348 





CHAPTER IV. 



PROBLEM OF DIFFERENT SOUNDS OF THE SAME 

 STRING. 



IT had been observed at an early period of acous- 

 tical knowledge, that one string might give 

 several sounds. Mersenne and others had noticed 1 

 that when a string vibrates, one which is in unison 

 with it vibrates without being touched. He was 

 also aware that this was true if the second string 

 was an octave or a twelfth below the first. This 

 was observed as a new fact in England in 1674, 

 and communicated to the Royal Society by Wallis '. 

 But the later observers ascertained further, that the 

 longer string divides itself into two, or into three 

 equal parts, separated by nodes, or points of rest ; 

 this they proved by hanging bits of paper on differ- 

 ent parts of the string. The discovery so modified 

 was again made by Sauveur 3 about 1700. The 

 sounds thus produced in one string by the vibration 

 of another, have been termed Sympathetic Sounds. 

 Similar sounds are often produced by performers on 

 stringed instruments, by touching the string at one 

 of its aliquot divisions, and are then called the 

 Acute Harmonics. Such facts were not difficult to 



1 Harm. lib. iv. Prop. 28, (1636.) Ph. Tr. 1677, April. 

 3 A. P. 1701. 



