OVERTONES 365 



vdbrate freely through its whole length, we shall find, 

 n general, that the divided string also begins to vibrate. 

 [t follows that a vibrating string will induce vibrations 

 n another, not only when the latter performs the same 

 mmber of vibrations, but also when it makes twice, 

 hrice, four times, &c., as many as the former ; in other 

 vords, when it emits an harmonic of the first string. 

 3ut, as we have previously seen, resonance can be 

 produced only if the second body is capable of vibrating 

 exactly at the same rate as the first ; and, we here see 

 hat resonance takes place when the vibrations of the 

 econd string are the harmonics of the first ; hence it 

 bllows that in the note of the first string not only the 

 undamental tone is contained but also its harmonics. 

 That this is really the case is proved by further investi- 

 gation, which shows that a string which swings as a 

 vhole vibrates at the same time in halves, thirds, fourths, 

 ec., of its length, and that its motion is indeed very 

 ornplex. A practised ear can detect in the sound of an 

 >pen string, mingled with the fundamental tone, the 

 everal harmonics to it. These overtones appear more 

 .istinct when the fundamental tone is dying away ; 

 irst the octave is heard, then the twelfth, and sometimes 

 everal others besides. Different persons possess differ- 

 nt degrees of delicacy of perception in this respect, but 

 - is by no means absolutely requisite to possess a 

 oecially trained musical ear, in order to be able to dis- 

 nguish these tones. 



If the overtones of the string of the monochord are 

 ot immediately distinguished, they may be more 

 isily heard by plucking the string and then touching a 

 ode with the finger. The fundamental tone will there- 



