ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 259. 
vertheless, the interval which is observed between the sounds of the two 
systems being always very small, and not being constant in different cry- 
stals, it appears more natural to attribute this difference of elasticity to 
an irregularity of structure than to suppose that it depends on a deter- 
minate 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 differ- 
ence 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 a X b 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.1. 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, trans- 
form 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, PI.III. In a crystal of quartz there are three planes analogous 
to the preceding, since the phznomena which are presented by the 
plates cut round the edge a6 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 
Cede f. 
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 
