The Stones of Venice, Volume 1 (of 3)

by John Ruskin

3. The length of slope of bell, b d;

4. The inclination of this slope, or angle c b d;

5. The depth of abacus, d e.

For every change in any one of these quantities we have a new proportion of capital: five infinities, supposing change only in one quantity at a time: infinity of infinities in the sum of possible changes.

It is, therefore, only possible to note the general laws of change; every scale of pillar, and every weight laid upon it admitting, within certain limits, a variety out of which the architect has his choice; but yet fixing limits which the proportion becomes ugly when it approaches, and dangerous when it exceeds. But the inquiry into this subject is too difficult for the general reader, and I shall content myself with proving four laws, easily understood and generally applicable; for proof of which if the said reader care not, he may miss the next four paragraphs without harm.

§ XIV. 1. The more slender the shaft, the greater, proportionally, may be the projection of the abacus. For, looking back to [Fig. XXIII.], let the height a b be fixed, the length d b, the angle d b c, and the depth d e. Let the single quantity b c be variable, let B be a capital and shaft which are found to be perfectly safe in proportion to the weight they bear, and let the weight be equally distributed over the whole of the abacus. Then this weight may be represented by any number of equal divisions, suppose four, as l, m, n, r, of brickwork above, of which each division is one fourth of the whole weight; and let this weight be placed in the most trying way on the abacus, that is to say, let the masses l and r be detached from m and n, and bear with their full weight on the outside of the capital. We assume, in B, that the width of abacus e f is twice as great as that of the shaft, b c, and on these conditions we assume the capital to be safe.

But b c is allowed to be variable. Let it become b2 c2 at C, which is a length representing about the diameter of a shaft containing half the substance of the shaft B, and, therefore, able to sustain not more than half the weight sustained by B. But the slope b d and depth d e remaining unchanged, we have the capital of C, which we are to load with only half the weight of l, m, n, r, i. e., with l and r alone. Therefore the weight of l and r, now represented by the masses l2, r2, is distributed over the whole of the capital. But the weight r was adequately supported by the projecting piece of the first capital h f c: much more is it now adequately supported by i h, f2 c2. Therefore, if the capital of B was safe, that of C is more than safe. Now in B the length e f was only twice b c; but in C, e2 f2 will be found more than twice that of b2 c2. Therefore, the more slender the shaft, the greater may be the proportional excess of the abacus over its diameter.

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.