vertheless, the interval which is observed between the sounds of the two systems being always very small, and not being constant in different crystals, it appears more natural to attribute this difference of elasticity to an irregularity of structure than to suppose that it depends on a determinate and regular arrangement, the more so as in very large crystals, like those I have employed, it is very rare not to meet with irregularities of structure sufficiently obvious even to be recognised by the naked eye.
The plate No. 2, inclined 78° to the axis, begins to present a difference in the disposition of these two systems of nodal lines; one of the two transforms itself into two hyperbolic branches, which become more straightened in the plate No. 3, inclined 75° to the axis, and which afterwards approach each other again, and become two straight lines, which intersect each other at right angles in the plate No. 4, inclined about 51° to the axis, and which consequently is nearly perpendicular to the face of the pyramid fig. 1; the inclination of the faces of the pyramid to those of the hexahedron being 140° 40′.
The numbers of vibrations which were nearly the same for No. 1, from which only the sounds D and D+ were obtained, differ more as the plate approaches No. 4, when the gravest sound being C, the second is the G of the same octave, although the two modes of division are the same as those of No. I . It is this sound C, given by one of the modes of division of the plate perpendicular to the face of the pyramid, which I have taken as the term of comparison, and to which the sounds of all the other plates are referred. Recommencing with the plate No. 4, the variable system separates once more, but in the contrary way; the curves which form it continue to straighten, whilst their summits recede from each other, and at the same time the two sounds approximate until they are sensibly the same in No. 8, inclined about 12° to the axis. The hyperbolic system ceases to assume a determined position, and it can, without the sound undergoing any change, transform itself gradually into the rectangular system which form the axes, so that this plate appears to be exactly in the same conditions as No. 5 of fig. 8, PL III. In a crystal of quartz there are three planes analogous to the preceding, since the phænomena which are presented by the plates cut round the edge of the base of the prism, are, as I have satisfied myself, precisely the same as those which are presented, for the same degrees of inclination, by plates cut round the two other edges , .
Beyond No. 8. the sounds begin to differ from each other, and the branches of the hyperbola continue to straighten until No. 11, parallel to the second face of the pyramid. There the distance between their summits is greater than for any other degree of inclination of the plates, and the sound of the rectangular system is the same as that of
