Page:Scientific Memoirs, Vol. 1 (1837).djvu/268

256 planes perpendicular to the preceding and passing through the axis, although it be different in the latter from what it is in the former; lastly, it was necessary to verify whether the plates cut parallel to the faces $$a X b$$, $$e X f$$, $$c X d$$ of the pyramid were really susceptible of assuming the same modes of division, and whether these modes were different from those of the three plates cut parallel to the faces $$b X c$$, $$d X e$$, $$a X f$$, these latter being besides similar to each other. Experiment having shown the affirmative of these positions, it is evident that all the series of plates perpendicular to a plane normal to any two parallel faces of the prism, and passing through its axis, ought to present identical phænomena for the same degrees of inclination, and that the same ought to be the case for the series of plates perpendicular to any plane passing through two opposite edges of the hexahedron. All the plates we have employed are 23 or 27 lines in diameter and 1 line in thickness; they have been cut with great care and are polished, in order that the phænomena they exhibit with respect to light might be compared with those they present relative to sonorous vibrations. Lastly, although they have been taken from five or six different crystals and from different countries, it may be supposed that they belong to the same piece of quartz, because, whenever it was necessary to pass from one crystal to another, the precaution was taken of causing to be cut in the new specimen a certain number of plates, for the sole purpose of repeating the experiments already made; and by this process we may assure ourselves that crystals of very different appearance, such as those of Madagascar and of Dauphiny, do not however present remarkable differences in their structure.

Before proceeding to the description of the phænomena which are related to each series of plates, we shall observe, that in all the figures the line $$x y$$ represents the axis itself of the crystal when it is contained in the plane of the plate, or its projection in the contrary case, and that the position of this axis has been determined with great care, for each plate individually, by means of polarized light; so that with this datum and the details into which we shall enter, the position occupied by any plate within the mass of the crystal may easily be represented to the mind.

If we consider first the plates ., v., ., fig. 2. and 2, bis, which are parallel to the faces of the hexahedron, we see that they assume exactly the same modes of division: one of these modes, that which is represented by dotted lines, consists of two nodal lines, which cross each other rectangularly, whilst the other resembles the two branches of a hyperbola, to which the two preceding lines serve as axes. The sound of the first system being F, that of the second is the D# of the