HERMANN VON HELMHOLTZ. 715 



notes which were a j^osteriori found to obey certiiin natural laws was 

 voluntary. The scale itself is not natnral, in the sense that it is not 

 a necessary conseqnence of the construction of the ear. On the con- 

 trary, it is the product of artistic invention. Music is thus not a mere 

 branch of mechanics, but an art. The architect and the composer alike 

 deal with materials which are subject to mechanical laws, but they are 

 alike free to fashion from these forms determined not by calculation, 

 but by the sense of beauty. 



Von llelmholtz was at work on optics while still engaged in the study 

 of sound. The Handbu<;h der Physiologischen Optik appeared in sec- 

 tions in 1856, 1800, and 1860. It is, as he himself has said, a complete 

 survey of the whole held of that science. In the first place he treated 

 the eye as an optical instrument, traced the path of the rays through 

 it, and discussed the mechanism by which it can be accommodated to 

 distinct vision at different distances. To investigate the last point 

 it was necessary to measure the images formed by reflection from the 

 surfaces of the crystalline lens. For this purpose he invented a special 

 instrument — the opthalmometer — by which such measurements can be 

 made on the living patient with great accuracy. 



In an interesting course of popular lectures, published in 1868, and 

 since translated by Dr. Atkinson, Yon Helmholtz insisted that far from 

 being, as was often supposed, a perfect organ, the eye has many optical 

 defects; and that our unconsciousness of these is due not so much to 

 its perfection from the instrument-maker's point of view, as to the ease 

 with which it adapts itself to different circumstances, and to the skill 

 with which long ])ractice enables us to interpret the messages it conveys 

 to the brain. 



The se(;ond section of the work was devoted to the sensation of sight. 

 The theories of color and of intensity, the duration of the sensation of 

 light, the phenomena of contrast and subjective aj)pearances were all 

 discussed with a fullness never before attained. The last part was 

 devoted to such problems as our visual appreciation of three dimensions 

 in space and binocular vision. 



The theory of color, originally due to Young, was adopted and 

 enlarged by Helmholtz. It assumes that all the sensations of color are 

 compounded out of three fundamental sensations, which are respec- 

 tively a red, green, and violet or blue. Nearly if not all the phenomena 

 of color-blindness can be explained on the hypothesis that, in the case 

 of i^ersons so affected, the power of appreciating one or other of these 

 sensations is wanting. 



It was hardly to be expected that differences of opinion would not 

 arise as to some of the points discussed in two works so wide in their 

 scope and so novel in their methods as the treatises on the sensations 

 of tone and on physiological optics. Koenig, the celebrated instrument 

 maker, has demonstrated the existence of beats which in the case of 

 compound sounds could be explained as due to the upper partials, but 



