256 FELIX SAVART’S RESEARCHES ON THE 
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 X6, 
eX f, eXd 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 Xe, d Xe, aX 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 phenomena 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 phenomena 
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 coun- 
tries, 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 experi- 
ments 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 phenomena 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. 
First Series. Plates parallel to the Axis of the Hexahedron. 
If we consider first the plates 1., v., 1x. fig. 2. and 2, b¢s, which are 
parallel to the faces of the hexahedron, we see that they assume ex- 
actly 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 DQ of the 
Dogeew. » 
