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 lies in the fact that in them In and Yo stand symbolized and
contrasted. They no longer obey a law of utility, but an abstract
law of beauty, for in becoming sexually expressive as it were, the
construction itself is sometimes weakened or falsified. The familiar
classic console or modillion is an example: although in general
contour it is well adapted to its function as a supporting bracket,
embedded in, and projecting from a wall, yet the scroll-like ornament
with which its sides are embellished gives it the appearance of
not entering the wall at all, but of being stuck against it in some
miraculous manner. This defect in functional expressiveness is
more than compensated for by the perfection with which feminine
and masculine characteristics are expressed and contrasted in the
exquisite double spiral, opposed to the straight lines of the moulding