Let, then, the quantity e d, and angle d b c, at A of [Fig. XXIII.], be invariable, and let the length d b vary: then we shall have such a series of forms as may be represented by a, b, c, [Fig. XXIV.], 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.
§ 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.
| 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]
§ 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 In proportion to the strength of these edges, this function of the abacus is superseded, and these edges are strong in proportion to the steepness of the slope.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.
| Fig. XXVI. |
§ 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. So Law 3 says that capitals of great excess must have steep slopes; but it does not say that capitals of small excess may not have steep slopes also, if we choose. And lastly, Law 4 asserts the necessity of the thick abacus for the shallow bell; but the steep bell may have a thick abacus also.
§ XIX. It will be found, however, that in practice some confession of these laws will always be useful, and especially of the two first. The eye always requires, on a slender shaft, a more spreading capital than it does on a massy one, and a bolder mass of capital on a small scale than on a large. And, in the application of the first rule, it is to be noted that a shaft becomes slender either by diminution of diameter or increase of height; that either mode of change presupposes the weight above it diminished, and requires an expansion of abacus. I know no mode of spoiling a noble building more frequent in actual practice than the imposition of flat and slightly expanded capitals on tall shafts.