ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 267 



directions perpendicular to eacli 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 whicli these axes are rect- 

 angular. It appears therefore that we may conclude from tiiis oljser- 

 vation that rock crystal possesses, like carbonate of lime, supernumerary 

 planes of cleavage parallel to the diagonal planes of its primiti\'e 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 accuracj' of this assertion, it is suffi- 

 cient to cut, in a rhombohedron of carbonate of lime, a jjlate 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, whicli 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, 

 his, 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 difl'erence 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- 

 fi-action, and the other with repulsive (negative) double refraction. 



It ajipears, therefore, to result from this approximation between the 

 phsenoraena 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 tliis conclusion. For thin plates of 

 this substance break according to two directions inclined to each other 

 at lists'; and experiment shows that the two modes of division of 

 which they are susceptible are two nearly similar hyperbolic curves, one 

 of whicli apj)ears to have for its iisym})totes the directions of cleavage, 

 and the otlier for its princii>al axis tiiat one of these two directions in 



