§ 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.
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 In proportion to the strength of these edges, this function of the abacus is superseded, and these edges are strong in proportion to the steepness of the slope.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_.
§ 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.