The chancel arch, again, demands height, and the more so if it be wide, as in our own day is necessary. The nave arcades are better pointed than round, as are any others carrying any considerable weight. Buttresses remain necessary at the ends of the arcades, and are desirable as a steadiment to the outer walls, particularly where roofs without a direct tie are made use of, and are further useful as permitting the introduction of larger windows than might be safe without them. In all cases, indeed, where roofs or floors are so constructed as to concentrate pressure upon points, it is clear that buttresses are desirable; and when the efficient size cannot be given them without inconvenience or dissight, it is equally clear that the deficiency may be readily compensated by loading them with lofty pinnacles. It is wrong to use buttresses without any object but appearance, but there are numbers of cases where they are of great advantage, besides those in which we know them to be indispensable. If so many of our arched and vaulted buildings in these days were not mere pretences in lath and plaster, we should have more practical experience of the need of the buttress and of the pointed arch. I was once told by the English Commissioner in Scinde that the European engineers had difficulty in making the native builders there believe that any but a pointed arch will stand.
Let us now inquire as briefly as may be into the rationale of ribbed vaulting as distinguished from the arris vaulting of the Roman and earlier Romanesque builders.
A groined vault does not of absolute necessity demand the use of ribs any more than the plain waggon-head vault. Even the latter was from an early period frequently divided into compartments or bays by transverse ribs, which were useful as a means of giving it rigidity; but in groined vaulting these were of nearly constant use, both for the same reason, and because the vault, being reduced at its springing to so narrow a footing, required this additional strength. The arrises, however, or diagonal lines of intersection, were always left without ribs.
Why, then, was the custom changed? For two important reasons. The first was this: that the intersection forms naturally a feeble line, both from the difficulty, particularly with the rough materials usually employed, of making its construction sound; from its forming an arch of greatly increased width without corresponding increase of height: and from its reduction at the springing level to a pin’s point.
The second was of a more intricate nature, and requires to be explained more in detail. When the two intersecting vaults of a groin are similar and equal in their section, or when the section of one is the mathematical resultant of that of the other, the line of intersection falls in a plane. When vaulting, however, became general, all sorts of irregularly-formed spaces would have to be so covered, and would present problems of considerable difficulty, in which it would be impossible in all cases that the vaulting surfaces should be portions of cylinders or regular cylindroids, and in which the intersecting lines could not, without much twisting of the surfaces, be brought to fall into planes.
The introduction of the diagonal rib met both of these difficulties. It strengthened the weak angle and gave it a substantial footing; and it at the same time gave to the lines of intersection a certain degree of independence of the vaulting surfaces; so that, instead of the surfaces governing the intersection, they were thenceforth governed by the ribs, and the latter could be made to fall into planes, and to avoid unsightly forms even in vaulting spaces of the most irregular and abnormal forms.
The substitution of the rib for the arris worked as great a revolution in the principles of vaulted construction as did the pointed arch itself. Nothing in the way of vaulting was now impracticable or unsightly; the architect was absolutely master of his work, and could do what he liked with it. The facilities it offers are quite marvellous in the eyes of the modern practical man when once they are opened to them. I have myself found one of the most practical men I ever met with, who had for years taken the leading management of the business of the greatest builder of our day, though hitherto uninitiated in Gothic construction, almost in ecstasies at finding a difficult problem in vaulting he had been puzzled over for days and making models of in vain, solved in an instant by seeing the absolute liberty of action exercised in a similar case in Westminster Abbey. The old builders themselves perfectly luxuriated in their newly-discovered liberty: not only could they vault spaces of any conceivable plan, every dimension of it varying, and the difficulties increased by the necessity of pushing up windows in its sides in all kinds of difficult positions, but they could make the result so pleasing and apparently so straightforward and natural, that not one observer out of a thousand ever finds out that there was any difficulty to be got over at all. Sometimes, indeed, we find them rejoicing so much in their freedom as to set themselves needless puzzles for the very luxury of solving them. There is a most remarkable instance of this in the crypt under Glasgow Cathedral, where the pillars which support the floor have been placed in a variety of intricate positions for no reason, apparently, but to produce curious perplexities in the vaulting and create strange problems, for the mere pleasure to be derived from their solution and the beauty of the puzzle when solved.[59]
It has been argued that the Gothic vault is less refined than some of the previous forms, because less strictly mathematical; that a refined system of construction should in all cases possess an exact mathematical solution, though the builder may, when once master of the true theory, depart from it in execution; that the work, in short, though irregular in execution, should be perfect and mathematically accurate in its theoretical type.
I agree with this doctrine in the main; but I hold that the Gothic vault complies with its conditions.
The square groined vault, with semicircular arches, is perfect in its theory, and gives elliptical arches for its arris lines. The same, if vaulted with the pointed arch, is equally true in theory, for the diagonal ribs may be pointed arches, formed each of portions of two ellipses. The oblong vault, again, is perfect if the wide arch is a semicircle, the narrow one a vertical semi-ellipse, and the arrises horizontal semi-ellipses of the same height; but the ancients generally chose to stilt the narrow arch instead of using the vertical ellipse, and by doing so threw the diagonal arris out of the plane and out of shape; but the theoretical form remained, nevertheless, perfect. In like manner, if the same figure be vaulted across its widest span by a pointed vault, and if the narrow vault have a pointed arch composed of two portions of ellipses, and the intersections be of the same figure as resulting geometrically from the intersection of the two vaults, the theoretical form is perfect. Now, if in either case the architect thinks the elliptical pointed arches inferior in beauty to those composed of parts of circles, and by using ribs finds himself enabled to throw the error resulting from the substitution of the latter form into the vaulted surfaces where it will be invisible, surely he is only using that discretionary power of introducing irregularities upon a perfect theory which is claimed as his right; and this is exactly what the Gothic architects introduced.