350 HISTORY OF ACOUSTICS. 



explanation ; and it cannot be denied that the sub- 

 ject has its difficulties ; but still these do not deprive 

 Bernoulli of the merit of having pointed out the 

 principle of coexistent vibrations, or divest that 

 principle of its value in physical science. 



Daniel Bernoulli's Memoir, of which we speak, 

 was published at a period when the clouds which 

 involve the general analytical treatment of the pro- 

 blem of vibrating strings, were thickening about 

 Euler and D'Alembert, and darkening into a contro- 

 versial hue ; and as Bernoulli ventured to interpose 

 his view, as a solution of these difficulties, which, 

 in a mathematical sense, it is not, we can hardly be 

 surprized that he met with a rebuff. The further 

 prosecution of the different modes of vibration of 

 the same body need not be here considered. 



The sounds which are called Grave Harmonics, 

 have no analogy with the acute harmonics above- 

 mentioned ; nor do they belong to this section ; for 

 in the case of grave harmonics, we have one sound 

 from the co-operation of two strings, instead of 

 several sounds from one string. These harmonics 

 are, in fact, connected with beats, of which we have 

 already spoken ; the beats becoming so close as to 

 produce a note of definite musical quality. The 

 discovery of the grave harmonics is usually ascribed 

 to Tartini, who mentions them in 1 754 ; but they 

 are first noticed" in the work of Sorge On tuning 

 Organs, 1744. He there expresses this discovery 

 8 Chladni. Acoiist, p. 2">4. 



