exposed workmanship of the worst kind; even in the outside or ashlar courses, stone chips and pieces of slate and even deal chips were commonly found packed and wedged in to compensate for the leanness of the stones in both beds and joints." same manner. In modern bridges, the piers consist wholly of squared stones, each course being of equal height quite through the body of the pier. The thick arches, combined with the height of the piers. At the bridge of Neuilly the thickness is only one-ninth part of the span from the springing of the arches. The height is regulated according to circumstances, attention being given to the highest point to which the waters have ever been known to have risen. which was further to diminish the already contracted waterway, and to raise the flood-waters to the head Fl requisite to scour it away, with the gravel under it, by which means the sand was exposed, and the piers at once undermined, so that the bridge fell. The river Tyne, in the part where the bridge stood, was Some of the piers of Old London Bridge were about 530 or 540 feet wide, at the height of freshes larger than the original openings of the arches; they or ordinary floods; this width the piers and abutment consisted of small rubble stones laid in lime-mortar, reduced one-fifth, leaving but 424 feet opening be-surrounded by a thin casing of squared stones. The tween the piers where they are thinnest, and the Roman bridges were probably constructed in the diminished width was further reduced below summer water-level by the greater substance of the piers at their footings, and by the defences of rubble packed around them, which had the effect of making an imper-ness ought to be regulated by the span and rise of the fect dam, or sunken weir, at every archway. "But the flood-waters had on previous occasions risen above bridge to the height of the springings of the arches without injury to the works, notwithstanding the pressure of a head of 3 feet of water, accumulated by the obstructions of the piers and their defences, and a scour arising from a velocity of from 800 to 900 With respect to the shape of the piers, the portion feet per minute resulting from that head. Above the which supports the arch is usually oblong with right level of the springings, however, the arches them-lined parallel sides. Under low-water the pier inselves began to be immersed, and these in a rise of 3 feet in height above the springings, will have further diminished the water-way full 30 feet, when the pressure became sufficient to break up the crust of gravel that lay exposed between the toes of the rubble defences of the piers, to wash out the sand and loam from between the rubble, and to scour out a channel deep enough to compensate for the space that the piers of the bridge, with their defences, and the immersed haunches of the arches occupied." It is probable, in cases of this kind, if the bed of the river were deepened sufficiently to make the section of the water-way in the bays equal to the whole section of the bed or trough occupied by water before the erection of the piers, no danger would ensue. Under ordinary circumstances, the current will effect such deepening of itself; but while doing so, the piers are exposed to a great wearing action, which, in the case before us, proved fatal. Fig. 294 represents a longitudinal section of the central arch and its piers. The lower water-level is that of summer-water, and the top dotted line is the height above bridge of the flood which undermined and overthrew it. Mr. Hosking remarks, that the substance in thickness of which bridge piers may be built, must depend in a great degree upon the materials of which they are composed, the height to which it may be necessary to carry them, and the weight of the arches, upper works, and load; it being taken for granted that the workmanship is good, as the thickest piers, badly wrought and built, may be unable to bear the weight they are intended to carry, though piers of half their substance might be sufficient. "If the piers of Westminster and Blackfriars bridges had been one-eighth or one-ninth the span of the arches resting upon them, instead of one-fourth and one-fifth of that proportion, as they are respectively, it is not improbable that both these bridges would have failed. The late operations for the repairs to their piers have creases in breadth to the foundation. The rate of increase is regulated by the nature of the foundation, and the proportions which the body of the pier bears to the span of the arches. In many modern bridges this increase is at the rate of three inches for every foot in height. Large offsets are convenient for supporting the centres, but three or four inches in the stonework is sufficient for that purpose, the wooden platform projecting considerably more around the pier. The ends of the piers should be provided with salient angles to act as cutwaters. Some recommend that the shape of these cut waters should be triangular, and that they should differ in the size; and others, where heavy craft are navigated, consider circular cutwaters best calculated to resist the effects of concussion. The form of a gothic pointed arch diminishing to its apex, seems best fitted for the division of the stream and for resisting the impulse of heavy bodies. The shapes of the points of the piers are various, such as acute-angled, right-angled, semicircular, or two segments of a circle intersecting each other. Telford preferred the second and fourth of these forms. These projecting points are usually diminished from the limits of each side of the piers. Each course of stone around the outside should be laid header and stretcher alternately. The stretchers should be from eighteen inches to two feet in breadth, and the headers about one-third of the whole face, or each from three to four feet long. The upright, or end joints, should be correctly squared at least one foot in from the face, and in no part should be more than one inch in width. The interior, or filling-in stones, should be of equal height with the outside stones, and should have their upright joints not more than one inch wide: they should break joint at least one foot; the first and all succeeding courses should be laid flushed, with both their bed and upright joints in proper mortar. There should be an allowance for the thickness of the out side mortar joints of about onc-eighth inch when I passage of small craft up and down the river. It compressed. All the joints should be run full of grout where there is any vacancy. The hardest and most perfect stones should be used for the projecting points of the piers, especially those on the upper side of the bridge. The points should be carried up at least to above high-water mark, and at that height to be usually finished by sloping them back to the face of the spandrels. The courses of stone may vary in thickness, eighteen inches being a good average. The abutments are managed in the same manner as the piers, only their backing is generally made of good rubble stone laid in lime mortar. This rubble work must be levelled and grouted at the height of cach course of square masonry, the whole to be properly bonded and connected together. If the bridge be wide, a buttress or counterfort should be placed behind the middle part of the abutment; it should be of rubble work well bonded into the body of the abutment, and having thin hoop-iron, laths, or half-inch boards laid in as they are carried up. 3. The centres. In the construction of an arch, a timber-framing called a centre or center (from the French verb ceintre or cintre), is necessary for supporting the voussoirs until they are keyed in. The centre must be strong enough to bear the weight or pressure of the voussoirs without any sensible change of form throughout the whole progress of the work, or fatal results may ensue, as in the case of a large arch erected over the river Derwent, on the line of the Glossop and Sheffield road. The men were procecding to lay the keystone, when the centre gave way and fell with a tremendous crash into the river, causing the loss of several lives. A centre should also admit of being easily and safely removed, and so designed that it may be erected at a moderate cost. In navigable rivers, where a certain space must be left for the passage of vessels, and in deep and rapid rivers, where it is difficult to establish intermediate supports, the frames should span the whole width of the archway. In other cases the framing may be constructed upon horizontal tiebeams, supported in several places by piles or frames fixed in the bed of the river. Dr. Robison remarks that the general principles of carpentry furnish a rule for the construction of centres. To give the utmost possible strength to a frame of carpentry, every piece should be so disposed that it is subject to no strain but what either pushes or draws it in the direction of its length; and if we depend on timber alone for the strength of the centre, we must rest all on the first of these strains; for when the straining force tends to draw a beam out of its place, it must be held there by a mortice and tenon joint, which possesses but a trifling force, or by iron straps and bolts. Cases occur where it may be difficult to make every strain a thrust, and the best artists admit of tics; and indeed, where a tiebeam can be admitted connecting the two feet of the frame, no better security need be sought. But this may in some cases be inconvenient. In supporting the arch of a bridge, such a tie-beam would stop the would often be in the water, and thus exposed to accidents by freshes, &c. Interrupted ties must therefore be employed, whose joint or meetings must he supported by something analogous to the king-posts of roofs. When this is judiciously done, the security is good. But great judgment is necessary in the disposition of the pieces. It is by no means an easy matter to decide whether a beam in a centre is in a state of compression or of extension. In some works we see pieces considered as struts and relied on as such, while they are certainly tie-beams, and should be secured accordingly. It is of great consequence not to be mistaken in this point; for in such case if the piece be stretched when we imagine it to be compressed, we are not only deprived of some support which was expected, but the expected support has become an additional load. To ascertain this point we may suppose the piers to yield a little to the pressure of the arch-stones on the centre frames. The feet therefore fly outwards and the shape is altered by the sinking of the crown. The frame must be drawn again for this new state of things, and we must notice what pieces must be made longer than before. All such pieces have been acting the part of tie-beams. The centre has also to keep the arch in form that is, while the load on the centre is continually increasing, as the masons lay on more courses of arch-stones, the frame must not yield and go out of shape, sinking under the weight on the haunches and rising in the crown, which is not yet carrying any load. The frame must not be supple; and must derive its stiffness not from the closeness and strength of its joints, which are quite insignificant when set in competition with such immense strains, but from struts or ties properly disposed, which prevent any of the angles from changing its amplitude. The strength and stiffness of the whole centre must be found in the triangles into which this frame of carpentry may be resolved. The strain which one piece produces on two others with which it meets in one point, depends on the angles of their intersection, and these are greater as an obtuse angle is more obtuse or an acute angle more acute. This suggests the general maxim, to avoid as much as possible all very obtuse angles. Acute angles which are not necessarily accompanied by obtuse ones, are not so hurtful; because the strain here can never exceed the straining force; whereas in the case of an obtuse angle it may surpass it in any degree.1 Centres are composed of separate vertical frames or trusses, placed from four to six feet apart, connected together by horizontal ties and stiffened by braces. When the frames have to span the whole width of the archway, the offsets of the stone-work afford a most substantial abutment for the support of the centre. There is generally one frame under each of the external rings of arch stones, and the intermediate space is equally divided by the intermediate frames. A bridge of three arches requires (1) Robison, "System of Mechanical Philosophy;" edited by Brewster. two centres; one of five arches three centres, and the arch-stones are small, the pressure upon the so on. In the designing of centres, it is important to determine the point at which the arch-stones first begin to press upon the centre, and also the pressure upon it at different periods of the formation of the arch. It has been found by experiment that a stone placed upon an inclined plane does not begin to slide until that plane has an inclination of 30° from the horizontal, and until a stone begins to slide upon its joint, or bed, it does not of course press upon the centre. When a hard stone is laid with a bed of mortar, it will not slide until the angle becomes 34° or 36°. A soft stone bedded in moitar will stand when the angle which the joint makes with the horizon is 45°, if it absorb water quickly, because in that case the mortar becomes partially set. The pressure may in general be considered to commence at the joint which makes an angle of 32° with the horizon. This angle is called the angle of repose, and if we consider the pressure to be represented by the radius, the tangent of this angle will represent the friction: and considering the pressure as unity, the friction will be 0.625. The next course above the angle of repose will press upon the centre, but only in a small degree; and the pressure will increase with each succeeding course, so that when the plane of the joint becomes so much inclined that a vertical line passing through the centre of gravity of the arch-stone does not fall within the lower bed of the stone, the whole weight of the arch-stone may be considered as resting upon the centre. Mr. Tredgold' has given a method of estimating the weight upon a centre at any period of the construction, or when any portion of the archstones is laid, as well as when the whole weight which it has to sustain is laid upon it. As the pressure increases very slowly until the joint begins to make a considerable angle with the horizon, the strength of the centre should be directed to the parts where the strain is greatest. For example, at the point where the joint makes an angle of 44° with the horizon, the arch-stone only exerts a pressure of one-fourth of its weight upon the centre; where the angle of the joint is 58°, the pressure exceeds half the weight; but near to the crown, the stones rest wholly upon the centre. Now it is of course unnecessary to make the centre equally strong at each of these points, and if this were done there would not be the means of applying strength where it is really required, without interfering with ties and braces, which are only an incumbrance to the framing. When the depth of the arch-stone is nearly double its thickness, the whole of its weight may be considered to rest upon the centre, when the joint makes an angle of about 60° with the horizon. If the length be less than twice the thickness, it may be considered to rest wholly upon the centre, when the angle is below 60°, and if the length exceed twice the thickness, the angle will be considerably above 60°, before the whole weight will press upon the centre. When (1) Elementary Principles of Carpentry. London, 1820. centre is greater than when they are large. In order to make a centre sufficiently strong to support any part or the whole of the pressure, the strains must not act very obliquely upon the supporting pieces, and the magnitude of the parts must be proportioned to the strain upon them. In order to support any part without a sensible change of form, the parts of the centre must be so disposed, that the stress may prevent any part from rising instead of causing it to rise; for there is this danger in large arches, when the arch-stones are laid to a considerable height, that they often force the centre out of form by causing it to rise at the crown, rendering it often necessary to load the centre at the crown to prevent such rising. When arches are of small span the centres are easily managed, and when it is possible to obtain intermediate supports without great expense, large centres are not difficult. The centering of Conon Bridge, of which the span is 65 feet and the rise 21.8 feet, is a good example of this kind of construction: it was designed by Mr. Telford. trived to suit the general scantlings of timber so as to save labour, and to have the timber in as useful a state as possible when it had served its purpose. "What I had in view," he says in his Reports, "was to distribute the supporters equally under the burden, preserving at the same time such a geometrical connexion throughout the whole, that if any one pile or row of piles should settle, the incumbent weight would be supported by the rest. With respect to the scantlings, I did not so much contrive how to do with the least quantity of timber, as how to cut it with the least waste; for as I took it for granted the centre would be constructed of east country fir, I have set down the scantlings, such as they usually are in whole balks or cut in two length wise." The arch which this centre carried was of stone, its chord 60 feet 8 inches, versed sine 18 feet, and width across the vertex 25 feet. The centering consisted of 5 frames or ribs. Where intermediate supports cannot be obtained, centres require more care in the construction. The placing of a load upon the haunches must have a tendency to raise the centre at the crown, unless the frame be so contrived that it cannot rise there under the effect of any force that it may have to sustain at the haunches. In some of the centres constructed by the French engineers, there was a change of form with every course of stones that was laid upon them. Thus in the centre designed by Perronet, for the bridge of Neuilly, Fig. 297, it is obvious that such a centre loaded at A and B must rise at c, and the timbers being nearly parallel, the strains produced by a weight resting on any point must have been very great, and the consequent yielding at the joints considerable. "It is a kind of framing well enough adapted to support an equilibrated load, distributed over its whole length; but is one of the worst that can be adopted for a centre, or for supporting any variable load. It must have consumed an immense quantity of timber, and yet without the advantage of connexion. The quantity is crowded into so small better disposition of its timbers, a load at a could not cause the centre to rise at c without reducing the length of the beam DE, and the one opposite it. There is an excess of strength in some of its parts, and it is complicated in the extreme; but on the whole it is a very judicious combination." Where timbers meet at an angle, it is desirable to let them abut into a socket of cast-iron, as was done in this case, Fig. 298. If possible the principal beams should abut end to end, and intersect one another as little as possible, as every joining causes some degree of settlement, and halving the timbers together destroys nearly half their strength. Fig. 299, is a design for a centre by Mr. Tredgold. "Let the built beams EF, FF', and F'E' be each trussed and abut against each other at F and F'; then it is obvious that when the loads press equally at DD', they will have no tendency to raise the beam FF' in the middle, unless it be not sufficiently strong to resist the pressure in the direction of its length; and as it is easy to give it any degree of strength Fig. 299. that may be required, a centre of this form may with a little variation in the trusses be applied with advantage to any span which will admit of a stone bridge. When timber is not to be had of sufficient length, the beams EF, FF', and F'E' may be built in the manner directed for building beams." These beams constitute the chief support; the arch is an ellipse, and consequently a considerable part of it will bear almost wholly on the centre. But if we take the whole weight of the ring between D and C and consider it to act in the direction HF at the joining F, it will be the greatest strain that can possibly occur at that point from the weight of the arch-stones. Produce the line HF to f and let hf represent the pressure; draw he parallel to the beam EF. Then as hf represents the pressure of the arch between D and c, he will be the pressure in the direction of the beam FE; and ef the pressure in the direction of the beam FF': and these beams must be of such scantlings as will sustain these pressures. Let the weight of the arch from н to н' be estimated, and if two-thirds of this weight be considered to act at c in a vertical direction, it will be the greatest load that is likely to be laid at that point, and the dimensions for the parts of the truss FCF must be found so as to sustain that pressure. The frame EDF may be calculated to resist half the pressure of the arch-stones between B and H. From D to c the whole weight of the arch-stones together with the weight of the centre itself may be considered as acting in a vertical direction at E, and the supports at GE should be sufficient to sustain the action of this pressure. Perronet's general maxim of construction was to make the truss consist of several courses of separate trusses, independent as he supposed of each other, and thus to engage the joint support of them all. This centre consisted of a number of struts, set end to end, and forming a polygon. The trusses were so arranged that the angles of one were in the middle of the sides of the next, as when a polygon is inscribed in a circle, and another of the same number of sides is circumscribed by lines which touch the circle in the angles of the inscribed polygon. By this construction the angles of the alternate trusses lie in lines pointing towards the centre of the curve. King posts were therefore placed in this direction between the adjoining beams of the trusses. These king posts consisted of two beams, one on each side of the truss, and embraced the truss beams between them, meeting in the middle of their thickness. The abutting beams were mortised half into each half of the post. The other beam, which formed the base of the triangle, passed through the post, and a strong polt was driven through the joint and secured by a key or a nut. In this manner the whole was united, and it was expected that when the load was laid on the uppermost truss it would all butt together, forcing down the king posts, and therefore pressing them on the beams of all the inferior trusses, causing them also to abut on each other, and thus to bear a share of the load. This method of construction is the invention of Perrault. Its merits are fully discussed by Dr. Robison, in the first volume of his System of Mechanical Philosophy. This construction, somewhat modified, was used by Perronet for the centering of the Bridge of Neuilly. The arch has 120 feet span and 30 feet rise, is 5 feet thick, and is remarkable for the flatness of its crown. The frames of the centering were 6 feet apart, and each carried an absolute load of 350 tons. The strut Fig. 300 CENTERING OF THE PONT DE NEUILLY. beams were 17 by 14 inches in scantling. The king posts were of 15 by 9 each half; and the horizontal bridles which bound the different frames together in five places were also 15 by 9 each half. There were 8 other horizontal binders of 9 inches square. As the stiffness of the framing depended on the transverse strength of the beams, care was taken not to weaken them by bolts. But notwithstanding this, the framing sunk upwards of 13 inches before the key-stones were laid; and during the progress of the work the crown rose and sunk by various steps as the loading was extended along it. When 20 courses were laid on each side, and about 16 tons laid on the crown of each frame, it sunk about an inch. When 46 courses were laid and the crown loaded with 50 tons, it sunk about half an inch more. It continued sinking as the work advanced, and when the key-stone was set it had sunk 13 inches. But this sinking was not general; on the contrary, the frame had risen greatly at the haunches, so as to open the upper part of the joints, many of which gaped an inch, and this opening of the joints gradually extended from the haunches towards the crown, in the neighbourhood of which they opened on the under side. This evidently arose from a want of stiffness in the frame. But these joints closed again when the centres were struck. Dr. Robison remarks that the movements and twisting of this centre seem to indicate a deficiency not only of stiffness, but of abutment among the truss beams. The whole was too flexible because the angles were too obtuse. This arises from their multiplicity. Indeed, this centre should have consisted of fewer pieces, and their angles of meeting been proportionally more acute. Dr. Robison gives by way of favourable contrast the details of Mr. Mylne's centre used for the arches of Blackfriars Bridge. The span of the arch is 100 feet and its height from the spring about 43. The leading maxim in this centre seems to be, that every part of the arch shall be supported by a simple truss of two legs resting one on each pier. The exterior joints are strengthened and the ring made as stiff as possible by apron pieces, from the ends of each of which proceed the two legs of the trusses. These legs are 12 inches square: they are not of an entire piece, but of several, meeting in firm abutment. Some of their meetings are secured by the double king posts, which grasp them firmly between them, and are held together by bolts. At other intersections the beams appear halved into each other; a practice which must weaken them and would endanger their breaking by cross strains, if it were possible for the frame to change its shape. But the great breadth of this frame is an effectual stop to any such change. No sinking or twisting was observed during the progress of the mason work. Three points in a straight line were marked on purpose for this observation, and were observed every day. The arch was more than 6 feet thick, and yet the sinking of the crown before setting the key-stones did not amount to one inch. This centre employs more timber than Perronet's, but is in every way stronger. But with every care in the construction of centres there is always a sinking in the crown of the arch. Dr. Robison describes this in his peculiarly lucid manner. He says:-" By gradually withdrawing the centering, the joints close, the arch-stones begin to butt on each other and to force aside the lateral courses. This abutment gradually increasing, the pressure on the haunches of the centering is gradually diminished by the mutual abutment, and ceases entirely in that course which is the lowest that formerly pressed it: it then ceases in the course above, and then in the third, and so on. And in this manner not only the centering quits the arch gradually from the bottom to the top, by its own retiring from it, but the arch also quits the centering by changing its shape. If the centering were now pushed up again, it would touch the arch first at the crown; and it must |