The mould for cutting the ends of the boards, which are to cover the ribs of the centres of the lesser openings, will be found as follows:

On any straight line, C5, as on the diameter AC produced, set off the equal parts A1, 12; 23, 34, 4B, of the quadrant AB, on the straight line C5, from C to 1, from 1 to 2, from 2 to 3, from 3 to 4, from 4 to 5, and draw the straight lines lu, 2v, 3w, 4x, 5y, perpendicular to C5. Make lu, 2v, 3w, 4x, 5y, each respectively equal to each of the ordinates comprehended between the base AC, and the plan line of the rib AD; then, through all the points C, u, v, w, x, y, draw a curve Cuvwxy, as before; then the shadowed part, of which the curve line Cuvwxy is the edge, is the mould for one side, which may also be made use of for the other.

To apply this mould, all the boards should be laid together, edge to edge on a flat or plane surface, to the breadth C5. Draw a straight line C5, perpendicular to the edge of the first board, at the distance of 5y from the end. At the distance C5 draw a perpendicular 5y, and set off the distance 5y. Then apply the proper edge of the mould from C to y, as exhibited in the plate, and draw a curve across the boards, and cut their ends off by the line thus drawn ; then the ends, thus formed of the remaining parts, will fit upon the boarding of the greater vault, after being properly bevelled, so as to fit upon the surface of the said boarding.

No. 4, of fig. 1, exhibits the curve, in order to draw or discover the line on the boarding of the greater vault, in order to place the boarding of the lesser vault.

Nos. 2 and 3, fig. 1, show the method of forming the inner edges of the angle ribs, so as to range with the small opening in plaster groins. The under edge of the rib must be formed so as to correspond to the curve which is the plan line of its angle; and the little distances, between the straight line and the curve, must be set off on the short lines, shown at Nos. 1, 2, and 3; then a curve may be drawn through the points of extension, and the superfluous wood taken away; then, the rib being put in its real place, the angle will exactly fall over its plan. The diagram, figure 1, and its different numbers, answer both the purposes of centring for brick or stone, and of ribbing for plaster-ceilings.

Figure 2, pl. XXXIX, exhibits the method of forming the Cradleing, or ribs, for plasterceilings of Welsh groins. Here principal ribs are used only across at the piers. The ribs of double curvature, which form the groins, though here exhibited, in order to fix the ribs, are not always used by men of experience: but young workmen require every assistance, in order to acquire a comprehensive idea of the subject; it is, therefore, proper to show how the groined ribs may be found. The other ribs, for lathing upon, are made of straight pieces of quartering, fixed equi-distantly

In

Figure 3, pl. XXXIX, is a plan in which common groins and Welsh groins both occur. London, an example may be seen in the gate-way leading from the Strand, into the court of Somerset-house.

176. To find the seats of the intersections of groins formed by the intersection of an annular and a radial vault, both being at the same height, the section of the annular vault being a semi-circle, and that of the radiating vault a semi-circle of the same dimensions, the plan being given. Fig. 4, pl. XXXIX.

Perpendicular to the middle line, or axis, AC, of the radial vault, draw a straight line, ab, from any point of that middle line; from the point thus drawn, set off ab equal to the radius of the circle of the annular vault; from the point b draw a line, parallel to the axis, AC, of the radiating vault, to meet the side of the plan as at d. From the point of meeting draw a straight line de, perpendicular to the axis, to meet the other side of the plan of that radiating vault: on the perpendicular thus drawn, between the two sides, as a diameter, describe a semi-circle: divide

each quadrantal arc of this semi-circle, and each quadrantal arc of the semi-circle DE, which is the section of the annular vault, into the same number of equal parts. Draw lines through the points of division in each arc, perpendicular to its base or diameter, to meet the said diameter. Through the points of section in the diameter of the annular vault, and from the centre, C, of the radiating vault, describe arcs. From the same centre C, and through the points of section of the diameter cd of the semi-circle, which is equal to the section of the radiating vault, draw lines to meet the arcs. Then, through the intersection of these lines, and the arcs drawn from the points of section in the diameter of the semi-circle, which is the section of the annular vault, trace curves, which will be the plan lines of the groin. The method of fixing the timber is exhibited at the other end of the figure. The ribs of both the annular vault and the radiating vault are all fixed in right sections of these vaults, as must appear evident from what has been shown.

OF THE CONSTRUCTION OF WOODEN BRIDGES.

177. BRIDGES of that sort adapted for gardens and pleasure-grounds are often of wood; they are cheaper, lighter, and make a great shew for little labour; but even in the great and serviceable kind of bridges this material is far from being excluded.

The first point to be considered, in the construction of a bridge, is that the timber be sound and well-seasoned: the next, that it be in sufficiently large pieces; as the timbers must be substantial and well-joined, or all will presently be in ruin.

It is not only the pressure above that must be guarded against in these bridges, but also the power of the water in an encreased quantity and forced rapidity. Fifty wooden bridges are destroyed by floods for one that fails beneath the weight above: the broader the river the larger will be the bridge; and in proportion to this the timber must be more massive; and the rapidity of the river, not only in its common state, but as increased by floods, must be computed, and the strength of the fixing proportioned accordingly.

178. There are many reasons for building a bridge of a single arch, and where the extent of the river is any thing considerable, no piece of wood-work will require more skill in the fabricator, nor will any do him more honour.

We have, in the preceding part of this work, Art. 57 to 83, and in treating of the framing of roofs, Art. 102 to 104, and other timber-work, shown the best modes of joining piece to piece; and it may be shewn that there is scarcely any length to which timbers may not be carried by this admirable art.

The advantages of a single arch are very great, because the common accidents which throw down bridges will have no power over one of this kind. And for one fabric which fails by any natural decay, thousands are torn or thrown down by torrents from land-floods, or by loads of ice or floating timbers, which the swelling of the water has brought from their places; and its force throws with an irresistible violence against the piers.

There are many places where a bridge is an annual charge, and whenever the extent is not beyond all reasonable proportion for a single arch, that should be the method of avoiding the accidents; and, if ten times the price were paid, it would be frugality; but, indeed, skill is required more than price in such a fabric. No bridge is more beautiful than one of a single arch; none more convenient; and besides the numerous accidents which are avoided, and from

which security there results a promise of great duration, none is stronger; for a single arch, when well formed, composes a body more firm than if cut in a vast thickness from a single piece, the parts and the directions of the grain being combined in the framing so as to strengthen and support one another.

Palladio has given a figure of a Bridge of one arch which he laid across the Cismone, where the breadth of the river was a hundred Vicentine feet;* its strength appears incontestible from the structure, and experience showed it to be what it seemed; but there is yet another great advantage in this bridge, which is, that it lies level with the rest of the road, and does not tire the traveller with an ascent and descent.

179. In plate XL, fig. 1 is the elevation of a wooden bridge, similar to one of Palladio's designs, supported on the principle of an arch, and may be used with advantage where the ground rises on one side more than on the other. In order that this bridge may be sufficiently strong, and the road or path-way easily surmounted by passengers and carriages, the curvature of the lower or supporting arch is much greater than that above, which forms the road or path-way.

Figure 2 is a design for a wooden bridge, supported by brackets, projecting more and more as they rise. This design, as well as the following one, is adapted to a straight road or foot-way. Figure 3 is a design of a bridge, with piers and any number of arches, in which the intrados of each arch is the arc of a circle. It is supported by wooden beams over the posts, acting as brackets; and, to prevent the ends of the supporting brackets from having a sharp edge, small keys are let in from the underside.

In order that this bridge may be sufficiently strong, when the space between the posts or piers is considerable, a truss is placed in the middle, so as to form part of the railing, which increases the strength, so that the span may be extended to two, or even three, times the length that it could be without it.

180. THE TIMBER FOOT-BRIDGE, Over the Clyde, at Glasgow, is represented in plate XLI. This very neat and elegant structure was designed and superintended by Mr. Peter Nicholson, in the year 1808.

Figure 1 exhibits the elevation of the bridge. The form of the road-way is a flat curve, said to be the arc of a parabola. The land abutments are strong masses of masonry, to which the timbers of the floor, or foot-way, are well secured by cramps of iron bolted to the stone-work. This bridge was constructed with the view of admitting a certain class of vessels to pass under it. Therefore, to keep the opening between the posts clear, the foot-way is suspended by trusses, formed in the railing. The breadth of the foot-way is about ten feet. Figure 2 is a plan of the beams, which support the planking of the road-way. Figure 3 is an elevation of the middle opening, or arch of the bridge. Figure 4 is an elevation of an opening adjoining one of the land abutments.

Figure 5 is a transverse section, showing also the elevation of the posts and braces which form the piers.

Figure 6 exhibits the scarfing of one of the beams, the manner of bolting the parts together, and their junction with the post by which they are supported.

Figure 7 exhibits the manner of joining the braces and posts in the railing.

This bridge has resisted the most tremendous ice-floods; though the floods have risen sometimes to such a height, as only to leave a small part in the middle of the road-way dry; and

The foot of Vicenza is equal to 1.136 English feet, hence the span of the bridge over the Cismone would be nearly 114 feet. See Ware's Palladio, Book III, Chap. vii.