built and tower-like shaft appears to have been the result of a loss of this sense of symmetry consequent on the employment of intractable materials.
§ XII. But farther: we have up to this point spoken of shafts as always set in ranges, and at equal intervals from each other. But there is no necessity for this; and material differences may be made in their diameters if two or more be grouped so as to do together the work of one large one, and that within, or nearly within, the space which the larger one would have occupied.
§ XIII. Let A, B, C, Fig. XIV., be three surfaces, of which B and C contain equal areas, and each of them double that of A: then supposing them all loaded to the same height, B or C would receive twice as much weight as A; therefore, to carry B or C loaded, we should need a shaft of twice the strength needed to carry A. Let S be the shaft required to carry A, and S2 the shaft required to carry B or C; then S3 may be divided into two shafts, or S2 into four shafts, as at S3, all equal in area or solid contents;40 and the mass A might be carried safely by two of them, and the masses B and C, each by four of them.
Fig. XIV.
Now if we put the single shafts each under the centre of the mass they have to bear, as represented by the shaded circles at a, a2, a3, the masses A and C are both of them very ill supported, and even B insufficiently; but apply the four and the two shafts as at b, b2, b3, and they are supported satisfactorily. Let the weight on each of the masses be doubled, and the shafts doubled in area, then we shall have such arrangements as those at c, c2, c3; and if again the shafts and weight be doubled, we shall have d, d2, d3.
§ XIV. Now it will at once be observed that the arrangement of the shafts in the series of B and C is always exactly the same in their relations to each other; only the group of B is set evenly, and the group of C is set obliquely,—the one carrying a square, the other a cross.
Fig. XV.
You have in these two series the primal representations of shaft arrangement in the Southern and Northern schools; while the group b, of which b2 is the double, set evenly, and c2 the double, set obliquely, is common to both. The reader will be surprised to find how all the complex and varied forms of shaft arrangement will range themselves into one or other of these groups; and still more surprised to find the oblique or cross set system on the one hand, and the square set system on the other, severally distinctive of Southern and Northern work. The dome of St. Mark’s, and the crossing of the nave and transepts of Beauvais, are both carried by square piers; but the piers of St. Mark’s are set square to the walls of the church, and those of Beauvais obliquely to them: and this difference is even a more essential one than that between the smooth surface of the one and the reedy complication of the other. The two squares here in the margin (Fig. XV.) are exactly of the same size, but their expression is altogether different, and in that difference lies one of the most subtle distinctions between the Gothic and Greek spirit,—from the shaft, which bears the building, to the smallest decoration. The Greek square is by preference set evenly, the Gothic square obliquely; and that so constantly, that wherever we find the level or even square occurring as a prevailing form, either in plan or decoration, in early northern work, there we may at least suspect the presence of a southern or Greek influence; and, on the other hand, wherever the oblique square is prominent in the south, we may confidently look for farther evidence of the influence of the Gothic architects. The rule must not of course be pressed far when, in either school, there has been determined search for every possible variety of decorative figures; and accidental circumstances may reverse the usual system in special cases; but the evidence drawn from this character is collaterally of the highest value, and the tracing it out is a pursuit of singular interest. Thus, the Pisan Romanesque might in an instant be pronounced to have been formed under some measure of Lombardic influence, from the oblique squares set under its arches; and in it we have the spirit of northern Gothic affecting details of the southern;—obliquity of square, in magnificently shafted Romanesque. At Monza, on the other hand, the levelled square is the characteristic figure of the entire decoration of the façade of the Duomo, eminently giving it southern character; but the details are derived almost entirely from the northern Gothic. Here then we have southern spirit and northern detail. Of the cruciform outline of the load of the shaft, a still more positive test of northern work, we shall have more to say in the 28th Chapter; we must at present note certain farther changes in the form of the grouped shaft, which open the way to every branch of its endless combinations, southern or northern.
Fig. XVI.
§ XV. 1. If the group at d3, Fig. XIV., be taken from under its loading, and have its centre filled up, it will become a quatrefoil; and it will represent, in their form of most frequent occurrence, a family of shafts, whose plans are foiled figures, trefoils, quatrefoils, cinquefoils, &c.; of which a trefoiled example, from the Frari at Venice, is the third in Plate II., and a quatrefoil from Salisbury the eighth. It is rare, however, to find in Gothic architecture shafts of this family composed of a large number of foils, because multifoiled shafts are seldom true grouped shafts, but are rather canaliculated conditions of massy piers. The representatives of this family may be considered as the quatrefoil on the Gothic side of the Alps; and the Egyptian multifoiled shaft on the south, approximating to the general type, b, Fig. XVI.
§ XVI. Exactly opposed to this great family is that of shafts which have concave curves instead of convex on each of their sides; but these are not, properly speaking, grouped shafts at all, and their proper place is among decorated piers; only they must 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.
§ 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,
