Page:Scientific Memoirs, Vol. 1 (1837).djvu/276

264 the first and the last, was rectangular, whilst in rock crystal this mode of division may establish itself.

1st. The elasticity of all the diameters of any plane perpendicular to the axis of a prism of rock crystal, may be considered as being sensibly the same.

2nd. All the planes parallel to the axis are far from possessing the same elastic state; but if any three of these planes be taken, restricting ourselves only to this condition, that the angles which they form with each other are equal, then their elastic state is the same.

3rd. The transformations of the nodal lines of a series of plates cut round one of the edges of the base of the prism are perfectly analogous to those which are observed in a series of plates cut round the intermediate axis in bodies which possess three unequal and rectangular axes of elasticity.

4th. The transformations of a series of plates perpendicular to any one of the three planes which pass through two opposite edges of the hexahedron are, in general, analogous to those of a series of plates cut round a line which divides into two equal parts the plane angle included between two of the three axes of elasticity in bodies where these axes are unequal and rectangular.

5th. By means of the acoustic figures of a plate cut in a prism of rock crystal, nearly parallel to the axis, and not parallel to the two faces of the hexahedron, we can always distinguish which are the faces of the pyramid susceptible of cleavage. The same result may be obtained by the disposition of the modes of division of a plate taken nearly parallel to one of the faces of the pyramids.

6th. Whatever be the direction of the plates, the optical axis, or its projection on their plane, always occupies a position on them which is intimately connected with the arrangement of the acoustic lines: thus, for example, in all the plates cut round one of the edges of the base of the prism, the optical axis, or its projection, invariably corresponds with one of the two straight lines which compose the nodal system formed of two lines which intersect each other rectangularly.

Although there is doubtless a great analogy between the phænomena which rock crystal has just presented to us, and those we have observed in bodies in which the elasticity is different according to three directions perpendicular to each other, nevertheless we are forced to acknowledge that, with respect to the mode of experiment we have employed in these researches, rock crystal cannot be placed in the number of substances with three rectangular and unequal axes of elasticity, and still less in the number of those all the parts of which are symmetrically arranged round a single straight line. For the same phænomena