2627. The ratios that have been deduced by comparing the void and solid parts, if there be any reason in the considerations had, show that this law of making arches in arcades of the height of 2 diameters is not empirical, the following being the results of the use of the ratios in the arcade without, and that with pedestal, of which we shall presently treat. Thus in the

2628. In the examples of the arcades with pedestals, we shall again repeat the process by which the results are obtained, first merely stating them in round numbers. Fig. 903. is a

Tuscan arcade from Vignola's example, as will be the following ones.

In this the whole area is 306, omitting fractions, the area of the void is 156, that of the entablature 50, and the supports 100. The ratio of the supported part (the entablature), therefore, is 5, and the supports and weights are very nearly equal to the void. The height of the pedestal is almost 3 modules and 8 parts, the opening 9 modules 6 parts, and the width of the whole pier 4 modules and 3 parts.

50

100

The detail of the above result is as follows:

The whole area, 22.30 x 13.75

Area of semi-arch,

9.5x9.5x 7854

= 35.43

=306'62

Entablature, 13.75 x 3'66
Leaves for supporting parts

Total voids, therefore,

=156.55

150-07 = 50.32

99.75

It will be seen that we have taken the numbers in the preceding paragraph without supplying strictly the decimal parts that arise from the multiplication and subtraction of the several portions compared. The coincidence of the hypothesis with the apparent law is no less remarkable in this example than it will be found in those that follow; and, sceptical as we at first were on the appearances which pointed to it, we cannot, after the examination here and hereafter given, do otherwise than express our conviction that, in carrying out the principles, no unpleasant combination can result.

2629. Fig. 904. exhibits the Doric arcade, whose whole area from centre to centre of columns is 374. The area of the void is 189, that of the entablature 62, and of the supporting parts 112. The ratio of the entablature to the supports is therefore =55, and that of the supports and weights to the voids 9. The height of the pedestal is almost 5 modules and 4 parts, the opening 10 modules, and the width of a pier 4 modules and 9 parts.

As in the preceding example, we think it will be useful to detail the process by which the general results stated have been arrived at. It is curious and interesting to observe the similarity between the cases. It is scarcely possible to believe that accident could have produced it. May not the freemasons of the middle ages have had some laws of this nature which guided their operations? But we will now proceed to the calculation.

Herein, as before, the general result in the preceding paragraph has been given in round

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,

146.80

Leaves for supporting parts 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