numbers, that the mind of the reader may not be distracted from the general proportions. The detail again corroborates the hypothesis, as in the preceding subsection was predicated, and the further we proceed, as will be presently seen, its truth becomes more manifest.

2630. The Ionic arcade with a pedestal is shown in fig. 905. The whole area is 448 between the axes of the columns; that of the void, 228. The entablature's area is 73, and the supporting parts 146. The ratio, therefore, of the load to the support is 75, and supports and weights are very nearly equal to the void. The height of the pedestal is 6 modules, the opening 11 modules, and the width of a pier 4 modules and 12 parts.

Once more returning to the detail on which the above proportions are based, and which in this as in the following example we think it better to supply, observing, as before, that the numbers above stated are given roundly, we shall have in the Ionic arcade,

Whence it will be seen that the round numbers first given are shown to be sufficiently accurate for exemplification of the law, and that the further we examine the hypothesis the more closely we find it connected with the theory of weights and loads that has occupied a very considerable portion of this Book, and which we hope may not have had the effect of exhausting the reader's patience. We trust we shall have his pardon for pursuing the course we have taken.

2631. Fig. 906. is an arcade with pedestals of the Corinthian order. Its total area is 528, that of the void 284, the area of the entablature 84, and that of the supporting parts 159. Hence, the ratio of the load to the support is 52, and the supports and weight are equal in area to the void within a very small fraction. The height of the pedestal is 6 modules, the opening is 12 modules wide, and the width of a pier is 4 modules and 9 parts.

We here close the curious proofs of a law whose existence, we believe, has never been suspected by modern architects. It was clearly unknown to Rondelet, and but for the work of Lebrun already quoted, we might never have been led to the investigation of it. That author himself, as we believe, did not entertain any notion of it.

In the Corinthian arcade with pedestal we have

Thus, again, the law seems to be borne out, and to prove that the assumptions we have been making are not those of empiricism.

2632. In fig. 907. are collected the imposts and archivolts used in the arcades of the different orders.

2633. We are not of the opinion of Sir William Chambers in respect of the arcades which Vignola has given; that author had not, we think, critically examined their composition, and we confess we do not think his own examples are improvements on those of the master in question; but we are willing to admit that in the examples of arcades with pedestals, they would have been much improved by assigning a greater height generally to the plinths of the pedestals, which are, doubtless, much too low, and might be well augmented by adding to them a portion of the dies of the pedestals.

2634. Great as is our admiration of Palladio, we do not think it necessary to say more relative to his arcades, than that he has given only designs of arches with pedestals, and that their height is from one and two thirds to two and a half of their width. His piers are generally 3 modules, except in the Composite order, wherein they are 4 modules. 2635. Scamozzi makes his Tuscan arch a little less than double its width, increasing the height gradually to the Corinthian arch with pedestals to nearly twice and a half the width. He diminishes his piers as the delicacy of the order increases, his Corinthian piers being only 3 modules in width. We do not, however, think it necessary to dwell longer on this part of the subject, and shall close it by observing that the impost of the arch should not much vary from half a module in height, and that the width of the archivolt, which should touch the shaft of the column or pilaster in the geometrical elevation, at its springing, is necessarily prescribed by the width of pier left after setting out the column upon it. Where columns are used on piers, their projection must be such that the most prominent member of the impost should be in a line with the axis of the column on the transverse section. In Ionic, Composite, and Corinthian arcades, however, it may project a little beyond the axis of the columns, to avoid the disagreeable mutilations which are otherwise rendered necessary in the capitals. Arcades should project not less than their width from the front of the wall which backs them." With regard to their interior decoration," says Chambers, "the portico may either have a flat ceiling or be arched in various manners. Where the ceiling is flat, there may be on the backs of the piers, pilasters of the same kind and dimensions with the columns on their fronts; facing which pilasters there must be others like them on the back wall of the portico. Their projection as well as that of those against the back of the piers may be from one sixth to one quarter of their diameter. These pilasters may support a continued entablature, or one interrupted and running across the portico over every two pilasters to form coffers; or the architrave and frieze only may be continued, while the cornice alone is carried across the portico over the pilasters as before, and serves to form compartments in the ceiling, as is done in the vestibule of the Massini palace at Rome, and in the great stable of the King's mews, near Charing Cross," no longer in existence, having been destroyed to make way on its site for the execrable mass of absurdity to which the government who sanctioned it have facetiously

given the name of National Gallery. Chambers thus continues:-"Where the portico is arched, either with a semi-circular or elliptical vault, the backs of the piers and the inner wall of the portico may be decorated with pilasters, as is above described, supporting a regular continued entablature, from a little above which the arch should take its spring, that no part of it may be hid by the projection of the cornice. The vault may be enriched with compartments of various regular figures, such as hexagons, octagons, squares, and the like, of which, and their decorations, several examples are given among the designs for ceilings." Of these we shall hereafter give figures in the proper place. "But when the vault is groined, or composed of flats, circular or domical coves, sustained on pendentives, the pilasters may be as broad as are the columns in front of the piers, but they must rise no higher than the top of the impost, the mouldings of which must finish and serve them instead of a capital, from whence the groins and pendentives are to spring, as also the bands or ares-doubleaux which divide the vault."

2636. In the examples of arcades, we have followed those given by Chambers, as exhibiting a variety which may be instructive to the student, and at the same time afford hints for other combinations. Fig. 908. is one of the compositions of Serlio, and is an

expedient for arching in cases where columns have been provided, as in places where the use of old ones may be imposed on the architect. The larger aperture may be from 4 to 5 diameters of the column in width, and in height double that dimension. The smaller opening is not to exceed two thirds of the larger one, its height being determined by that of the columns. Chambers thinks, and we agree with him, that this sort of disposition might be considerably improved by adding an architrave cornice or an entablature to the column, by omitting the rustics and by surrounding the arches with archivolts. It is not to be inferred, because this example is given, that it is inserted as one to be followed except under very peculiar circumstances. Where an arrangement of this kind is adopted, care must be used to secure the angles by artificial means.

2637. Fig. 909. is given from the cortile of the castle at Caprarola by Vignola, a structure which in the First Book of this work we have (346.) already mentioned. The height of the arches is somewhat more than twice their width. From the under side of the arch to the top of the cornice is one third of the height of the arch, the breadth of whose pier is equal to that of the arch, and the aperture in the pier about one third of its breadth.

2638. A composition of Bramante, executed in the garden of the Belvedere at Rome, is given at fig. 910. The arch in height is somewhat more than twice its width, and the

Fig. 910.

Fig. 911.

breadth of the pier equal to the opening. By dividing the latter into twelve parts we have a measure which seems to have prevailed in the mind of the architect, inasmuch as two of them will measure the parts of the pier supporting the archivolts, four the space for the two columns, two for the intervals between the niche and the columns, and four for the niche. Half the diameter of the arch measures the height of the pedestal; the columns are of the height of ten diameters, and their entablature one quarter of the height of the columns. The impost and archivolt are each equal to half a diameter of the column.

2639. Fig. 911. is an example whose employment is not uncommon in the designs of Palladio, and was considered by our great countryman Inigo Jones to be worthy of his imitation. The arch may be taken at about twice its width, and the pier not less than one nor more than two thirds of the width of the aperture.

2640. The example in fig. 912. is from the hand of Vignola, and was executed for one of the Borghese family at Mondragone, near Frascati. In it the arch is a little more in height than twice its width, and the breadth of the pier columns supporting the arch includes a little less than the width of the arch itself. We are not quite satisfied in having here produced it as an example, though, compared with the following one, we scarcely know whether we should not on some accounts prefer it.

2641. The last, example (fig. 913.) is one by that great master, Palladio, from the basilica at Vicenza. From the figure it is impossible to judge of its beauty in execution, neither can any imitation of it, unless under circumstances in every respect similar, produce the sensation with which the building itself acts on the spectator; yet in the figure it appears meagre and nothing worth. We can therefore easily account for the conduct of the critics, as they are called, who, never having seen this master's works, indulge in ignorant speculations of the pictorial effects which his compositions produce. Though not entirely agreeing with Chambers in his concluding observations on arcades and arches, we may safely transfer them to these pages. "The most beautiful proportion," he observes, "for compositions of this kind is, that the aperture of the arch be in height twice its width; that the breadth of the pier do not exceed that of the arch, nor be much less; that the small order be in height two thirds of the large columns, which height being divided into nine parts, eight of them must be for the height of the column, and the ninth for the height of the architrave cornice, two fifths of which should be for the architrave and three for the cornice. The breadth of the archivolt should be equal to the superior diameter of the small columns, and the keystone at its bottom must never exceed the same breadth."

SECT. XI.

ORDERS ABOVE ORDERS.

2642. Vitruvius, in the fifth chapter of his book "On the Forum and Basilica," in both which species of buildings it is well known that orders above orders were employed, thus instructs his readers: "The upper columns are to be made one fourth less than those Delow" (quarta parte minores quam inferiores sunt constituenda), "and that because the latter, being loaded with a weight, ought to be the stronger; because, also, we should follow the practice of nature, which in straight-growing trees, like the fir, cypress, and pine, makes the thickness at the root greater than it is at top, and preserves a gradual diminution throughout their height. Thus, following the example of nature, it is rightly ordered that bodies which are uppermost should be less than those below, both in respect of height and thickness." It is curious that the law thus given produces an exactly similar result to that