omposed of such
spheroids, there is great reason to believe that the particles are
shaped and ranged in the same way.

[Illustration: {Pyramid and section of spheroids}]

There is even probability enough that the prisms of this crystal are
produced by the breaking up of pyramids, since Mr. Bartholinus relates
that he occasionally found some pieces of triangularly pyramidal
figure. But when a mass is composed interiorly only of these little
spheroids thus piled up, whatever form it may have exteriorly, it is
certain, by the same reasoning which I have just explained, that if
broken it would produce similar prisms. It remains to be seen whether
there are other reasons which confirm our conjecture, and whether
there are none which are repugnant to it.

[Illustration: {paralleloid arrangement of spheroids with planes of
potential cleavage}]

It may be objected that this crystal, being so composed, might be
capable of cleavage in yet two more fashions; one of which would be
along planes parallel to the base of the pyramid, that is to say to
the triangle ABC; the other would be parallel to a plane the trace of
which is marked by the lines GH, HK, KL. To which I say that both the
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 pol