size of them: they must not be less than three feet even in small buildings, because, as Sir William Chambers seriously says, "there is not room for a fat person to pass between them." 2616. Before leaving the subject which has furnished the preceding remarks on intercolumniations, we most earnestly recommend to the student the re-perusal of Section II. of this Book. The intervals between the columns have, in this section, been considered more with regard to the laws resulting from the distribution of the subordinate parts, than with relation to the weights and supports, which seem to have regulated the ancient practice: but this distribution should not prevent the application generally of the principle, which may without difficulty, as we know from our own experience, be so brought to bear upon it as to produce the most satisfactory results. We may be perhaps accused of bringing a fine art under mechanical laws, and reducing refinement to rules. We regret that we cannot bind the professor by more stringent regulations. It is certain that, having in this respect carried the point to its utmost limit, there will still be ample opportunity left for him to snatch that grace, beyond the reach of art, with the neglect whereof the critics are wont so much to taunt the artist in every branch. SECT. X. ARCADES AND ARCHES. 2617. An arcade, or series of arches, is perhaps one of the most beautiful objects attached to the buildings of a city which architecture affords. The utility, moreover, of arcades in some climates, for shelter from rain and heat, is obvious; but in this dark climate, the inconveniences resulting from the obstruction to light which they offer, seems to preclude their use in the cities of England. About public buildings, however, where the want of light is of no importance to the lower story, as in theatres, courts of law, churches, and places of public amusement, and in large country seats, their introduction is often the source of great beauty, when fitly placed. 2618. In a previous section (2524.) we have spoken of Lebrun's theory of an equality between the weights and supports in decorative architecture: we shall here return to the subject, as applied to arcades, though the analogy is not, perhaps, strictly in point, because of the dissimilarity of an arch to a straight lintel. In fig. 898. the hatched part AEMFDCOB is the load, and ABGH, CDIK the supports. The line GK is divided into six parts, which serve as a scale to the diagram, the opening HI being four of them, the height BH six, NO two, and OM one. From the exact quadrature of the circle being unknown, it is impossible to measure with strict accuracy the surface BOC, which is necessary for finding by subtraction the surface AEMFDCOB; but using the common method, we have Fig. 898. to that surface; or, in figures, ADX AE 6 x 3 BC2 x 7854 =11.72. Now the suports will be IK x IC x 2 (the two piers) 1 x 6 x 2 = the piers; or, in figures, = 12.00. That is, in the diagram the load is very nearly equal to the supports, and would have been found quite so, if we could have more accurately measured the circle, or had with greater nicety constructed it. But we have here, where strict mathematical precision is not our object, a sufficient ground for the observations which follow, and which, if not founded on something more than speculation, form a series of very singular accidents. We have chosen to illustrate the matter by an investigation of the examples of arcades by Vignola, because we have thought his orders and arcades of a higher finish than those of any other master; but testing the hypothesis, which we intend to carry out by examples from Palladio, Scamozzi, and the other great masters of our art, not contemplated by Lebrun, the small differences, instead of throwing a doubt upon, seem to confirm it. 2619. In fig. 898. we will now carry, therefore, the consideration of the weights and supports a step further than Lebrun, by comparing them with the void space they surround, that is, the opening HBOCI; and here we have the rectangle HBCI-HB x HI, that is, 6 x 4 =24, and the semicircle BOC equal, as above, to =6-28. Then 24+6.28 30.28 is the area of the whole void, and the weight and support being 11 72+ 4x4x7854 12=23-72, are a little more than two thirds the areas of the whole void; a proportion which, if we are to rely on the approval of ages in its application, will be found near the limits of what is beautiful. 2620. We shall now refer to the examples of Vignola alluded to; but to save the repetition of figures in their numbers, as referred to, each case is supposed in what immediately follows as unconnected with the entablatures which they exhibit, it being our intention to take those into separate consideration. 2621. Suppose the Tuscan example (fig. 899.) without an entablature, we have the The area of the void is 16'6+975 × 6·5=79.97, whereof 53′025, the portion of solid parts, is not widely different from two thirds. In Vignola's Doric example, (fig. 900.), again without the entablature, we have The area of the void is 19.24 + 10.5 × 7=92.74, whereof 67.26, the portion of solid parts, is not much different from two-thirds. In the Ionic example (fig. 901.), still without considering the entablature, the following will result : 105 82, whereof 74.10, the portion of In the Corinthian example (fig. 902.), not taking into consideration the entablature, the following is the result: The area of the void is 23 65+ 14·111 × 7·76=133·15, whereof 83-06, the portion of solid parts, is somewhat less than two thirds of the void. 2622. The result which flows from the above examination seems to be that, without respect to the entablature, the ratio of the solid part to that of the void is about 666. Bearing this in mind, we shall next investigate the ratio of the supports and weights, considering the entablature above the arcade as a part of the composition; and still following Vignola, whose examples, as we have above stated, do not so much differ from those of other masters as to make it necessary to examine those of each, we will begin with that architect's Tuscan arcade, without pedestals, exhibited in fig. 899. on the preceding page. In this example, from centre to centre of pier, The whole area, in round numbers, 17.5 x 9.5 6.5x6.5x 7854 Area of semi-arch, 2 Rectangle under it, 9.75 x 6.5 Entablature, 9.5 x 3.5 = 166.2 =16.6 Total void, therefore, 79.9 86.3 =33.2 Leaves for the supporting parts 53.1 In this example, therefore, the supporting parts are 53, those supported 33, and the voids 79. The ratio between the solid and void parts = 9, and the ratio of the supports to the weights is }}='62. The distance between the axes of the columns is 9 modules and 6 parts; the height of the semi-arch, 3 modules and 3 parts; and between the crown of it and the under side of the architrave is 1 module; the whole height, including entablature, being 17 modules and a half. 2623. Following the same general method, we submit the Doric arcade (fig. 900.) without pedestal. Measuring, as before, from centre to centre of piers, The whole area, in round numbers, 20.2 × 10 Area of semi-arch 7×7x7854 2 Entablature, 10 x 4.2 Leaves for the supporting parts 67.3 In this example, therefore, the supporting parts are 67, those supported 42, and the voids 92. The ratio between the solid and void parts is 85, and the ratio of the supports to the weights is = '63. The distance between the axes of the columns is 10 modules, the height of the semi-arch is 3 modules and 6 parts, and between the crown of it and the underside of the architrave is 2 modules; the whole height, including the entablature, being 20 modules 3 parts. 2624. The Ionic arcade, without pedestal, is shown in fig. 901. The measurements, as above, from centre to centre of pier, The whole area, 22·64 × 10·88 in round numbers =246.3 Leaves for the supporting parts 88.3 Hence, in the example, the supporting parts are 88, those supported 52, and the voids 105; so that the ratio of the voids to the solids, in this order, is 8, and the ratio of the supports to the weights does not materially differ from the other orders, being = 6. The distance between the axes of the columns is 10 modules 16 parts, the height of the semi-arch is 3 modules 3 parts, and between the crown of it and the under side of the architrave is 2 modules; the whole height, including the entablature, being 22 modules 13 parts. 2625. Fig. 902. represents the Corinthian arcade without pedestal. The measurement, as before, is from centre to centre of pier. The whole area, 25·2 × 11·33, in round numbers =288.5 In the Corinthian example, therefore, the supporting parts are 97, those supported 58, and the voids 133. The ratio between the solid and void parts = 8, and the ratio of the supports to the weights 59. The distance between the axes of the columns is 11 modules and 6 parts, the height of the semi-arch is 3 modules 16 parts, and between the crown of it and the under side of the architrave is 2 modules 3 parts; the whole height, including the entablature, being 25 modules 3 parts. 2626. The laws laid down by Chambers for regulating arcades are as follow: "The void or aperture of arches should never be much more in height nor much less than double their width; the breadth of the pier should seldom exceed two thirds, nor be less than one third of the width of the arch, according to the character of the composition, and the angular piers should be broader than the rest by one half, one third, or one fourth." ... "The height of the impost should not be more than one seventh, nor need it ever be less than one ninth of the width of the aperture, and the archivolt must not be more than one eighth nor less than one tenth thereof. The breadth of the console or mask, which serves as a key to the arch, should at the bottom be equal to that of the archivolt, and its sides must be drawn from the centre of the arch. The length thereof ought not to be less than one and a half of its bottom breadth, nor more than double." 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 50 6 Fig. 903. 12 13 14 Modules 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 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. The detail of the above result is as follows: The whole area, 22:30 x 13.75 Area of semi-arch, =306'62 95x95x7854 = 35.43 2 |