CHAP. IV., 7.] MECHANICS (ACOUSTICS). CHLADNI SAV ART. 



93 



7. Progress of Acoustics. CHLADNI SAVART. Laplace's Correction of the Theory of Sound. 

 Vibrating Plates and Acoustic Figures. Cagniard de la Tour's " Sirene." 



of the 

 theory. 



(433.) The mathematical theory of the propagation of 

 Mathema- sound, considered as a branch of analytical mecha- 

 tl f c ^* he ^Jnics, made far greater progress during the eighteenth 

 pagation century, in harmony with the general character of 

 of sound, the science of that period, than the inductive doc- 

 trines of acoustics. Newton here, as in other de- 

 partments, overstepping the limits of knowledge of 

 his day, left a legacy of toil to his immediate suc- 

 cessors. Lagrange had the most distinguished good 

 fortune in reducing the theory of aerial tremors under 

 their most general conditions to the laws of mecha- 

 nics by the calculus of partial differentials ; and La- 

 place supplied the link which was wanting to recon- 

 cile the result with the known mechanical properties 

 of air. As the former of these matters belongs more 

 properly to the period of the previous Dissertation, 

 Laplace's and as the beautiful discovery of Laplace has been 

 correction m ore especially touched upon by Sir John Leslie, 

 it will be sufficient here to recall the fact that the 

 spring of air, or the effort by which it tends to re- 

 expand under sudden compression or to contract to 

 its former bulk when suddenly dilated, is increased 

 by the heat extricated in the former case, as well as 

 by its absorption in the latter. And as sonorous 

 pulsations are held to consist of a series of com- 

 pressed and rarified waves whose velocity is affected 

 by the recoil of air, it appears certain that the velo- 

 city must be increased by this circumstance, though 

 it is difficult to determine experimentally the exact 

 amount. 



(434.) The revival of experimental acoustics is due to 

 Chladni ERNST CHLADNI a native of Saxony, but of Hungarian 



the reviver . . , . -. *.,. n T , i i -i 



of experi- extraction, born in 17o6. Little had been done in 

 mental this department since the time of Sauveur, who as- 

 acoustics. certained the nature of the harmonic vibrations of 

 strings, and that of Daniel Bernouilli, who considered 

 the analogous case of organ pipes. We are indebted 

 to Chladni for two classes of original experiments 

 his measure of the velocity of sound in a variety of 

 bodies by peculiar and ingenious methods ; and his 

 observations on the vibrations of plates by means of 

 the ingenious expedient of strewing them with sand 

 and other powders. 



We shall say a few words under each of these 

 heads : 



I. Chladni observed the velocity of sound in air 



of different densities, and in different gases, by using 



lifferent a nut e of metal which was sounded by means of the 



uedia ; elastic fluid required, and the resulting note enabled 



him to determine by an easy calculation the speed of 



propagation of the tremor. This method (using an 



organ pipe) has been more lately resorted to by 



Dulong for the purpose of deducing the properties 



of different gases with respect to heat, by ascertain- 

 ing from experiment the co-efficient in Laplace's 

 correction for the velocity of sound. Chladni was 

 also probably the first to notice the longitudinal os- 

 cillations of strings and rods which always yield a 

 note immensely sharper than the lateral vibrations. 

 By means of the former he ascertained the velocity 

 of sound in a variety of woods and metals, in some 

 of which it is no less than seventeen times greater 

 than in air. These observations are not only inte- 

 resting in themselves, but as throwing light on the 

 constitution of solid bodies. To Chaldni we like- 

 wise owe a knowledge of the twisting vibrations of 

 rods, which exhausts the modes of vibration of such 

 bodies. To connect theoretically the periods of these 

 different kinds of movement, has been a favourite 

 problem with recent mathematicians, but has not even 

 yet been quite successfully performed. 



The determination of the velocity of sound in (436.) 

 water, an experiment by no means difficult, was re- In water - 

 served for MM. Colladon and Sturm, who ob- 

 served it on the Lake of Geneva, and found it to be 

 4708 English feet per second, a result closely con- 

 forming to the theoretical amount deduced from 

 Oersted's observation on the compressibility of water. 



II. But Chladni' s experiments on the vibrations (437.) 

 of plates are of still greater interest and originality. Chladni on 

 Though it has been affirmed that Galileo strewed JfoVof 1 *" 

 sand or light substances upon the sounding boards plates. 

 of musical instruments, 1 Chladni deserves the entire 

 credit of rendering this an exact method of ascertain- 

 ing the nodal lines or points of rest in bodies vi- 

 brating in a stable or permanent manner. He first 

 applied it to plates round, square, or of different 

 figures, supported horizontally and caused to vibrate 

 by applying a violin bow to their edges. Dust or fine 

 sand strewed or sifted uniformly over such a plate, 

 arranges itself in a variety of beautiful figures, being Acoustic 

 tilted from the greater part of the surface, and heaped fig 1 "" 68 - 

 up on those parts which are at rest in consequence of 

 the vibratory motion of adjacent parts taking place 

 simultaneously in opposite directions ; just as the 

 nodal points of a string vibrating harmonically are 

 without motion on the same account. The number 

 and variety of figures thus producible in the same 

 plate is very great, and corresponds, as Chladni 

 clearly saw, to different simple harmonical vibrations 

 of the elastic plate, being accompanied by their ap- 

 propriate notes ; or by the superposition of several 

 such modes of vibration, and of the corresponding 

 sounds. The tract published by him in 1787 en- 

 tituled, Entdeckungen iiber die Theorie des Klanges, 

 contains numerous figures of these appearances, which, 



This, however, is very doubtful. See Dove, Repertorium, iii. 106. 



