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should be dated, is the latter end of the ninth century, when the crypt of St. Peter's church, Oxford, was built by Grimbald; and it is from that time that we shall attempt to trace its development.

But, first, it may be as well to mention some of the peculiarities of the early arched buildings in Rome, and to point out the ease and simplicity with which they met the difficulties which the architects of the middle ages were so much perplexed to evade. By-and-by it will be our endeavour to show how these difficulties operated in suggesting the peculiarities of the Gothic style.

We may observe, then, that it was the object of the Roman architects to avail themselves of the great additional power with which the arch furnished them in extending their general designs, and yet to preserve the details of the Grecian system. To effect this amalgamation of new and old principles was their constant effort; but their success does not appear to have been progressive; they arrived almost immediately at that sufferable mediocrity which they never passed; and they have left us nothing to admire but the size of their works, and the dexterity of their execution.

These remarks will be illustrated in those singular structures, the Temple of Peace and the Baths of Diocletian; and of these it will be necessary to give a somewhat minute description, with a view to contrasting them by-and-by with the happily unsuccessful imitations of after times. First, then,

the reader must be at the trouble to impress upon his mind the form resulting from the intersection of two equal cylinders, whose axes cut one another at right angles; of this form, and others which are akin to it, we shall have frequent occasion to speak in the sequel; and by describing it here, we shall consult expedition as well as clearness.

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The above figures will convey some idea of its appearance, Fig. I. on the concave surface, Fig. II.

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on the convex.

It will be observed, that the points A, B, C, D, stand in the four corners of a square, and that three distinct arches spring from each; from B, for instance, there spring the arches B F A, B G D, BEC; of these B F A, B G D, are semicircles, being direct sections of the two intersecting cylinders. But B E C being an oblique section, is an ellipse, of which the long axis equals the diagonal of the square A B C D, and the short axis its side. This elliptic arch is the line in which the two cylinders cut one another, and is called a groin.

The whole figure, consisting of the four circular arches AF B, B G D, D K C, C H A, and the two elliptic groins A E D, BEC, is, in architectural language, called a bay. Such a bay as has been here described is the simplest form which can be adopted for the stone roof of a square building ; two such bays, in juxta-position, will form the roof of a building twice as long as it is broad; and a succession of them may be always used when the length of the building to be roofed is any exact multiple of its breadth. Such a succession of bays is called a groined vault.

If the bay represented in Fig. I. was one of such a succession, then of the two semi-circular arches. which spring from the point B, one (say BFA) would rest flat against the wall; the other (B G D) would cross the building at right angles to the wall. In this case B FA would be called a longitudinal arch, B G D a transverse arch; and thus each bay would consist of two transverse arches, two longitudinal, and two diagonal, or groins.

It will be seen at once that such a groined vaulting is only applicable where the length of the vault is a given multiple of its breadth; where this is not the case, it will be necessary to use bays of a less simple form: e. g., if the length of a building is twenty-one feet, and the breadth ten, it will be impossible to cover it exactly by two bays, such as that represented in Fig. I., where the longitudinal and transverse arches are of equal dimensions. In

this case we must employ three bays, of which the longitudinal arches are seven feet in span, and the transverse ten. However, the height of each must still be the same, in order that the cylinders, of which they are sections, may, as before, cut one another in the point E, and form the groin.

Of this species of groining, the Temple of Peace and the Baths of Diocletian are magnificent specimens. Each consists of three bays, of which the longitudinal and transverse arches differ in span. In the Temple of Peace all the three bays, when perfect, were exactly alike; and as the breadth of the building was less than a third of its length, the longitudinal arches were necessarily of greater span than the transverse; but that their height might be equal, while their span was unequal, the former were built semicircular, the latter elliptic, with the long axes vertical. Thus the bay was formed, not of the intersection of two cylinders, as is Fig. I., but of a cylinder and a cylindroide, the cylinder forming the longitudinal arch, and cylindroide the transverse.

The Baths of Diocletian exhibit a more complicated arrangement. The vaulting of this remarkable structure is still perfect; its central bay differs from the extremes, being nearly square, whereas their breadth very materially exceeds their length. The cylinder is studiously avoided in all three ; even in the central bay, where the longitudinal and transverse arches are nearly equal, and where consequently there was very little to deviate from the

semicircular form, the ellipse, with its long axis vertical is wantonly substituted, and the bay itself formed by the intersection of two cylindroides; in the two extremes the arrangement is such, that the form of the groins, which, in ordinary cases, would be elliptic, with the long axis horizontal, is here accurately semicircular. This arrangement is worthy of notice, as it is frequent in our finest cathedrals.

From what has been said, it is evident that the architect who constructed these vaultings must have been acquainted with practical methods of describing on a large scale almost every variety of ellipse; and of determining à priori the exact curve in which cylinders and cylindroides would intersect each other. Without such knowledge, and that too in such a compendious form as to enable workmen to apply it, no architect could have undertaken a work of this magnitude: for though on a small scale an accurate eye may sometimes stand in the place of rules, yet the case is widely different with a structure like the Temple of Peace, where the span of each arch is more than double the breadth of St. Paul's Cathedral. In a scientific point of view, then, these works have no ordinary merit.

As works of taste, their claim to admiration is much more questionable, combining as they do the details of the pure Grecian temple with a new feature to which these have no reference. For instance, the vast roof of the Baths of Diocletian is apparently supported on four Corinthian columns,

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