600 ADDITIONS. 



rind Xote), have a known material dependence, and each may be em- 

 ployed in determining the other : for instance, the Note ruay be 

 employed in determining the velocity of sound and the elasticity of 

 the vibrating substance. 



O 



Chladni, 1 and the Webers, 2 had made valuable experimental inqui- 

 ries on such subjects. But more complete investigations of this kind 

 have been conducted with care and skill by M. Wertheim. 3 For in- 

 stance, he has determined the velocity with which sound travels in 

 water, by making an organ-pipe to sound by the passage of water 

 through it. This is a matter of some difficulty ; for the mouthpiece 

 of an organ-pipe, if it be not properly and carefully constructed, pro- 

 duces sounds of its own, which are not the genuine musical note of 

 the pipe. And though the note depends mainly upon the length of 

 the pipe, it depends also, in a small degree, on the breadth of the 

 pipe and the size of the mouthpiece. 



If the pipe were a mere line, the time of a vibration would be the 

 time in which a vibration travels from one end of the pipe to the 

 other ; and thus the note for a given length (which is determined by 

 the time of vibration), is connected with the velocity of vibration. 

 He thus found that the velocity of a vibration along the pipe in sea- 

 water is 1157 metres per second. 



But M. Wertheim conceived that he had previously shown, by gene- 

 ral mathematical reasoning, that the velocity with which sound travels 

 in an unlimited expanse of any substance, is to the velocity with 

 which it travels along a pipe or linear strip of the same substance as 

 the square root of 3 to the square root of 2. Hence the velocity of 

 sound in sea-water would be 1454 metres a second. The velocity of 

 sound in air is 332 metres. 



M. Wertheim also employed the vibrations of rods of steel and other 

 metals in order to determine their modulus of elasticity that is, the 

 quantity which determines for each substance, the extent to which, in 

 virtue of its elasticity, it is compressed and expanded by given pres- 

 sures or tensions. For this purpose he caused the rod to vibrate near 

 to a tuning-fork of given pitch, so that both the rod and the tuning- 

 fork by their vibrations traced undulating curves on a revolving disk. 

 The curves traced by the two could be compared so as to give their 

 'elative rate, and thus to determine the elasticity of the substance. 



Traite ffAvmstique, 1809. 2 Wellenlehre, 1852. 



Memoires de Pliysique Mecanique. Paris, 1S48. 



