Cuap. IV., § 7.] 
MECHANICS (ACOUSTICS).—CHLADNI—SAVART. 
891 
§ 7. Progress of Acoustics. CHLADNI—SavARt. Laplace’s Correction of the Theory of Sound. 
Vibrating Plates and Acoustic Figures. 
(433.) The mathematical theory of the propagation of 
Mathema- sound, considered as a branch of analytical mecha- 
pee, nics, 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- 
a overstepping the limits of knowledge of 
is day, left a legacy of toil to his immediate suc- 
cessors. Lagrange had the most distinguished good 
fortune in reducing the theory of aérial tremors under 
their most gerieral 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, 
and as the beautiful discovery of Laplace has been 
more 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, 
Laplace’s 
correction 
of the 
theory. 
(484.) The revival of experimental acoustics is due to 
see 8 Ernst Cutapnta native of Saxony, but of Hungarian 
of experi. Xtraction, born in 1756, 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 
Tose Aa of different densities, and in different gases, by using 
different % flute of metal which was sounded by means of the 
media; —_ 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 
(435.) 
Cagniard de la Tour’s * Sirene.” 
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 (486.) 
water, an experiment by no means difficult, was re- ! 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 tle 9 
sand or light substances upon the sounding boards plates. 
of musical instruments,! 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 “gures- 
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, 
1 This, however, is very doubtful. 
See Dove, Repertorium, iii, 106. 
