ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. Q57. 
same octave. Thus, in any plate taken parallel to the faces of the 
hexahedron, one of the nodal lines of the rectangular system always 
corresponds with the axis of the crystal. In this case everything 
occurs the same as in plates composed of parallel fibres and which con- 
tain in their plane at least one of the axes of elasticity; but this is no 
longer the case for the plates 111., viI., xI., perpendicular to two paral- 
lel faces of the hexahedron, although they are also parallel to the axis 
like the preceding: instead of a system of lines crossed rectangularly 
and a hyperbolic system, they exhibit only two hyperbolic systems, 
which appear exactly similar, and which however are accompanied by 
very different sounds, since one of them gives D and the other Ff 
of the same octave. The principal axes 7m, I'm! of each of the two 
hyperbolic curves appear to intersect each other at the centre of the 
plate; their mutual inclination is from 51° to 52°, so that the branches 
of these curves intersect each other ; and if a line 0 p be drawn through 
the centre of the plate equally inclined to each of the axes Im, I m’, 
and this line be supposed to be the section of a plane perpendicular to 
the plate, this plane will, for the plate 111., be parallel to the face eX f 
of the pyramid fig. 1.; for the plate vir., to the face aX; and lastly, 
for the plate x1., to the face eXd; so that it must hence be concluded 
that the six faces of the pyramid do not possess the same properties, 
and that the three we have just indicated perform an important part in 
the phenomena in question. It must be remarked that the modes of 
division of these plates are exactly the same as those of the plate No. 3 
of fig. 14, Pl. III.*, which contains neither of the axes of elasticity in its 
plane. Now, if we consider the plates 11., Iv., VI., VIII., X., XII. inter- 
mediate to the preceding and to those which are parallel to the faces 
of the hexahedron, we find also in them properties which seem to de- 
pend on both jointly, as well with respect to the nodal lines of the two 
systems as to the sounds they produce. Thus with reference to the pro- 
cess of investigation which we have employed, all the plates parallel to 
the axis do not possess the same properties, whilst with regard to light 
it is well known that they exhibit exactly the same appearances. 
Although this result has been verified many times, it was still impor- 
tant to verify it again, which I did in the following manner: I took, 
first, two plates like Nos. 1. and v., and then two plates like 11. and 
vul., and after having crossed their optic axes, I placed successively 
_ each of these pairs in the path of a large pencil of light polarized by 
_ a black glass, the plane of the plates being placed perpendicularly to 
_ the luminous rays, and their axes making an angle of 45° with the plane 
_ of polarization. It is known that if we look through a similar pair by 
means of a tourmaline, the axis of which is in the plane of polarization, 
_ We perceive two systems of coloured hyperbolas, the tints of which 
* For Pl. III. see Scientific Memoirs, Part I. 
