4:2 HISTORY OF ACOUSTICS. 



made to sound. His first investigations on this subject, Entdeckun- 

 f/en ilber die T/teorie des Klangs, were published 1787; and in 1802 

 and 1817 he added other discoveries. In these works he not only 

 related a vast number of new and curious facts, but in some measure 

 reduced some of them to order and law. For instance, he has 

 traced all the vibrations of square plates to a resemblance with 

 those forms of vibration in which Nodal Lines are parallel to one 

 side of the square, and those in which they are parallel to another 

 side; and he has established a notation for the modes of vibra- 

 tion founded on this classification. Thus, 5-2 denotes a form in 

 which there are five nodal lines parallel to one side, and two to 

 another ; or a form which can be traced to a disfigurement of such a 

 standard type. Savart pursued this subject still further ; and traced, 

 by actual observation, the forms of the Nodal Surfaces which divide 

 solid bodies, and masses of air, when in a state of vibration. 



The dependence of such vibrations upon their physical cause, 

 namely, the elasticity of the substance, we can conceive in a general 

 way ; but the mathematical theory of such cases is, as might be 

 supposed, very difficult, even if we confine ourselves to the obvious 

 question of the mechanical possibility of these different modes of 

 vibration, and leave out of consideration their dependence upon the 

 mode of excitation. The transverse vibrations of elastic rods, plates, 

 and rings, had been considered by Euler in 1779 ; but his calculation 

 concerning plates had foretold only a small part of the curious pheno- 

 mena observed by Chladni ;' and the several notes which, according 

 to his calculation, the same ring ought to give, were not in agreement 

 with experiment. 2 Indeed, researches of this kind, as conducted by 

 Euler, and other authors, 3 rather were, and were intended for, exam- 

 ples of analytical skill, than explanations of physical facts. James 

 Bernoulli, after the publication of Chladni's experiments in 1787, 

 attempted to solve the problem for plates, by treating a plate as 

 a collection of fibres ; but, as Chladni observes, the justice of this 

 mode of conception is disproved, by the disagreement of its results 

 with experiment. 



The Institute of France, which had approved of Chladni's labours, 

 oroposed, in 1809, the problem now before us as a prize-question : 4 

 ' To give the mathematical theory of the vibrations of elastic su: 



1 Fischer, vi. 587. * Ib. vi. 596. 



3 See Chladni, p. 4V4. * See Chladni, p. 357. 



