Page:Scientific Memoirs, Vol. 1 (1837).djvu/269

 

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 contain in their plane at least one of the axes of elasticity; but this is no longer the case for the plates iii., vii., xi., perpendicular to two parallel 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 F# of the same octave. The principal axes $lm$, $l^{\prime }m^{\prime }$ 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 $lm$, $l^{\prime }m^{\prime }$ 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 $eXf$ of the pyramid fig. 1.; for the plate vii., to the face $aXb$; and lastly, for the plate xi., to the face $cXd$; 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 phænomena 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.^[1], which contains neither of the axes of elasticity in its plane. Now, if we consider the plates ii., iv., vi., viii., x., xii. intermediate 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 process 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 important 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 iii. 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

1. For Pl. III. see Scientific Memoirs, Part I.