XIV., of
which _a_ is a proportion for a colossal building, _b_ for a moderately
sized building, while _c_ could only be admitted on a very small scale
indeed.

Sec. XVI. 3. _The greater the excess of abacus, the steeper must be the
slope of the bell, the shaft diameter being constant._

This will evidently follow from the considerations in the last
paragraph; supposing only that, instead of the scale of shaft and
capital varying together, the scale of the capital varies alone. For it
will then still be true, that, if the projection of the capital be just
safe on a given scale, as its excess over the shaft diameter increases,
the projection will be unsafe, if the slope of the bell remain constant.
But it may be rendered safe by making this slope steeper, and so
increasing its supporting power.

[Illustration: Fig. XXV.]

Thus let the capital _a_, Fig. XXV., be just safe. Then the capital _b_,
in which the slope is the same but the excess greater, is unsafe. But
the capital _c_, in which, though the excess equals that of _b_, the
steepness of the supporting slope is increased, will be as safe as _b_,
and probably as strong as _a_.[48]

Sec. XVII. 4. _The steeper the slope of the bell, the thinner may be the
abacus._

The use of the abacus is eminently to equalise the pressure over the
surface of the bell, so that the weight may not by any accident be
directed exclusively upon its edges. In proportion to the strength of
these edges, this function of the abacus is superseded, and these edges
are strong in proportion to the steepness of the slope. Thus in Fig.
XXVI., the bell at _a_ would carry weight safely enough without any
abacus, but that at _c_ would not: it would probably have its edges
broken off. The abacus superimposed might be on _a_ very thin, little
more than formal, as at _b_; but on _c_ must be thick, as at _d_.

[Illustration: Fig. XXVI.]

Sec. XVIII. These four rules are all that are necessary for general
criticism; and observe that these are only semi-imperative,--rules of
permission, not of compulsion. Thus Law 1 asserts that the slender shaft
_may_ have greater excess of capital than the thick shaft; but it need
not, unless the architect chooses; his thick shafts _must_ have small
excess, but his slender ones need not have large. So Law 2 says, that as
the building is smaller, the excess _may_ be greater; but it need not,
for the excess which is safe in the large is still safer in the small.
S