refraction.
That, similarly, by cutting the crystal by any plane through the axis
SS, such as the plane of the figure is, the perpendicular ray ought to
suffer no refraction; and that for oblique rays there were different
measures for the irregular refraction according to the situation of
the plane in which the incident ray was.
Now these things were found in fact so; and, after that, I could not
doubt that a similar success could be met with everywhere. Whence I
concluded that one might form from this crystal solids similar to
those which are its natural forms, which should produce, at all their
surfaces, the same 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
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