[Illustration: Fig. XXIV.] § XV. 2. _The smaller the scale of the building, the greater may be the excess of the abacus over the diameter of the shaft._ This principle requires, I think, no very lengthy proof: the reader can understand at once that the cohesion and strength of stone which can sustain a small projecting mass, will not sustain a vast one overhanging in the same proportion. A bank even of loose earth, six feet high, will sometimes overhang its base a foot or two, as you may see any day in the gravelly banks of the lanes of Hampstead: but make the bank of gravel, equally loose, six hundred feet high, and see if you can get it to overhang a hundred or two! much more if there be weight above it increased in the same proportion. Hence, let any capital be given, whose projection is just safe, and no more, on its existing scale; increase its proportions every way equally, though ever so little, and it is unsafe; diminish them equally, and it becomes safe in the exact degree of the diminution. 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. [Illustration: 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._