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 sufficient 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 determine 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, having been stopped in these investigations by the difficulty of procuring a sufficient quantity of rock crystal very pure and regularly crystallized, 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 rhombohedron, 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 phænomena 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 , fig. 6, be a rhombohedron of carbonate of lime, of which is one of the obtuse solid angles; corresponding to the face of cleavage of the pyramid of rock crystal, the diagonal will be the line round which all the plates must be supposed to be cut; and they are consequently normal to , 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 . We will first remark that the modes of division of the plate No. 1, fig. 7, bis, perpendicular to the axis, are the same as those of the corresponding plate of rock crystal, and that the plate No. 5, perpendicular to , 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 analogy between the two orders of phænomena. The inspection of fig. 7, bis, shows then that the branches of the nodal hyperbola of No. 3, parallel to , consequently to the plane , are straighter than those of the plates which precede or follow it; and admitting that this maximum of recession occurs equally in quartz for the corresponding diagonal 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 pyramid forming with this axis an angle of 38° 20′; thus the projection of this plate on the plane of fig. 3. will be the line .
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 phænomena of fig. 8, Pl. III., and those of fig. 3, bis,
