DIFFERENT SOUNDS OF THE SAME STRING. 349 



explain on Taylor's view of the mechanical condi- 

 tion of the string ; but the difficulty was increased 

 when it was noticed that a sounding body could 

 produce these different notes at the same time. 

 Mersenne had remarked this, and the fact was more 

 distinctly observed and pursued by Sauveur. The 

 notes thus produced in addition to the genuine note 

 of the string, have been called secondary notes; 

 those usually heard are, the octave, the twelfth, and 

 the seventeenth above the note itself. To supply a 

 mode of conceiving distinctly, and explaining me- 

 chanically, vibrations which should allow of such an 

 effect, was therefore a requisite step in acoustics. 



This task was performed by Daniel Bernoulli in 

 a memoir published in 1755* He there stated and 

 proved the principle of the coexistence of small 

 vibrations ; it was already established, that a string 

 might vibrate either in a single swelling (if we use 

 this word to express the curve between two nodes 

 which Bernoulli calls a ventre,) or in two or three 

 or any number of equal swellings with immoveable 

 nodes between. Daniel Bernoulli showed further, 

 that these nodes might be combined, each taking 

 place as if it were the only one. This appears suffi- 

 cient to explain the coexistence of the harmonic 

 sounds just noticed. D'Alembert, indeed, in the 

 article Fundamental in the French Encyclopedie, 

 and Lagrange in his Dissertation on Sound in the 

 Turin Memoirs*, offer several objections to this 



4 Berlin Mem. 1753, p. 147. 5 T. i. pp. 64, 103. 



