the case of a thrown ball. A liquid has the added
power of lateral extension. Its tendency, when intercepted, is to
spread out in the two dimensions of a _plane_--as in the case of a
griddle cake; while a gas expands universally in all directions, as
shown by a soap-bubble. It is a reasonable inference that the fourth
state of matter, the corpuscular, is affiliated to some
four-dimensional manner of extension, and that there may be states
beyond this, involving even higher development of space.

Next glance at the vegetable kingdom. The seed, a _point_, generates
a _line_ system, in stem, branches, twigs, from which depend _planes_
in the form of leaves and flowers, and from these come fruit,
_solids_.

"The point, the line, the surface and the sphere,
In seed, stem, leaf and fruit appear."

A similar sequence may be noted within the body: the _line_-network
of the nerves conveys the message of sensation from the _surface_ of
the body to some center in the _solid_, of the brain--and thence to
the Silent Thinker, "he who is without and within," or in terms of
our hypothesis, "he who dwells in higher space."

MAN THE GEOMETER

When man essays the role of creator he cannot do otherwise than
follow similar sequences: it is easy to discern dimensional
progression in the products of man's ingenuity and skill. Consider,
for example, the evolution of a building from its inception to its
completion. It exists first of all in the mind of the architect, and
there it is indubitably higher-spatial, for he can interpenetrate
and examine every part, and he can consider it all at once, viewing
it simultaneously from without and from within, just as one would be
able to do in a space of four dimensions. He begins to give his idea
physical embodiment by making with a pencil-_point, lines_ on a
_plane_ (a piece of paper), the third dimension being represented
by means of the other two. Next (if he is careful and wise) he makes
a three-dimensional model. From the architect's drawings the engineer
establishes his points, lays out his angles, and runs his lines upon
the site itself. The mason follows, and with his footing courses
makes ponderable and permanent the lines of the engineer. These
lines become in due course walls--vertical planes. Floors and
roofs--horizontal planes--follow, until some portion of
three-dimensional space has been enclosed.

Substantially the same sequence holds, whatever the kind of building
or the