ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 261 



to one of the cleavage planes ; thus the direction of this line, in a plate 

 parallel to the axis and normal to two faces of the hexahedron, is suffi- 

 cient to enable us to ascertain which of the faces of the pyramid are 

 susceptible of cleavage. 



In order to complete all that relates to the transformations of the 

 nodal lines of this series of plates, it would have been important to de- 

 termine with accuracy the degree of inclination to the axis, of the 

 plane situated between No. 3 and No. 4, for which the summits of the 

 nodal hyperbola are at the greatest distance from each other : but, hav- 

 ing been stopped in these investigations by the difficulty of procuring 

 a sufficient quantity of rock crystal very pure and regularly crystal- 

 lized, I have been reduced to determine this maximum of recession 

 on another substance, and I have chosen for this purpose the ferriferous 

 carbonate of lime, a substance whose primitive form is a rhonibohe- 

 dron, which differs from that of rock crystal only in the angles formed 

 by its terminating planes. As we have already observed, there is a 

 sufficiently great analogy between the phsenomena presented by these 

 two substances, with respect to sonorous vibrations, to enable us to 

 admit that what occurs in one occurs also in the other : thus, let A E, 

 fig. 6, be a rhombohedron of carbonate of lime, of which A is one of 

 the obtuse solid angles ; A B C D corresponding to the face of cleavage 

 of the pyramid of rock crystal, the diagonal B D will be the line round 

 \\ hich all the plates must be supposed to be cut ; and they are conse- 

 quently normal to A C E G, represented separately in fig. 7, in which 

 the lines 1, 2, 3, &c., are their projections, and indicate at the same time 

 the angles which they make with the axis A E. We will first remark 

 that the modes of division of the plate No. 1, fig. 7, 6?*, perpendicular 

 to the axis, are the same as those of the corresponding plate of rock 

 crystal, and that the plate No. 5, perpendicular to A C, assumes also 

 the same modes of division as the plate perpendicular to the cleavable 

 face of the pyramid of rock crystal, which establishes a sufficient ana- 

 logy between the two orders of jihaenomena. The inspection of fig. 7, bis, 

 shows then that the branches of the nodal hyperbola of No. 3, parallel 

 to A G, consequently to the plane B D F H, are straighter than those 

 of the plates which precede or follow it ; and admitting that this maxi- 

 mum of recession occurs equally in quartz for the corresponding dia- 

 gonal plane of its rhombohedron, as this plane forms with the cleavable 

 face of the pyramid an angle of 96" 0' 13", the plate in question will 

 be inclined 57° 40' 13" to the axis of the crystal, the face of the pyra- 

 mid forming with this axis an angle of 38° 20'; thus the projection of 

 this plate on the plane m w X op Y of fig. 3. will be the line A B. 



Now since the maximum of recession of the summits of the nodal 

 hyperbola is in this manner determined, it is easy to recognise a great 

 analogy between the phaenomena of fig. 8, PI. III., and those of fig. 3, bis. 



Vol. I Part I. t 



