Page:Scientific Memoirs, Vol. 1 (1837).djvu/274

 

Pl. IV.; for, supposing several intermediate plates between Nos. 3 and 4, that which would be inclined 57° to the axis would correspond to No. 1 of fig. 8, Pl. III.; No. 4 in the crystal would correspond to No. 3 in the wood; and lastly, No. 11 of the crystal plates, in which a second maximum of recession of the summits of the hyperbola occurs, would correspond to No. 6 of the plates of wood; so that the same phænomena, which are included, in a body having three rectangular axes of elasticity, in an arc only of 90°, to be afterwards reproduced in a contrary direction in the following quadrant, are included in rock crystal in an arc of 96° 0′ 13″, and cannot be entirely reproduced, because similar phænomena to those we have just observed for a series of plates cut round $ab$, fig. 1 , Pl. IV., occurring, for the same degrees of inclination, in the two series of plates which might be cut round $cd$ and $ef$, both are confounded together in the vicinity of the plate perpendicular to $XY$.

 

Third Series. Plates cut round the diagonal $ac$, fig. 1, and according to the different Azimuths of the Plane $be^{\prime }Yb^{\prime }eX$, fig. 4.

These plates present phænomena much more complicated than those of the two preceding series. It may be easily conceived that this ought to be the case, since the plates parallel to the two adjacent faces of the pyramid assume very different modes of division, which supposes that their elastic state also greatly differs: consequently the plates perpendicular to the plane which passes through the two opposite edges of the hexahedron ought to participate in the properties of both. It is thus that the plates perpendicular to two parallel faces of the prism, and passing through its axis, assume a disposition of nodal lines in which the direction of the planes of cleavage, parallel to one of the faces of the pyramid, exercises a considerable influence.

In the plates of this series (fig. 4, bis,) neither mode of division is constant; nevertheless, in order that they may be easily distinguished from eacli other, I have continued to indicate them, one by uninterrupted lines, the other by dotted lines. And for the purpose of preserving, in all the plates, the projection $xy$ of the axis parallel to the axis $XY$ of fig. 1, I have here supposed that the crystal had been turned round until its edge $be^{\prime }$ was in front. This is besides sufficiently indicated by figure A, which represents the modes of division of the plate perpendicular to the axis, as it also does the section of the hexahedron by a plane parallel to this plate.

The inspection of figures A, B, C, D, E. … shows that the nodal system indicated by the perfect lines is formed of two hyperbolic branches which at first straighten themselves, and the summits of which recede more from each other, so far as the plate E inclined 51° to the axis,