nes which constitute the principal
sections intersect one another at right angles, whether the
neighbouring surfaces are parallel or not, then the ray which has come
by the regular refraction, as DG, undergoes only an irregular
refraction in the lower piece; and on the contrary the ray which has
come by the irregular refraction, as CE, undergoes only a regular
refraction.

But in all the infinite other positions, besides those which I have
just stated, the rays DG, CE, divide themselves anew each one into
two, by refraction in the lower crystal so that from the single ray AB
there are four, sometimes of equal brightness, sometimes some much
less bright than others, according to the varying agreement in the
positions of the crystals: but they do not appear to have all together
more light than the single ray AB.

When one considers here how, while the rays CE, DG, remain the same,
it depends on the position that one gives to the lower piece, whether
it divides them both in two, or whether it does not divide them, and
yet how the ray AB above is always divided, it seems that one is
obliged to conclude that the waves of light, after having passed
through the first crystal, acquire a certain form or disposition in
virtue of which, when meeting the texture of the second crystal, in
certain positions, they can move the two different kinds of matter
which serve for the two species of refraction; and when meeting the
second crystal in another position are able to move only one of these
kinds of matter. But to tell how this occurs, I have hitherto found
nothing which satisfies me.

Leaving then to others this research, I pass to what I have to say
touching the cause of the extraordinary figure of this crystal, and
why it cleaves easily in three different senses, parallel to any one
of its surfaces.

There are many bodies, vegetable, mineral, and congealed salts, which
are formed with certain regular angles and figures. Thus among flowers
there are many which have their leaves disposed in ordered polygons,
to the number of 3, 4, 5, or 6 sides, but not more. This well deserves
to be investigated, both as to the polygonal figure, and as to why it
does not exceed the number 6.

Rock Crystal grows ordinarily in hexagonal bars, and diamonds are
found which occur with a square point and polished surfaces. There is
a species of small flat stones, piled up directly upon one another,
which are all of pentagonal figure with rounded a