n still, shallow water, find their
complement in the curved lily-pads which lie horizontally on its
surface. Trees such as pine and hemlock, which are excurrent--those in
which the branches start successively (i.e., after the manner of time)
from a straight and vertical central stem--are Yo; trees such as
the elm and willow, which are deliquescent--those in which the trunk
dissolves as it were simultaneously (after the manner of space) into
its branches--are In. All tree forms lie in or between these two
extremes, and leaves are susceptible of a similar classification. It
will be seen to be a classification according to time and space,
for the characteristic of time is _succession_, and of space,
_simultaneousness_: the first is expressed symbolically by elements
arranged with relation to axial lines; the second, by elements
arranged with relation to focal points (Illustrations 6,7).

The student should train himself to recognize In and Yo in all
their Protean presentments throughout nature--in the cloud upon the
mountain, the wave against the cliff, in the tracery of trees against
the sky--that he may the more readily recognize them in his chosen
art, whatever that art may be. If it happens to be painting, he will
endeavor to discern this law of duality in the composition of every
masterpiece, recognizing an instinctive obedience to it in that
favorite device of the great Renaissance masters of making an
architectural setting for their groups of figures, and he will
delight to trace the law in all its ramifications of contrast between
complementaries in line, color, and mass (Illustration 8).

[Illustration 8: THE LAW OF POLARITY CLEOPATRA MELTING THE PEARL. BY
TIEPOLO]

With reference to architecture, it is true, generally speaking,
that architectural forms have been developed through necessity, the
function seeking and finding its appropriate form. For example, the
buttress of a Gothic cathedral was developed by the necessity of
resisting the thrust of the interior vaulting without encroaching upon
the nave; the main lines of a buttress conform to the direction of the
thrust, and the pinnacle with which it terminates is a logical shape
for the masonry necessary to hold the top in position (Illustration
9). Research along these lines is interesting and fruitful of result,
but there remains a certain number of architectural forms whose origin
cannot be explained in any such manner. The secret of their undying
charm