t be named here in order to mark
their exact opposition to the foiled system. In their simplest form,
represented by _c_, Fig. XVI., they have no representatives in good
architecture, being evidently weak and meagre; but approximations to
them exist in late Gothic, as in the vile cathedral of Orleans, and in
modern cast-iron shafts. In their fully developed form they are the
Greek Doric, _a_, Fig. XVI., and occur in caprices of the Romanesque and
Italian Gothic: _d_, Fig. XVI., is from the Duomo of Monza.

Sec. XVII. 2. Between _c3_ and _d3_ of Fig. XIV. there may be evidently
another condition, represented at 6, Plate II., and formed by the
insertion of a central shaft within the four external ones. This central
shaft we may suppose to expand in proportion to the weight it has to
carry. If the external shafts expand in the same proportion, the entire
form remains unchanged; but if they do not expand, they may (1) be
pushed out by the expanding shaft, or (2) be gradually swallowed up in
its expansion, as at 4, Plate II. If they are pushed out, they are
removed farther from each other by every increase of the central shaft;
and others may then be introduced in the vacant spaces; giving, on the
plan, a central orb with an ever increasing host of satellites, 10,
Plate II.; the satellites themselves often varying in size, and perhaps
quitting contact with the central shaft. Suppose them in any of their
conditions fixed, while the inner shaft expands, and they will be
gradually buried in it, forming more complicated conditions of 4, Plate
II. The combinations are thus altogether infinite, even supposing the
central shaft to be circular only; but their infinity is multiplied by
many other infinities when the central shaft itself becomes square or
crosslet on the section, or itself multifoiled (8, Plate II.) with
satellite shafts eddying about its recesses and angles, in every
possible relation of attraction. Among these endless conditions of
change, the choice of the architect is free, this only being generally
noted: that, as the whole value of such piers depends, first, upon their
being wisely fitted to the weight above them, and, secondly, upon their
all working together: and one not failing the rest, perhaps to the ruin
of all, he must never multiply shafts without visible cause in the
disposition of members superimposed:[41] and in his multiplied group he
should, if possible, avoid a marked separation between the large ce