to be borne, and the scale
of the building. The proportions of a wooden column are wrong in a stone
one, and of a small building wrong in a large one,[20] and this owing
solely to mechanical considerations, which have no more to do with
ideas of beauty, than the relation between the arms of a lever, adapted
to the raising of a given weight; and yet it is highly agreeable to
perceive that such constructive proportion has been duly observed, as
it is agreeable to see that anything is fit for its purpose or for ours,
and also that it has been the result of intelligence in the workman of
it, so that we sometimes feel a pleasure in apparent non-adaptation, if
it be a sign of ingenuity; as in the unnatural and seemingly impossible
lightness of Gothic spires and roofs.

Now, the errors against which I would caution the reader in this matter
are three. The first, is the overlooking or denial of the power of
apparent proportion, of which power neither Burke nor any other writer
whose works I have met with, take cognizance. The second, is the
attribution of _beauty_ to the appearances of constructive proportion.
The third, the denial with Burke of _any_ value or agreeableness in
constructive proportion.

Sec. 11. The value of apparent proportion in curvature.

Now, the full proof of the influence of apparent proportion, I must
reserve for illustration by diagram; one or two instances however may be
given at present for the better understanding of its nature.

We have already asserted that all curves are more beautiful than right
lines. All curves, however, are not equally beautiful, and their
differences of beauty depend on the different proportions borne to each
other by those infinitely small right lines of which they may be
conceived as composed.

When these lines are equal and contain equal angles, there can be no
connection or unity of sequence in them. The resulting curve, the
circle, is therefore the least beautiful of all curves.

When the lines bear to each other some certain proportion; or when, the
lines remaining equal, the angles vary; or when by any means whatsoever,
and in whatever complicated modes, such differences as shall imply
connection are established between the infinitely small segments, the
resulting curves become beautiful. The simplest of the beautiful curves
are the conic, and the various spirals; but it is as rash as it is
difficult to endeavor to trace any ground of superiority or inferiority