Page:Scientific Memoirs, Vol. 1 (1837).djvu/154

142 itself on them in a single position; and that there is a second position in which two hyperbolic curved lines are obtained which are accompanied, according to the different cases, by a sound which differs more or less from that which is produced when the crossed lines occur. Plates are also met with which are incapable of assuming the mode of division formed of two straight lines, and in which only two systems of hyperbolic curves are obtained, sometimes similar, yet giving different sounds. In short, I have yet found no body for which the same nodal figure can place itself in every direction; which seems to indicate that there are very few solid substances which possess the same properties throughout. But what appears still more extraordinary is, that if in the same body, a mass of metal for instance, plates are cut according to different directions, some are susceptible of the mode of division consisting of two lines which cross each other rectangularly, whilst others present only two systems of hyperbolic curves. In both cases, the sounds of the two systems may differ greatly: there may, for example, be an interval between them of more than a fifth.

To arrive at the discovery of the experimental laws of this kind of phænomena, it would be necessary therefore to be able to study them, at first in the most simple cases, for example, upon bodies the elastic state of which, previously known, would differ only according to two directions. This would obtain in a body which might be composed by placing flat plates formed of two heterogeneous substances upon each other in such a manner that all the odd plates might be of one substance, and all the even plates of another, the elasticity in all directions of the plane of each of them being the same. But it has appeared to me difficult to attain this condition, since I have yet found no body the elasticity of which was the same in all directions.

The most simple structure after the preceding would be that of a body composed of cylindrical and concentric layers, the nature of which should be alternately different for the layers next each other, as is nearly the case in the branch of a tree free from knots. It is evident that the elasticity ought to be sensibly the same in every direction of the plane of a plate cut perpendicularly to the axis of the cylinder, and it ought to differ greatly from that which is observed in the direction of the axis. Consequently we shall commence by examining this first case; after which we shall pass to that in which the elasticity would be different according to three directions perpendicular to each other, as would take place in a body composed of flat plates alternately of two different substances, and the elastic state of which would not be the same, according to two directions perpendicular to each other. Wood fulfills again these different conditions; for in a tree of very considerable diameter, the ligneous layers may be considered as sensibly plane for a small number of degrees of the circumference; and if we confine ourselves to plates of