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 different from those of the preceding plates. It 
appears therefore to result from this identity of phenomena 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 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 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 primi- 
tive 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, dis, 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 
