 of violet light-strokes thrown upon the retina in each second. The phrase "_millions of millions_" is used in the text, because few people realize the idea of any arithmetical whole beyond a million. [95] "What we hear" writes Professor Max Müller "when listening to a chorus or a symphony is a commotion of elastic air, of which the wildest sea would give a very inadequate image. The lowest tone which the ear perceives is due to about 30 vibrations in one second, the highest to about 4,000. Consider then what happens in a _Presto_ when thousands of voices and instruments are simultaneously producing waves of air, each wave crossing the other, not only like the surface waves of the water, but like spherical bodies, and, as it would seem, without any perceptible disturbance; consider that each tone is accompanied by secondary tones, that each instrument has its peculiar _timbre_, due to secondary vibrations; and, lastly, let us remember that all this cross-fire of waves, all this whirlpool of sound, is moderated by laws which determine what we call harmony, and by certain traditions or habits which determine what we call melody--both these elements being absent in the songs of birds--that all this must be reflected like a microscopic photograph on the two small organs of hearing, and there excite not only perception, but perception followed by a new feeling even more mysterious, which we call either pleasure or pain; and it will be clear that we are surrounded on all sides by miracles transcending all we are accustomed to call miraculous, and yet disclosing to the genius of an Euler or a Newton laws which admit of the most minute mathematical determination." _Science of Language_, Second Series, p. 115.