28 HISTORY OF ACOUSTICS. 



CHAPTER II. 

 PROBLEM OF THE VIBRATIONS OF STRINGS. 



rjlIIAT the continuation of sound depends on a continued minute i,nd 

 J- rapid motion, a shaking or trembling, of the parts of the sounding 

 body, was soon seen. Thus Bacon says, 1 " The duration of the sound 

 of a bell or a string when struck, which appears to be prolonged and 

 gradually extinguished, does not proceed from the first percussion ; 

 but the trepidation of the body struck perpetually generates a new 

 sound. For if that trepidation be prevented, and the bell or string be 

 stopped, the sound soon dies : as in spinets, as soon as the spine is let 

 fall so as to touch the string, the sound ceases." In the case of a 

 stretched string, it is not difficult to perceive that the motion is a 

 motion back and forwards across the straight line which the string 

 occupies when at rest. The further examination of the quantitative 

 circumstances of this oscillatory motion was an obvious problem ; and 

 especially after oscillations, though of another kind (those of a pendu- 

 lous body), had attracted attention, as they had done in the school of 

 Galileo. Mersenne, one of the promulgators of Galileo's philosophy in 

 France, is the first author in whom I find an examination of the details 

 of this case (Harmonicorum Liber. Paris, 1636). He asserts, 2 that the 

 differences and concords of acute and grave sounds depend on the 

 rapidity of vibrations, and their ratio ; and he proves this doctrine by 

 a series of experimental comparisons. Thus he finds 8 that the note of 

 a string is as its length, by taking a string first twice, and then four 

 times as long as the original string, other things remaining the same. 

 This, indeed, was known to the ancients, and was the basis of that 

 numerical indication of the notes which the proposition expresses. 

 Mersenne further proceeds to show the effect of thickness and tension. 

 He finds (Prop. 7) that a string must be four times as thick as another, 

 to give the octave below ; he finds, also (Prop. 8), that the tension 

 must be about four times as great in order to produce the octave above. 

 From these proportions various others are deduced, and the law of the, 



Hist. Son. et And vol. ix. p. 71. 2 L. i. Prop. 15. 3 1 . ii Pron. 



