int.

This law of Radiation enters largely into architecture. The Colosseum,
based upon the ellipse, a figure generated from two points or foci,
and the Pantheon, based upon the circle, a figure generated from a
central point, are familiar examples. The distinctive characteristic
of Gothic construction, the concentration or focalization of the
weight of the vaults and arches at certain points, is another
illustration of the same principle applied to architecture,
beautifully exemplified in the semicircular apse of a cathedral, where
the lines of the plan converge to a common center, and the ribs of the
vaulting meet upon the capitals of the piers and columns, seeming
to radiate thence to still other centers in the loftier vaults which
finally meet in a center common to all.

[Illustration 30]

[Illustration 31]

[Illustration 32]

The tracery of the great roses, high up in the facades of the
cathedrals of Paris and of Amiens, illustrate Radiation, in the one
case masculine: straight, angular, direct; in the feminine: curved,
flowing, sinuous. The same _Beautiful Necessity_ determined the
characteristics of much of the ornament of widely separated styles
and periods: the Egyptian lotus, the Greek honeysuckle, the Roman
acanthus, Gothic leaf work--to snatch at random four blossoms from
the sheaf of time. The radial principle still inherent in the debased
ornament of the late Renaissance gives that ornament a unity, a
coherence, and a kind of beauty all its own (Illustration 35).

[Illustration 33]

[Illustration 34]

Such are a few of the more obvious laws of natural beauty and their
application to the art of architecture. The list is by no means
exhausted, but it is not the multiplicity and diversity of these laws
which is important to keep in mind, so much as their relatedness and
cooerdination, for they are but different aspects of the One Law, that
whereby the Logos manifests in time and space. A brief recapitulation
will serve to make this correlation plain, and at the same time fix
what has been written more firmly in the reader's mind.

[Illustration 35]

[Illustration 36]

First comes the law of _Unity_; then, since every unit is in its
essence twofold, there is the law of _Polarity_; but this duality is
not static but dynamic, the two parts acting and reacting upon one
another to produce a third--hence the law of _Trinity_. Given this
third term, and the innumerable combinations made possible by