GOTHIC Vaults. SAGITAL SHAPE AND ITS MEANING

At the beginning of the study of medieval architecture, the importance of the pointed arch was greatly exaggerated and was even considered as the predominant feature of Gothic art. For a long time, a semicircular arch was considered characteristic of Romanesque art, while a broken, pointed arch was considered characteristic of Gothic art.

What we said above about Romanesque vaults, and in particular about Cluny, saves us from the need to again prove that such a distinction has no basis: starting from 1100, Romanesque architects widely used the pointed arch, showing an amazing understanding of the advantages that could be extracted from its weakened thrust.

Gothic architects adopt it from imitation; it seems that for some time they do not even realize its static advantages: they use it along with the semicircular arch; on rice. 165 it is clearly visible what idea guided them in this combination. This drawing depicts in general terms two buildings dating back to the beginning of Gothic art: G - choir in Saint-Germain des Pres; N- choir in Noyon.

Rice. 165

Let's look first at the choir in Noyon (TV). In the lower floor, in the triforium and in the upper floor - everywhere we find a pointed arch along with a semi-circular one; The transition from a semi-circular arch to a pointed arch is explained by the desire to keep the locks of the arches at the same level.

Moreover, on the lower floor the pointed arch is found only in the corner part, where the rounding forces the distance between the supports to be narrowed. In the triforium, the initial span, the widest, is covered with a semicircular arch, while the remaining spans are covered with pointed ones, so that the locks of all arches are on the same level.

In the upper floor, the spans along the straight parts of the plan are covered with semicircular girth arches, and the spans at the curve are lancet. In the choir of the church of Saint-Germain des Prés (drawing G), the pointed form is introduced into the triforium purely for decorative reasons; but in the two main floors, the lower and upper with high windows, the pointed arch appears only at the curve, that is, at the place where the supports come together.

And here the only reason for its appearance is the desire to give the rounded arches a height approaching the arches of the straight part of the plan: the desire to align the locks of the arches, and nothing more. Because of the same desire to establish a single level for the cheek arches and diagonal arches, Romanesque architects introduced pointed form into groin vaults.

When Gothic architects built cross vaults on ribs, their starting point would not be a cheek pointed arch, but a diagonal one, and this arch would be semicircular in shape.

Thus, the semi-circular, rather than pointed, outline is the main one for the Gothic vault; we can say that until the 13th century. the pointed outline is adopted more out of necessity than out of desire: only when the boldness of the plans forces the use of all means to reduce the thrust, the static advantages of the pointed arch begin to play a decisive role.

Let us limit ourselves to these instructions regarding one of the architectural elements, essentially secondary, and move on to vault systems, the choice of which affects the overall economics of the building.

Rib Vault WITH UNCONNECTED FORMWORKS AS THE BASIC IDEA OF THE SYSTEM

The difficulty in constructing Romanesque cross vaults lies solely in the laying of the rib capstones connecting the parts of the vault: the slightest mistake deprives these ribs of stability.

This difficulty would disappear if the ribs of the vault were supported by diagonally placed arches, which would form under the ribs something like permanent circles of stone. Then the correctness of the ligation of the seams would matter little, even the ligation itself could be completely absent, and the execution of the vault would be equally simple, regardless of the irregularities of the plan on which it is being built.

The chain leading from the Romanesque vault to the Gothic is this: Gothic architecture discards all concerns about masonry, adding to the Romanesque vault a rib under each of its edges; Gothic vault - the same cross vault, the formwork of which is independent and supported by ribs.

Construction method. - Rice. 166 gives an idea of ​​the usual methods of constructing a Gothic vault: the ribs are lined with cut stone, the formwork is made of small stones, and the backfill, raised to the level of the vault sinuses, does not allow deformation of the thin formwork.

Gothic ribs resemble the brick frame of Roman cruciform vaults. But the meaning of both is far from the same. Among the Romans, the frame plays only a temporary role: it is designed to absorb part of the load falling on the circles; upon completion of the work, it remains included in the mass of the vault, and the vault functions as a monolithic structure.

Gothic architects give the ribs an essential and permanent role - it is on them that the vault rests; Instead of introducing ribs into the thickness of the massif, they are taken out, and the massif itself is replaced with light, non-rigid formwork, almost unconnected with each other. The ancient vault was an inert monolith, the Gothic vault was a connection of non-rigid formwork on a ribbed skeleton.

Efforts arising in Gothic vaults.- At one glance at rice. 166 the nature of the forces arising in the arch is clarified. The ribs, laid out with larger masonry than the vault strippings, give less shrinkage and form in the mass of the vault a kind of frame, which takes on most of the load, causing compression forces in it, distributed along the ribs and taking a vertical direction.

The main efforts are concentrated in the ribs; their direction, at least theoretically, is quite definite. Then follow relatively minor forces, the influence of which, however, should be noted: the formworks located on the outer sloping surface of the ribs have some tendency to slide in the direction of the arrow ( rice. 166).

Consequences of using a rib vault.- The properties of the new code that we have considered allow us to now evaluate the significance of this innovation. Thanks to the ribs, the main thrust is strictly localized. There are no distributed forces that obscure the issue of the location of the support pillars. Therefore, counteraction is sufficient in those places where the thrust acts.

By skillful placement of the ribs the architect can direct the thrust to those points of resistance at his disposal; the entire balancing system is in his hands. The ribbed vault not only allows the expansion of the expansion, which could not be achieved by any tricks in conventional masonry, but it makes it possible to even reduce this expansion.

A cross vault is inevitably heavy, because the rib stones form a sufficient connection to the masonry only if they are of a certain thickness, and this circumstance entails a significant thickness of the entire vault.

We do not encounter any of this in the case when the vault is erected on ribs. The vault, the formwork of which becomes only filling, acquires extreme lightness; along with a decrease in gravity, the thrust also decreases, therefore the support elements may be less powerful.

Finally, the entire structure loses the rigidity that inextricably accompanied the cross vault: in the event of subsidence, there is no longer any reason to fear irreparable cracks in the masonry, all parts of which are interconnected. The rib vault, so to speak, is flexible and changeable: the support points can settle, the abutments can deviate, and the rib vault will follow these movements.

So, no matter what point of view one takes, the use of a ribbed vault provides a significant simplification and additional guarantees: it is the starting point of all techniques that ensure balancing - techniques that made it possible to realize the most daring attempts of Gothic art. If it were necessary to indicate distinctive feature architecture that replaced Romanesque art, then such a feature would not be a pointed outline, but a rib vault. Gothic art is characterized not by the use of one or another outline of the arch, but by the very idea of ​​​​an original design that distinguishes its active frame from the mass of the arch.

EXECUTION DETAILS: PROFILING, MASONRY, CIRCLES
Profiling.- The method of profiling the Gothic vault is the same as for the Cluny cross vaults. The diagonal arch, which in the Middle Ages was called “augive” *, is almost always semicircular; As for the cheek arches (doubleaux, tormerets), they are given a pointed shape to make their height approximately equal to the height of the diagonal arch.

Note: Augive - literally translated, taking into account the Latin root of the name, means auxiliary, supporting the arch of the section. The term pointed architecture, proposed for Gothic by some French experts, did not survive.

This is explained at rice. 167. Let ABCD be the rectangle that needs to be covered with a vault; the diagonal arch of the “ogive”, running along the diagonal AC, will be a semicircle AS "C; the cheek arches will be pointed, like AE"B. Now all that remains is to divide the parts of the filling into sectors.

Let's look at the ASE stripping. The diagonal semi-arch AS" and the cheek semi-arch AE" are divided into the same number of equal parts.

Let m, m ",..., u, u "... be horizontal projections of the separation points: straight lines m u, m " u "... are projections onto the plan of masonry joints; in vertical projection, these lines of masonry seams will be slightly curved, so that each sector forms a small, very flat arch, spanned between the diagonal and cheek arches.

This is normal profiling. As an exception, we cite several rarely encountered vaults in which the diagonal arch is not strictly semicircular. In the early period of Gothic art, we find in the vaults of Morianval a lowered diagonal arch, oval in shape. In the 13th century, in the cathedrals of Chartres * and Reims, the diagonal arches were elevated and oval in shape.

Note:Chartres Cathedral emerged in its Gothic form after a fire in 1191, which almost destroyed the Romanesque church built 60 years earlier. In 1220 the covering of the vaults was completed, and in 1260 the cathedral was consecrated. It is 130 m long, the width of the transept is 61 m, the height is 36.55 m, the left tower reaches a height of 115 m. The sculpture of Chartres is extremely important for its contrasts with the earlier semi-Romanesque sculpture of the 12th century. and with developed Gothic sculpture of the 13th century. See Melet R., La cathedrale de Chartres, Paris 1909.

Details of the masonry: the support part is wedge-shaped and the support part is in the form of a “pillow”.- In the earliest Gothic vaults, the ribs from top to bottom are lined with wedge-shaped stones and are independent of one another until the very bottom ( rice. 168, A).

To install a bundle of such independent ribs, you need a fairly wide supporting surface, a relatively massive supporting abutment. Often, in order to compress this bundle, the ribs seemed to be intertwined, thinning them towards the base; but these were only attempts to get out of the difficulty.

The solution to this difficult problem was found only in the 13th century. and lies in the fact that the lower rows of the masonry bundle of ribs are laid out in the form of a “pillow,” that is, horizontal rows of solid stones.

On rice. 168 Both successive methods of laying the supporting part of the vault are compared:
In drawing A, the ribs, starting from the very base, are independent of the supporting abutment, in which recesses are made for their installation. Instead of resting the already branched bundle of ribs on the ledges made in the abutment, the abutment itself was widened upward (Fig. B); the ribs branch only at the moment when the widening of the abutment is already large enough to serve as a foundation for them. In this way, not only is excavation in the abutment avoided, but the wedge part of the rib masonry, which causes expansion, is reduced by the height of the cushion: in reality, the support column rises, widening to level N, and only at this level does that part of the structure begin that is kept in balance corresponding play of forces.

The pillows along their entire height are like an interlacing of ribs; According to the original drawing reproduced by Willis *, the profile of the pillow is as follows:

Note: To the works of the English scientist architect Willis, quoted in the notes to Chapter Three, it should be added here: Willis R., The architectural History of Cambridge, 1886.

They are content to mark the upper and lower surfaces of the block according to the dimensions of the ribs ( rice. 169, M); the contour thus obtained on the surface limits the mass of stone that must be left; everything that protrudes beyond the lines is cut away.

If we think theoretically, this technique gives only approximate results: applying the same profile along the width to the horizontal planes of section a, b, c, we obtain a rib (N), the section of which is deformed (detail X).

It is not difficult to avoid this error, but in most cases the masons were satisfied with the approximate drawing obtained using this simplified method.

Supporting parts of ribs in the form of a cushion, as we have already said, are found only since the 13th century. In the nave Notre Dame Cathedral, completed around 1220, we do not yet find these support pillows. In the Soissons Cathedral, which was founded around the time that Notre Dame Cathedral was being completed, all the supporting parts of the ribs are already laid out in the form of pillows.

Note: The cathedral in Soissons was founded around 1180. The nave and choir were built around 1200; in 1212 it was already possible to perform services. Wed. Le fevre - Montalis, Architecture religieuse dans l "ancien diocese de Soissons". 1894.

Circular method. - Gothic vaults, the formworks of which are curved in different directions, would seem to force the use of a rather complex system of circles; in fact, the latter were extremely simple.

The experience of restorers of French Gothic monuments has shown that in cases where the spans of the vaults are not particularly large, you can get by with one circle truss under each rib and draw out the filling sectors using only sliding small circles, as shown in drawing C ( rice. 170).

Was this ingenious method used in the Middle Ages? We do not have any indisputable data. In many vaults, including the vaults of the cellars in Provins, imprints of the formwork on which their fillings were laid out have been preserved. Often the span of the sectors seems too significant, and their boom is too small in order to be able to get by with sliding circles alone.

Finally, there are vaults whose ribs are not located in the same vertical plane and which, therefore, could not be made on simple wooden trusses.

As an example, we provide rice. 170, V plan of the ribs of the circular galleries of the Cathedral in Bourges *. Here, obviously, a wide, level flooring was needed as a circle, a kind of temporary scaffolding on which the wedge-shaped stones of the vault were laid.

Note: The city cathedral of Bourges began construction around 1175 and was consecrated in 1324. The length of the plan is 118 m, width 50 m, height inside 38 m. The cathedral does not have a transept, otherwise it is closest to Notre Dame Cathedral. See Boinet, La cathedrale de Bourges, Paris 1911.

If small circles were used to lay out formwork, then they were placed precisely on such temporary scaffolding, and not on inconvenient ribs; it is more likely that they used continuous formwork, and this formwork was arranged quite simply, as indicated in drawing A.

Rice. 171 explains the designs of circles adopted for the most ordinary vaults of Gothic cathedrals: each rib S is sandwiched between two ribs of wooden trusses, being their integral part; From one farm to another there is a flooring of the required shape, on which rubble filling stones are laid.

Auguste Choisy. History of architecture. Auguste Choisy. Histoire De L'Architecture

Romanesque vault

An important task of Romanesque building art was the transformation of a basilica with a flat wooden ceiling into a vaulted one. At first, the vault covered the small spans of the side naves and apses; later, the main naves also began to be covered with the vault. The thickness of the vault was sometimes quite significant, so the walls and pylons were designed thick with a large margin of safety. Due to the need for large covered spaces and the development of construction technical ideas, the construction of initially heavy vaults and walls began to be gradually lightened.

The vault makes it possible to cover larger spaces than wooden beams. The simplest in shape and design is the cylindrical vault, which, without moving the walls apart, presses on them from above with enormous weight, and therefore requires especially massive walls. This vault is most suitable for covering rooms with a small span, but it was often used in the main nave - in France in the regions of Provence and Auvergne (Notre-Dame du Port Cathedral in Clermont).

Later, the semicircular shape of the vault arch was replaced with a pointed one. Thus, the nave of the Cathedral in Otyun (early 12th century) is covered with a pointed vault with so-called edge arches.

The basis for new types of vaults was the old one roman straight cross vault above a square room in plan, obtained by the intersection of two half-cylinders. The loads arising from this arch are distributed along the diagonal ribs, and from them are transferred to four supports at the corners of the space being covered. Initially, the ribs that appeared at the intersection of the semi-cylinders played the role of arches, which made it possible to lighten the entire structure (St. Stephen's Cathedral in Cana, 1064-1077; the monastery church in Lorsch was the first completely covered with basilica vaults).

Monastic church in Cluny. Romanesque cross vault:
1 - end ribs; 2 - diagonal ribs; 3 - lock; 4 - stripping.

If you increase the height of the vault so much that the diagonal intersection curve turns from elliptical to semicircular, you can get the so-called raised cross vault.

The vaults most often had solid masonry, which, as we said, required the construction of massive pylons. Therefore, a big step forward was Romanesque composite pylon: semi-columns were added to the main pylon, on which the edge arches rested, and as a result, the expansion of the arch was reduced. A significant structural achievement was the distribution of the load from the vault over several specific points due to the rigid connection of the transverse edge arches, ribs and pylons. The rib and edge arch become the frame of the vault, and the pylon becomes the frame of the wall.

In more late time First, the end (cheek) arches and ribs were laid out. This design was called ribbed cross vault. During the heyday of the Romanesque style, this vault was made higher, and its diagonal arch acquired a pointed shape (Church of the Holy Trinity in Cana, 1062-1066).

To cover side naves, instead of a cross vault, they sometimes used semi-cylindrical vaults, very often used in civil engineering.

Romanesque designs are, first of all, a raised ribbed vault, a pointed arch and the suppression of oblique lateral thrusts from the vaults by a system of supports. They create the basis for the subsequent Gothic style in architecture.

Stone vaults were nowhere as common as among the Romans: the ruins are full of their remains, everywhere vaults made of rubble and mortar, boldly thrown over the space, cover the ancient halls; or at least the remains of a stone structure in the form of a ledge hanging over the surface of the walls have been preserved as witnesses of the original structure and reveal to us the design of the vaults destroyed by time. These vaults made of small-sized material are varied, so to speak, indefinitely; They cover sometimes rectangular fences, sometimes round, sometimes polygonal in area, sometimes exedra. Made using formwork, they adapted equally well to the most diverse plans and to the most varied requirements for the location of premises. In addition, many of them seemed designed to last for centuries, and the noble simplicity of their forms gave the buildings a strict, majestic appearance. Never have construction techniques corresponded so well to the material and spiritual needs of the people; and it becomes clear to us why the Romans based their entire architecture on the use of such a structural system.
The problem of replacing wooden structures with others that are both stronger and more durable is as old as the art of construction; but until the advent of vaults made in the form of a monolithic stone structure, no truly practical solution was known. The slab flooring and stone architrave ceilings of Egyptian and Greek temples required materials obtained through hard labor and used at great expense. We find in the construction of primitive architecture several vaults made of horizontal rows of stones gradually overhanging each other; we even find vaults consisting of wedge-shaped stones, the lines of the seams of which converge at one point on the horizontal axis; but, out of ignorance or submission common system, the builders of these early years almost always laid the wedge stones of their vaults dry, without placing between the two blocks any cement, no mortar, no substance to compensate for the unevenness of the hewn. Hence the need arose to give the stones used a very regular shape, hence the practical difficulties that arose, which, undoubtedly, should have limited the possibilities inherent in ashlar vaults. Among all the ancient peoples, ashlar vaults were most common among the Etruscans; however, their use was very limited; they covered with vaults sewers, underground drains serving to drain damp plains, aqueducts, city gates, but in Etruscan buildings intended to satisfy ordinary life needs, and even in religious buildings, the vaulted structure never received constant use; were used wooden logs, similar to those described by Vitruvius in the Tuscan temple, or stone architraves, similar to those reproduced in the facades of several extant buildings carved into the rock.
As for the Greeks, despite their constant connection with Etruria, they apparently never thought of reproducing the varieties of Etruscan vaults whose seam lines intersect at one point. We find in the original Greek buildings, at Mycenae and especially on the island of Euboea, false vaults made with overlapped masonry, but vaults of wedge stones, the lines of the joints of which meet at one point, were not used by the Greeks until the Roman conquest; in forms of construction with a flat ceiling, their architects gave the highest expression of the ideas of proportionality and correctness; and the Greeks treasured these forms as the most beautiful creation of their genius; they were, as it were, part of their national glory and lasted as long as Greek independence lasted. Therefore, the Greeks, being witnesses of the appearance of vaulted buildings, did not take part in them and left them to the Romans. Architects are honored to have propagated this structural system, which they have made simple and practical through the use of small-dimensional materials artificially combined into one whole.
Whether the Romans were the inventors of vaults made in the form of a monolithic stone structure, that is, made of small stones tightly cemented with mortar, or not, be that as it may, before them, no people had thought of building from small stone materials vaults of large spans. The Romans themselves, apparently, for a long time neglected the possibilities that such a design could provide, or did not know them; and we find it continually applied only towards the end of the last century B.C.; Apparently, it developed during the period of material prosperity that followed the end of conquests in distant countries and the cessation of civil strife. Her successes were rapid at that time; A real revolution was taking place in the art of construction. The use of vaults in the large halls of public buildings entailed a complete change in plans; the supports, which were now subjected to a new kind of effort, had to take forms hitherto unknown; it was necessary to change the grouping of the hall to ensure a clear perceived spread of the vaults. Until now, builders lived as if at the expense of the funds of Greece and Etruria; only during this period did construction techniques free themselves from the shackles of tradition; a whole constructive system, truly Roman, is emerging, or at least receiving correct and widespread development.
This transformation, which took place in the last years of the republic, was, of course, prepared for a long time; but did the first examples of monolithic vaulted structures disappear during the long interval of time separating us from the Romans, or rather did these primitive structures be pulled down and give way to the magnificent structures erected by the emperors, and the traces of this interesting series of experiments and improvements preceding the age of Augustus were as if erased by time?
Be that as it may, the Pantheon stands before us simultaneously as a masterpiece of Roman architecture and as one of the first monuments of its history; and examples of earlier times are too rare and doubtful to indicate the successive successes of the building art of the Roman Republic. We will not attempt to reconstruct by guesswork the picture of its origin - we immediately began to study the vaults, made in the form of a monolithic stone structure and reaching complete completion; we will describe the conditions under which they were built, and try to connect these collected facts with a small number of simple ideas which seem to have dominated the whole system of vaulted buildings among the Romans.
If we turn to some Roman building with stone vaults, if we examine, for example, one of the rows of aqueducts that line the outskirts of Rome, we will notice at the ends the main arches made of bricks or stones, the lines of the masonry seams converging in one common center, and behind these main arches is rough stonework made of pieces of tuff or tiles, similar to concrete. A compact mass of rubble and mortar, enclosed between two arched facings, the lines of the masonry joints of which converge at one point - such is the structure revealed by a superficial examination of the ruins. But upon closer examination of these outwardly homogeneous rough masses, we will find ribs embedded in them of a completely different structure, real built-in ribs, sometimes entire brick lattices, forming an internal skeleton in the body of the fillings, a light frame, branching, subdividing and extending inside the rough stone structures that make it clothe.
One should not look at the skeleton of the vault as a system of rigid arches, erected simultaneously with the masonry of the structure, made of crushed stone and mortar, and intended to strengthen it, in a word, as something similar to stone pillars in the walls of modern buildings. The brick frames placed in the masonry of the Roman vaults were erected earlier, and the rough stonework was made later, as evidenced by the discrepancy in the arrangement of courses of infill and frame masonry (Fig. 8).
This light frame, this frame embedded in the vault, consists, like the main arches with which it ends, of bricks; the lines of the seams of its masonry converge at one point, and in this respect its construction is to some extent similar to our stone vaults; but here is an analogy. ends, and if we leave aside the internal structure of the vaults and consider the filling itself, we will be convinced of the simplicity of the design, which is completely unusual for modern buildings.

Rice. 8.

The very name of the vault evokes the idea of ​​a structure made of stones laid so that the lines of the masonry seams converge in one common center; and this idea actually corresponds to the construction of Roman vaults of cut stones laid dry; Likewise, this idea is correct, as we have just said, in relation to arches made of bricks placed in the form of a strong frame inside the masses; but to extend it to the masses themselves would be completely erroneous; the rows that make up the filling masonry of the Roman vault, made in the form of a monolithic stone structure, maintain a strictly horizontal position from the base to the top; and seeing how the traces of these rows are indicated in the destroyed parts of the ruins, you involuntarily remember the even layers, sometimes outlined quite clearly in the dimensions of layered soils. This arrangement of seams is a rather unusual phenomenon, and therefore we find it useful to explain it graphically. In two comparative sketches I give cross-sections of the vaults built according to one and the other system.
In a modern vault, the seams are located as shown in Fig. 9.
The joints in a Roman dry-laid ashlar vault are located in exactly the same way.
On the contrary, in a Roman vault made of small-sized material forming a monolithic stone structure, the seams invariably have the direction shown by shading in the second of the above-mentioned schematic sections (Fig. 10). Thus the Romans, depending on whether they were building with ashlar or with mortar-cemented rubble, consistently placed the joint lines either converging at one common center or strictly parallel. These two opposing methods, however, do not contain any discrepancy, no contradiction in the ancient methods, for there is a deep difference between the conditions for balancing vaults made of stones laid dry and vaults made in the form of a solid monolithic stone structure.

Rice. 9	Rice. 10

In one case, the stones are held together only due to their shape, and it is necessary to give the seam lines a direction leading to their intersection at one point; in the second case, the binding material turns everything into a whole single block, in which layers of mortar and rows of stones are mixed
into one continuous homogeneous mass; therefore, the direction of these rows is not particularly important from the point of view of the strength of the structure; and the Romans took advantage of this circumstance to introduce significant simplification into their work: they decisively freed themselves from any complications that could have resulted from the arrangement of the seams so that their lines converged at one point. Thus, the masonry of their vaults is nothing more than a continuation of the supports, which seem to hang over the span; abolish the frame embedded in the filling, and what remains is a stone structure, very similar in the direction of the rows to the structure of the walls supporting it.
We said about ancient walls that the Romans used two types of monolithic masonry, namely, those made without compaction and with compaction; and we noticed that only the first was used for the construction of walls faced with thin bricks, because only this can be done without auxiliary devices and solid formwork. Considerations of the same order apply to vaults, and they make it possible to predict which of the two types of masonry should have been used in them. For the vaults, it was inevitable that internal formwork would be installed, giving the filling the appropriate shape, but if this formwork was necessary, in other words, if circles were needed for the vaults, then at least it was necessary to try to make these circles as cheaply as possible, and this condition should have influenced the Romans had a choice between two known masonry designs. If they had used masonry that required compaction, they would have subjected the circles to shocks that could have loosened their joints, but first of all, this method would have caused severe deformations in the supporting frame of the circles: the circles would have been jammed in places located close to the supports of the arch (Fig. 11 ), and at the same time the outer cladding would begin to expand outward.
To accommodate such efforts, it would be necessary, in addition to the circles, to arrange formwork on them; The frame and formwork, this entire temporary wooden structure, would have to be extremely strong to withstand the thrusting forces and the incessant impact of impacts: in the face of these difficulties, the best solution was to abandon the rammed masonry.
This is how Roman architects reasoned; The masonry of their vaults, wherever I could establish its structure, was made with exact adherence to the techniques that were used in the construction of ordinary walls. Sometimes lighter materials are used for vaults than for walls, but the method of execution is the same in both cases - the stone masonry of the vaults is never compacted.

Rice. eleven	Rice. 12

Although when choosing the type of construction they had in mind to save on the circles, the impact exerted by the vaults on their supports was, nevertheless, in some cases very strong. As long as the masonry of the vault rose slightly above the heels, it held up almost by itself; its rows with successive overlaps actually joined the vertical, continuation of the supports, like some kind of shoot ABS in the form of a protrusion attached along a line AB(Fig. 12); - the shape of this protrusion ABS did not differ significantly from the theoretical profile of a beam of equal resistance, suitable for a solid body embedded in the wall at one end and loaded only with its own weight, and therefore, these parts of the vaults did not require difficult and expensive supports for their construction. In an extreme case, the vault in this lower part could do without scaffolding - a template was enough to give its lower surface the curvature and outline that it was supposed to have.
But this ease of execution decreases as the arch becomes higher; its overhanging parts, the further away, the more they put pressure on the circles, and the load near the top of the arch increases with extreme speed.
Soon the vault appears as if it were a semi-liquid mass, resting its entire weight on the supporting devices; from the circles, which were almost redundant just now, energetic resistance is now required, the higher the more dense and massive the arches must be; Roman vaults were never light: the rough structure of their fillings forced them to sometimes be given enormous dimensions.
Moreover, it was necessary to support this pile of materials, which had not yet achieved a sufficiently strong connection, with supports incapable of bending.
This was a serious difficulty: the slightest settlement, as a result of which the stone structure would be forced to work, just during the setting process would cause internal displacements, and perhaps even cracks, in the masonry, which consisted of crushed stone and mortar.
In an ordinary vault, the lines of the masonry seams are directed to one point, the settlement circles, although annoying, rarely causes a catastrophe: cracks may form in several seams, but the stability of the building does not depend solely on the integrity of these seams; the mortar in this type of vault serves primarily for adjustment, for pressure distribution, this is not a binder, it is simply a layer between the wedge stones; even if this mortar cracks or disappears, it will not necessarily threaten the integrity of the vault, and its presence is so little necessary that the ancients never used mortar in their cut stone structures.
But in vaults made in the form of a monolithic stone structure, as the ancients thought of them, the role of mortar ceases to be auxiliary; here he, and he alone, provides the connection between the elements of the structure; as soon as this connection is broken, all that remains of the structure is something similar to a broken, collapsed, previously monolithic mass.
Thus, in order to construct a Roman vault from small materials, it was necessary to ensure complete immutability of the circles: this, so to speak, was the first condition for success, and this condition could only be fulfilled with great difficulty when simple wooden circles were used. But even using more wood, multiplying the number of joints, giving them impeccable accuracy, it is impossible to resolve all the difficulties: the tree with the best joint is bent, warped, deformed, and a monolithic vault, unable to follow all the deformations of the wooden structure that serves as its formwork, will constantly be under threat to lose support due to possible settlement or shift of circles.
It should be added that it would have been too unusual for Roman builders to attach such importance to temporary devices: it would be surprising if they, who usually considered useful only those works that were designed to last a long time, and especially accustomed to always looking for simple solutions, suddenly In a single case, such complex and expensive auxiliary work would be used.
Finally, if we pay attention to the composition of workers employed in construction sites, then, although in different ways, we will come to the same conclusion. The Romans, who had an unlimited number of workers in all parts of their empire, did not, however, find workers everywhere with equal ease who could be entrusted with responsible carpentry work. When the structures being built require simple physical effort, it is easy to dial labor among conquered peoples, in armies, among slaves. But as soon as it comes to complex and difficult structures, such as durable and deformable circles, the possibilities of execution become more limited; the architects will be forced to assemble, at considerable expense, a multitude of skilled artisans, and in addition they will have to come to terms with the inevitable delays. And when, having spent money and time, they are able to erect entire scaffolding to support the filling of their enormous vaults without the risk of them settling, then the next day after the completion of the work, all the expenses for these temporary devices, so to speak, will be wasted, all this expensive equipment will disappear without a trace will disappear. Sacrificing expensive and hard labor in vain, of course, was unprofitable; the ancient builders tried to avoid this, and their efforts aimed at partially getting rid of dependence on temporary scaffolding inspired them with an idea that was as ingenious as it was simple - to introduce this into the designs of vaults. a semblance of an internal brick frame that supported the mass of the infill masonry during construction and thereby unloaded the circle,

Rice. 13.

The first tables appended to this work give a general view of the various frames of the vaults, showing them embedded in the filling which they supported, and the drawings placed in the text explain some of the structural details, which we can immediately understand, at least in general features, nature and significance of the functions performed by them.
I took a simple type from among various frame systems and tried to reproduce it in Fig. 13 view of the structure during construction.
The figure shows temporary circles C, lightweight brick frame D, placed directly on the circles, and finally, filling M from crushed stone and mortar, from which, upon completion of the work, a vault in the proper sense of the word is formed.
In accordance with modern construction techniques, temporary circles C would carry the entire vault; they would have to be made extremely strong, therefore, they would be very expensive. Here, on the contrary, the wooden circles carry, so to speak, only the skeleton of the vault; this is a significant difference that makes it possible to reduce the load-bearing capacity of the circles, that is, to make them significantly less powerful, which will entail a significant reduction in costs.
By the attachment of this strong frame structure, which covers and protects them, the temporary circles are secured from all danger of destruction, they form the desired shape for filling, without being burdened by its weight; Once erected, the brick frame becomes a real system of circles, extremely durable vaults that remain in the body of the masonry, merging with it into one whole and contributing, along with rough monolithic masonry, to the strength and durability of the structure.
These second brick circles, thus included in the body of the masonry, are undoubtedly more expensive than the amount of filling material whose place they occupy; but how insignificant these extra costs will seem if you compare them with the savings achieved by installing a temporary wooden structure. Moreover, this extra expense in itself was quite insignificant.
The material used for the frames was simple brick, albeit of large size, but its production in the outskirts of Rome was inexpensive.
On the other hand, this brick, despite its cheapness, was used truly remarkably economically.
Instead of making this frame solid, we see that the Romans made it through, thus eliminating about half of the bricks that would have been necessary to construct such a load-bearing solid shell over the circles (Table I).
Often they were limited to individual ribs, so to speak, girth arches, immersed in the thickness of the filling of crushed stone and mortar (Plates IΙ, III, VII, VIII, IX, Χ, XI). And these supporting arches are made of ordinary stone masonry; they were never made solid, but openwork in all directions; These are lattice structures made of bricks covering narrow strips of the arch at a certain distance.
Finally, in some cases, in order to reduce the costs that, given the thickness of the vault, required installing bricks on edge, the Romans used frames of bricks laid flat and forming a kind of curved flooring on the surface of the circle (Table IV, Fig. 1). Sometimes two floorings of this kind were laid one above the other, but then the second one was usually no longer continuous (Pl. IV, Fig. 3). It was impossible to go further in the economical use of materials.
As for labor costs, they were less than might be expected, judging by the ingenious and in some cases sophisticated combinations that we see in the pictures: everything was done quickly, I would even say that it was perhaps quite rough work. Inspecting a Roman building, you feel that the ancient builders learned, through practice, to lay out the brick frames of vaults in a hurry and achieved in them all the savings of time and labor compatible with such work; the appearance of these auxiliary devices speaks of the most hasty execution, and the irregularity of the forms in them is sometimes so striking that I was forced, in order to make the thoughts of the builders clear, to give these frames in my drawings a correctness that was often far from being detected by the most careful examination of the ruins.
However, in no case should the Romans be reproached for their unreasonable sloppiness; in this case, the speed of work at the expense of its accuracy was more an advantage than a disadvantage. Any waste of time in auxiliary construction work, unless justified by the strict requirements of urgent necessity, must be considered useless; and the rough appearance given by the Roman builders to the frames of their vaults shows that they correctly understood their purpose. It was enough to install the brick frame so reliably that it would only last until the completion of laying the filling: as soon as the stone monolithic design was ready, everything turned out to be built in, walled up in its mass; and during decorative works the last traces of the frame, which could still remain visible from the inside, disappeared under a thick layer of plaster; What advantage would a more careful execution give under these conditions? The very crude frames of the Roman vaults were good enough; and to try to carry them out more accurately would be labor in vain.

Rice. 14

But besides considerations of economy, the Romans had another more important reason for avoiding delay. In order to fully understand the reason for their haste in completing the vault frames, one must clearly imagine the state of the construction site at the moment when auxiliary structures were to be installed. brick structures. The laying of the supports has been completed and the circles have just been installed in place. The architect then faces a difficult choice. By continuing to lay the infill, he risks crushing the circles; if, on the contrary, he pauses the work of laying the infill in order to take it up again when the laying of the vault frame is completed, this forces him to leave the entire artel of workers and slaves unoccupied.
The only way to coordinate everything is for him to hastily install these frames and complete their laying while the filling still does not put pressure on the circles. If, for example, AB indicates the level where the pressure begins, it is necessary that at the moment when the filling reaches the level AB, the frame arches were locked and the structure would have the appearance shown in Fig. 14.
Thus, the laying of the frames and the infill of the entire structure as a whole begins and is carried out simultaneously, but the frames must be laid out and completed with masonry so that they can already fulfill their purpose during that short period of time while the infill masonry stands on its own. Hence this such noticeable haste; the reason for it, as we see, was serious, otherwise there would have been a temporary inactivity of the numerous laborers whom the Romans used to carry out the simplest and most labor-intensive part of the construction work in their large structures.
This initial period, when the internal frame of the vaults had to be erected entirely and with great haste, was, however, the only critical moment in the work: the masonry of the vaults was completed on these rigid supports as easily as ordinary masonry; and when, finally, the moment of untwisting them arrived (an operation quite complicated in other constructive systems), it was carried out without any danger, or, rather, untwisting no longer represented any serious operation. It was possible without any risk to remove the wooden structure that carried the formwork: it was real circles. the frame itself; and hidden in the masonry fillings of crushed stone and mortar, these brick circles blocked the span, bearing the weight of the vaults until the mortar completely hardened.
Now we can cover in general both the course of Roman construction and the advantages associated with the constructive system of ancient vaults: it, as we see, is based on very simple and practical principles; some of the principles on which it is based are so natural and so easy to come to mind that they can be found in another form in architecture most externally different from the Roman one; I'm talking about French architecture of the Middle Ages. The ribbed vaults in our (French) cathedrals, of course, are not similar to the vaults of the Romans either in their external appearance or in the static conditions of their work; some hold on thanks to a deliberately created complex combination of forces and thrusts; in others, stability is created simply by the monolithic structure of their masonry; but with regard to construction techniques, the analogy is indicative, and it is all the more remarkable that it is perhaps accidental. Indeed, who wouldn’t notice that the ribs of medieval vaults are equivalent to ancient frames. In one case the ribs are made of bricks and are placed in a mass of masonry infill of crushed stone and mortar, in the other they project in relief and support infills of real stone masonry. But the differences in shapes and materials are not important here: the main one. the installation is the same on both sides; hidden or protruding ribs play, at least during the execution of work, the same role; and the less similarity there is in their appearance, the more one can feel how natural and generally understandable the idea of ​​erecting vaults on the second row of circles, built of stone material, is. I do not undertake to predict the transformations that this ingenious idea will experience in the future; but the applications that it successively received in two radically different architectures speak, in my opinion, of its fruitfulness; and the study of the possibilities which such a solution can afford in these days is certainly worthy of the full attention of builders.
Concluding this first study of the monument codes, it would be useful to compare all our hypotheses as a whole with the indications in the texts. Unfortunately, positive information on this matter is very incomplete, and the hints are very dark.
Vitruvius mentions the names of the vaults several times, but does not provide any details regarding the methods of their construction; if we analyze his entire treatise, we will hardly find at least one place in it that seriously illuminates this, perhaps the most important issue in the entire history of ancient architecture. He talks about the method. reproducing the design of the vault using a wooden structure made of boards arranged in a curve, intertwined with reeds; and plastered; As for the real vaults, it is in vain to look for their description from him. Should we see in this strange gap an omission on the part of the author or the result of a complete distortion of his works? Or, finally, is this a sign indicating the state of the art of construction at the time of Vitruvius? I would readily incline to this latter assumption; and the date of construction of the oldest large vaults that have survived to our time makes it, it must be admitted, very plausible.

Rice. 15.

Despite these gaps and ambiguities, Vitruvius always remained an authority among the Romans; and later authors" were content for the most part with repeating in a less ponderous, less lengthy, but often less precise form the instructions of his text. Thus, Pliny, writing at a time when frame vaults were very common, does not go into any detail regarding methods of their construction; the agricultural expert Palladius and the anonymous author who abridged Vitruvius remain equally silent regarding construction techniques relating to vaults in the proper sense of the word, but they spread, following the example of the original author from whom they copied, about these very uninteresting structures, imitating the outward curvature of arches, possessing neither their strength nor their durability.

Rice. 16.

But, if we are deprived of the possibility of checking the texts, then at least we can find out what the traditions say. The Italians even now use temporary wooden structures very sparingly when it comes to circles for the construction of vaults; Thus, you can often see that they use such a design as shown in Fig. 15.
The permanent brick circles of the Romans are here represented in the form of a row of bricks laid flat, supported on a cross-piece of rejected wood, and several bricks placed on edge; Sometimes the Italians remove the bricks laid flat during unwinding, but the Romans usually left them in place. However, even in modern Italian buildings, I have repeatedly encountered already completed vaults, covered inside with such a curved brick flooring, which originally served as formwork and circles.
Here (Fig. 16) is another system of brick circles, conceived in approximately the same spirit.
The circles on which the vault is displayed consist of two curved protruding ribs starting at the heels, turning at the top into a through brick wall located on a wooden beam.
Finally, I will give as a last example (Fig. 17) the design of a circle, consisting of two wooden beams, resting one against the other and supporting a through wall of bricks, similar to a tympanum, not made correct masonry, the purpose of which is to support the masonry of the vault during the work.

Rice. 17.

Probably none of these three types of circles correspond exactly to ancient designs; but it seems to me that one cannot help but recognize here and there the remarkable identity of principles: for example, the same desire to limit oneself to the simplest wooden structures, brick, which in both cases plays an important role as a material for circles, and its use for the sake of economy and ease of flat laying in the laying of floorings or in the laying of through walls. However, with further study, the observation of modern techniques will repeatedly help us understand the practical techniques of the Romans, obscurely visible in the ruins, or, at least, add new evidence in favor of the explanatory hypotheses that we have outlined above.
Let us now return to Roman frame designs. They are divided, as we see, into two groups, of which one covers all structures based on the use of arches or lattice frames of such masonry, the lines of the seams of which converge in one center, and the other - all those that are based on the use of brick floorings, laid flat. We will tackle both solutions in turn in different types of vaults and the first duty - in barrel vaults.

a) Vaults on frames with radial seams.

Frames, the lines of the masonry seams of which intersect in one center, are usually made of two types of bricks: square with a side length of 2 Roman feet (slightly less than 0.60 m) and rectangular bricks with side dimensions of 2 feet and about 1/2 foot ( 0.15 m).
Arches and ribs were made from rectangular bricks, placing the latter at a distance of 2 feet between the axes, and with large square bricks, with a side length of 2 Roman feet, these ribs were connected to each other in the same way as shown in Fig. 18.

Rice. 18.

In this way they obtained something like a lattice, which can be considered the most complete type of Roman frame with radial seams.
Sometimes (but this case is an exception and seems to be the result of carelessness rather than deliberate calculation) large square bricks used for connection, instead of being laid as shown in Fig. 18, that is, one after the other along one line - along the generatrix of the cylindrical vault, they overlap one another so that each square brick covers the entire width of both arches connected by it (Fig. 19).
The arrangement is doubly defective - because a) the same amount of materials can cover a much smaller part of the vault, and b) it is more difficult to fit the filling into the reduced cells of the frame.
Perhaps somewhat greater strength is provided by the larger number of these arches; but even with another system, apparently, a strength is obtained that is quite sufficient even for the widest vaults; and since the frames were here essentially auxiliary structures, the ancients acted wisely in sacrificing this weak increase in strength for the more important conditions of economy and lightness.
We find a remarkable example of a structure made using the first method (Fig. 18) in the hall of the Caesars' Palace in Rome, which is part of the group of buildings surrounding the Circus Maximus. I present this summary on the table. I; in order to give a clearer idea of ​​its general structure and to show how it is connected with its supports, I have drawn a series of sections in which all the details of the structure are revealed and at the same time summarized. ideas that we have been able to form up to now both about the design of the vaults and about the usual structure of Roman massive stone structures. These drawings will make it possible to establish the identity between the construction of the masonry of the vaults and the supports, the horizontal arrangement of the rows in the fillings of the vault and, finally, and especially, the presence of a common frame, which is replaced from the inside during the transition from the cylindrical vault to the supports by facing of triangular bricks.
This table gives perhaps the most complete type of antique structural frame system: the brick frame, which is shown here, combines the valuable qualities of a rigid load-bearing support and a continuous cladding.

Rice. 19.

But this design still required a quantity of bricks that may seem enormous, and the Romans, sacrificing this costly advantage, gradually abandoned such construction in favor of moving from a solid brick frame to free-standing arched ribs hidden in the masonry. I will try to show the consequences of these simplifications and variations. But, connecting all subsequent examples that I want to give with the first type of construction, I, of course, do not pretend to restore the historical chain of events and the path in which changes in constructive techniques took place in reality: the relative dates of the construction of the various vaults that we will have to compare, usually little known; and therefore it would be too bold to set the goal of finding, in the current state of archaeological knowledge, [the end of the 19th century. - Ed.] real continuity of Roman ideas; my intention is only to identify, among the many different forms, the leading basic idea underlying the design of the permanent circles - the frames of ancient vaults.
Moving on after this reservation to a comparison of the arch shown in Table. I, with various vaults shown on the same scale on the plate. II and III, we will see that they are obviously connected by one common idea, which found its most complete expression in the Palatine vault.
In Fig. 1 table The II arches of the frame are no longer directly connected. with each other using large square bricks-links: instead of this overall connectivity, the arches are simply located closer to each other.

Rice. 20.	Rice. 21.

The frame of the vault is now, so to speak, reduced to a system of free-standing ribs; these ribs are no more than 0.15 m wide in the direction of the arch forming, and the spaces between them exceed the dimensions of ordinary Roman square bricks. Thus, the space between the arches is not divided into cells; but to the right and left on each side of the arch protrude the ends of large square bricks, laid interspersed with bricks 0.15 m wide; Without dividing the space between the arches into separate cells, they still clearly outline these divisions in it and, so to speak, compensate for the discontinuity of the frame structure. Each arch, taken separately, would have the appearance shown in Fig. 20: these protrusions made of large bricks seemed to capture the mass of filling and did not allow it to put pressure on the circles; in any case, it is certain that the close connection of the filling with these small projections of the ribs of the frame helped to transfer most of its weight to the arches, instead of allowing them to bear their entire weight on the temporary structure of the circle.
The vaults shown in Fig. 1 table II, are a typical example of the attempts of builders to get rid of the dependence and expense of constructing a solid lattice frame, while retaining almost all the advantages afforded by solid construction: this vault is taken from the arcades of an aqueduct, which is considered the aqueduct of Nero, and the remains of which are built into the walls of the gardens , stretching on both sides of the street leading to the church of S. Stefano Rotondo in Rome.
In order to distinguish the structure shown in our drawing on the spot, rather intense attention is required: the filling of the vault consists of fragments of tiles of the same color as the frames, and the frames themselves are so crudely made that, without prior knowledge of their existence, it is very difficult to notice them in a mass reminiscent of rock with veins, a rock of the same shade that envelops them and further complicates the examination, already difficult due to the ruined state and barbaric execution. I already warned at the beginning that it is necessary for me, for the sake of clarity, to give in my drawings a certain correctness to the load-bearing structures that the Romans built; in this case, more than anywhere else, I had to allow myself this liberty; and more than anywhere else, this curious aqueduct shows how important the Romans attached to the speed of erecting these frames. We already know quite well the reasons for this extreme haste, but nowhere is it reflected so clearly as in the irregular forms of this arcade.
Such free-standing arches as those shown in our sketch (Fig. 20) were easily feasible, but due to the insignificant size of their cross-section (about 0.15 m), their stability was questionable: these arches could be deformed from longitudinal bending in their plane or out of plane; the Romans invented a way to compensate for their lack of stability; they began to pair these arches, replacing the design shown in fig. 20, the one we see in Fig. 21.
The rib, made from two arches thus paired, is nothing more than a narrow strip cut from a lattice frame, similar to that found in the Palatine: the grouping of the arches, which increased the area of ​​their cross-sections, reduced the possibility of longitudinal bending. The advantages of the new design compared to the previous one were significant, and we see that these paired arches are widely used in a number of structures, of which we will mention the Colosseum (Table II, Fig. 2).
The figure occupying the upper half of the table. II, depicts part of the galleries that form the outer enclosure of the amphitheater. The drawing simultaneously shows two parallel and adjacent galleries, the spans of which are almost identical; only one of them was built on frames, while the monolithic masonry of the other was made directly on the circles.
Therefore, we should not consider the constructive technique that interests us as systematically used by the builders of the Colosseum: The Colosseum, in relation to its structures, is, so to speak, a huge summary of all the achievements of ancient construction art, where all the ancient constructive techniques were used in turn. Were the vaults rebuilt in different time, whether its construction was entrusted: at the same time to several contractors who were given a certain freedom in the use of certain techniques, be that as it may, but in different vaults of this structure, and sometimes in different parts of the same vault, one can notice the most opposite construction techniques. In general, the barrel vaults appear to have been built along arches hidden in the masonry, the shape and placement of which are clearly shown in our drawing. However, no absolute law prevails either in the placement of these ribs or in their design: sometimes they begin at the level of the height of the heels, sometimes, on the contrary, much higher; sometimes their axes correspond to the axes of large architectural divisions, then (Table II, Fig. 2) the arches resting on stone pilasters are located eccentrically with respect to the axis of the supports on which their heels are placed. With some effort, architects could use these arches as decorative element for their vaults, but they prefer, at the cost of inaccuracies in the work, to eliminate the risk associated with the too slow execution of these elements, intended only to ensure strength, in order then, after completion of the construction, to hide the irregularity of their design under a thick layer of plaster. This carelessness of execution is characteristic of most of the frames that we will consider later; but before going any further, it is necessary to more carefully analyze the true purpose of the frame that we have just described.
I may be told that the functions of the brick frames of the Palatine (Pl. I), which can serve as circles during the construction of the vault, are self-explanatory: it is a single lattice structure, working as one unit; there is nothing more logical. Even in the aqueduct of Nero (Table II, Fig. 1), where the arches, although very close together, but the brick projections coming from one arch still do not meet the projections of the neighboring arch, it is clear that the brick frame can withstand the great weight of the masonry filling during the construction of the vault; but will everything be just as clear when the frame of the vault is reduced to a series of girth arches hidden in the masonry infill, to ribs not only located separately, but separated by intervals of about 3 m? Doesn't it seem that the arches here will simply carry the load of only that part of the infill that is located above them? But in the spaces between the two arches, won’t the filling, being in a semi-liquid state, rest on the formwork laid in temporary circles in exactly the same way as it would lie on it if these free-standing arches were absent? That's the doubt; I believe that it can be solved as follows.

Rice. 22.

Imagine (Fig. 22) a vault of a similar design, limited at the top by a horizontal plane; in other words, imagine a vault whose construction has been suspended; let's assume that D And Ε - its two arched ribs.
It is clear that both of these arches, despite the empty space DE, left between them, will be enough to carry the masonry filling the vault, if each of the horizontal rows of this array ends in a non-straight line NAR, but curved like an arc DBE: the result will then be achieved, no matter how irregular the rough fragments of which the horizontal rows of the vault are composed, provided that sufficient lift is given to the various curves, like AB in an arc DBE. In accordance with this, you can mentally divide each row of monolithic masonry into two parts: the part of the row located behind some imaginary line DBE, will hold on its own, forming something like a horizontal arch, the seam lines of which converge in one common center and which rests on the ribs D And E. Filling part S, located between the curve DBE and the inner surface of the arch, will be, as it were, suspended from the first, in some way stuck to it, thanks to the adhesion that the solution has until it completely hardens.
This explanation puts an end to objections that might be based on the lack of integrity of the frames, and proves how little importance the Romans attached to thickness and regularity. wooden planks formwork even when there was a very large distance between the ribs of the frame: for formwork, the shapes of the elements of which can be imagined from the many places where they left an imprint, long thin boards were usually taken, which had many defects, as if carelessly thrown onto small circular trusses . Their purpose was indeed not so much to support the stone structure as to serve as its form: the most that they had to carry, until the mortar hardened, was a slight load of that part of the massif, which is indicated by the letter S in our last schematic sketch.
The same frame construction of individual ribs, but on a larger scale, we find in the Basilica of Constantine (Pl. III). Above, we considered vaults that covered the galleries with a span of about 5 m, while the largest span of the vaults of the Basilica of Constantine is 23 m; this is almost the width of the nave of St. Peter's in Rome.
With such a span, the vaults required load-bearing ribs of exceptional strength; Therefore, the architect, obviously fearing the insufficiency of such simple arches as in the Colosseum, added to them the same additional supporting arches, so that the ribs of the frame in the Basilica of Constantine consist of two brick arches located one above the other (Pl. III and Fig. 24 ). This idea of ​​​​arranging the ribs of the frame in such a way as to correspondingly increase the load-bearing capacity of the vaults of a very long span was quite natural; Meanwhile, wouldn’t it be better, instead of placing the arches one above the other, to place them directly next to each other, carefully bandaging them. In this case, the cladding of the inner surface of the vault could have been more satisfactorily completed and both a larger support area and greater stability of the ribs would have been provided, while the amount of brick used would have remained the same.
This is fair: however, such an arrangement of arches directly next to each other did not change anything regarding the consumption of bricks, but the situation was different with the costs of temporary circles. When two arches are located one above the other, as in the Basilica of Constantine, then only for one, the lower one, circles are necessary; when this internal arch is installed, it itself can already serve as a support for the one that is thrown above it. On the contrary, if you pair these arches, placing them side by side instead of placing one above the other, then both of them will simultaneously load the circles; and since their weight is approximately the same, the strength of the temporary devices should be doubled. Thus, for the sake of saving on temporary circles, it was advantageous to do as the Romans did, that is, to make each edge from two brick arches overlapping one another.
It remains to be seen whether this achievement of savings on circles is devalued by the fact that with a given arrangement of arches the danger of longitudinal bending increases.
There is no doubt that an arch with a span of over 23 m and a cross-section of 0.60 m wide should collapse and collapse from its own weight when the circle is removed. But when determining the strength that a vault frame made of crushed stone and mortar should have, it should not be stipulated that the frame must remain stable and bear additional load immediately upon completion of its construction.
In fact, it is not so important that the frame has sufficient strength at the moment when it is already built and completed, as long as it has sufficient strength and stability at the moment when it is loaded with infill masonry made of crushed stone and mortar? Meanwhile, if we consider the issue from this point of view, undoubtedly the only correct one, we will be convinced that arches with a cross-sectional width of 0.60 m fully satisfied their purpose and here’s why:

Rice. 23

1. During the entire period, while the infill masonry held itself and did not yet load the circle, the frame, of course, was not exposed to any risk, being, moreover, sandwiched between the beams by wooden formwork, the purpose of which was to serve as a form forming the octagonal caissons of the vault ( Table III and Fig. 25).
2. Subsequently, when the pressure from the weight of the masonry began to be transmitted, it gradually increased, at first very slowly, and then more and more energetically, as the structure rose.
By the time pressure is transferred from the weight of the infill masonry to the arch (Fig. 23), the actual span of the arch AB was already significantly less than the span of the entire cylindrical vault. In addition, as the masonry of the vault rose higher, the working part of the arches of the frame gradually shortened and remained only on that segment of them that was not yet hidden in the infill masonry, and we see that the load-bearing capacity of the frame continuously increased along with the load, which she needed to endure; and it is quite possible that at that moment, when the upper, still wet masses of the infill masonry were in great need of support, the span of those parts of the arches that were not yet hidden by the infill masonry from. crushed stone and mortar, decreased so much that at this value the strength of the frame fully corresponded to the magnitude of the load.
In short, the strength of these ribs and their resistance to longitudinal bending increased as the span decreased AB, that is, as the need for resistance increased. Thus it is explained that such slender arches could serve as frame ribs in the construction of one of the colossal vaults built by the ancients: such a result undoubtedly represents a most remarkable achievement.

Rice. 24.	Rice. 25.

If the design of the vault is perfect, then it must be admitted that the caissons decorating this vault are not linked to the distribution of the elements of the frame, which played an important role in its construction. I give on a large scale (Figs. 24 and 25) a detail of one part of the ribs of the vault of the Basilica of Constantine.
To the left (Fig. 24) is an exposed rib, to the right (Fig. 25) is the same rib embedded in the infill masonry. As can be seen in the figure, the ribs ran along the projections on the surface of the vault separating the large octagonal caissons of the vault from each other and in this respect their location was chosen well. But the architects who were entrusted with the decorative decoration of the building came up with the idea of ​​filling the gaps between the large caissons with small square recesses, and for the sake of this fantasy the builder was forced to make recesses in these ribs to a depth corresponding to the depth of the small square caissons located on the ribs (Fig. 25) . He got out of the difficulty by resorting to a method that at first glance seems strange, but I believe that he should not be judged too harshly for these liberties with respect to architecture. To allow a contradiction between the architectural forms and the basic structure of the building, to hide the skeleton that is essential to the stability of the masses, is to create a work that condemns the mind, it is to show a lack of taste, insulting the mind with the spectacle of obvious deception. But do we have sufficient grounds to say that by hiding the brick frames of their rows, the Romans were hiding from the viewer one of the main elements of the design of these vaults? I don't think so. What exactly is the structural system of the Roman vault frames? Just an ingenious technique used during the execution of the work: these internal frames served only during construction, they made it possible to remove the vault, giving it a monolithic masonry; finally, after the solution has hardened, their independent existence seems to cease, and they appear in the arch only as its component part. From this moment on, the Roman architect no longer sees in this whole either a frame or fillings, but a homogeneous monolithic mass, and he is truly allowed not to emphasize in the external decorative finishing a distinction which, in his opinion, disappeared in the structure of the vault.

Rice. 26

That is why cases when the ancients reveal the frame of a vault in the exterior of a completed structure are extremely rare; As an example of vaults in which complete consistency between the frame and external forms is achieved, I can only cite the barrel vault in the Temple of Venus and Roma. Unfortunately, the entire upper part of this remarkable vault is destroyed, and the fragments of the lower part are insufficient and too damaged by time to make any assumptions on the basis of which its original appearance could be restored. Therefore, I present, not as reliable, but at least as very probable, those structural elements that could to some extent be identified during examination of this vault and which appear to me in the form as they are depicted in Fig. 26.
The caissons were square in shape, and the directions of the ribs of the caisson coincided with the direction of the sides of the caissons, which are located continuously, some in the direction of the axis of the vault, and others perpendicular to this axis: all of them together formed a continuous lattice of large cells, some longitudinal sides of which are horizontal, and others coincide with the direction of sections normal to the axis of the arch.
The transverse ribs of this vault are smaller in width than the same ribs in the Basilica of Constantine, but they are continuous, and not through, as in most other Roman buildings.
As for the method of erecting these brick frames, these protruding ribs outlined in relief on the inside of the vault, it is self-explanatory. As shown in our drawing, the brick ribs, together with the formwork, probably wooden, formed a strong whole before the infill was laid: horizontal ribs reinforced the transverse arches; both of them, maintaining their position thanks to the formwork used to make the caissons, formed a light vault, partly wooden, partly stone, between the circles and the infill masonry, which played the role of a frame, similar to the role of the end-to-end brick frame structure shown in the table. I. Here we find complete harmony between the structural system and the architectural forms; the architect accidentally used a brick frame as decoration, but nothing forced him to do this, he was free to choose the architectural design; and the consistency of external architectural forms with construction, observed in the temple of Venus and Roma, is not, in my opinion, serious evidence of the superiority of this building compared with others.
We have now examined the main types of frames, the lines of the masonry seams of which converge in one common center. Having now taken a general look at the types of their applications, it will be possible, without the need for any additional data, to evaluate both their useful functions and the results that they provide in the construction of vaults. But along with the advantages that they provide, is there still no reason to consider their use as fraught with some dangers? These frames, immersed in the thickness of the masonry of the vaults, apparently formed, in the still damp mass of crushed stone and mortar, a core that could not be compressed; included in a monolithic stone structure, which settles independently, without external influence, they may have interfered with the progress of shrinkage and caused the appearance of large and small cracks. If this were really the case, then the frame systems that facilitated the construction of the vaults would hasten or cause their destruction, but fortunately the situation is completely different. In fact, the masonry of the infill of the vaults is not a mass laid in one step, and it is curious how the gradual progress of construction in level, very thin layers reduces the danger of shrinkage; each layer very quickly acquires its final volume, each row shrinks in turn; and since the general shrinkage has been eliminated, there is no longer any fear of cracks. However, this remark does not apply specifically to the type of frames that we described below: it also applies to another type of structure, which we are now considering, and therefore we will not repeat it in the future.

b) Vaults on frames made of bricks laid flat.

Compared to solid brick frames shown in table. I, frames of free-standing brick arches, similar to the frame of the vault of the Basilica of Constantine, had the advantage of requiring less material; Moreover, they fulfilled their purpose quite satisfactorily. However, even if the costs are the same, a solid frame is easier to construct, and therefore it was natural to strive to create a structure that, while possessing all the advantages of a structure made of free-standing arches, would at the same time create a continuous load-bearing surface; This seems to be the origin of the new frame construction, the use of which is found in Roman vaults.

These large bricks, laid on high-quality gypsum or quick-setting mortar, formed, as it were, a thin continuous shell over the entire convex surface of the formwork; this shell, reproducing the shape of the inner surface of the vault, was a kind of curved brick flooring (Fig. 27).
In some cases, the entire frame of the vault consisted of one such flooring, but usually another flooring, similar to it, but consisting of smaller bricks, was laid on it, forming a second shell, firmly connected to the first layer of gypsum or mortar.
Thanks to this layering, a kind of protective crust was created over the entire surface of the formwork, like a light arch ABCDE(Fig. 28), which could not be moved immediately upon completion of its construction without the danger of its destruction from its own weight (Fig. 29); it gained strength as the main vault was built until it was strong enough to bear the load of the infill masonry lying on it.
In fact, the reason that prevented the immediate uncircling of this auxiliary vault was not so much the small thickness of its strong walls, but rather its semicircular outline. The stability of a brick vault laid flat is ensured by two conditions: firstly, the outline of the vault in the form of a gentle circular arch with a very small lifting boom, and secondly, its pinching in two unshakable supports. In the case of a semicircular outline, the rigidity of the arch is insufficient; to give it sufficient rigidity, you need to fill the side parts of the arch AB And DE(Fig. 28). This backfill counteracts the bending of the arch and prevents its thin walls from collapsing under the influence of its own weight. In Roman vaults, similar vaulted flooring made of brick laid flat was apparently used precisely in such cases.

Rice. 29.

The masonry of the vault had not yet loaded the circle, while its first rows were already clamping the brick auxiliary flooring to a certain level BD(Fig. 28); that part of the brick vaulted flooring that was supposed to actually bear the load, that is, its working part, reduced to a simple circular arch BCD, ended up in best conditions work. At the moment when the masonry of the main vault reached the level BD, it was already possible to remove the circles and, if necessary, move them to another place, i.e., in other words, build the vault in parts and use the same circles when constructing subsequent parts of the vault.
The Romans actually often used this technique. To be convinced of this, it is enough to pay attention to the fact that the bricks of the vaulted flooring, instead of being laid alternately and forming masonry with tied seams, are laid with through seams, like the squares of a chessboard (Fig. 27). This circumstance is fully consistent with the idea of ​​​​building a vault in separate links: if we assume that the bricks were laid in a band, then the edge of each link would be jagged; this would cause some difficulties in connecting the links to each other. By thus abolishing any connection, the Roman builders thereby eliminated all difficulties of fitting.
Savings on circling do not require proof - it is obvious.
In accordance with the remark made above regarding a similar case, it is enough for the circles to withstand the load from the weight of the vaulted flooring alone; The first row of bricks serves as formwork for the second row, and both together form a strong frame that bears the load from the masonry of the entire vault.
The vault detail shown in the following figure (Fig. 30) illustrates the application of the described vault design. This example is taken from the Baths of Caracalla, which are perhaps the most significant building of all built using this structural system.
In this example, the first of two vaulted decks is made of square bricks, with sides measuring 2 Roman feet (0.60 m) and 4 to 5 cm thick; the second flooring is made of smaller bricks - with sides ⅔ of an antique foot or approximately 20 cm. In addition, a number of bricks are placed on edge in the thickness of the second flooring; these bricks form, as it were, butts or anchor protrusions on the outer surface of the vaulted flooring.

Rice. thirty.

The purpose of the various parts of this peculiar structure is given in the previous description, and the order of the work is quite obvious.
Instead of continuous formwork, individual boards were placed on the circular truss at a distance of 2 feet from axis to axis (Fig. 30); A flooring of large square bricks was quickly laid over these milkings. Thus, the cost of wooden cladding was low, and thanks to the large size of the bricks, the first row of flooring could be laid extremely quickly.
Once the first row had been laid, the second row could be laid with less haste using smaller bricks. Indeed, the second flooring is always made of small bricks; I know of only one example of the use of bricks of the same large size for both rows in the vaults of the Pantheon (overlapping wall niches, plate XIII). The second row of bricks was supposed to overlap the seams of the first row, as we will see later; the dimensions of the second row of bricks - 20x20 cm - corresponded well to this purpose.
However, it was necessary not only to design load-bearing frame for laying the filling of the vault: it was also necessary to provide some connection between this frame and the filling, so that after unwinding the entire structure would be a single monolithic mass; It was for this purpose that bricks were used, placed on edge and included in the masonry of the lower vaulted flooring at some distance from each other (Fig. 31). These bricks, placed on edge and serving as a connection, tended to topple under the influence of their own weight; in some structures of Hadrian's Villa they tried to prevent them from tipping over by laying small bricks, leaning against the butts (Fig. 31).

Rice. 31.

This was the design of the vaults at the time of their construction; we should not, however, expect that we will find it intact in their ruins. The vaulted flooring of brick laid flat has mostly disappeared; its remains can be found at the heels of the vault, in the reentrant corners formed at the junction of the vault with the walls, in a word, in those places where these fragile vaulted floorings were best protected from destruction. In the spans of the vault, the double vaulted flooring collapsed; the original placement of square bricks can only be judged by the more or less clear imprints they left in the monolithic masonry filling the vault; Only the bricks, placed on edge, have survived everywhere, now protruding from the surface of the surviving remains of the vault (Pl. IV, Fig. 2); in some cases, these piers and brick linings, embedded in the masonry filling of the vault, survived and remained in their places, while only fragments remained of the entire flooring-frame.
Moving on to the conclusions, we can say that by using a frame made of bricks laid flat, the ancient builders pursued two goals: firstly, to provide the masonry filling of the vault with a strong and continuous supporting surface; secondly, to ensure a strong connection between the frame and the masonry. We have just examined how they fulfilled this double condition in the vaults of two famous buildings - Hadrian's Villa and the Baths of Caracalla; in ordinary cases the type of frame used in their gigantic vaults could be greatly simplified, since its advantages could be achieved at less expense.
Let us proceed to study the improvements introduced by the Romans in this design to achieve greater economy in work or materials.
In Fig. 32 shows a frame that is closest in type to the two previous examples. The first vaulted flooring is still solid, and the bricks of the second row only overlap the seams of the first flooring; The vaults of some of the halls of the Caesars' palace were laid out using this simplified method. Judging by the prints, the vaults of Sette Sale (a reservoir near the Baths of Titus) were of approximately the same type. This placement of bricks in the second row of the vaulted flooring combined the advantages that, requiring less brick consumption, it ensured a good connection between the frame and the masonry of the vault filling.

Rice. 32.

Rice. 33.

Roman builders went further - instead of covering all the seams of the lower vaulted flooring, they limited themselves to laying bricks only along the seams perpendicular to the axis of the vault (Fig. 33). Thus, the frame as a whole is a solid brick flooring, reinforced with ribs made of smaller bricks, which, according to the builders’ plans, served both to cover the seams and as stiffening ribs.
This design is found in the vaults of several tombs on the Appian Way; on the table IV, Fig. Figure 3 shows a perfectly preserved detail of the vault of one of the tombs. The bottom deck bricks measure 45 cm (11/2 ft) sideways; the size of the bricks of the ribs covering the seams is only 22 cm. The gypsum, which served as a binder, has leached over time, so that traces of the bricks of the vaulted flooring can hardly be detected. Its remains are more easily discovered in the ruins of the so-called Villa Quintilii, preserved to the left of the Appian Way, not far from the tombs just mentioned.
In several other monuments of the Appian Way, the idea of ​​​​using the upper vaulted flooring only to cover the seams is expressed even more clearly and openly; in these structures, the bricks of the upper floor are no longer laid in a continuous layer, but are located at distances from each other (Fig. 34) and precisely in those places where the action of shaking or too much load could be destructive, i.e. at the common junction point four adjacent corners of the bricks of the bottom row of flooring.

Rice. 34.

To achieve even greater savings, the top flooring should be completely eliminated. The Romans took this last bold step towards simplifying the design and reached the point that they began to build vaults with a single-row flooring; However, cases of the use of such a frame, consisting of a single-row flooring, are comparatively rare: in Roman barrel vaults I was able to find only one clearly defined example in the so-called Circus of Maxentius behind the Gate of St. Sebastian (Porta San Sebastiano) (Pl. IV, Fig. 1), where all the vaults on which the amphitheater is erected are made with a single-row flooring of large bricks.

Rice. 35.

The use of vaulted brick flooring became widespread in ancient vaults; such frames are found not only in simple cylindrical vaults, but also in vaults of the most complex shapes; they were equally used in vaults covering vast halls, as, for example, in the Baths of Caracalla, as well as in the most modest vaults of narrow aqueducts in galleries; in this latter case, the flooring is often reduced to two brick slabs measuring 60x60 cm, installed at an angle and supporting each other; in Fig. 35 shows the design of one of the many aqueduct galleries overlooking the Colosseum arena.
In other cases, instead of two inclined square bricks, they were limited to one horizontal slab that served as a ceiling (Pl. XIII).
The vaulted flooring made of brick laid flat served as a supporting structure not only for the vaults laid out in horizontal rows of crushed stone and mortar; in cases where the Romans even built free-standing arches with radial joints, they invariably provided them with a similar brick flooring from below for reinforcement. As an example of the use of such an arch with radial seams, built with an auxiliary flooring, we can point to the porticoes of the amphitheater near the Church of the Cross in Jerusalem.

Rice. 36

The same type includes overlap over water pipe in the Baths of Caracalla (Fig. 36).
Finally, I must pay attention to the four large vaults that cover the lowered sides of the huge central hall in the Baths of Caracalla. In the entire building, these vaults alone are made of masonry, the seam lines of which intersect at one point; we can say that these four barrel vaults are the only ones not only in this building, but also among all the vaults of Roman buildings that I examined in Italy. Their masonry consists of alternating rows of large bricks and tiles laid on mortar. On the table V depicts one of these arches: radial brickwork This vault, as well as the monolithic masonry laid in layers of crushed stone and mortar of other vaults, is laid out on a double vaulted flooring, which is in every way similar to the floorings of brick laid flat described above.
Based on all the examples given, one can judge the general nature of the auxiliary vaulted flooring, which was used in ancient architecture as a frame - the supporting structure of the vault. These frames, so common in antiquity, are still used in Italy. I have more than once been present at the laying of such vaulted flooring in those areas where they were used two thousand years ago with success, which is sufficiently evidenced by the surviving ruins.
Such vaulted floorings are often used to this day even in Rome itself; the closed vaults that decorate modern villas are mostly built on a floor of bricks laid flat, just like the vaults in the Baths of Caracalla; the inner surface of the vault is usually formed by one row of bricks laid flat on gypsum mortar; the rest of the masonry of the vault is a monolithic masonry made from fragments of rubble stone and mortar.

Rice. 37.

Over time, the importance of the frame and backfill in the design of vaults has changed. The Romans considered the brick frame merely as an auxiliary structural element supporting the main body of masonry infilling the vault; the latter was the main part of the structure, ensuring its strength and durability. Now the vaulted flooring has become the main, load-bearing element of the structure; in some modern vaults, this clearly expressed purpose of the main masonry of the vault - to serve only as filling - is revealed especially clearly: these vaults are made only from the bottom at the heels with regular masonry on mortar, while the upper parts of the masonry filling the vaults are simply backfilled with rubble. Italian masons call this type of vault construction volte alla volterrana and sometimes give it the expressive name volte a foglio (leaf vaults)..
In France this vault design is now rarely used, but in the last century it was used frequently. Detailed description of these vaults, given by Blondel, deserves mention (see "Cours d"architecture", t VI, chap. II). Flat, lowered vaults, which are the subject of our study, unexpectedly began to be used in French architecture in the 18th century. In in essence, their use was only a revival old tradition, preserved from time immemorial in the construction techniques of Roussillon masons; For a description of these techniques, see below.
Along the walls of the room, covered by a vault, longitudinal beams were laid, which served as supports for mobile circles, 21/2 feet wide (Fig. 37); along these circles a double flooring of bricks laid flat was laid; the bricks of each row and both rows were tightly bound together with gypsum mortar in exactly the same way as in Italy, and in the same way as the ancient Romans did. When the part of the masonry corresponding to the circular link was completed, the link moved along the guide beams for a small distance (Fig. 37); then the next part of the vaulted flooring was laid on the same circular link, etc. The backfill was laid on the thin-walled vault thus created; all this, apparently, corresponded, being much more modest in size, to the masonry of ancient vaults.
It is quite obvious that such a design is fully consistent with the ancient Roman principles of vaulting. Since the area where these vaults were used borders the Roman colonies in Provence, it is quite possible that this method of laying vaults is only a reminiscence of Roman techniques. This similarity is so obvious that the above description is quite modern system The masonry is of great interest, especially because it exhaustively confirms our conclusions based on the study of the ruins of Roman monuments.

2. Cross vaults.

So far we have looked at examples of barrel vaults. Moving now to the study of cross vaults, I would like to note their significance in Roman architecture, clarify the question under what circumstances they were used, and show with examples the use of the vault laying techniques described above in them.
We know that, as a rule, the Romans avoided crossing vaults. In the amphitheaters at Arles and Nimes we do not find a single cross vault, although their annular corridors and radial passages intersect in all directions; in the Verona Circus, only a few cases of small cylindrical vaults intersecting can be noted; in the ruins of the Colosseum, you are surprised at the insignificant number of intersecting vaults with such a large number of intersections of countless galleries.
To avoid the intersection of the vaults with each other, the Romans usually placed the heels of one of the vaults above the shelyga of the other vault (Fig. 38).

Rice. 38.

Where such a solution was feasible, it removed all difficulties; but often the insufficient height of the galleries did not make it possible to place intersecting vaults at different levels, and inevitably it was necessary to resort to cross vaults.
Another circumstance in itself entailed the use of cross vaults: the Romans often had to cover buildings consisting of a central and two side naves with vaults. With this solution, there are only two options to give access to natural light to the middle nave: either the vault should be raised at a sufficient height to place light openings below the level of the heels, or they should be pierced in the vault itself. The Romans usually settled on the second solution: this is the origin of the cross vaults above the large nave of the Basilica of Constantine (Pl. III) and the vaults above the two halls of the Baths of Caracalla - above the central and another, perfectly preserved hall, which in the 16th century. was converted into the church of Santa Maria degli Angeli. In some cases, the use of cross vaults was caused not by design requirements, but by the desire to add variety to the architectural composition. However, such cases are extremely rare; almost always the use of cross vaults was justified by both aesthetic considerations and structural requirements.

Rice. 39.	Rice. 40.

But we will not touch upon the question of exactly in what cases the Romans used cross vaults - our task is to indicate what techniques they resorted to when choosing their outlines and during construction.
Let us first consider what the outline of the ancient test vault was.
Giving preference everywhere to simpler solutions, the Romans sought to solve the cross vault in the form of the intersection of two cylindrical vaults of equal spans. Thanks to this solution, they could adopt circular curves for the outlines of the vaults and thereby avoid the elliptical outlines of circular trusses.
The Romans, in rare cases, strove for strict equality of spans of intersecting vaults; if there was an insignificant difference in the sizes of their diameters, they neglected it and limited themselves to placing the shelygi at the same level, preserving semicircular outlines in both vaults.
The central nave of the Basilica of Constantine was covered in exactly this way (Fig. 39). The size of the wider one is taken as the total height of the intersecting vaults; the cross-section of the other arch is a semicircle with a raised center, the total length of the lifting boom of which AB equal to CD. The fact that the heel of the less wide arch was slightly raised did not harm the appearance of the arch at all and even gave it a more elegant appearance. However, the difference in the size of the sides of the building covered by the vault was often too great to allow this technique to be applied. In these cases, the Romans tried to bring the solution to the design of a cross vault to the solution to the design of a vault on a square plan; in doing so, they resorted to a very simple technique, shown in Fig. 40.
The actual cross vault covered only the square ABCD, allocated in the middle part of the room; the size of the side of this square was equal to the size of the smaller side of the rectangle covered by the vault; parts of the rectangle not covered by the cross vault were covered by a continuation of the longitudinal cylindrical vault ( A.E.).

Rice. 41.

This solution was very common, but it should not be considered the only one: the Romans did not at all abandon either the solution of cross vaults on rectangular plans, or the vaults with an elliptical section that were the result of this decision. In the Baths of Diocletian, three sections of one perfectly preserved hall are covered with cross vaults, the ratio of the spans was approximately 2:3; in Fig. 41 shows the plan of these vaults, and their general view is given in Table. IX.
This vault is the most remarkable example of cross vault solutions known to me over an elongated rectangular plan; this example, however, is not the only one. Vaults of elliptical shape lasted until Byzantine architects, heirs to the traditions and aspirations of Roman art, applied a very appropriate technique in classical cross vaults, shown in Fig. 42.
Thanks to the new ingenious design of the vaults, larger or smaller irregularities in the plan no longer led to a complication of the outline of the vaults. The cheek curves could be semicircles (regardless of whether the sides of the overlapped rectangle were equal or unequal to each other); the room covered by the vault could be a quadrangle with unequal angles; the curves at the intersections of the vaults became arbitrary, and nothing prevented them from giving them a semicircular outline; all circles could be made in the form of semi-circular trusses.
Having noted the connection that exists between Roman principles and Byzantine innovation, let us return to the study of ancient cross vaults and consider the methods of their construction.
Whatever the shape of the cross vault, the Romans simplified their design, using techniques very close, at least in their basic principles, to the techniques they used in the construction of barrel vaults. The design of the cross vaults, as well as the cylindrical ones, consisted of two independent parts: a monolithic infill masonry and a through brick frame or a lightweight vaulted brick flooring that supported the infill masonry during the construction of the vault and thereby replaced, at least partially, temporary circles .

Rice. 42.

In cases where the Romans laid a cross vault on a vaulted floor, they made the corner ribs of the vault from large brick slabs; no matter how small the dimensions of the flooring bricks were, these slabs were never less than 45 cm apart; usually the size of their sides was 60 cm and the thickness was 5 cm. In most cases, these rib slabs were not preserved, but their size and shape can be judged from their imprints; You can mentally reproduce the general appearance of the frame. In Fig. 43 shows such a structure of the vaulted flooring before laying the main masonry of the vault filling.

Rice. 43.

This example is taken from the ceiling design of one of the halls of the Baths of Caracalla. Very similar versions of this solution are found in the Palace of the Caesars, Hadrian's Villa, etc. The issue of the design of the intersection of vaults is resolved even more simply in cases of using through frames. Ribs M And N were located along the lines of intersection of the arches (Table IX), and if necessary, additional arches were introduced R in the transverse direction from one abutment to another. The latter were no different from the brick arches used in laying the cylindrical vaults. In the future, we will consider only the design of the corner ribs of the cross vaults (Fig. 44).
Three parallel brick arches, connected in pairs by baked clay tiles, formed a load-bearing frame located along the corner edge. To finally complete this structure, it was only necessary to slightly trim the bricks so that the rib was shaped to match the protruding corner of the cross vault. The bricks were not pre-cut according to a template, but were simply trimmed on site. This simple treatment cost almost nothing and did not delay the work.
Difficulties arose only when laying the upper parts of the diagonal arches. Without much difficulty it was possible to close one of the arches, for example the arch M(Table IX); but at the moment when it was necessary to connect the arch to it N, difficulties inevitably arose: both parts of this second arch press on the arch on both sides M, threatening to crush her. Obviously, before laying the last bricks of the arch N, it was necessary to fill the upper cells of the through arch M. Arch M with filled cells could already withstand pressure from adjacent parts of the arch N. Thus, the construction of the vault was completed without further difficulties.

Rice. 44.

The vaults in the baths of Diocletian were made using this method. Typically, this design was used for vaults with a span of at least 15 m. In vaults with smaller spans, the load-bearing part of the structure correspondingly becomes more and more lightweight; the brick frame is gradually simplified in accordance with the reduction in the weight of the main masonry filling the vault. Following a logical series of possible changes, the Romans first abolished the intermediate paired arches of the arches type R, shown in table. IX; next they eliminated one of the three arches that formed the compound diagonal arches; finally, of these three component arches, the Roman builders destroyed two, so that the frame of the vault was reduced to arches of a single section running along each rib. Thus, in Roman architecture one can find all possible vault design options, which are transitional from a frame system to a system of vaults made of monolithic masonry without any frame.
Let us try, using examples, to characterize the various types of brick frame structures found in this successively changing series:
1. In one of the galleries of the Palatine, located in the southern part of the hill (see Table VIII), there is a frame structure that, in its appearance, is closest to the frame we took as the main type. The rib arches are located exactly the same as in the baths of Diocletian; they consist of the same number of arches, connected to each other in the same way. But in this case, due to the smaller size of the hall, the intermediate arches were considered unnecessary. In other words, the design is reduced to that shown in the table. IX, less intermediate arches R.
2. As an example of the use of diagonal ribs consisting of only two arches, I will give the cross vault over the central part of the Janus Quadrifrons arch in Rome. General form the vault is shown in the table. VII, fig. 1 ; in Fig. 45 shows a detail of the rib, freed from the masonry infill. After the previous detailed study, the order of the work is quite obvious: first, one diagonal arch was erected without finishing the laying of the other; then the top two or three cells were filled with concrete, after which the masonry of the second arch was completed.

Rice. 45.	Rice. 46.

3. Let us finally consider structures in which diagonal arches were allowed, consisting of only one row of bricks. An example of such a solution is found in the vaults of one of the halls of the Caesars' palace, the ruins of which, located separately on the Palatine site, rise above the recess of the Circus Maximus. Each of these diagonal arches (Fig. 46) consists of a single course of narrow bricks, and the masonry of the arches includes large square tiles, hewn in place. These nlits protrude from the arch to the right and left, and, entering the thickness of the monolithic masonry of the vault, thus provide a strong connection between it and the brick frame.
After going through a series of transformations, the structure of the antique vault frame came to its simplest form. A study of its further development over subsequent centuries to the present day would take this work beyond the scope of the study of Roman building art; we would have to move on to the Middle Ages and consider the vaults of Western Europe, erected between the 11th and 17th centuries. In these vaults we find the same diagonal ribs and projecting double girth arches; but in this case the purpose of these arches is different. In Roman vaults, the frame is important only during the time when the masonry is not yet fully strengthened and needs additional support; after the final hardening of the frame masonry, it merges with the surrounding infill masonry and works equally with the entire masonry due to the adhesion of all parts. The Gothic frame, which was no less important during the construction of the vault, retained its independent significance even after the unwinding; it completely bears the load from the filling of large cut stone between the ribs and transmits this load in the form of a thrust, which is carried by massive buttresses or the back support of flying buttresses. The balancing systems in ancient vaults and in Gothic vaults are significantly different. The similarity between these types of vaults can only be established by comparing them during construction; but under these conditions the similarity is undeniable. Gothic vaults provide only a new interpretation of the basic elements of cross vaults from the time of the Roman Empire. A detailed study of the common features and differences between ancient and Gothic vaults goes beyond the scope of the task set in our work. We have given the main options for frame designs in Roman vaults and will indicate in the next section how the same design principles extended to vaults with a round plan, i.e., domes and semi-domes.

3. Vaults on bases that are round in plan.

Of all types of vaults, spherical vaults place the least load on the circles. Each horizontal section of such a vault is a closed ring, which itself strives to maintain balance. It is obvious that a dome with a plan in the form of a regular circle requires less a strong frame than with a plan free form consisting of irregular curves.
A number of ancient domes were erected using only simple wooden circles; an example is the vault of a large building erected at the gates of Rome in honor of the mother of Emperor Constantine.
However, these properties, which are a consequence of surface curvature, decrease as the radius increases. In domes with a span approaching that of the Pantheon in Rome, the curvature is so small that all the advantages resulting from it lose all significance. Even with smaller spans, the Romans apparently feared the possibility of the circles collapsing under the load of the weight of the masonry; in cases where the span reached 20 m, they resorted to constructing a frame, considering it capable of facilitating the work of temporary circles.
To facilitate the work of the circle, the Romans in some cases used a brick frame, similar to that shown in tab. I.
The implementation of this frame was made difficult by the convex shape of the arch. It was necessary to lay rows of bricks along meridians with changing directions. The dimensions of the frame cells changed all the time, consistently decreasing. Obviously, these difficulties should have limited the use of this system. Domes of this design are extremely rare; Of these, the most interesting is the dome of the building known as Torre de Schiavi, to the left of the road leading from Rome to Praeneste. To avoid the difficulties caused by the reduction of cells, the use of a frame laid over the entire surface of the vault was replaced by individual meridional ribs dividing the vault into a number of sections in the form of spherical wedges.
An example of a vault of such a design is the vault of the ancient baths adjacent to the Pantheon in Rome; on the table X shows part of the frame of the lower part of the vault; the upper part is difficult to restore due to the lack of accurate data. It is difficult to determine whether these belts of bricks were interrupted suddenly, resting on rings, as in the Pantheon (Fig. 49), or whether they intersected like ribs in cross vaults. The vault is now cut in half by the street, and its surviving ruins provide no more information than that which formed the basis for the schematic reconstruction of the vault shown in Table 1. X. These ruins are of great interest from another point of view: it can be assumed that they are the remains of the baths of Agrippa and, therefore, date back approximately to the time when speaking of which Vitruvius barely mentions building materials made of baked clay. If this assumption is correct, then the described example of the use of a brick frame in vaults is one of the most ancient in the history of building art. The general appearance of the ruins does not contradict this: the entire structure, down to the smallest detail, was made extremely carefully - the caring attitude and painstaking attention of the builder is felt in everything; careful execution indicates the use of a new construction technique. With the acquisition of sufficient skills, the Romans began to pay less attention to the thoroughness of the work; in this case, a successful solution to the design of the vaults fully corresponds to excellent execution; in the vaults of a later period one can find frames of lighter construction, but we will not find such careful finishing and forms of such impeccable regularity.
The dome of the building, which bears the controversial name of the Temple of Minerva the Physician, is an example of the same vault design, but differs sharply from the one described in its rough execution. Part of this vault is shown in the table. XI, and the general plan is in Fig. 47; From this drawing one can fully judge the incorrectness of this plan.

Rice. 47.

The general composition of the building is quite clear: in front of us is a vault supported by small sails on a decagonal drum. The vertices of the polygon serve as the bases of ten arches, dividing the dome into ten equal parts. Some of these spherical triangles are in turn divided by secondary arches. The entire structure as a whole is a well-designed frame diagram, understandable at first glance and not requiring additional explanation.
However, upon closer examination, we will notice some uncertainty in the execution of such a simple design and discover strange errors in its details. The frame at the heel is extremely massive, as if an error was made in the calculation when determining its dimensions; then, at a height of several meters above the heel, it becomes much lighter - apparently, during work, the builders noticed the excessive strength of the frame and abandoned their original intentions for reasons of economy. The main arches, the supports of which are located at the vertices of the polygonal plan, are composed of five branches at the heel, and only three at the apex. The decrease in the number of branches could be explained by the desire to increase the cross-section of the main arches in accordance with the increase in the cross-section of the vault at the heel. This explanation in itself would be completely justified, but taking into account the entire set of facts, the first assumption should be recognized as the only correct one. In other words, the structure of the frame was undoubtedly disfigured, due to the fact that its original design underwent radical changes during construction. This deviation from the main plan is especially clearly expressed in the execution of the secondary arches located in separate sections of the dome.
In some sections we see two arches, breaking off almost at the very beginning; they have no constructive meaning because they are not closed; in other sections there is only one arch, rising to an insignificant height and suddenly breaking off, and therefore as unnecessary as in the first case; finally, in a number of sections the builders, having become convinced of the uselessness of these auxiliary arches, completely abandoned them. Thus, in the case under consideration, we find in the same vault sections subdivided by two open arches, separated by one arch, and, finally, sections without any dividing arches. These arches, begun with masonry at the heel, then changed or finally interrupted, showed an indecision unusual in Roman architecture. The Temple of Minerva the Healer was apparently built in the last years of the Roman state; both in the plan and in the external appearance of this building there are many features characteristic of an era close to the heyday of Byzantium. In the vaults of the baths of Agrippa we see the emergence of new construction techniques, and in the vault of the temple of Minerva the Healer we see decline. These vaults seem to embody. represent the extreme limits in the development of a building tradition that lasted with amazing constancy throughout the long period of the Roman Empire.
It is worth mentioning how the techniques discussed in relation to spherical domes were modified in semi-domed vaults and vaulted niches, and how structures with vaulted brick flooring were implemented in them. Table XI, XII and XIII give fairly clear answers to these questions: in Table. XII and XIII show two different designs for covering niches with vaulted brick floorings; on the table XI - design of ceilings for large niches with a frame of individual arches.
You should pay attention to how successfully the thrust of the meridional arch, directed at the mouth of the hemiarch, is perceived by means of its end resting on the powerful cheek arch.
In spherical vaults, making the frame is always a difficult job, and therefore the Roman builders, less than any others, considered it necessary to start it from the very heel of the vault; the entire lower part of the masonry was built up to a certain level without any brick frame, sometimes even without any circles; in this case, the curvature of the dome was controlled using only a cord fixed in the center of the dome, the length of which was equal to the radius of the dome.

Rice. 48.

Other examples include the vaulted ceilings of the niches in the Baths of Caracalla - it is very likely that they were built in the same way (Fig. 48).
In order not to deviate from the task set before me - to become familiar with the design of ancient vaults through personal study of individual monuments - I should not mention the Pantheon, since its dome, being covered with a thick layer of plaster, is a system of caissons without any visible indication of presence of a frame. However, in view of the extreme importance of this structure, I will still turn to this example, using the testimony of another person.
During the renovation of the vault under Pope Boniface, Piranesi took the opportunity to study the details. It was necessary to beat off and restore the plaster, which had been damaged and collapsed over time in various parts of the vault; For this purpose, movable scaffolding was installed, moving along the ledge of the cornice and rotating around an axis fixed at the top of the dome. This ingenious device made it possible for Piranesi, who immortalized the monuments of ancient Rome in his drawings, to study in great detail the entire inner surface of the vault. In Piranesi's works we often find too loose assumptions, but in this case his testimony deserves more confidence. The position from which Piranesi was able to examine the vault ensures to a certain extent the veracity of its depiction. The careful reproduction of parts visible today only partially confirms the authenticity of the image and those details that we are not able to see.

Rice. 49.

Rice. 49 accurately reproduces Piranesi's drawing of the construction of the internal frame of one-eighth of the dome.
In the Pantheon, as well as in the Temple of Minerva the Healer, the vault frame consists of meridian arches CC(Fig. 49). On unloading arches BB the load is transferred from them, thereby achieving the possibility of leaving voids that facilitate the laying of the drum, and, finally, the intermediate arches subdivide the part of the dome surface enclosed between the two meridional arches into smaller parts. Thus, the purpose of the frame elements in the lower part of the dome is clearly visible from their designs.
Let us now consider the construction of the brick frame in the upper part of the dome. A comparison of two figures (50 and 51), depicting two successive views of the structure of the upper part of the dome, shows the order of construction of the structure, which was apparently carried out in two stages.
Meridian arches at the top CC usually ended as shown in the left figure (Fig. 50). Their desire to get closer was extinguished by a brick ring framing a round hole at the top of the vault, and the pressure from them was transmitted to the ring through eight touching arches.
The upper ring, compressed by these eight arches, could withstand the pressure of the meridional arches only for a certain time; as the filling was laid, the force grew and threatened to crush the ring Ε . Ring strength Ε was considered sufficient until the masonry filling of the vault reached the level Ν ; from this moment it was considered necessary to strengthen the entire structure of the frame of the upper part of the vault; the second concentric ring was laid out SSS, which, just like the ring bordering the upper hole, was supported by arches OO, - was also supported by a system of arches, indicated in the right figure by the letters TT.

Rice. 50.	Rice. 51.

This is the origin of arches TT and rings S, which make up the difference in Figures 50 and 51. This interpretation is completely justified: the ring S, concentric to the ring bordering the upper hole, could not be realized without auxiliary arches T; the latter, in turn, could not be erected until the filling reached the level N, since otherwise there would be nothing to install them on and something to absorb their thrust. In other words, the necessary sequence of construction of the upper part of the dome is completely justified and justified. At the beginning, the meridional arches rested with their upper ends only on the ring E; as soon as the masonry filling the dome reached the level N, this ring was reinforced by a ring S, placed at some distance from it. When adopting such a sequence in the construction of the frame, its purpose and its entire structure, as well as the order of work itself, become quite clear.
I present this explanation as an assumption that is subject to further verification, and draw the attention of researchers to those circumstances that can serve as an explanation for the questions that arise when studying this huge dome: nineteen centuries of its existence serve as the best proof of the correctness of the techniques used; reliable knowledge and study of these methods would contribute to the development of the art of construction and would illuminate an important fact in the history of ancient architecture.
The dome of the Pantheon rests directly on a round drum; This was also the solution for the first Roman domes, such as the dome over the round hall of the Baths of Agrippa (Plate X) and the domes over all round rooms in the first years of the empire. The design on sails, which we mentioned when describing the dome of the temple of Minerva the Healer, penetrated into Roman architecture very late. Examples of its use mostly date back to the period of decline that followed the reign of Diocletian and preceded the heyday of Byzantium. In the temple of Minerva the Healer, sails are used to transition from a spherical vault to a ten-sided base; in Torre de Schiavi the dome is erected using rather crude sails on an octagonal plan. The dome of the central part of the tomb of Placidia in Ravenna, a monument closer to ancient than to Byzantine art, is erected on a square plan.
Thus, gradually ceilings in the form of domes on sails appeared in Roman buildings, from which in the 6th century, under Justinian, architects created a completely new, independent structural system.

4. Special types of vault construction; ways to give vaults greater strength: the use of buttresses, etc.

The auxiliary structures of the frame type that we considered, used by the Romans in the construction of vaults, can be divided into two types: to one type we can include arched brick frames with radial seams, and brick lattice frames. frames and free-standing arches made of brick; the second includes vaulted flooring made of brick laid flat, and other types of auxiliary structures of this type. This classification, due to its great imperfections, cannot fully cover all possible solutions.
Often the Romans used only one of these types of vault frame structures; sometimes we find a combination of both types in their buildings; An example of such a solution is the vault covering one of the halls of the Palatine (Pl. VI) and representing a system of supporting arches, led along a vaulted flooring from slabs laid flat. These two structural systems complement each other, and the architect combined a continuous deck with a rigid frame of brick arches with radial joints in the design of the vault.
It can be assumed that the Romans did not recognize their constructive solutions universal and strict rules; They did not consider it possible, given the endlessly changing conditions of construction and the demands placed on buildings, to use the same unshakable methods. In this regard, one cannot help but notice a clear preference in the choice of certain building materials or techniques in performing construction work: in Rome, brick frames are used in the construction of vaults; in Pompeii, for example, the frame is made of completely different materials, and the appearance of the vaults changes dramatically. The architect does not limit himself to the use of brick frames or the construction of a vaulted flooring of brick laid flat; he introduces an auxiliary structure between the formwork and the masonry filling the vault, in which, however, one should not look for similarities to the skillfully lightweight frame that we described above. This structure consists of a continuous layer of tuff fragments and mortar covering the formwork in the form of a shell, the process of which is similar to crushed stone paving. The purpose of the vault frame is performed here by an auxiliary thin vault made of almost raw materials, which takes on the load from the weight of the infill masonry, as in the case of using a vaulted brick flooring laid flat. This type of vault construction, most often found in Pompeii, is most clearly expressed in the vaults of the corridors of the arena, the galleries of both theaters and in the halls of the lower floor of the so-called house of Diomede, etc.
In Verona we no longer see the use of tuff or brick; they are replaced by pebbles mined in the river Ech (Adiga), from which a similar thin-walled vault is laid, used to support the infill masonry of the arches of the amphitheater corridors.
In cases where the vaults have small spans and are at a small height from the ground, the Romans changed the methods of their construction and abandoned the use of circles and frames; they erect vaults directly on an earthen embankment, which serves as a kind of formwork; The vault found in the ancient cemetery in Vienna was built in this way, and the vaults in the basement of one of the main temples on the Palatine were built using the same method. In this case, the earthen embankment, which served as formwork during the construction of the vault, remained not removed and was preserved in the form in which it was completed by the builders.
We see how ways to achieve savings on auxiliary devices are changing, while the basic principles of vault construction remain unchanged; I want to show with a number of examples what various forms this idea took among the Romans when it was resolved.
So far I have described vaults with a curved lower surface; the curvilinearity of the outlines of the circles in itself already presented difficulties in the work, and the Romans began to look for more economical solutions in abandoning curvilinear outlines. We see an attempt at such a solution in the theater in Taormina. The covering of large niches was designed in the form of a lintel with a broken outline, replacing a cylindrical vault (Pl. XV, Fig. 5). The easiest way to understand this extraordinary design is to imagine a pointed arch made up of rectilinear elements resting against each other; It is clear that with this outline of the ceiling, the circles could have been two thick boards resting against each other. This trick cannot be called an exception in the Roman building art: in the plain surrounding Rome, near the rounded end of the Circus of Maxentius, I discovered ancient structures of modest appearance, in which the cross-section of vaults, oblong in plan, is similar to these ceilings of niches in Taormina. The circles of such a simplified vault exactly correspond to the rafters of gable roofs. It seems to me that it would be difficult to find a better example of the freedom with which the Romans found solutions based on the principle of economy that I have tried to highlight.
Freely choosing examples of the implementation of this idea, the Romans did not miss a single opportunity from which they could benefit. Realizing that the pressure on the circles from the weight of the masonry was much greater at the top of the vault than at its supports, they tried to use masonry of various designs in the corresponding parts of the vault.
An example of such a solution is the double arch shown in Fig. 2 tables XV; its lower part is made of solid masonry made of large bricks, and the upper part is a brick frame filled with crushed stone and mortar. In Fig. 1 of the same table shows the large arches of the lower floor of the Pantheon, the lower parts of which are tied together; the upper parts are three separate arches, laid out independently, without ligation; the lower arch was used as a circle for laying the upper arches.
The Romans, in addition, used the adhesive force of the mortar and erected small vaults without any circles; in some water supply galleries in Greece we find such a solution, and an example is the covering of the water supply galleries in the porticoes of Eleusis (Fig. 52).

Rice. 52.

Sectorial bricks were laid here on thick layers of mortar; the two bottom bricks were laid quite simply; after they had already been installed in place and the mortar fastening them to the previously laid part of the masonry had hardened, the keystone was placed in the place prepared for it; In this way, the laying of the vault could be carried out without any auxiliary devices.
In the case of a concentrated load or the need to create support for a transverse wall, it was necessary to strengthen a certain section of the vault structure; in these cases, Roman builders abandoned the usual frame hidden in the infill masonry and resorted to constructing girth arches protruding from the masonry; sometimes the heels of these arches rested on pilasters, but more often the Romans limited themselves to the fact that the arches protruded from the surface of the vault only in the upper part of the vault, while the lower parts of the girth arches remained hidden in the infill masonry (Fig. 53).
Thanks to this technique, in an overloaded area the arch receives the necessary reinforcement; at the same time, the pilasters are completely abolished, and the room is freed from unnecessary protrusions, while the walls along the entire perimeter are given a continuously flat surface.
There is no need to increase here the number of examples of these special techniques and their application in individual particular cases; they clearly demonstrate the principle of reasonable economy, which is visible in all cases with equal clarity, despite all the variety of techniques.
Considering that the questions about the methods of constructing vaults have been sufficiently clarified, let us move on to consider the issue of constructing support elements that perceive thrust. At first glance, it seems that this issue does not apply to the structural vault systems we are considering. Indeed, in these structures, the perception by special devices of the thrust that usually occurs in an arch made of wedge stones is not so important; the entire vault is a monolithic massive body, and the main task is to create sufficiently strong supports that can withstand the pressure from the weight of the vault.

Rice. 53.

The ability of monolithic vaults to maintain their shape without any additional supporting abutments was, it would seem, their main advantage; this property is too elementary for the Roman builders to not notice; they, however, did not lose sight of the dangers that this design of the vaults concealed. The erected vault is loaded gradually, and its deformations sometimes occur for quite a long time; the top of the arch gradually descends, and its lower lateral parts tend to diverge. If the possibility of these movements is not prevented, there is a danger of serious damage as a result of these deformations; after their completion, internal stresses accumulate in the masonry of the vault, and the vault can be compared to a loaded powerful spring resting on two supports. It is clear that the masonry of the vault should not be exposed to such working conditions; it is necessary to combat the appearance of deformations, and the best way for this is to firmly secure the expanding elements of the vault with powerful buttresses. This, in my opinion, is the origin of the buttresses used in ancient vaults. The figure shown here. 54 gives a clear idea of ​​their shape, size and location.
The buttresses of the Church of Santa Maria degli Angeli, the Temple of Peace and almost all the great Roman cross vaults, with a few exceptions, have a similar appearance. In buildings with barrel vaults, buttresses are spaced less frequently and have a smaller overhang; in buildings with a circular plan, the use of buttresses is an exception. This sequence, however, is so natural that it does not require additional explanation.
In general, the Romans used external buttresses in very rare cases; taking care to ensure the stability and strength of the vaults, as well as other parts of the buildings, they avoided such devices; Instead of erecting special buttresses, they looked for solutions that would ensure the stability of the vaults by the appropriate arrangement of individual parts of the building. In this regard, a number of fruitful lessons can be learned from studying the layout of large Roman structures.

Rice. 54.

We will not give here a number of examples of such techniques, which are equally understandable and witty, but which, however, do not lend themselves to precise calculations; the direction of thought that guided the Romans can be considered fairly established. The essence of their methods is easy to understand from a detailed study of the plans of such large structures as the baths of Caracalla, Diocletian and Titus, the Palatine and the like; you are convinced with what persistence and with what various techniques the Romans avoided work intended solely to ensure the stability of the vaults; in almost all cases, structural elements intended for this purpose are simultaneously used in connection with the main purpose of the structure.
In the case, for example, when a rectangular room is covered with a cross vault, the Romans placed the heels A of the vault not exactly in the corners of the room, which would have caused the construction of protruding buttresses, but at some distance from the outer walls B.C., as shown in Fig. 55.

Rice. 55.

With this decision, areas AB the transverse walls were replaced by buttresses; in the case where the width of the room was less than its depth, the advantages of this solution are further complemented by the advantages of the cross-vault design with a square floor plan (see Fig. 40); buttresses are introduced inside the room, being part of the internal walls and increasing the usable area of ​​the room without additional costs. We find this solution in almost all cases of intersecting barrel vaults; We find a large number of wonderful examples of such a solution in the baths of Caracalla.
The plan for the Basilica of Constantine is an example of another type of solution to the same problem: the cross vaults of the middle nave were too large a span to not be strengthened by the construction of powerful buttresses. Such buttresses are the transverse walls indicated in Fig. 56 letters A, B, C And D.

Rice. 56.

However, these walls are not given the appearance of ordinary buttresses attached to the supporting pylons of a large cross vault; cylindrical vaults were thrown from one wall to another, which formed the space AB, used as a side nave.
In this way, they ensured that the buttresses stopped blocking the building from the outside; they were no longer elements that were specifically designed to impart strength to the structure, but were included in the usual solution in which the individual parts of the building mutually support each other, without causing the need for additional and unnecessary devices.
In cases where there was a possibility of free choice of means, Roman architects still instinctively settled on the most simple solution, which consisted in increasing the size of the supports of the vaults, however, arranging large voids in the thickness of these supports to save masonry when constructing stone masses of increased sizes; This method was used in the construction of the Pantheon of Agrippa (Table XIII).
The walls of the Pantheon along the entire perimeter are a solid stone drum, lightened by a number of internal voids located one above the other, the placement of which I try to make clear by showing them without the wall cladding hiding them.
In the spaces between these voids, which facilitate the masonry of the walls, and the covered arches, there are recesses in the form of niches, covered with arches, convexly facing in the direction opposite to the direction of action of the thrust.
The Romans lightened their stone structures, subject to thrust, in two ways; they either left voids inside them, covered with cylindrical vaults, or arranged niches in them with half-domed ceilings; similar constructive techniques can be found in the supporting walls of ancient vaults, in retaining walls (Table XIV, Fig. 1).
In all these cases, their purpose is the same: by allowing the overall thickness and base area of ​​the wall to be increased, they increase its stability without significantly increasing its cost.
Simultaneously with the construction of powerful stone massive supports, the Romans tried to reduce the danger of the thrust by using very light materials to build vaults; during the construction of ancient vaults, pumice was constantly used; The large number of examples that confirm the use of pumice precisely in those parts of the arch where weight reduction is especially important does not give us the right to consider this an accident. Most of the vaults in the Colosseum, in the Baths of Titus and Caracalla are built from very porous volcanic tuff, from which all dense stones have been carefully removed.
Given in the compilation work of Isidore of Seville short description, borrowed, apparently, from one of the Roman authors, absolutely accurately sets out the custom of leaving the lightest building materials for laying vaults.
Another circumstance is often associated with the idea of ​​​​lightening the vaults, but, in my opinion, too much importance was attached to it. This is the presence of monolithic fillings of the vaults of clay pots in the masonry.
The insignificant part of the total volume of the vaults that pots usually occupy, and mainly the way they are placed, rather lead us to believe that their use is completely inconsistent with theoretical considerations based on the use of the light weight of these hollow pots. Indeed, if the Romans hoped to reduce the weight, and therefore the expansion, by introducing these pots into the masonry of the vaults, we should have found them in the upper parts of the vault, where the greatest weight of materials should be avoided.
We don't actually see this; Moreover, most often we see exactly the opposite.
The use of these clay pots can be studied from a 4th century monument called in this connection Torre Pignatarra (Pot Tower); baked clay pots embedded in masonry were also found in the vault of the temple of Minerva the Healer (Minerva Medica) (Pl. XI); Finally, I examined the use of these pots in a number of tombs located along the Via Labicana and mainly in the vaults of the Circus of Maxentius, located outside the Gate of St. Sebastian: in all these cases they are found placed in the lateral parts of the vaults. In Fig. 1 table IV shows the placement of pots in the masonry of the last mentioned monument; Sometimes they are found in the masonry of the ceilings of openings, but more often they are located directly above the supporting walls, and their number is increasing! in those places where their main quality - low weight - cannot be used at all. I met them even in the thickness of the wall; I will give one of many examples of such unexpected placement: when studying the main facade of the Temple of Minerva the Healer (Minerva Medica), you can find such a pot on the right side, slightly above the arch of the doorway, hidden in the masonry of the wall, directly behind the cladding. In short, we can conclude from the above facts that when placing these clay pots, the possibility of using their light weight was not taken into account.
Apparently, the origin of the use of pots found in the masonry of Roman monuments can be explained as follows.
Liquid food products for the population of Rome were delivered to the city in clay pots; The townspeople did not have anything to send to them in exchange for the products they received, and the large number of such already used and little valuable dishes greatly constrained them. Together with the rest of the garbage, they took these pots to what is now called Monte Testaccio (Pot Mountain); this hill with such a characteristic name consists entirely of fragments of pottery. The builders came up with the idea of ​​using this pottery as building material; these pots were artificial material of excellent quality, not exceeding the cost of the rubble stone that they replaced. Due to the significantly lower weight of pots compared to ordinary stone, they were used mainly in the masonry of the upper parts of the building. However, the desire to achieve them by reducing the weight and load of the vaults seems alien to the Romans; we find such a solution in the buildings of Ravenna and Milan; it is difficult to decide whether the vaults, lightened by embedding clay pots into the masonry, are the own invention of the Lombard architects, but in any case it can be considered most likely that this ingenious solution was not borrowed by them from the Romans. More plausible is the assumption that this solution, applied in the dome of the Church of St. Vitale (San Vitale), came to Italy the same way as architectural solution this temple. This assumption thus attributes all the credit for the first conscious use of clay pots in the masonry of vaults to the architects of the Byzantine school.
In general, when studying purely Roman buildings, it should be recognized that the use of clay pots in their history is secondary, and. the study of their application does not provide grounds for any important conclusions that would complement or clarify the principles we set out in our study.

Rice. 57.	Rice. 58

One of the given drawings (Fig. 54) reveals one significant feature of ancient vaults: these vaults simultaneously serve as the top covering for the buildings they cover; the Romans never built roofs according to wooden rafters over the vaults. Roman builders apparently considered the protection of stone vaults by roofing over wooden rafters, that is, the use of a structure made of expensive, unstable and short-lived material, as a vicious system of duplicating the structure. The Roman architect either uses wooden rafters for roofing, abandoning vaults, or resorts to vaulted structures; in this case, the yun does not make a wooden roof; vaults perform all functions: metal sheets or tiles are laid on their outer surface to protect from rain; sometimes the leveled flat surface of the arch is covered with a thin layer of thick, thick cement mortar (Fig. 57).
This type includes whole line vaults in the Baths of Caracalla: the masonry of the vaults at the top ends with an almost horizontal platform; The last layer of masonry is covered with a mosaic of colored marble and serves as the floor of a magnificent terrace.
In cases where the outer surface of the vault is covered with tiles or metal sheets, it is given the shape of a pitched roof, which it replaces.
An interesting example of such a solution is the vault of the Church of Santa Maria degli Angeli (Fig. 54). Inside it is covered with a series of cross vaults; if you imagine a special roof over each of the barrel vaults, then their mutual intersections will create exactly the shape that is given to the outer surfaces of the vaults; the location of the valleys exactly corresponds to the ribs of the cross vaults; this solution is the most natural and best ensures the free flow of rainwater. A similar solution is found in the Parisian baths, in the Basilica of Constantine, etc.; Only in the case of spherical domes the shape of the outer surface corresponds to the convex shape of the dome, and the section along such a dome has the form shown in Fig. 58.
This exception to general admission the decision is quite justified if we take into account that to create a horizontal outer surface it would be necessary to increase the volume of the masonry to a volume significantly exceeding half the useful volume of the dome. The Romans saw this decision as an unacceptable excess; in this we see one of the most characteristic expressions of the Romans of how, having a certain system of views, the principles of which cannot be absolute, they knew how to refrain from extreme decisions resulting from the usual methods they adopted.
In our study of ancient vaults, only the following questions remained unclear. What ensured the safety of a number of vaults? What reasons led to the destruction of other vaults? Finally, what methods did the Romans use to restore partial damage to the vaults and prevent their final destruction?
Among the reasons for the destruction of vaults made in monolithic masonry of crushed stone and mortar, we should first of all mention the influence of tremors and uneven soil settlement. As the next reason in order, it is necessary to note the destructive effect of large plants growing on arches; at first glance it seems insignificant, but the Romans attached very serious importance to it. Roman laws reflect the measures by which they tried to prevent this danger, establishing gaps between green spaces and aqueducts, for which the appearance of cracks is especially dangerous. The Senate adopted a resolution prohibiting, starting from 11 BC. e., plant plants less than 15 feet from aqueducts; We learn about this from the treatise “On Aqueducts” by Frontin, and three centuries later this decree is confirmed and receives even greater clarification in the constitutions of Emperor Constantine.
And indeed, the danger that they tried to prevent was very serious; It is difficult to imagine the size of those parts of the masonry that peel off under the influence of plant roots. Perhaps the destructive effect of these imperceptibly acting forces can only be compared with the devastation caused by human hands.
Regardless of the causes of damage, the restoration of Roman vaults was carried out by bringing up a second brick vault with radial seams.
In the vicinity of Rome there are a number of examples of aqueduct vaults reinforced with such an additional vault, erected from the inside and compensating for the insufficient strength of the frame supporting the damaged masonry of the vault; rice. 2 on the table XIV depicts such an arch erected from below, strengthening the arch of the aqueduct.
The example shown in the figure was taken by me from an arcade near Lateran, the ruins of which adjoin the chapel of Scale Santa.
The method of erecting these subsidiary arches is as simple as it is ingenious. A new arch to support the cracked arch was erected without an exact fit to the surface of the old arch; a gap was deliberately left between the upper surface of the new and the lower surface of the damaged arch; this gap was laid only on one front side in such a way that there was a void between both arches, which was then filled with dense concrete, forming a kind of spacer between them.
This was a technique that was sometimes simplified by the fact that additional arches were brought close to the cracked one - without installing this gasket. In this way, in my opinion, a number of monuments in Pompeii, damaged during the earthquakes that preceded the great eruption, were restored. Apparently, both the baths and the amphitheater were restored in the same way. As a final example, I will cite an ancient vault, known only by description, which was, as the original says, “supported by supporting arches” of double thickness, mounted on independent supports (Orelli, n° 3328). If desired, another explanation of the arches of Pompeii could be given, but the document I have just mentioned eliminates the need for a discussion on this issue, the results of which might not be sufficiently definite; one may doubt the choice of interpretation of the purpose of the Pompeian arches, but with even greater right one can assert that exactly the same arches were used by ancient architects to protect damaged vaults from collapse.

Here and below we are talking about Italy at the end of the 19th century. - Approx. ed.
Regarding the sense in which we need to understand the generality of scale here, as well as regarding our use of the conventional method of depiction, see the notes to the tables at the end of this work.
Minerva Medica.
As proof of the authenticity of his image, Piranesi cites the following: he says that he depicted. the internal view of the dome (Fig. 49) as the dome appeared before him when it was cleaned of antique plaster.
Now this vault has been destroyed, for more information about it, see Le Blant, Monuments of Christian Writing in Gaul, vol. II, p. 125. Found in the embankment that formed the core of the vault, a stone with an incised inscription left an imprint in the masonry of the vault , by which construction techniques can be judged.
The described arches serve as unloading arches, transferring the load from the overlying parts of the wall to the strong parts of the base. They are almost entirely covered with masonry, and it is quite obvious that they were laid with masonry after the completion of laying the arches along the circles. Using this masonry as formwork would be a mistake; Outwardly, it would give the impression of achieving unloading, but in fact we would have a single monolithic masonry in which all forces are transmitted vertically, as in the case of the absence of an unloading arch.
“Sfungia, lapis creatus ex aqua, levis ac fistulosus et cameris aptus” (“Spongy stone formed in water, light and spongy, suitable for laying vaults”). Origin., lib. XIX, cap. Χ.
It is worth remembering when studying the use of these clay pots in ancient masonry about clay vases, which, along with metal vessels, according to Vitruvius, served to improve the resonance of large meeting halls.
Such a comparison would, in my opinion, be purely coincidental. Indeed, as understandable as attempts to improve acoustics in theaters are, they are just as unnecessary in the construction of tombs like Torre Pignatarra, or monuments along the road to Praeneste. In addition, Vitruvius does not say that these vases were walled up in the thickness of the walls of theater buildings; they were simply installed under the stepped seats of the amphitheater (Vitruvius, book V, 5, 1). Thus, drawing an analogy between these two cases of using clay pots is devoid of any basis.
See the description of vaults made of hollow pipes in the work of de Dartein on the architecture of Lombardy, who made available to me the results of his research, which helped me to illuminate the question of the origin of vaults made of hollow clay pots. De Dartein believes that the beginnings of this system of construction go back to at least the 4th century; he notes its use not only in the church of St. Vitaliy in Ravenna, but also in the Baptistery of Ravenna, restored and decorated by Archbishop Neon (423-430) and in a very ancient chapel near the temple of St. Ambrose in Milan in the chapel of St. Satire.
Frontin. De aquaed., n. 126 and 127; Cod. Theod., lib. XV, tit. II, I. 1 ; Cf. Cassiod. Variaruir. lib. II, ep. 39; lib. V, ep. 38; lib. VII, form. 6.
Compare these instructions of ancient authors with the instructions of Alberti in the sixth chapter of the tenth book of his treatise “On Architecture”.

(straight or curved).

Vaults allow you to cover large spaces without additional intermediate supports; they are used mainly in round, polygonal or elliptical rooms.

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  Vault structures, i.e. arched-dome floor system was the next step in the development of architecture. She was preceded by post-beam system, which is based on the use of tree trunks as the main building material. Although stone blocks and bricks soon replaced wood, the post-and-beam system (i.e., a structure whose elements meet at right angles) remained the basic principle of construction in the Ancient World - in the architecture of Ancient Egypt and Ancient Greece. The bending strength of the stone limited the width of the span in a post-and-beam structure to approximately 5 m. (Those vaults that are still found in the architecture of these periods, for example, the casemates of the Tiryns acropolis and shaft tombs are called false codes, because unlike the classical versions, they did not transmit thrust forces and resembled them only externally).

  The situation changed only with the invention of fairly reliable binders - solutions such as cement and concrete, as well as with the development of science, which made it possible to calculate more complex curved structures. The use of curved vaults, where the stone no longer works in bending, but in compression, and therefore exhibits higher strength, made it possible to significantly exceed the above-mentioned span size of 5 meters of the beam-post system.

  Although barrel vaults appeared already in 4-3 thousand BC. in Egypt and Mesopotamia, the widespread use of the arched-dome ceiling system began only in the architecture of Ancient Rome. It is customary to attribute the invention of the arch and dome to this time, as well as the main types of vaults, which are based on these two structural elements. Over time, the number of these types has increased.

  The vaults in ancient Roman construction, as well as in its successors - Romanesque and Byzantine architecture, were quite heavy, therefore, in order to withstand the weight of the ceilings, the supporting walls for these vaults were built very thick and massive. The load in such structures was transferred directly to the walls. The next stage in the development of vaults came in Gothic architecture, the builders of which invented a new option for distributing the load.

  The massive wall that served as support for the heavy vault was replaced with a system of buttresses and flying buttresses. Now the force began to be transmitted not directly vertically downwards, but was distributed and diverted sideways along the flying buttresses, going into the buttresses. This made it possible to make the walls much thinner, replacing them with several reliable supporting buttresses. In addition, there was a change in the laying of the vaults themselves - if previously they were entirely laid out from massive stones and were the same throughout the entire thickness, now the vault began to consist of rigid ribs (ribs) that served for support and distribution of the load, and the spaces between the ribs were laid out with light brick, which now performed only a protective, but not a load-bearing function. This discovery allowed Gothic architects to constructively cover unprecedentedly large spaces of cathedrals with new types of vaults and create dizzyingly high ceilings.

  Finally, the next and, to date, final milestone in the evolution of vaults came in the 19th century with the invention of reinforced concrete. If before this, engineers had to calculate vaults laid on formwork made of brick with cement, or of stone with concrete (and they could crumble in the event of unsuccessful calculations or errors in masonry), now concrete is reinforced with iron and molded in pouring molds. This gave it extraordinary strength, and also gave maximum freedom to the imagination of architects. From the 2nd half of the 19th century. vaults were often created from metal structures. In the 20th century various types of monolithic and prefabricated reinforced concrete thin-walled shell vaults appeared complex design. They are used for coverings of long-span buildings and structures. From the middle of the twentieth century. Wooden laminated vaulted structures are also widespread.

  Purpose

  Vaulted ceilings have been used for centuries primarily for religious and public spaces because, when properly designed, a vault can cover a huge space - while a beam, regardless of material, has a limit to its length. (This is why in private construction, even in the same panel houses, the beam-post system still prevails, since there is no need for large footage and high ceilings). The greatest variety of vault types is demonstrated by sacred architecture, which was supposed to combine spaciousness and beauty, and in Stalinist architecture the metro had to correspond to these parameters, so at the moment Moscow metro stations show great variability in vault types.

  Vault elements

  Depending on the type of vault, it may have the following elements:

  • Castle, keystone, vault key- a medium wedge-shaped stone in the groove of an arch or vault. Sometimes it is emphasized by decoration.
  • Mirror- horizontal, flat plane of a mirror vault, ceiling lamp (initially - any smooth surface of slabs in masonry).
  • Trays- a curved plane of the vault, one end resting on the wall, and the other connecting with the rest of the trays, that is, a part of the vault that has the shape of a segment of a semi-cylindrical surface, dissected by two mutually intersecting planes.
  • Paddugi (padgugi)- the lateral cylindrical parts of a closed vault, in a mirror vault, are located under the mirror. Initially, there was a large fillet above the cornice, serving as a transition from the wall to the ceiling.
  • Spandrel- the space between the outer surfaces of adjacent vaults, or a vault and a wall.
  • Sail- a spherical triangle, providing a transition from the square under the dome space to the circumference of the dome.
  • Spring arch- a persistent arch that strengthens or supports a vault.
  • Span of the vault- its width
  • Skewback- the lower part of an arch, vault, resting on a wall or pillar; or the top stone of the support on which the arch or vault rests.
  • Strippings- a recess in a cylindrical vault in the form of a spherical triangle. Formed by the intersection of two mutually perpendicular cylindrical surfaces (usually of different radii). It can be either part of a cross vault, or an additional vault embedded in a cylindrical or mirror vault. It is installed above door and window openings when the top point of the opening is located above the heel of the arch.
  • Arch arrow- the distance from the axis of the arch in the key to the chord connecting the centers of its heels.
  • Shelyga (shalyga)- the upper line or ridge of the arch. Also - a continuous row of keystones (vault key).
  • Cheek vault (lunette)- end of the vault, its cut
  • Cheek arch- a girth side arch of the cross vault, located on the sides of the rectangle of its plan.
  • cheek wall- the end wall of the room covered with a cylindrical vault does not experience any load.
  Gothic designs:
  • Ribs- rib of a Gothic frame vault. Are divided into:
    • Ogiva- diagonal arch. Almost always semicircular.
    • Tierseron- an additional rib coming from the support and supporting rails in the middle.
    • Lierni- an additional rib running from the intersection point of the ogive to the slit of the cheek arches.
    • Controllers- transverse ribs connecting the main ones (that is, ogives, liernes and tiercerons).
  • Shuttering- in a rib vault, filling between the ribs.

  • Illustration	Definition
    	Cylindrical vault- forms in cross section semicircle (or half an ellipse, part of a parabola, etc.). This is the simplest and most common type of vault. The ceiling in it rests on parallel supports - two walls, a row of pillars or arcades. Depending on the profile of the arch that lies at the base, there are: semicircular lancet box elliptical parabolic
    	Box vault- a type of cylindrical vault; differs from it in that it forms in cross section not a simple arc, but a three-center or multi-center box curve. It has a large expansion, usually extinguished by metal ties, and is used to cover larger areas than can be covered with a cylindrical vault.
    	Cylindrical vault with strippings- a vault formed by the intersection at right angles of one vault with others of smaller span and lower height, that is, with the formation of formwork.
    	Cross vault- formed by the intersection of two cylindrical or box-shaped vaults of the same height at a right angle. It was used to cover square and sometimes rectangular rooms. It can rest on free-standing supports (pillars, columns) in the corners, which makes it possible to concentrate the pressure in plan only on the corner supports.
    	Closed vault- is formed by extensions of the walls inclined along a given curve - trays (cheeks), which rest along the entire perimeter on the walls and converge in the horizontal roof of the vault with a rectangular plan or at one point when overlapping a square one (in the illustration) in the plan of the room (in the latter case also may also be called "monastic"). It is derived from the cylindrical vault. Transfers vertical pressure and thrust along the entire length to the walls. It was known in the architecture of Central Asia, Rome and Gothic, but was rarely used, becoming more widespread in Renaissance architecture. Closed vault with strippings- the presence of formwork along the axes of the trays changes the structural system of the vault: forces are transferred to the corners.
    	Mirror vault- differs from a closed one in that its upper part is a flat horizontal slab-plafond (the so-called “mirror”). It is usually separated from the paddug (side edges) by a clear frame and is often used for painting. Such a vault is often used for decorative purposes, while the room itself can actually be covered with a beam or rafter structure from which a false vault is suspended. It became most widespread during the Renaissance.
    	Sail vault- vaulted vault on four supports. It is formed by cutting off parts of the spherical surface of the dome with vertical planes. Conventionally, it is divided into two zones: the lower - load-bearing, and the upper - carried, flat part of the sphere, called skufya. Sometimes the skufya was given a semi-circular shape.
    	Khreshchaty vault- a closed vault, cut through by two intersecting vaults of a different shape, at the intersection of which there is a light drum.
    List of architectural vaults Gothic vaults fan vault- formed by ribs ( ogiva And Tierserona), emanating from the same corner, having the same curvature, making equal angles to each other and forming a funnel-shaped surface. Typical of English Gothic. Star vault- the form of a cross Gothic vault. Has auxiliary ribs - Tierserons And liners. The main diagonal ribs of the cross vault are clearly visible in the frame. Gothic cross vault- cross vault, which is frame structure in the form of a network of ribs on which the formwork rests, which allows the pressure to be concentrated only on the corner supports. The main feature of the Gothic is clearly defined profiled diagonal ribs that make up the main working frame, which absorbs the main loads. The formworks were laid out as independent small vaults, supported by diagonal ribs. Schemes of the main types of vaults found in Russian architecture of the 11th - early 18th centuries: 1 - box(from the 11th century); 2 - quarter-cylinder(mainly XI-XV centuries and later); 3 - dome(from the 11th century); 4 - dome with sails without drum(XI century); 5 - dome on drum(from the 11th century); 6 - conha(from the 11th century); 7 - gable(XI century); 8 - crusade(XI-XII centuries, as well as from the end of the 15th century); 9 - tent(end of the 13th century); 10-12 - stepped-arched(XIV-XVI centuries); 13 - ripped cross(from the beginning of the 16th century); 14, 15 - closed on formworks converging to the corner(from the beginning of the 16th century); 16, 17 - vaulted ceiling of a single-pillar chamber on formwork converging to the corner(from the beginning of the 16th century);

  Structural elements

  Benefits received

  § Greater savings in building materials

  § Increasing the height of the building, as well as the illumination of its interior space

  § Combining the internal space into one whole

  § Reduced construction time

  

  Rosette - the keystone of a ribbed vault

  § Flying buttress- this is an external stone thrust arch that transfers the thrust of the arches of the main nave to supporting pillars spaced from the main body of the building - buttresses. The flying buttress ends with an inclined plane in the direction of the roof slope. In the early period of Gothic development, flying buttresses were found hidden under the roofs, but they interfered with the lighting of the cathedrals, so they were soon brought outside and became open to view from the outside. Flying buttresses can be two-span, two-tiered, or a combination of both of these options.

  § Buttress- in Gothic, a vertical structure, a powerful pillar that contributes to the stability of the wall by the fact that its mass counteracts the thrust of the vaults. In medieval architecture, they figured out not to lean it against the wall of the building, but to take it outside, at a distance of several meters, connecting it to the building with spanned arches - flying buttresses. This was enough to effectively transfer the load from the wall to the supporting columns. The outer surface of the buttress could be vertical, stepped or continuously inclined.

  § Pinnacle- a pointed turret, which was used to load the top of the buttress at the point where the flying buttress adjoined it. This was done to prevent shear forces.

  

  Reims Cathedral: pillar-abutment “bundle of columns”, capital “vault heel” and ribs supported on it

  § Post-support- could be of a simple cross-section, or could be "bundle of columns".

  § Rib- the edge of the arch of the vault, protruding from the masonry and profiled. The system of ribs forms a frame supporting the lightweight masonry of the vault. Are divided into:

  § Jaw arches- four arches along the perimeter of a square cell at the base of the vault.

  § Ogiva- diagonal arch. Almost always semicircular.

  § Tierseron- an additional rib coming from the support and supporting rails in the middle.

  § Lierni- an additional rib running from the intersection point of the ogive to the slit of the cheek arches.

  § Controllers- transverse ribs connecting the main ones (i.e. ogives, liernes and tiercerons).

  § Shuttering- in a rib vault, filling between the ribs.

  § Keystone (rosette)

  

  Pointed cross vault

  The most important element, the invention of which gave impetus to other achievements of Gothic engineering, was the ribbed cross vault. It also became the main structural unit in the construction of cathedrals. The main feature of the Gothic vault is clearly defined profiled diagonal ribs that make up the main working frame that carries the main loads.

  
  

  The background to its origin is as follows: first, a cross vault arose by intersecting two cylindrical vaults at right angles. In it, unlike a cylindrical one, the load does not go to two side walls, but is distributed over the corner supports. The weight of such vaults, however, was very great. In search of a way to lighten the vault, builders began to strengthen the frame arches that were formed at the intersections of the cross vaults. Then the filling between them became thinner and thinner until the vault became completely framed.

  Such frame arches are called ribs (fr. nervure- vein, edge, fold).

  

  Photo of the rib vault from below: 4 cheek arches and two diagonally intersecting.

  

  Church of San Francesco in Assisi. After the earthquake, the ribs were exposed and the infill masonry collapsed

  Rib vaults were square in plan cells. They connected the supports of the nave spans with each other. Over time, the so-called connected system- for each square of the wide main nave there were two smaller side ones. This system provided greater strength and a special rhythm to the internal space of the temple.

  

  Photo of the star vault from below

  The frame of the simplest ribbed vault consists of 4 arches around the perimeter of the square - cheek arches, and 2 diagonally intersecting - revived. With a semicircular profile, the cheek arches are lower than the diagonal ones, which forced the filling between them to be of a complex shape. With the introduction of the pointed arch, it became very easy to coordinate the height - the cheek arches began to be made pointed (as if folded in the slit - the ridge of the arch), and the ogives retained their semi-circular shape. The formworks are supported by ribs, which allows pressure to be concentrated only on the corner supports. These formworks were laid out as independent small vaults, supported by diagonal ribs.

  

  Star vault is a form of cross-shaped Gothic vault. Has auxiliary ribs - Tierserons And liners. The main diagonal ribs of the cross vault are clearly visible in the frame.

  As style and technology developed, architects began to introduce more and more additional details. So, sometimes they installed additional ribs running from the intersection point of the ogive to the arrow of the cheek arches - the so-called. liners. Then they installed intermediate ribs supporting the rails in the middle - Tierserons. In addition, they sometimes connected the main ribs together with transverse ribs, the so-called counterlayers.

  Thus, the number of ribs increased from six arches to 10, 12, etc.

  In the initial period of the development of Gothic architecture, the space (square or rectangle in plan), covered by one cross vault, represents (as in Romanesque architecture) an independent spatial unit. Late Gothic abandons the interpretation of space as a composite and gradually comes to understand it as a single whole. This was achieved by complicating the cross vault by introducing additional ribs, which split the vault into smaller parts.

  
  
  

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