\Ve have arrived at a theory which is very nearly consonant with what has become, among our modern builders, the most approved way of distributing the weight over the haunches of an arch. It was customary, in the construction of bridges, to fill up the haunch with solid matter, such as gravel, earth, or the like, until a roadway of a proper slope was procured. Where the arches were small, this might not be attended with any perceptible bad effect, provided the archstones were of a good depth. But the necessity of lightening the haunches has been forced upon the attention of builders, whenever large arches have been attempted. A more remarkable instance of this we cannot have than in the bridge of Pontypridd, in Wales, built by William Ed wards, a simple country mason of Cliamorganshire. It is one of the boldest arches in Britain, perhaps even in Europe, being t 40 feet span, and 35 feet rise ; a portion of a circle of 872 feet radius, and the depth of arch stones is only 3 feet.
In each haunch there arc three cylindrical openings running through from side to side : the diameter of the lowest is nine feet, of the next six feet, and of the up. permost three feet ; and the width of the bridge is about eleven feet. To strengthen it horizontally, it is made widest at the abutment, from whence it contracts to wards the centre, in the old and unartificial way, by se ven offsets, so that the roadway is one foot nine inches wider at the extremities than at the middle ; and is also very steep.
That this mode of lightening the haunches is effec tual, we have undoubted proof in the case before us. (Plate LXXXIII.) It is not ungraceful, but were it thought so, the tunnels might be concealed by the side walls. Indeed these tunnels might even become use ful, by affording additional passage for the waters in dangerous floods, as seems to have been intended in the ancient bridge of Merida, the Pont St Esprit over the Rhone, and in many other similar structures both an cient and modern. Nevertheless we cannot approve of this mode. It seems to press unequally on the arch, and only at a number of detached points ; and though the widest tunnel may be placed just where the greatest evacuation is necessary, yet this ill agrees with the gra dual approximation to solidity, which we should find in passing down the back of the arch. To make correct workmanship in these tunnels is troublesome and expen sive. The following mode, which has now become the customary practice of our most experienced bridge builders, is much preferable.
Thin longitudinal walls are built over the flank of the arch, parallerto the sides of the bridge, and about three or four feet asunder. The spaces between are covered at top with thin flat stones, or arched over by pointed or circular arches ; or they are covered by regularly projecting courses in the way of an Egyptian arch ; and in any case a platform is thus formed, upon which the gravel may be laid for a roadway.
In all probability, the first inventors of this mode of building, besides employing it with the view of equili brating the arch by lightening the part over the haunches, had also an idea of steadying it by the lateral abutment. They appear to have considered these spandrel walls as a sort of hoops, that would keep the parts of the arch together, and hinder any stone from moving, by their great friction, inertia, and mutual abutment. Hence various ingenious modes have been employed for lock ing them into the back of the archstones, propagating the pressure througn, and securing them from sliding away at the bases.
They indeed act in this way ; nevertheless the equili bration of the arch should be attended to in their con struction, that every unnecessary strain may be avoided. The thichnc33 of these walls may be varied indefinitely, and the vacant spaces made in any proportion to the so lid parts. The galls ought to be near each other, that their effect may be lelt over the whole arch, and perhaps they should spread out towards the bottom ; but this is not so very necessary, for the courses of archstones break joint with each other, and the inequality of pres sure in one course is immediately corrected by being propagated to the succeeding. We may determine readily the thickness proper for these walls, by the help of the table last given, provided we know the thickness of the arch, and of the roadway, (including the small arcade below it,) and the breadth of the whole structure. For example, let the breadth of the soffit be 20 feet, the thickness at crown of the radius, and the archstone alone ,4,-; being the same proportions as for the numbers in the example to last table. Then from that example we find the thickness of all the masonry in the spandrel must, near the crown, be or 5 feet ; at 30° from the crown, it must be 7 feet ; at 40°, 9 feet 44 inches; at 50°, 13 feet 11 inches ; and at 57° or the whole must be solid masonry. Suppose, in the next place, that the side walls are 18 inches thick, and the span drels 3 in number, of course there will be four open ings. The thickness of each wall must be at 50° from the crown 3 feet 8 inches ; at 40°, 2 feet q inches; at 30°, I foot 4 inches ; and diminishing from thence to half that thickness. Perhaps eighteen inches is too thin for the side walls, but they may be thickened towards their bases, diminishing the thickness of the spandrels in proportion. On the other hand, nine inches appears too little for the spandrel wall, when we consider that an arch is to be built on it ; but the height near the crown will be so small, that a little additional thickness there will be of no moment ; nay, it will enable the arch the better to resist any overload at the crown.