CONSTRUCTION VIII. THE SHAFT 125

developed form they are the Greek Doric, a, Fig. 16, and occur in caprices of the Romanesque and Italian Gothic: d, Fig. 16, is from the Duomo of Monza.

§ 17. (2.) Between c₃ and d₃ of Fig. 14 there may be evidently another condition, represented at 6, Plate 2 (opposite p. 130), 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 2. 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 2; 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 2. 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 2) 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:* and in his multiplied

* How far this condition limits the system of shaft grouping we shall see presently. The reader must remember, that we at present reason respecting shafts in the abstract only.

[Version 0.04: March 2008]