CH. xxx. VIBRATION OF STRINGS. 265 



many of these beats there are in a second, knowing that 

 between each beat A must have given nine puffs, you have 

 only to multiply the number of beats by nine, and that will 

 give you the number of vibrations of the note sounded by 

 that pipe. 



Sauveur tried the experiment in this way, and found that 

 when he sounded the low c in the 8-foot pipe it gave 122 

 vibrations in a second. He afterwards went on to apply 

 this to stringed instruments, and made many remarkable ex- 

 periments. Through his researches and those of Bernoulli, 

 Euler, and Lagrange, it was proved that the sound given 

 by a string when struck, depends upon four conditions, 

 namely, its length, thickness, weight, and its tension, or the 

 tightness with which it is stretched. When any one of these 

 conditions is altered the string will give a different note, 

 but when two strings are exactly alike in these four re- 

 spects they will give the same note, because they will both 

 make exactly the same number of vibrations to and fro in 

 any given time. If one of them is only half as long as the 

 other, it will make two vibrations while the longer string is 

 making one, and then it will give a note an octave higher ; 

 all the other notes between these two can also be sounded 

 by altering the relative lengths of the two strings. 



It would be too long to work out here the laws respect- 

 ing the intervals between different notes and the lengths of 

 the strings producing them, but there are some curious and 

 beautiful experiments with stretched strings which help us 

 to have some idea, of musical sound and its laws. If you 

 shetch a string upon a sounding-board and then draw a 

 violin bow across it, it will give a musical note. If you 

 then touch the middle of the string quite lightly with a 

 feather you will get the same note an octave higher, because, 

 although the whole string is sounding, yet the feather keeps 



