IN my former lectures I have endeavoured to trace out the history of that course of transition by which the rude arcuated architecture which prevailed in Western Christendom, during the dark ages between the fall of the Roman empire and the rise of modern civilisation,—commonly known as the “Romanesque” style,—first emancipated itself from its semi-barbaric character, and became a consistent round-arched style, and subsequently, by a perfectly logical series of changes, resulting from the suggestions partly of scientific construction, and partly of artistic refinement, developed itself into that new, original, and beautiful style which has in more modern times received the very absurd, but now unavoidable, name of Gothic architecture.

Having traced this development up to what I consider to be its culminating point—the form which it arrived at towards the end of the thirteenth century—it had been my intention, before I proceeded farther with the historical view of the subject, to have given a series of short practical treatises on several of the more important elements of the style whose history I have traced out; as, for instance, on the principles of Gothic vaulting, on tracery, on the system of mouldings belonging to the style; on roofing; on architectural carving and sculpture, etc., etc. Circumstances, however, having rendered it impracticable for me just now to devote to it the time which would be necessary to do justice to these subjects, I purpose on the present occasion to content myself—at the risk (I may say with the certainty) of repeating what I have already stated—with an inquiry into the rationale of the style of architecture of which I have been treating.

Such an inquiry is the more necessary from the extraordinary contrariety of opinion which we find to exist as to the real character of the style, as well as the external and internal causes of its development. Such opinions assume the most contradictory forms. One class of them may be denominated the religious view of the question. Under this head one party describes it as Christian, and another as Roman Catholic architecture. One attributes to its various parts a deep symbolisation of Christian truth; another discovers in them nothing but the mystic arcana of Romanism; while another cuts the knot by protesting that it is Mahometan architecture. A second class of opinions assumes an ethnological form. Under this head some have thought the style especially English; some pre-eminently German; some, again, in the most exclusive and straitened sense of the term, French; and others (in the widest sense) Teutonic; while the entanglement is again cut through by the champions of the Saracenic claim.

Then comes a political class of disputants. One declares the style to be nothing more or less than the visible exponent of feudalism. If the system of Durandus were applied to this view, we should perhaps have the orders of the arch shown to represent the divisions of feudal aristocracy.—The point of the arch to be the king; the outer voussoirs the great, and the inner the lesser, vassals; the clustered pillars to be the bishops surrounded by their clergy; the ashlar stones the freemen; the rubble stones the villains and serfs; the mortar to be the bond of union or of slavery by which the whole system was cemented together; and the painted glass to be that clerical monopoly of learning by which the pure light of knowledge was imparted through an artificially-coloured medium. Others have, however, shown that the style developed itself just when feudalism was giving way, and just among those very communities who were most resolutely exerting themselves for its overthrow; and that, in England especially, it synchronises with the foundation of those institutions to which we owe our liberties and our greatness; while our knot-cutting friends would contemptuously pooh-pooh the whole question by saying that it had nothing to do either with feudalism or Magna Charta, but was simply the natural result of the Crusades.

Again, as to its more practical characteristics; one party claims for it the most unbounded liberty, another denounces it as curbing the free following of practical and artistic requirements. The very same party sometimes describes it as excluding the light of day, and sometimes as offering no protection against the glare of sunshine. In fact, without going farther into these contrarieties, it may be sufficient to say that among those who have not gone much into the subject no opinions are too inconsistent either with one another or with facts to find ready advocates.

My object in this and the succeeding lecture will be to show that the style originated in no occult influences; that, if it can be called either Christian, Teutonic, French, English, German, or Western European, it is so only in a plain, straightforward, and historical, and not in any hidden, exclusive, or mysterious, sense; but that it, in fact, arose from the application of plain common sense to plain practical requirements; that many of these requirements were not peculiar to the period, but belong to all time; that many were not limited to a race or climate, but are common, with certain modifications, to different races and countries; and that the application of the same class of common sense to altered requirements would produce results by no means militating against those thus arrived at, but, on the contrary, tending to enrich, to amplify, and to add new life, variety, and harmony to the art which it had first suggested.

To judge of the practical reasonableness of a style of building, it is not enough to prove that it answers its purpose; we may pre-suppose that all civilised people would effect as much as that—indeed, that all people would do so who can construct at all; for if uncivilised, their aim would be more simple and more readily attained.

The question is, whether the purpose is provided for by means consistent with common sense, with the laws of nature, with the properties of the materials at hand, and without an expenditure of labour and material disproportioned to the result. In this I do not restrict the question to merely utilitarian results, but admit the artistic element in a degree proportioned to the rank and purpose of the edifice. I would also wish to guard myself against being understood to imply that the superior reasonableness of a style of architecture proves a higher state of civilisation among the people who use it. Inventions are often accidental, and independent of high civilisation. Thus, though an arch is a more rational means of spanning a wide opening than a single block of marble, the early Romans who used the arch were probably much less civilised than the early Greeks, who were ignorant of it.

The Egyptians and the Greeks used most nobly the means of spanning openings with which they were best acquainted, and for which their numerous quarries of granite and marble supplied them so liberally with the materials; but such a mode of construction is manifestly costly, dependent upon natural facilities of the most exceptional kind, and extremely limited in its application. The use of the arch obviates all these difficulties, and consequently a mode of construction which admits the arch is more rational than one which does not. Roman architecture, in short, than Greek.

The Romans were, in fact, eminently a practical race, and their architecture is in its construction in a high degree practical and rational; they by no means limited themselves to the use of costly and bulky materials, but united in their structures the use of all the materials of which their world-wide dominion gave them command, and were equally successful in employing in them the most stupendous masses of marble, as at Baalbec, the granite of Egypt, or the flint-nodules of Kent; and never hesitated at spanning the widest structure with vaults of domes of such solidity as almost to defy the ravages of the elements and of time.

The two great defects in the rationale of their architecture were—first, that, as the conquerors of the world, the resources at their command were so unlimited that economy of material seems to have been almost dismissed from their consideration, and their principle of statics seems to have been rather that of passive and inert resistance than of equilibrium of forces; and, secondly, that, having adopted the artistic features of Greek architecture, they attempted to unite them with their own totally different system of construction, in a manner which cannot always be said to be consistent with reason.

When the nations of modern Europe began to emerge from the chaos of centuries, and to generate for themselves a new civilisation, their aim, as regards architecture, seems rather to have been to recover that of ancient Rome, than to generate a new style for themselves; but their limited resources, and unfamiliarity with what is now denominated “Classic” art, freed them from the tendency to follow their great masters in the two defects which I have mentioned. True, they often built with needless massiveness; but this was not the result of profuseness, but of want of experience; and when they imitated or re-used the details of Roman architecture they applied them with more regard to practical utility then to Classic precedent.

At first the Romanesque builders were at a low level both as to constructive and artistic skill; but all their efforts being directed to practical improvement, they, in course of time, succeeded in generating a very consistent round-arched style, in which every feature may be said to have resulted, in a greater or less degree, from practical reasoning on immediate requirements and on their experience of preceding defects.

The observations I have to offer on the developments thus reasoned out are intended to apply mainly to those of the countries north of the Alps, but may in many points be found to be of general application.

One of the first practical principles aimed at throughout the whole range of Mediæval architecture was so to arrange their designs as to facilitate the use of small materials, and to render themselves independent of the accident of having quarries at command which would supply vast blocks of stone. It happened that in the great seats of early art this was of less consequence, for Egypt, Syria, Greece, and Italy contain such quarries in tolerable abundance, though even the Romans resorted to concealed arches for the security of their architraves; but in Northern Europe, though building-stone in most parts abounds, it is quite exceptional to find it at once in blocks of great dimensions and of strength which would render it a trustworthy covering to openings of any considerable bearing. With all our increased facilities at the present day, we never find the trabeated system carried out in its integrity when on a large scale; either the middle stones of architraves are suspended by concealed arched joints, as is the custom here, or are visibly arched-jointed, as in France, or the entire architraves consist of brick arches plastered over, to mimic the construction they affect but cannot follow. Even in our Gothic buildings, where every facility exists for the use of moderate-sized stone, it is often with much difficulty that blocks of a size suited to all purposes can be obtained. Thus with the Houses of Parliament, after the whole kingdom had been ransacked by a geological commission, not only was the quarry they recommended summarily rejected as incapable of furnishing stone of any reasonable size, but the second quarry, which was adopted in its place, and which produced an admirable material, was, after a time, abandoned, and a third selected, the productions of which have, in other respects than size, proved so lamentably inferior. The fact is that it is only here and there that we find quarries uniting quality and size which suit even our moderate requirements; and if such is the case now, with all our mechanical advantages and facilities of transit, how much more must it have been felt in days when the mechanical appliances of the ancients had been in a great measure lost, and the Roman roads broken up, while the means which were to supply these deficiencies were yet in their infancy.

While, then, at all times and everywhere, it is a desideratum to a rational system of construction that it should offer every facility for the use of ordinary and easily-obtained material, such was the case in a more than usual degree in those early ages of modern art.

Though the universal use of the arch by the Romanesque builders obviously promoted this object, it would not of necessity lead to its fullest attainment. Arches may be, and often are, constructed of enormous blocks of stone; and it had to be studied how to make good construction with small materials.

The most obvious means of doing this was by building the arches in rims, as we do our brick arches—a deep arch, consisting of several distinct arches laid one over the other, each forming the centre on which the next is built (Fig. 136). By this mode of building an arch of any degree of strength may be built of stones of the most moderate dimensions. This system, consequently, became general in the Romanesque buildings.

Now, a deep arch so constructed, and built square through the wall, has a heavy clumsy appearance, and forms a dark and cavern-like recess. You may ornament the voussoirs and vary their colour as you please, but still it is heavy, wanting in play of light and shade, and obstructive to the free passage of the rays of light. This was early felt and early obviated.

In an arch built in several rims, it is not necessary that any but the outer rim should be of the full width of the wall. This suggested the system of sub-ordinating the rims, or recessing them, one behind the other, so as to divide the arch into what are called orders (Fig. 137).

This gives us at once a new and beautiful mode of arching, economical, and adapted to all varieties of material, giving great play of light and shade, offering the greatest freedom for the admission of light, and suggesting (as we shall see) a perfectly new system of decoration.

This division of the arch into receding orders necessitated a corresponding form in the piers which supported it.

The first means of relieving the plainness of this block form was the introduction of an impost at the springing, defining the line which separates the pier from the arch (Fig. 138). Afterwards the orders of the jamb would receive pilaster capitals (Fig. 139), and finally decorative columns would be inserted in their place (Fig. 140), thus completing the general idea of the pier and arch as made use of during the Romanesque period.

The arch itself was at the same time subjected to various systems of decoration suited to its normal construction.

It is clear that the extreme angles of the orders contribute but slightly to their strength. These might, therefore, be rounded, chamfered, or moulded at pleasure. It became common to form them into large rolls between two hollows, and also to cut the order into various mechanical or other forms, as zigzag, etc. etc., according to the fancy of the architect, from which arose the whole system of Romanesque arch-decoration; and as the junction of the arch with the wall above was but slightly marked by the change in the direction of the joints, a small projecting moulding was introduced between them, which we call the dripstone or label, which not only drew the line more emphatically but also served to prevent the water which ran down the face of the walls from discolouring the arch-mouldings.

It will readily be seen that this logical and reasonable mode of constructing arched openings would, when applied to arches carried on pillars, lead to the clustered column.

If the wall was not thick, the arches might certainly continue to be of one order, and the most natural mode of supporting them would then, as heretofore, be single columns. Where, however, the wall was so thick as to give it a clumsy look if the arch ran square through it, it would be divided into two orders, and would assume at its springing a cruciform plan. The impost must break round this figure; and though the column might still remain (and often did remain) round (Figs. 141, 142), the abacus only assuming the cross form, the most natural thing would be to form a complex pillar composed of four shafts united in one, each apparently supporting its own order of the arch (Fig. 143).

If the arch were divided into three orders, a more complex form suggested itself, containing eight shafts; and as the system was carried out, many other combinations arose not necessary to enumerate.

Thus we see that the adoption of the arched system of construction, unbiassed by any pre-existing laws of art, but aided only by the very rational desire to utilise the materials most abundantly provided by nature, led to two of the most important characteristics common to Romanesque and Gothic architecture, viz., the sub-ordinated arch and the clustered column, with the whole system of decoration derived from them; than which no two features can be pointed out which have been more richly fruitful of architectural forms the most original and beautiful.

Again, in the mode of bringing down the arch upon columns, the Romanesque builders exercised a sound discretion. The Greeks and Romans in their trabeated construction, reasonably enough, made their architraves only as wide as the upper diameter of their columns, so that whatever projection the capitals had beyond the shaft, they had the same beyond the architrave also. When, however, you substitute two arches for two architraves, you bring down the weight by two opposite forces; its footing on the capital, therefore, requires as much steadiment as possible.

The Romans, as many of their modern followers, were for a time so inconsistent as not only to limit the arch, like the architrave, to the thickness of the upper diameter of the column, but actually interposed, without a shadow of use, a bit of entablature between the column and the arch; thus, instead of doing all they could to give steadiness to the spring of the arch, they made it as tottering in its construction as possible. This was corrected by the Romans of the Lower Empire, and the arch was placed by them, as reason would dictate, directly upon the capital, or (still more sensibly) on a strong flat impost laid on the capital; and for this most reasonable step they have in after ages been pronounced barbarous! The Romanesque architects, taught by common sense rather than by precedent, followed their example. If they imitated or re-used the Corinthian capital, they laid upon its fragile abacus a more trustworthy impost, and to give greater steadiment to the foot of the arch they made it somewhat wider than the diameter of the column—a practice which pervades Mediæval architecture, and contributes greatly both to its good construction and its beauty.

The system of constructing doorways is directly derived from what I have already described—as many recesses being given to the jambs as the arch has rims, and these decorated with columns if thought good. The head is often filled in with a tympanum supported by corbels in the jambs, both as a field for sculptured decoration, and to make the door itself square instead of arch-formed. If this is not done, the inner arches are made to spring from a higher level, to allow the doors to open without catching against them.

The windows show the same regard to reason. The inside is nearly always widely splayed, to spread the light equally in the room. The external recess depended partly on the degree of architectural character aimed at, and partly on the depth required for the arch. Where the openings were but narrow, and the resources small, one arch-rim would suffice; and this would often be chamfered at the edges, to prevent obstruction to light.

If the opening were wider, and so required a deeper arch, or if the architectural effect aimed at were greater, we find two or more such orders as the above, with, perhaps, columns supporting the outer ones; the receding orders, in either case, doing away with undue obstruction of light or view; the sill always well sloped, to throw off the water, and having usually a string-course below, to prevent it from running down and discolouring the walls. In all this, strict regard to practical reason and utility is manifest; every step is argued out on the basis of construction and requirement, and every decoration is founded on, and results from, the conclusions come to on these practical grounds.

In domestic architecture, if a window were beyond the width of a single casement, a small pillar was often interposed, and the inner order of the window was divided into two arches, while the outer one, if there were any, was in one, the casements or shutters falling into rebates in the back of the column, by which a window of double width, which would not otherwise be conveniently attainable was produced. In window-like openings in which glazing was not needed—as in triforiums, cloisters, and screens—this system was used for beauty where not demanded for the same reasons as in windows, and the subdivisions were often increased to three or four under one comprising arch.

In other instances of the same kind, where light arcading was needed, as in cloisters, and the wall was too thick to rest upon a single capital, two small columns were placed one behind another, or a sort of bar or double corbel placed on the capital of a single pillar to support the springer of the arch, for the sake of avoiding the use of thick piers, which were not needed for strength, and would obstruct view and light; and all these practical contrivances were made elements of beauty and varied effect.

Another legitimate exercise of reason on the part of the Romanesque builders, was the rejection of the fixed rules of proportion observed by the ancients between the diameter and height of their columns. These rules were good in their place, but they had been worked out for a totally different system; and we know that the ancients themselves were anything but as slavish in their adherence to them as their modern imitators. In a purely arcuated system, however, it became clear that such rules were out of place and inconsistent with reason. Circumstances, in a majority of cases, prescribed the height of a column, from reasons wholly irrespective of the question of its load. It followed, then, that the diameter must be regulated rather by the load than the height, so that every variety of proportion became admissible. Take, as an example, the crypt under the choir of York minster. Its height being prescribed by circumstances, and the portion of it required for the vaulting being fixed by the width of the arched bays, it followed that the height of the columns was also rigorously defined; but some of these columns had to carry those of the church above, and with them the whole superstructure, while others had no load but the vaulting of the crypt and the floor of the church. Surely, then, the simplest exercise of reason dictated that their diameters should vary with their load, irrespective of their height. The system of clustering columns both helped to moderate the extremes of such variation in proportion, and, at the same time, introduced still wider liberty; for, though a pier destined to carry a vast load might be subdivided, and its apparent proportions thus lightened, the individual shafts of which it was composed, not having each its own proper load, might be viewed as decorative only, and be made exceedingly thin for their height. The use of such thin shafts did not, however, originate in the Middle Ages. Canina shows in his work on Domestic Architecture Decorated with Ornaments of a Light Form, that it was frequent among the ancients, though not often adopted by modern Classic architects. Even for really constructive pillars it is admissible where the material is of remarkable strength, as in the case of metal columns, and, in a less degree, with those of marble or granite where the load is very small; but it is especially so where the columns are of a decorative rather than a functional character, in which case it is not only lawful, but correct, to show this by making them of slender proportions. The liberty, however, which I here defend, must, as all other liberty, be kept within reasonable bounds, and must be regulated by a correct eye and sound judgment.

Another sound exercise, as I think, of reason and liberty, which was universal among the Romanesque and Byzantine architects, was the departure from the rule of the ancients that all capitals and other recurring objects of a like nature should be worked to one and the same pattern. It may be that the unity of a colonnade, united by a single and unbroken entablature, demanded this. I am not finding fault with it in Grecian or Roman architecture; but where the capitals are separated by arches, or did not form a continuous range at all, the effect would be most painfully monotonous if the sculptured capitals were all alike, as if cast in a mould by the hundred. We accordingly find it established as a universal law that, though moulded or other mechanically-formed capitals might, if you please, be alike, no such slavery should be imposed upon the sculptor; but that he should have the fullest scope, within the reasonable limits suggested by the requirements and the general balance and harmony of mass and outline, for the freest exercise of his own imagination.

Now, though these and other developments of the Romanesque period were founded on a thoroughly practical and logical course of reasoning, it by no means follows that a perfected form of arcuated architecture had yet been arrived at, any more than that the decorative system had been brought into a thoroughly refined or artistic form.

Towards the middle of the twelfth century the efforts of the architects were redoubled towards the attainment of these two objects; and the advancement made, both in correcting defects in construction and refining the decorative system, were most strenuously followed up, and all improvements made were founded strictly on reason. The great constructive difficulty met with arose from the powerful outward pressure of the round arch when of great span or carrying any great load, and especially so when used in situations where it was difficult to give it any very massive abutment.

The cases of failure from this cause were most frequent; so much so, that besides the numerous instances recorded of buildings wholly or in part falling from the failure of the arches, we find among the buildings still remaining abundant evidences of the insufficiency of the round arches for their load, and of the abutments to resist their pressure. In ordinary architecture we cannot, as in bridges, viaducts, etc., give our arches an unlimited abutment proportioned to the pressure, whatever it may be; we are limited in our means of doing this by innumerable causes: thus, in a central tower, if the arms of the cross have aisles, the natural abutments of the tower arches are reduced to the frail aid of a continuous arcade upon detached pillars; and even if there are no aisles, the abutting walls are perforated with windows. The abutments, again, of a chancel arch are perforated either by arches or windows, while the gable over the arch loads it heavily at its weakest point. The abutment of an arch, again, has often to impinge upon a pier at half its height, as in the case of a nave arcade abutting upon the detached piers of a central tower. In all such situations the undue pressure of the round arch was found to be most prejudicial. Still more strongly was it felt where the nave was spanned by stone vaulting. The Romans had got over this, as in the Baths of Diocletian, by breaking the continuity of the aisles by vast abutting walls across them. But in a church this was impracticable. Its uses demanded continuity of aisle and moderation in the size of the pillars. Failures often occurred from these adverse causes, and the ingenuity of the architects was naturally directed to obviating the defect.

I have, in a previous lecture, described the series of tentative experiments, all of them dictated by constructive and practical requirements, by which it was attempted to avoid these difficulties. I will not weary you by recapitulating them. The two obvious desiderata were an arch of less pressure and an abutment of greater resistance; and these were the two objects aimed at in most of the succeeding developments. The first demand was met by the pointed arch; the second by the systematised use of the buttress, whether of the solid or arched description. It was perfectly well known that the outward thrust of an arch diminished as its height increased; that the resisting power of an abutment depended mainly on its extension in the direction of the pressure; and that where sufficient extension of abutment could not be obtained without inconvenience or dissight, the deficiency might be compensated by loading it from above: and by arguing on these three facts the constructive characteristics which distinguish Gothic from Romanesque, or the pointed-arched from the round-arched Gothic, were logically worked out.

The strictly mathematical mode of increasing the height of an arch would, I suppose, be by using a semi-ellipse, its major axis being vertical. The form is, however, most unpleasing to the eye and troublesome in execution, from its constant variation of curvature, so that by far the most natural and practical means of effecting the object is the adoption of an arch of two centres, or what is commonly called the “pointed arch.” We accordingly find, as I have shown by ample evidence in a previous lecture, that this form was in the first instance used just in those situations in which a reduction of outward pressure or an increased power of bearing weight were of the greatest importance. I have shown that this form was not adopted at first as a matter of taste, of fashion, or of fancy; nor even, as has been suggested by a highly talented writer, as a means of meeting the difficulties arising from the varied heights of the arches of vaulting, but simply from structural and mechanical necessity. It matters not whether the form was new or old, whether it occurred to them without external suggestion, or whether they saw it in the East, in their own intersecting arcades, or in the first proposition of Euclid. It was not the seeing of it in any such manner which caused its introduction, but the simple fact that they had arrived in the course of their constructive development at a practical problem of vital importance, which absolutely demanded the pointed arch for its solution.

The first situations in which the pointed arch was substituted for the semicircle are the wide spanning arches of vaulting and the arches carrying central towers and gables. We next find it in the wide arches of nave arcades; and it is not, as a general rule, till it became customary in those positions where it was demanded for practical reasons, that it began to be used as a matter of taste in other positions.

Having secured the first object—an arch of reduced pressure—the second, viz., the abutment of an increased resistance, was attained by the systematic development of the buttress—a feature very much neglected by the Romanesque builders; and, as the vaulting of a lofty nave could not be directly supported by the ordinary buttress, the arched or flying buttress was introduced, spanning the aisles and conveying the pressure to the buttresses beyond. That this was introduced for utility only, and not from taste, is proved by the attempts in early instances to conceal it; so that we may with certainty conclude that all these beautiful features of Gothic architecture originated not from taste or caprice, but from reasoning upon practical and urgently pressing constructional requirements, and that the beauties to which they gave rise proceeded from the application to them of the great principle of Gothic architecture, the decoration of constructive or useful features.

Let us, however, suppose for a moment that our building is not vaulted, but has timber roofs; there still remains an advantage in the use of the pointed arch. If it has, for instance, a central tower, the demand for an arch of reduced thrust is still greater than if the church had been vaulted, for the arms of the cross, from their reduced weight, are less effective as abutments.

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.

The fact is that, besides its unpleasing form, especially when the major axis is vertical, the use of the ellipse entails such an annoying series of difficulties as greatly to increase the trouble and consequent cost of execution. The constant change of curvature, the troublesome methods of striking it, and of finding the true lines of the arch-joints, not to mention the mathematical fact that the same joint line is never true both for the extrados and intrados, and that, if the rib-mould remains unchanged in depth, the extrados and intrados cannot be both true ellipses at all; all these furnish quite sufficient practical reasons for its rejection in cases where not only is there no necessity but an abstract mathematical idea to be satisfied by its use, but the beauty of the work is greatly improved by dispensing with it.

Though the pointed arch was introduced from purely constructive reasons, there was another of a more æsthetical nature, which rendered its adoption more general when once introduced. It was a double one; not only did the general tendency towards lofty proportions render it necessary to make use of an arch more in harmony with the general feeling of the architecture, but the rejection of a fixed code of proportions for pillars and other parts demanded for the arch an equal power of varying its own proportions. The semicircular arch is absolute and invariable, and though the use of smaller segments would meet the case in one direction, there were no means of proportioning it to features of increasing height. This was attempted both in Romanesque and Byzantine works by the expedient of stilting, but this is, after all, more a semblance than a reality. As in cases already cited, the mathematical solution of the problem is the ellipse; but only imagine anything so unpleasing as a series of elliptical arches placed the length-way upwards! Good taste would not suffer it. But the pointed arch at once met the difficulty. To illustrate my meaning, I will beg you to take an internal bay of a Norman cathedral (Fig. 146), and to suppose yourselves to have to increase its height throughout in the ratio of one-third (Fig. 147).