152 HERMANN VON HELMHOLTZ 



vibratory motion ; if the oscillations are transmitted through an 

 elastic medium, a simple wave-motion; he calls all other 

 oscillations that can be expressed, as was already known, as 

 a sum of such sine-functions with arguments, which again are 

 linear functions of time, a compound vibratory or wave motion. 

 Starting with the fact that wherever investigation by mathe- 

 matics and mechanics establishes the existence of compound 

 wave-movements, the trained ear is able to distinguish tones 

 which correspond with the simple wave-movements contained 

 in them, he next propounds the same question for simple wave- 

 motions, and tries to discover means of producing simple wave- 

 motions in the air. But since all resonant elastic bodies assume 

 various vibrational forms in which they can give out tones of 

 different pitch, Helmholtz selected a tone-producer, which 

 imparts its vibrations as little as possible to the air, while 

 another, the resonator, was so arranged that it was set in 

 sympathetic vibration with the first, and gave out its vibrations 

 easily and forcibly to the air. If the prime tone of the two 

 bodies is exactly the same, while all the higher partial tones 

 of the one are different from those of the other, the resonator 

 will only be excited by the prime tone, and will only give out 

 the vibrations of the prime tone to the air. Helmholtz chose 

 a tuning-fork, and as resonator took the string of a monochord, 

 or an air-chamber formed of cylindrical tubes made of paste- 

 board, closed at both ends with a round opening in the centre 

 r"*of one end. With the help of this arrangement it was found 

 that simple tones, as Helmholtz calls tones produced by simple 

 vibrations, on the analogy of the simple colours of the spectrum, 

 only give out clearly such deeper combination tones as have 

 a vibration number equal to the difference of the vibrational 

 numbers of the generating tones, and that when combination 

 tones of another order exist along with these, they are too 

 weak to be audible with generating tones of moderate strength. 

 When, therefore, combination tones of the higher order are 

 very perceptible in compound tones, they must be the com- 

 bination tones of the higher partials. Helmholtz also finds 

 a second class of combination tones, the vibration frequency 

 of which is equal to the sum of the generating tones, which 

 he calls summational tones, while he designates the others as 

 differential. 



