appreciable value; another some fractional part of a lodging house
in the slums. When this bloodless, but none the less deadly, contest
for space becomes acute, as in the congested quarters of great cities,
man's ingenuity is taxed to devise effective ways of augmenting his
_space-potency_, and he expands in a vertical direction. This
third-dimensional extension, typified in the tunnel and in the
skyscraper, is but the latest phase of a conquest of space which
began with the line of the pioneer's trail through an untracked
wilderness.


DIMENSIONAL SEQUENCES

Not only does nature everywhere geometrize, but she does so in a
particular way, in which we discover dimensional sequences. Consider
the transformation of solid, liquid, gas, from one to another, under
the influence of heat. A solid, set in free motion, can follow only
a _line_--as is 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_.