ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 265 



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 difi'erent from those of the preceding plates. It 

 appears therefore to result from this identity of phaenomena 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 deter- 

 mined by comparing the phaenomena 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 com- 

 posed 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 prirai- 

 ti\e 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. 1 1 , 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 con- 

 tain 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 no- 

 dal hyperbola, it must thence be concluded that this plane contains the 

 axis of least elasticity, and, at the same time, that this axis is perpendi- 

 cular to the intermediate axis, and forms with that of greatest elasti- 

 city 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 



