ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 257 



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 vith 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 in., 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 

 verj' different sounds, since one of them gives D and the other FJJ 

 of the same octave. The principal axes / »«, V 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 op be drawn through 

 the centre of the plate equally inclined to each of the axes /w, I' m'y 

 and this line be supposed to be the section of a plane perpendicular to 

 the plate, this plane will, for the plate iii., be parallel to the face eXy 

 of the pyramid fig. 1.; for the plate vii., to the face aXi ; and lastly, 

 for the plate xi., to the face cXrf; 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 phaenomena 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, PI. III.*, which contains neither of the axes of elasticity in its 

 plane. Now, if we consider the plates ii., 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. i. and v., and then two plates like in. and 

 VII., 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 PI. III. see Scientific Memoirs, Part I. 



