t occur about the
figure's _plane_ of symmetry, and in a higher--i.e., the _fourth_
dimension. Such a movement we can reason about with mathematical
definiteness: we see the result in the right- and left-handed
symmetry of solids, but we cannot picture the movement ourselves
because it involves a space of which our senses fail to give any
account.

Now could it be shown that the two-dimensional symmetry observed in
nature is the result of a three-dimensional movement, the right-and
left-handed symmetry of solids would by analogy be the result of a
_four_-dimensional movement. Such revolution (about a plane) would
be easily achieved, natural and characteristic, in four space, just
as the analogous movement (about a line) is easy, natural, and
characteristic, in our space of three dimensions.

OTHER ALLIED PHENOMENA

In the mirror image of a solid we have a representation of what
would result from a four-dimensional revolution, the surface of the
mirror being the plane about which the movement takes place. If such
a change of position were effected in the constituent parts of a
body as a mirror image of it _represents_, the body would have
undergone a revolution in the fourth dimension. Now two varieties of
tartaric acid crystallize in forms bearing the relation to one
another of object to mirror image. It would seem more reasonable to
explain the existence of these two identical, but reversed,
varieties of crystal, by assuming the revolution of a single variety
in the fourth dimension, than by any other method.

There are two forms of sugar found in honey, dextrose and levulose.
They are similar in chemical constitution, but the one is the
reverse of the other when examined by polarized light--that is, they
rotate the plane of polarization of a ray of light in opposite ways.
If their atoms are conceived to have the power of motion in the
fourth dimension, it would be easy to understand why they differ.
Certain snails present the same characteristics as these two forms
of sugar. Some are coiled to the right and others to the left; and
it is remarkable that, like dextrose and levulose, their juices are
optically the reverse of each other when studied by polarized light.

Revolution in the fourth dimension would also explain the change in
a body from producing a right-handed, to producing a left-handed,
polarization of light.

ISOMERISM

In chemistry the molecules of a compound are assumed to consist of
the a