The intradosses of the Roman domes, as we have al ready hinted, are of a semicircular section, as in the Pan theon, and the temple of Bacchus at Rome, the temple of Jupiter, and the vestibule of the palace of Dioclesian at Spalatro ; while the vertical section of the extrados through the axis, exhibits a much less segment, as may be seen in the first and last of the examples quoted. The latter observation, however, only applies to edifices built prior to the reign of the emperor Justinian ; after which period, from the completion of the dome of St Sophia at Constantinople, to the finishing of St Paul's cathedral at London, the domes are all of the surmount ed kind, and approach, in a certain degree, to the pro portions of spires or towers, so much affected in the middle ages. Since the labours and taste of Mr Stewart and others have revived the legitimate Grecian architec ture, the contour of the ancient Roman dome has been also restored, especially in cases where the structure is ornamented with any of the orders.
In the interior of the large towers of our Gothic ca thedrals, over the intersections of the cross, we find domes, rising from a squat c base, generally pierced with two windows over each wall, and forming beautiful groins, by their intersection with the interior domic ceiling.
Though the equilibrium and pressure of domes are very different from those of ordinary arches, yet they have some common properties, as will appear from the following comparison : If, in their cylindrical or cylin droidal Vaulting of uniform thickness, the tangent to the arch at the bottom be perpendicular to the horizon, the vault cannot stand ; neither can it be built with a concave contour in the whole, or in any part; and to make the arch in equilibrium, whether its section be circular or elliptical, supposing the intrados to be given, the ex tremes must be loaded vastly high, between the extrados of the curve, which runs upward, and the tangent to the arch, which is an asymptote, rising vertically from each foot or extreme of the arch. In like manner, in thin domical vaulting of equal thickness, if the curved surface rise perpendicular from the base, the bottom will burst, let the contour be as it may.
Notwithstanding this agreement, dome vaulting differs in other particulars very essentially front the common sort; for instance, to bring the figure of a dome into proper equilibrium, after the convexity has been carried to its full extent of equilibrium around, and equidistant from the summit on the exterior, the curvature may al ter into a concavity ; for, since the interior circumference of the courses is less than that of the exterior, the stones cannot fall inwardly, whatever be the outward pressure, unless they be squeezed into a less compass, which is supposed impossible ; consequently, they must be crush ed to powder before such a vault can give way. For the same reason, a vault may be constructed, that shall be convex within, and concave outwardly, and yet be suffi ciently firm. The strongest form, however, of a circular vault, intended to bear a load at the top, is that of a truncated cone, similar to Sir Christopher \Vren's con trivance for supporting the stone lanthorn and exterior dome of St Paul's. In this kind of vault, the pressure is communicated in the sloping right line of the sides of the cone perpendicular to the joints, consequently the conic sides have no tendency to bend to one side more than to the other, unless it be from the gravity of the materials tending towards the axis, which is counteract ed by the abutting vertical joints : A form so strong, as to be adequate to sustain or repel any force acting on its summit that we can possibly conceive.
In dome vaulting, on the contrary, the contour being convex, there is a certain load, which, if laid on the apex of the dome, must cause it to burst outwardly. The power of this load will be greater or less, according to the approximation of the contour towards, or its reces sion from, the chords of the arches of the two sides, or to a conic vaulting on the same base, carried up to the same altitude, and ending in the same circular course. In exemplification of this, if we begin at the keystone, and proceed downwards, from course to course, suppos ing a horizontal line to be a tangent at the eertcx, we shall discover, that every successive coursing-joint may be made to slope so much, and, consequently, the pres sure of the archstones of any course towards the axis may be so great, as to be more than sufficient to resist the weight of all the part above; hence it is evident. that a certain degree of curvature may be given to the contour, which will be just sufficient to prevent the stoncs, in any succeeding course, from being forced outwardly.
A circular vault, thus balanced, is what is called an equilibrated dome ; but it is the weakest of all vaults, be tween that of its own contour, and that of a cone upon the same base, rising to the same height, and ending in a key stone, or finished with an equal circular course.
From these data we may conclude, that the equilibrat ed dome has the boldest contour, but is only the limit of an indefinite number of inscribed circular vaults, all stronger than itself.
In other respects circular vaulting differs from the straight, in being built with courses in circular rings ; so that the stones in each course being of equal length, and pressing equally towards the axis, cannot slide in wardly. Hence circular vaults may be left open at the top, and even the equilibrated dome may carry a lantern of equal gravity with the part that would have been ne cessary to complete the whole. But domes of a more flat contour may carry more, according as they approach nearer to a cone, as already remarked ; and those circ u lar vaults that are either straight or concave on the sides, may he loaded without limit, and can never fail till the materials are crushed, provided they be hooped at the bottom. For a more complete investigation of this im portant subject, see DomE.
We have already observed, that, from the earliest pe riods of Roman architecture, ARCHES have been of im portance, and have been extensively used in the con struction of most sorts of edifices ; but, as their nature and principles have been treated of at sonic length under the term BRIDGE, we shall at present only observe, that they are introduced to cover openings to which lintels are inadequate, as drains and inverted arches in founda tions, in vaulting over cellars, halls, and passages ; also over doors, windows, and recesses. They are, indeed, be come so generally useful, and are capable of so nice and accurate adjustment, that we cannot too earnestly press upon the young architect, the propriety of rendering their principles and practice perfectly familiar to his