are constantly reproduced in it in three different positions; and it seems that everything in it has reference to the different directions of cleavage, to the faces, and to the edges of the primitive rhombohedron. Thus all the plates cut parallel to the natural faces of the hexahedron possess exactly the same properties, and these properties are very different from those of the plates equally parallel to the axis, but which are normal to two faces of the hexahedron. Likewise, the plates parallel to the cleavable faces of the pyramid produce the same sounds, and exhibit the same acoustic figures; whilst the plates parallel to the three other faces present figures different from those of the preceding plates. It appears therefore to result from this identity of phænomena for three distinct positions, that there are in rock crystal three systems of axes or principal lines of elasticity.
But in this point of view, what would be the precise directions of these axes for each system? This can, to a certain point, be determined by comparing the phenomena we have observed in rock crystal with those presented to us by wood. For, all the plates cut round one of the edges which result from the junction of a face of the pyramid with the adjacent face of the hexahedron, producing a nodal system composed of two lines cutting each other rectangularly, one of which always corresponds with the edge in question; and the transformations of the acoustic lines in it being entirely analogous to those of a series of plates cut round the intermediate axis in wood, it follows that this edge, which is nothing else than the great diagonal of the primitive rhombohedron, ought to be regarded as the intermediate axis of elasticity. In the next place, as the maximum of straightening and of deviation of the branches of the nodal hyperbola takes place in the plate No. 11 , fig. 3, bis, parallel to the cleavable face of the pyramid, and as at the same time this plate is a limit for the sounds which it produces, it is equally natural to suppose that it ought also to contain in its plane another axis of elasticity, which can correspond only to the second of the crossed nodal lines, that is to say, to that which serves as the second axis of the nodal hyperbola, and which is, at the same time, the smaller diagonal of the lozenge face of the primitive rhombohedron. This line may therefore be considered as the axis of greatest elasticity of each system. Lastly, following the same analogy, as the plate which is cut parallel to the diagonal plane, the intersection of which with the lozenge face of the rhombohedron forms its great diagonal, is besides a maximum of deviation for the summits of the nodal hyperbola, it must thence be concluded that this plane contains the axis of least elasticity, and, at the same time, that this axis is perpendicular to the intermediate axis, and forms with that of greatest elasticity an angle of 57° 40′ 13″, since such is the inclination of the face of the rhombohedron to the diagonal plane. Thus, first, the axis of
