264 EIGHTEENTH CENTURY. PT. in. 



stretched strings. But, curiously enough, it was a deaf 

 man, or one who heard very imperfectly, who made the 

 first accurate experiments as to the number of vibrations 

 which produce any particular note. 



Joseph Sauveur, the geometer, was born in 1653. He 

 was dumb for seven years after his birth, and his speech 

 as well as his hearing remained very imperfect during his 

 whole life. Yet this man, who was a splendid mathe- 

 matician, found his greatest pleasure in studying the mathe- 

 matical theory of sound. Sauveur had remarked that a 

 great confusion was created in music because there was no 

 fixed note from which every one could agree to start, and 

 in order to get this, it was necessary to fix upon some one 

 note of a known number of vibrations. But how were the 

 vibrations to be counted? 



Sauveur devised the following method : Musicians 

 knew already that when two organ pipes of different lengths 

 are sounded together, then, because the air-wave in the 

 shorter one is driven back, sooner than in the longer one, 

 the puffs of sound will come more rapidly from the shorter 

 pipe, just as the footfalls of a man who takes short steps 

 will be more frequent than those of a man who strides. 

 Now let us suppose two organ pipes, one, A, 8 feet, and the 

 other, B, 9 feet long. A being one-ninth shorter than B, 

 the puffs from that pipe will be one-ninth quicker, so that 

 by the time A has made nine puffs it will have gained 

 one whole step upon B, which will only have had time to 

 make eight. Now all the time it is gaining, its puffs will 

 come somewhere between those of B, but as soon as it has 

 gained one whole stride the two pipes will sound simul- 

 taneously. This produces what musicians call 'beats,' or 

 loud gusts of sound at regular intervals whenever the two 

 pipes sound together, and it is clear that if you count how 



