me regular and irregular refractions as the natural
surfaces, and which nevertheless would cleave in quite other ways, and
not in directions parallel to any of their faces. That out of it one
would be able to fashion pyramids, having their base square,
pentagonal, hexagonal, or with as many sides as one desired, all the
surfaces of which should have the same refractions as the natural
surfaces of the crystal, except the base, which will not refract the
perpendicular ray. These surfaces will each make an angle of 45
degrees 20 minutes with the axis of the crystal, and the base will be
the section perpendicular to the axis.

That, finally, one could also fashion out of it triangular prisms, or
prisms with as many sides as one would, of which neither the sides nor
the bases would refract the perpendicular ray, although they would yet
all cause double refraction for oblique rays. The cube is included
amongst these prisms, the bases of which are sections perpendicular to
the axis of the crystal, and the sides are sections parallel to the
same axis.

From all this it further appears that it is not at all in the
disposition of the layers of which this crystal seems to be composed,
and according to which it splits in three different senses, that the
cause resides of its irregular refraction; and that it would be in
vain to wish to seek it there.

But in order that any one who has some of this stone may be able to
find, by his own experience, the truth of what I have just advanced, I
will state here the process of which I have made use to cut it, and to
polish it. Cutting is easy by the slicing wheels of lapidaries, or in
the way in which marble is sawn: but polishing is very difficult, and
by employing the ordinary means one more often depolishes the surfaces
than makes them lucent.

After many trials, I have at last found that for this service no plate
of metal must be used, but a piece of mirror glass made matt and
depolished. Upon this, with fine sand and water, one smoothes the
crystal little by little, in the same way as spectacle glasses, and
polishes it simply by continuing the work, but ever reducing the
material. I have not, however, been able to give it perfect clarity
and transparency; but the evenness which the surfaces acquire enables
one to observe in them the effects of refraction better than in those
made by cleaving the stone, which always have some inequality.

Even when the surface is only moderately sm