ACOUSTICS. “kL 
powder is thrown up into the air when it falls upon the vibrating portions, 
and finally accumulates on the nodal lines, or lines of no vibration. They 
remain constant, therefore, and form the well known sound figures, first dis- 
covered by the eminent natural philosopher, Chladni. By taking sand 
moistened with gum water and finely pulverised, and placing a damp 
piece of paper on the plate, the figures may be removed and _ rendered 
permanent. 
Different figures result with a variation of the point of support of the 
plate, the rapidity of the vibrations, and the point of application of the 
vibrating cause ; of the hundreds fixed by Savart in the manner described 
above, we shall represent a few (figs. 68-74). The simple cross is pro- 
duced when the plate is fastened in the middle and intonated at one corner ; 
if the latter take place at the middle of one side of the plate, the cross (pl. 
19, fig. 71) is formed, &c. Other of the four-sided figures represented, are 
obtained by preventing the vibrations of one or more points of an edge of 
the plate. in which case several nodal lines are formed; symmetrical 
figures, however, are always produced, as the vibration which is hindered 
on one side ceases also in the corresponding parts of the other three. 
Triangular and polygonal plates give similar results. In circular plates 
very different tones may be produced, and each tone has its proper figure. 
Here may be distinguished three kinds of figures: diametral, concentric, 
and mixed. The diametral figures are obtained in a manner similar to the 
method employed for figs. 63 or 71, and the nodal lines are then radii. In 
the concentric the nodal lines form concentric circles, and are obtained 
by piercing the centre of the plate, drawing the hair of the bow through the 
hole, and thus producing the intonation. The plate then needs only to be 
supported in some of the points through which the nodal lines are to pass. 
The figures of the mixed system consist of diametral and concentric more 
or less curved lines, as seen in figs. 75-83, and are obtained by fixing the 
plates in the centre, and pressing the figures upon the points through which 
the nodal lines are to pass. Stretched skins or membranes act in the same 
manner as the plates, and Marx has exhibited the sound figures of these by 
means of his instrument, the Eoline. 
Normal vibrations occur in bells as in plates; and here also nodal lines 
are formed, which are, however, sometimes exceedingly irregular. To 
render these vibrations visible, we make use of a large wine-glass with 
a foot (fig. 84), filled with water or mercury, and intonated on the edge. 
There are then formed two very evident diametral nodal lines, between 
which the fluid remains in constant vibration, sufficiently violent at times 
to throw up drops into the air. 
In vacuo nodal lines are obtained which do not always agree with those 
formed in the air, particularly when the powder employed is very light, as 
lycopodium. | 
Plates, bells, &c., which do not possess equal elasticity on all! sides, 
likewise form peculiar figures, which, however, cease to be strictly sym- 
metrical. 
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