one and the other, though practicable, are more difficult than those
which were parallel to any one of the three planes of the pyramid; and
that therefore, when striking on the crystal in order to break it, it
ought always to split rather along these three planes than along the
two others. When one has a number of spheroids of the form above
described, and ranges them in a pyramid, one sees why the two methods
of division are more difficult. For in the case of that division which
would be parallel to the base, each spheroid would be obliged to
detach itself from three others which it touches upon their flattened
surfaces, which hold more strongly than the contacts at the edges. And
besides that, this division will not occur along entire layers,
because each of the spheroids of a layer is scarcely held at all by
the 6 of the same layer that surround it, since they only touch it at
the edges; so that it adheres readily to the neighbouring layer, and
the others to it, for the same reason; and this causes uneven
surfaces. Also one sees by experiment that when grinding down the
crystal on a rather rough stone, directly on the equilateral solid
angle, one verily finds much facility in reducing it in this
direction, but much difficulty afterwards in polishing the surface
which has been flattened in this manner.
As for the other method of division along the plane GHKL, it will be
seen that each spheroid would have to detach itself from four of the
neighbouring layer, two of which touch it on the flattened surfaces,
and two at the edges. So that this division is likewise more difficult
than that which is made parallel to one of the surfaces of the
crystal; where, as we have said, each spheroid is detached from only
three of the neighbouring layer: of which three there is one only
which touches it on the flattened surface, and the other two at the
edges only.
However, that which has made me know that in the crystal there are
layers in this last fashion, is that in a piece weighing half a pound
which I possess, one sees that it is split along its length, as is the
above-mentioned prism by the plane GHKL; as appears by colours of the
Iris extending throughout this whole plane although the two pieces
still hold together. All this proves then that the composition of the
crystal is such as we have stated. To which I again add this
experiment; that if one passes a knife scraping along any one of the
natural surfaces, and downwards as it were from the equilateral obtuse
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