Page:Scientific Memoirs, Vol. 1 (1837).djvu/157

Rh experiments is, that in wood in which the annual layers are nearly cylindrical and concentric, the elasticity is sensibly uniform in all the diameters of any section perpendicular to the axis of the branch. We shall see further on, that plates of carbonate of lime or rock crystal, cut perpendicularly to the axis, very seldom present this uniformity of structure for all their diameters, although the modifications which such plates impress on polarized light appear symmetrical round this same axis.

In the case which we have just examined, two of the three axes of elasticity being equal, the phænomena are, as we have just seen, exempt from any great complication. It is not so when the three axes possess each a different elasticity: it would then be indispensable to cut, first a series of plates round each of the axes, then a fourth series round a line equally inclined with respect to the three axes, and lastly, it would be necessary again to take a series round each of the lines which divide equally into two the angle contained between any two of the axes; and notwithstanding the great number of results which would be obtained by this process, the end would be far from attained, since these different series would want connexion with each other, and consequently this process cannot give a clear idea of the whole of the transformations of the nodal lines. Nevertheless, I shall content myself to follow this route, which appears to me less complicated than any other, and is sufficient to render fully evident all the principal peculiarities of this kind of phænomena.

In order that the relative positions of the lines round which I have cut the different series of plates of which I have spoken, and the relations they have to the planes of the ligneous layers, as well as to the direction of their fibres, may be more easily represented, I shall refer them all to the edges of a cube $$A E$$ fig. 5, the face of which $$A X B Z$$ I shall suppose is parallel to the ligneous layers, and the edge $$A X$$ to the direction of the fibres, which will allow the three edges $$A X$$, $$A Y$$, $$A Z $$ to be considered as being themselves the axes of elasticity. Afterwards I shall indicate the different degrees of inclination of the plates of each series, on a plane normal to the line round which they are to be cut; the position and outline of this plane being at the same time referred to the natural faces of the cube.

But before commencing to describe the phænomena which each of these series presents, it is indispensable to endeavour to determine the ratio of the resistance to flexion, in wood, in the direction of each of the three axes of elasticity: this may be easily done by means of vibrations, by cutting three small square prismatic rods, of the same dimensions, according to the three directions just indicated; for, the degree of their elasticity can be ascertained by comparing the numbers of the vibrations which they perform, for the same mode of division, knowing besides