4.06 tECTURE XXXIV. 



a similar conclusion from reasoning still less accurate: his merits with respect 

 to the theory of acustics in general are, however, by no means contemptible. 

 Lagrange and Euier have corrected and much extended the investigations 

 of Newton, and of Taylor; and Bernoulli and Daleinbert have also materi- 

 ally contributed to the coijiplete examination and discussion of the 

 subject. 



About the year 1750, Daniel Bernoulli succeeded in obtaining a solution 

 of a problem still more diificult than those which relate to the motions of 

 chords: he determined the frequency of the vibrations of an elastic rod 

 fixed at one end, as well as the relations of its subordinate sounds. Thesolution 

 is not indeed absolutely general, but it may perhaps be adapted to all possible 

 cases, by considering the effect of a combination of various sounds produced 

 at the same time. Euler has also great merit in extending and facilitating the 

 mathematical part of this investigation, although he has committed several 

 mistakes respecting the meclianical application of it, some of which he 

 has himself corrected, and others have been noticed by Riccatiand Chladni, 



The grave harmonics produced by the combination of two acute sounds 

 were noticed about the same time by Romieu and by Tartini, but first by 

 Romieu: their existence is not only remarkable in itself, but particularly as 

 it leads to some interesting consequences respecting the nature of sound and 

 hearing in general. 



Bernoulli has also investigated, in a very ingenious manner, the sounds 

 produced by the air in pipes of various forms, although confessedly on 

 suppositions deviating in some measure from the truth: the results of his 

 computations have, however, been amply confirmed by the experiments of 

 Lambert on the sounds of flutes. 



Dr. Chladni's method of examining the sounds of plates has affbrded a 

 Very interesting addition to our knowledge of the nature of vibrations; his 

 discovery of the longitudinal sounds of solids is of considerable importance, 

 and he is said to be engaged in an extensive work on tlie subject of acustics 

 in general. Some remarks which I have made in the Philosophical Trans- 



