PKOBLEM OF THE VIBRATIONS OF STRINGS. 2b 



phenomena of this kind may be considered as determined. Merscnne 

 also undertook to measure the phenomena numerically, that is to 

 determine the number of vibrations of the string in each of such cases ; 

 which at first might appear difficult, since it is obviously impossible to 

 count with the eye the passages of a sounding string backwards and 

 forwards. But Mersenne rightly assumed, that the number of vibra- 

 tions is the same so long as the tone is the same, and that the ratios 

 of the numbers of vibrations of different strings may be determined 

 from the numerical relations of their notes. He had, therefore, only 

 to determine the number of vibrations of one certain string, or one 

 known note, to know those of all others. He took a musical string of 

 three-quarters of a foot long, stretched with a weight of six pounds and 

 five eighths, which he found gave him by its vibrations a certain stand- 

 ard note in his organ : he found that a string of the same material 

 and tension, fifteen feet, that is, twenty times as long, made ten recur 

 rences in a second; and he inferred that the number of vibrations 

 of the shorter string must also be twenty times as great ; and thus 

 such a string must make in one second of time two hundred vibra- 



O 



tions. 



This determination of Mersenne does not appear to have attracted 

 due notice ; but some time afterwards attempts were made to ascer- 

 tain the connexion between the sound and its elementary pulsations in 

 a more direct manner. Hooke, in 1681, produced sounds by the strik- 

 ing of the teeth of brass wheels, 4 and Stancari, in 1706, by whirling 

 round a large wheel in air, showed, before the Academy of Bologna, 

 how the number of vibrations in a given note might be known. Sau- 

 veur, who, though deaf for the first seven years of his life, was one of 

 the greatest promoters of the science of sound, and gave it its name 

 of Acoustics, endeavored also, about the same time, to determine the 

 number of vibrations of a standard note, or, as he called it, Fixed 

 Sound. He employed two methods, both ingenious and both indi- 

 rect. The first was the method of beats. Two organ-pipes, which 

 form a discord, are often heard to produce a kind of howl, or wavy 

 noise, the sound swelling and declining at small intervals of time. This 

 was readily and rightly ascribed to the coincidences of the pulsations 

 of sound of the two notes after certain cycles. Thus, if the number 

 of vibrations of the notes were as fifteen to sixteen in the same time, 

 every fifteenth s'ibration of the one would coincide with every six 



4 Life, p. xxiii. 



