716 HERMANN VON HELMHOLTZ. 



as they are prodiuted wlieu the notes are as i^nre as it is possible to make 

 them, they do not appear to be accounted for by the original theory. 

 A writer ( Voigt. Wiedemann's Aunaleu, 1890, 40, p. (JGO) who has recently 

 examined the matter, concludes that both the combination tones of Von 

 Hehuholtz and the beat tones of Koenig can theoretically be produced 

 without the unsymmetrical arrangement which the former regarded as 

 essential, and that the one system or the other will tend to predominate 

 according to circumstances. The more nearly the energies of the two 

 vibiations api)roach equality the greater is the probability that the 

 combination tones will be heard. The less nearly the condition of equal 

 energy is fultilled, themoi-e important will the beat notes become. 



Several other points of considerable interest have been raised, but 

 those who on one ground or another have objected to the views of Von 

 Helmholtz, have not been entirely in accord among themselves. It is 

 probable that the theory will finally be accepted in its broad outlines, 

 but will require modifications of some nnportance in its details. 



The theory of color, too, with which the name of Von Helmholtz is 

 associated, is not without its difficulties. A new edition of his Optics 

 is appearing in parts, and in this alterations have been made which 

 prove that the author regarded the original hypothesis as capable 

 of modification and improvement. A strong committee of the Koyal 

 Society, which has recently reported on color vision, adopted the 

 terminology of the Young-Helmholtz theory, but pointed out that it 

 fails to explain some curious cases of diseased vision, in which the sen- 

 sation of color is confined to the blue end of the spectrum, while all 

 the other tints appear as white. On the other hand, the rival theory 

 of Hering also fails to account for some of the known facts. Thus the 

 problem is not finally solved, but the importance of the contribution to 

 its solution made in the Physiologischen Optik is not disputed even by 

 those who feel that there is need for further inquiry in the future. 



In these investigations on the eye and the ear, on light and sound, we 

 see Von Helmholtz at his most characteristic work; but the shortest 

 sketch of his scientific achievements would be incomplete without 

 reference to his eminence as a mathematician. 



He was, as might have been expected, deeply interested in the 

 electro-magnetic theory of light, and develo]>ed it in a form Avhich is 

 even more general than that adopted by Clerk Maxwell; but it seems 

 probable that, while Von Helmholtz has indicated possibilities. Max- 

 well has taken account of all that is necessary to explain the facts. 



Another inquiry of the first importance, and conducted with the 

 greatest ability, was that on the laws of vortex motion. The move- 

 ments of a liquid may be so complicated that it is at first sight an 

 almost hopeless task to analyze the motion into its simplest elements. 

 Changes of shape of the most exaggerated character may occur. A 

 compact mass may be drawn out into long threads. Particles at one 

 time far apart may be brought close together and again separated. 



