CH. xxx. MUSICAL VIBRATIONS. 263 



CHAPTER XXX. 



SCIENCE OF THE EIGHTEENTH CENTURY (CONTINUED). 



Calculation of Musical Vibrations Sauveur Bernoulli, Euler, La- 

 grange Nodes and Segments Chladni Plates, Bells, and Gongs 

 Sand Figures produced by Vibration. 



Calculation of Musical Vibrations Sauveur, 170O. 



After Newton had published his theory of sound, and some 

 clearer ideas prevailed about the manner in which sound 

 vibrations are conveyed to the ear, many mathematicians 

 occupied themselves in working out the laws of those 

 regular sound - vibrations which produce musical notes. 

 Among the most celebrated of these were Sauveur (1653- 

 1716), Daniel Bernoulli (1700-1782), Euler (1707-1783), 

 and Lagrange, of whom we shall speak presently in connec- 

 tion with astronomy. 



It will be remembered that Pythagoras by stretching a 

 string on a sounding-board (p. 12) had obtained musical 

 notes, whose intervals depended upon the lengths into 

 which the string was divided. Galileo also had pointed 

 out (p. 80), that in order to produce a musical note and 

 not rrlere noise, the shocks given to the air must follow 

 each other at regular intervals, and that the more rapidly 

 the vibrations strike upon our ear, the higher is the note 

 we hear ; and two men, Noble and Pigot, had made in 

 1676 some very interesting experiments on the divisions of 



