When elastic plates on which sand has been strewed are thrown into sonorous vibrations, the grains of sand arrange themselves in lines which indicate the quiescent parts of the plate, and have been called the nodal lines. This fact was discovered by Chladni, who also observed that the minute shavings cut by the edge of a glass plate from the hairs of the violin bow employed to produce the vibration, collected together on those parts of the plate that were most violently agitated, that is, at the middle of the lines of oscillation, or portions into which the plate is divided by the nodal lines. The same phenomenon is exhibited by lycopodium, or any other very light and finely divided powder. This subject was investigated by M. Savart, who, in a paper read to the Royal Academy of Sciences at Paris in the year 1817, endeavoured to account for this latter class of phenomena by deducing from the primary divisions of the parts of vibrating bodies, certain secondary modes of division, comprising parts that remain horizontal during every stage of the vibration, and which therefore may admit of the settlement there of light powders, while heavier powders can be stationary only at the points of absolute rest. This explanation not appearing to the author to be satisfactory, he made a great number of experiments, which are detailed at length in the present paper, showing that the immediate cause of these motions exists in the surrounding medium, and is to be found in the currents arising from the mechanical action of the plate, while vibrating upon that portion of the medium which is in contact with the plate. These currents are directed from the quiescent lines towards those parts where the oscillation is the greatest, and meeting from opposite sides at these central points, thence proceed perpendicularly from the vibrating surface to a certain distance; and finally, receding from each other, return again in a direction towards the nodal lines. The combination of these motions constitutes vortices carrying with them any light particles which may lie in the way of the currents. While in motion, the powders sustained by these vortices appear in the form of clouds, the particles of which have among themselves an intestine motion of revolution, rising in the centre of the heap, and rolling down again on the outer sides. The powders are collected in the same situations on the vibrating plate, although the plate may be considerably inclined to the horizon, and remain there even when the inclination is so great as to prevent grains of sand from resting on the nodal lines. A piece of gold leaf laid upon the plate was raised up in the form of a blister at that part which corresponded with the centre of the clouds, even to the height of one-twelfth of an inch.
Inertial-particle accelerations in turbulence: a Lagrangian closure