Page:Scientific Memoirs, Vol. 1 (1837).djvu/155

Rh a small diameter, cut at a little distance from the surface, we may suppose without any very notable error, at least for the whole of the phænomena, that the experiments have been made on a body the elasticity of which is not the same, according to three directions rectangular to each other, since, as is well known, this property does not exist in the same degree according to the direction of the fibres, according to that of the radius of the tree, and according to a direction perpendicular to the fibres and tangential to the ligneous layers.

After these two cases — the most simple that we have been able to study — we shall pass to the much more complicated phænomena which regularly crystallized bodies, such as rock crystal and carbonate of lime, present.

Let us suppose that fig. 1 (Plate III.) represents a cylinder of wood the annual layers of which are concentric to the circumference; let $$B C D E$$, fig. 2, be any plane passing through the axis $$A Y$$ of the cylinder, and let $$n n'$$ be a line normal to this plane: it is obvious that the plates taken perpendicularly to $$B C D E$$, and according to the different directions 1, 2, 3, 4, 5, &c. round $$n n'$$, ought to present different phænomena, since they all will contain the axis of least elasticity $$n n'$$ in their plane, and the resistance to flexure, according to the lines 1, 2, 3, 4, 5, will go on increasing in proportion as the plates shall more nearly approach being parallel to the axis of greatest elasticity $$A Y$$.

For the plate No. 1, fig. 3, perpendicular to this axis, all being symmetrical around the centre, the mode of division consisting of two lines which intersect each other at right angles, ought to be able to place itself in all kinds of directions, according as the place of excitation shall occupy different points of the circumference: this is really the case; but it is no longer so, for the plate No. 2 inclined 22° 5' to the preceding. In the latter, the elasticity becoming a little greater in the direction $$r s$$ contained in the plane $$B C D E$$, than in the direction $$n n'$$ normal to this plane, this circumstance ought to determine the nodal lines to place themselves according to these two directions. However, as this difference is very slight, the system of these two lines may still be displaced, when the place of excitation is made to vary; but it will change its form a little, and it will assume the appearance of two hyperbolic branches when it has arrived at 45° from its first position. In the plate No. 3, inclined 45° to the axis $$A Y$$, the difference of the two extreme elasticities being greater, the system of crossed lines becomes entirely fixed, or rather it can only move through a few degrees to the right or left of the position which it assumes in preference; but the hyperbolic system, the summits $$a$$ and $$b$$ of which recede more from each other than in fig. 2, will present the remarkable peculiarity of