angle, that is to say from the apex of the pyramid, one finds it quite
hard; but by scraping in the opposite sense an incision is easily
made. This follows manifestly from the situation of the small
spheroids; over which, in the first manner, the knife glides; but in
the other manner it seizes them from beneath almost as if they were
the scales of a fish.
I will not undertake to say anything touching the way in which so many
corpuscles all equal and similar are generated, nor how they are set
in such beautiful order; whether they are formed first and then
assembled, or whether they arrange themselves thus in coming into
being and as fast as they are produced, which seems to me more
probable. To develop truths so recondite there would be needed a
knowledge of nature much greater than that which we have. I will add
only that these little spheroids could well contribute to form the
spheroids of the waves of light, here above supposed, these as well as
those being similarly situated, and with their axes parallel.
_Calculations which have been supposed in this Chapter_.
Mr. Bartholinus, in his treatise of this Crystal, puts at 101 degrees
the obtuse angles of the faces, which I have stated to be 101 degrees
52 minutes. He states that he measured these angles directly on the
crystal, which is difficult to do with ultimate exactitude, because
the edges such as CA, CB, in this figure, are generally worn, and not
quite straight. For more certainty, therefore, I preferred to measure
actually the obtuse angle by which the faces CBDA, CBVF, are inclined
to one another, namely the angle OCN formed by drawing CN
perpendicular to FV, and CO perpendicular to DA. This angle OCN I
found to be 105 degrees; and its supplement CNP, to be 75 degrees, as
it should be.
[Illustration]
To find from this the obtuse angle BCA, I imagined a sphere having its
centre at C, and on its surface a spherical triangle, formed by the
intersection of three planes which enclose the solid angle C. In this
equilateral triangle, which is ABF in this other figure, I see that
each of the angles should be 105 degrees, namely equal to the angle
75