ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 267 
directions perpendicular to each other ; this explains the production of 
the nodal lines crossed at right angles, as in the series of plates cut 
round one of the axes of elasticity, in bodies in which these axes are rect- 
angular. It appears therefore that we may conclude from this obser- 
vation that rock crystal possesses, like carbonate of lime, supernumerary 
planes of cleavage parallel to the diagonal planes of its primitive rhom- 
bohedron, and that it is to the existence of these supernumerary joints 
that the principal peculiarities of the elastic state of this substance 
must be attributed. 
The only striking difference there appears to be between the struc- 
ture of carbonate of lime and that of quartz consists in this, that, in 
the first of these substances, the small diagonal of the rhombohedron is 
the axis of least elasticity, whilst it is that of greatest elasticity in the 
second. To be convinced of the accuracy of this assertion, it is suffi- 
cient to cut, in a rhombohedron of carbonate of lime, a plate taken 
parallel to one of its natural faces, and to examine the arrangement of 
its two nodal systems, one of which consists of two lines crossed rect- 
angularly, which are always placed on the diagonals of the lozenge, 
the primitive outline of the plate, and the other is formed of two hyper- 
bolic branches, to which the preceding lines serve as axes (see fig. 7, 
bis, No. 6); but with this peculiarity, that it is the small diagonal 
which becomes the first axis of the hyperbola, whilst it is its second 
axis in the corresponding plate of rock crystal (see fig. 3, bis, No. 11). 
It may be here asked how far this difference of structure may influence 
the phenomena of light which are peculiar to each of these two sub- 
stances, one of which is a crystal with attractive (positive) double re- 
fraction, and the other with repulsive (negative) double refraction. 
It appears, therefore, to result from this approximation between the 
phznomena presented by carbonate of lime and rock crystal, with 
respect to. sonorous vibrations, that the arrangement of the acoustic 
figures, and the numbers of vibrations by which they are accompanied, 
are always found intimately connected with the directions of cleavage 
in each plate; and it may be said in general, that if these directions 
intersect each other at right angles, in the plane of the plate, one of 
the two modes of division will always consist of two lines crossed rect- 
angularly ; whilst if they are inclined to each other the two nodal 
systems will be hyperbolic curves. 
The disposition of the nodal lines upon circular plates of sulphate 
of lime gives additional support to this conclusion. For thin plates of 
this substance break according to two directions inclined to each other 
at 113° 8’; and experiment shows that the two modes of division of 
which they are susceptible are two nearly similar hyperbolic curves, one 
of which appears to have for its asymptotes the directions of cleavage, 
and the other for its principal axis that one of these two directions in 
