336 HISTORY OF ACOUSTICS. 



Sauveur's other method is more recondite, and 

 approaches to a mechanical view of the question 6 . 

 He proceeded on this basis ; a string, horizontally 

 stretched, cannot be drawn into a mathematical 

 straight line, but always hangs in a very flat curve, 

 or festoon. Hence Sauveur assumed, that its trans- 

 verse vibrations may be conceived to be identical 

 with the lateral swingings of such a festoon. Ob- 

 serving that the string C, in the middle of a harpsi- 

 chord, hangs in such a festoon to the amount of 

 1 -323rd of an inch, he calculates, by the laws of 

 pendulums, the time of oscillation, and finds it 

 1-1 22nd of a second. Thus this C, his fixed note, 

 makes one hundred and twenty-two vibrations in a 

 second. It is curious that this process, seemingly 

 so arbitrary, is capable of being justified on me- 

 chanical principles ; though we can hardly give the 

 author credit for the views which this justification 

 implies. It is, therefore, easy to understand that 

 it agreed with other experiments in the laws which 

 it gave for the dependence of the tone on the 

 length and tension. 



The problem of satisfactorily explaining this 

 dependence, on mechanical principles, naturally 

 pressed upon the attention of mathematicians when 

 the law of the phenomena was thus completely 

 determined by Mersenne and Sauveur. It was de- 

 sirable to show that both the circumstances and 

 the measure of the phenomena were such as known 

 6 Ac. Sc. Hist. 1713. 



