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Fig. 267. cnorLAND Itridge.

which, meeting in the middle, form pointed arches, their bases or abutments standing upon the points of nn equilateral triangle.

Old London Bridge was commenced in the reign of Henry II., under the direction of Peter of Colchester, in 1176, the same year that the bridge of Avignon was begun. TbeFrench bridge was completed in twelve years: the erection of the English bridge occupied eighty-three; but this arose from the interruptions which must be experienced in a river where the tide rises twice every day, from 13 to 18 feet. The piles were principally of elm, and remained for six centuries without material decay, although a portion of the bridge fell, and was rebuilt, about one hundred years after it was begun. The stone bridge at Neweastle-upon-Tyne (built in 1281), and that over the Medway, at Rochester, consisting of 11 arches, were erected about the same time as the bridges of St. Esprit and Lyons, already noticed. During several centuries there were houses along each side of London Bridge; but these were removed in 1758. The middle pier was also taken away. The piles were drawn by a very powerful screw, commonly used for lifting the wheels of the water-works; and

the space including the two adjacent arches converted into one arch, of 72 feet span. The remaining old arches were very narrow, and the piers of vast size, being from 15 to 25 feet in thickness above the sterlings. Many of the old English bridges were fortified with gateways. In 1636, Inigo Jones designed a bridge, which was erected at Llanwst, in Denbighshire, consisting of 3 arches, segments of cireles: the middle one is 58 feet span, and rises 17 feet; the piers are 10 feet thick, and the breadth of the soffit of the middle arch is 14 feet. The archstones of the largest arch are only 18 inches deep; the covering over them is small, and the approaches are very steep, so that the bridge has a very light appearance.

In 1738, the situation of the present decayed structure, Westminster Bridge, was agreed on, and Mr. Labalyc, the architect, was allowed, after much doubt and difficulty on the part of the commissioners appointed by Parliament, to lay the foundations of the piers in caissons, or chests, filled with masonry, of a form and size suitable to the piers intended to be erected, and floated to the sites of the piers, where they were sunk, the bed of the river having been previously levelled by dredging. This method was adopted instead of placing the foundations upon piles, in the ancient manner, cut off above the level of low water, or using batterdeaux or cofferdams formed around the foundations, and pumping the water from the inside, as had been done in more moder n times. The bridge was surmounted by a lofty parapet, the object of which was to secure a sufficient weight of masonry to keep the caissons in place. Labalye states that this bridge contained twice the number of enbic feet of stone used in St. Paul's Cathedral. The bridge was finished in 1747, and was about to be opened, when the following accident happened :—Some workmen employed to get gravel out of the bed of the river, to cover the roadway of the bridge, finding some very suitable near the third pier on the western side of the centre arch, excavated considerably lower than the foundation, and too near it; consequently, the gravel escaped from under the platform, and the pier sunk so much as to make it necessary to take down the two arches which rested upon it. The opening of the bridge was therefore delayed until the I8th November, 1750. This bridge consists of 13 large and 2 small arches: their forms are semicircular; the middle one is 76 feet span, and the breadth over the parapets 44 feet. The system of building on caissons, as illustrated by the subsequent history of this bridge, has proved a failure, and has not been adopted in England. After the removal of old London Bridge, the bed of the river, on which the caissons rest, became undermined so much by the body of water, and increased velocity of the tide, that some of the piers gave way in 1846, so that in August of that year it was found necessary to close the bridge. Portions of the heavy masonry about it were removed, and the bridge itself was considerably lowered. It now remains standing, as it were, upon crutehes, awaiting its dissolution. Mr. Barry has furnished a design for a new bridge, which will probably be adopted when the new Palace at Westminster shall be completed.

Blackfriars Bridge was commenced from a design by Robert Mylne, about ten years after the completion of Westminster Bridge. It consists of 9 elliptical arches. The middle arch is 100 feet span; the length of the bridge is 995 feet from wharf to wharf; the breadth across the bridge is 43 feet 6 inches. The piers were built in caissons; but piles were previously driven for the caissons to rest upon. The arches being of wider span and of an elliptical form, and the piers of proportionally less thickness, and having less masonry over the top of the arches, this bridge has a much lighter appearance than that of Westminster. The expense of Blackfriars Bridge, inclnding the purchase of premises, was about 260,000/.: that of the building was only 170,000/. Westminster Bridge cost about 400,000/. Blackfriars Bridge was made passable as a bridle-way on the 19th November, 1768, and was generally opened on the 19th November, 1769. There was a toll of one halfpenny for every foot passenger, and one penny on Sundays, until the 22d June, 1785, when Government bought the toll, and made the bridge free. A few years ago, the bridge was lowered, and the open balustrade removed. It is impossible in this brief sketeh to notice the various bridges erected in modern times in Great Britain and Ireland. Some of them will be incidentally noticed in the different sections of this article. We cannot, however, refrain from giving a few details respecting the beautiful bridge which has taken the place of old London Bridge.

The old method of laying the foundations of piers, which was introduced soon after the Conquest, was very defective, and was particularly exemplified in the old London Bridge. "The masonry commenced above low-water mark, being supported on piles, which would have been exposed to the destructive alternation of moisture and dryness, with the access of air, if they had not been defended by other piles, forming projections, partly filled with stone, and denominated sterlings, which, in their turn, occasionally required the support and defence of new piles surrounding them, since they were not easily removed

when they decayed; so that, by degrees, a great interruption was occasioned by the breadth of the piers, thus augmented, requiring, for the transmission of the water, an increase of velocity, which was not only inconvenient to the navigation, but also carried away the bed of the river under the arches and immediately below the bridge, making deep pools or excavations, which required from time to time to be filled up with rubble-stones; while the materials which had been carried away by the stream were deposited a little lower down, in shoals, and very much interfered with the navigation of the river." From these circumstances, as well as from the effects of time and decay, it happened that the repairs of the old London Bridge often amounted, for many years together, to 4,000/. a-ycar. "It is true that the fall produced the trifling advantage of enabling the London water-works to employ more of the force of the tide in raising water for the use of the city; and this right being established as a legal privilege, long delayed the improvements which might otherwise have been attempted for the benefit of the navigation of the river. The interest of the proprietors of the water-works had been valued at 125,000/., and it had been estimated that 50,000/. would be required for the erection of steam-engines to supply their place; while, on the other hand, from thirty to forty persons, on an average, perished annually, from the dangers of the fall under the bridge."

The consequence of removing the centre pier was somewhat to diminish the fall; but it was found necessary to obstruct the channel again, in order that the stream might have force enough for the waterworks. But it was very difficult to secure the bottom from the effects of the increased velocity under the arch. A number of strong beams were fixed firmly across the bed of the river; but only two of them remained for any length of time, and the materials carried away were deposited below the middle arch, so as to form a shoal which was only sixteen inches below the surface at low water.

At length, after the bridge had been for more than six hundred years exposed to the constant action of a rapid current, it was determined to erect a new bridge. The loss of life and property was frequent, in consequence of the great velocity with which barges and smaller craft were carried by the stream through its arches, and of their descent, by means of a considerable fall, from one level to another. In 1823, an Act was obtained for rebuilding the bridge, and for making suitable approaches to it. John Rennie was appointed architect; but, as he died before the bridge was begun, the execution of his plan was confided to his son, Sir John Rennie. The new bridge, consisting of five elliptical arches, was intended to be on the site of the old one, and to correspond with the old approaches. It was, however, afterwards determined to construct it I80 feet higher up the river, so as to avoid the steep ascent of Fish Street-hill. The first pile of a cofferdam for the south pier was driven on the 15th March, 1824, and the first cofferdam was completed on the 27th April, 1825. It consisted of three rows of piles, dressed in the joints, and shod with iron; and many of them were 80 or 90 feet long. The first stone of the bridge was laid on the 15th June. The foundations of the piers are of wood, piles of beech being first driven in the interior of the dam, to a depth of nearly 20 feet, in the stiff blue clay which forms the natural bed of the river; two rows of horizontal sleepers, about 12 inches square, were then laid on the head of these piles, and covered with beech planking, 6 inches thick, on which the lowermost course of masonry was laid. another was considered to involve the whole question of the stability of the arch. Let a structure, Mnlk, Fig. 271, composed of a single row of unccmented stones, of any forms, and placed under any given circumstances of pressure, be intersected by a surface 1, 2, and let the resultant a A of all the forces which act upon one of the parts, Mn21, be taken. Then let this intersectingsurface change its form and position, so as to coincide in succession with all the common surfaces of contact, 3 4, 5 6, 7 8, 910, of the stones which compose the structure, and let b n, cc, do, ez, be the resultants, similarly taken with a A, which correspond to those several planes of intersection. In each such position of the intersecting surface, the resultant spoken of, having its direction produced, will intersect that surface either within the mass of the structure, or, when that surface is produced, without it. If it intersect it without the mass of the structure, then the whole pressure upon one of the parts, acting in the direction of this resultant, will cause that part to turn over upon the edge of its common surface of contact with the other part; if it intersect it within (he mass of the structure, it will not. Thus, if the direction of the resultant of the forces acting upon the part M N 1 2 had been" a' A', not intersecting the surface of contact 1 2 within the mass of the structure, but supposed to be produced beyond it into a ; then the whole pressure upon this part acting in a'k. would have caused it to turn upon the edge 2 of the surface of contact 12. So, also, if the resultant had been in a" A", then it would have caused the mass to revolve upon the edge 1. But the resultant having the direction a A, the mass will not be made to revolve on cither edge of the surface of contact 1 2.

The obstruction caused by the works of the new bridge rendered it necessary to throw two of the small arches of the old bridge at each end into one, which was done in about six weeks.

The centerings for supporting the arches of the new bridge were required to be of great strength, because the flatness of an elliptical arch produces a greater load on the centering, while building, than the semicircular arch does. Each centre consisted of ten frames, or ribs, supported at the two ends on piles driven into the bed of the river. These frames were boarded over on the top with stout planks. The arches, being unequally wide, required four sets of centres, each containing nearly 800 tons of timber. The first arch was keyed in on the 4th August 1827, and the last on the 10th November, 1828. Instead of filling up the spandrels of the arches with loose rubble-work, according to the usual practice, longitudinal or hance walls were built over the arches, and over these large blocks of stone were bedded, surmounted by heavy stone landings, on which is a course of cement, and over that the roadway. The approach from the city side is brought to the level of the bridge by a series of land arches in continuation of the bridge. The bridge was completed on the 31st July, 1831. It consists of five elliptical arches: the centre arch is 152 feet span, with a rise of 29£ feet above high-water mark. The two arches next the centre are 140 feet span, with a rise of 27£ feet; and the two abutment arches are 130 feet span, with a rise of %i\ feet. The piers arc solid, and rectangular in form. The great diminution in masonry work, in consequence of the form of the arches, allowed the piers to be greatly diminished in size. The line of roadway is a segment of a very large circle, the rise being only 1 in 132. The abutments are each 73 feet wide at the base, and spread out backward, so as to sustain the thrust of the bridge with best effect. The length of the bridge, from the extremities of the abutments, is 982 feet, and, within the abutments, 728 feet. The roadway is 53 feet between the parapets, being 8 feet wider than the old bridge, and 11 feet wider than any other bridge on the Thames. The foot-ways occupy 9 feet each, and the carriage-way 3j feet. The bridge is of the finest granite, from the quarries of Aberdeen, Ilcytor, and Penryu. The total quantity of stone was about 120,000 tons.

Section II.—Theory Of Stoxe Bridges.

The theoretical principles of stone bridges contain the mathematical demonstrations of the properties of

arches, the thickness of the piers, the force of the water against them, and other abstruse but necessary caleulations. This branch of the subject, which has exercised the talents and ingenuity of some of the greatest mathematicians in modern times, is not sufficiently elementary for the present work; but it may be interesting to give a short abstract of Professor Moseley's theory of the arch, chiefly abridged from Mr. Weale's beautiful work, already referred to, with occasional reference to the accomplished Professor's popular works, entitled, "Illustrations of Mechanies," third edition, London, 1846, and "Mechanies applied to the Arts," third edition, London, 1847. We will, however, first describe the various parts of an arch.

An arch may be defined as a collection of wedgeformed bodies, named voussoirs, or arch-stones, v r, Fig. 268, the first and last of which are sustained by a support or abutment, A B, while the intermediate ones are sustained in their Fig- 26Spositions by their mutual pressures, and by the adhesion of the cement interposed between their surfaces. The centre voussoir, k, or that in the highest part or crown, c, of the arch, is called the key-stone. The inferior surface of the arch, sfhf/>, is called its intrados, and sometimes its soffit; but this latter term is also occasionally restricted to the under surface of the arch, h, at its key-stone or crown. s/fs are the flanks of the arch. The exterior surface, e C d, is called its extrados, or back. The points s s, where the intrados meets the abutment, are called the springings, their horizontal direction, sis, the span, and the distance i h the rise or height of tho arch.

Such a structure, or, indeed, any structure, built up with uncemented stones, may fall, either by the opening of some of the joints, causing the stones to tarn on the edges of one another after the manner of a hinge, or by the stones slipping upon one another.

These two cases are represented in the following figures. In Fig. 209, an arch is falling by the turning

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Thus, the condition that no two parts of the mass should be made by the insistent pressures to turn over upon their common surfaces of contact, is involved in this other, that the direction of the resultant, taken in respect to every position of the intersecting surface, shall intersect that surface actually within the mass of the structure.

If the intersecting surface be imagined to take up an inGnite number of other positions, 1 2, 3 4, 5 (J, &c., and the intersections with it, abed, &c. of the directions of all the corresponding resultants be found, the curve line abedef, joining these points of intersection, is named by Professor Moscley the line of resistance. This line can be completely determined by the methods of analysis, in respect to a structure of any given geometrical form, having its parts in contact by surfaces also of given geometrical forms. And conversely, the form of this line being assumed, and the direction which it shall have through any proposed structure, the geometrical form of that structure may

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be determined, subject to these conditions. Or lastly, certain conditions being assumed, both as it regards the form of the structure and its line of resistance, all that is necessary to the existence of these assumed conditions may be found. Let the structure A B C B, Fig. 272, have for its line of resistance the line p Q. Now, it is evident that if this line cut the surface m N of any section of the mass in a point », without the surface of the mass, then the resultant of the pressures upon the mass cmn will cut through n, and cause this portion of the mass to revolve about the nearest point N of the intersection of the surface of section Mn with the surface of the stricture.

It is thercfore a condition of the equilibrinm, that the lii.o of resistance shall intersect the common surface of contact of each two contiguous portions of the structure actually within the mass of the structure; or, in other words, that it shall actually go through each joint of the structure, avoiding none: this condition being necessary, that no two portions of the structure may revolve on the edges of their common surface of contact.

Let us borrow from the same competent authority another illustration of this great condition of the equilibrinm of an edifice. Let the extreme stone, Fig. 273, of an edifice of uncemented stones have impressed upon it any given foree, p. In addition to this force, the stone is acted upon by gravity, which may be supposed to be collected in its centre of gravity. The resultant of these two forces will represent the whole force by which the first stone is pressed upon the second. If this resultant have its direction anywhere within the edges of the joint or surface of contact of the first stone with the second, the one will rest upon the other; if not, it will turn over u|>on it. The second stone may be considered to have its upper surface acted upon by the resultant force just spoken of, and this to be the only force pressing it downwards, besides its own weight, collected in its centre of gravity. If, then, a second resultant be taken, being that of two forces, of which the first resultant is one, and the weight of the second stone the other, then this second resultant will be that force by which the second stone may be supposes to be pressed upon the third. If its direction lie within the edges of the joint of the second and third stones, the second will rest upon the third; if not, the superstructure will turn upon the third stone. So, also, if a third resultant be taken, being that of two forces, of which one is the second resultant, and

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the other the weight of the third stone, then this third resultant will be that foree by which the third stone is pressed upon the fourth; and the conditions of the equilibrinm of this third stone are, that this resultant shall have its direction within the edges of the joint of the third and fourth stones: and so on of the rest. If we now suppose that the intersections of all these resultants with the planes of the joints of the successive stones are found, by mathematical investigation, and a line be drawn through all these points of intersection, we get the line of resistance before spoken of. If this line, which is a curve, have its direction anywhere beyond the joints of the stones, the edifice will be overthrown at such joints; but if the curve nowhere lie without the mass of the edifice, it will nowhere be overthrown by the turning of its stones.

But there is a second condition necessary to the stability of the structure. Its surfaces of contact must nowhere slip upon one another. That this condition may be satisfied, the resultant corresponding to each surface of contact must have its direction within certain limits. In Fig. 271, the line A B C D E, formed at the points of the consecutive intersections of the resultants a A, 4b, ec, do, &c., is termed the line of pressure. Its geometrical form may be determined under the same cireumstances as that of the line of resistance. A straight line, ec, drawn from the point e, whore the line of resistance abed intersects any joint 5 6 of the structure, so as to touch the lino of pressure A B C D, will determine the direction of the resultant pressure upon that joint: if it lie within a cone defined by Professor Moseley as a right cone, having the normal to the common surface of contact at the point of intersection of the resultant for its axis, and having for its vertical angle twice that whose tangent is the coefficient of friction of the surfaces, the structure will not slip upon that joint; if it lie without it, it will.

Thus, the whole theory of the equilibrinm of any structure is involved in the determination with respect to that structure of these two lines,—the line of resistance, and the line of pressure: the former determining the point of application of the resultant of the pressures upon each of the surfaces of contact of the system; the latter, the direction of that resultant.

In an upright pier or wall, the line of resistance is a ,hyperbola, the position and magnitude of which may be determined by construction. Resolve the foree p, Kg. 273, which acts upon the summit of the pier, into two others, one of which is in a vertical and the other in a horizontal direction. Caleulate the height of a mass which, being of the same substance and the same thickness as the pier, shall have a weight equal to the vertical foree of these two, and let this height be B U. Caleulate in like manner the height of a mass whose weight shall equal the horizontal foree, and let this height be A S. (The dotted lines, Fig. 273, represent these two imaginary masses.) Take >:, the centre of the width of the pier, and set off E G, equal to A s. Then draw the vortical G c. C will be the centre of the hyperbola, and the vertical

c E x will be its asymptote. Now, the curve cf a hyperbola always approaches, but never touches, its asymptote. The curve of resistance always, then, approaches, but never touches, the line c x; and if this line lie, as in the figure, within the mass of the sphere, then the line of resistance, never passing the line c x, can never cut the outward surface of the pier; and, however tall it may be, the pier can never be overthrown by the action of this foree. It is also a remarkable feature of the theory, that the pier will bear this insistent pressure p wherever in A G it is applied parallel to its present direction; the position of the centre of the hyperbola, c, not being changed by any alteration in the point of application of that pressure, but only in its magnitude.

Professor Moseley also gives the following method for determining the greatest height to which a pier can be built, so as to sustain a given pressure upon its summit. If A B, Fig. 273, be greater than half the width of the pier, or if G lie beyond B, then there will be some point in the outward surface or extrados of the pier where the line of resistance will cut it; and there will therefore be a certain height beyond which the pier cannot be carried without being overthrown. This height is thus determined. Let p, Fig. 274, be the point where the insistent pressure intersects the summit of the pier, and let A S, and A T, and E G be taken as before; join u G, and through p draw p z, parallel to u G. Z will be the point where the line of resistance cuts the extrados, and will indicate the greatest height to which the pier can be carried without being overthrown; or, if it can be carried higher, then is this the point to which an inclined buttress should be built to support it.

The details which have been given will enable the reader to form a general idea of the application of the theory of the line of resistance to the conditions of the equilibrinm of the areh. It is a general condition that this line, Rqaq' R, Fig. 275, (which represents an areh having the joints of its voussoirs perpendicular to the intrados, as they are usually made) touches the intrados or inner sur-1 face of the areh Fig. J75.

on both sides at its haunches, q Q_\ and the extrados at the crown, in A, and that afterwards, at lower points, it cuts the extrados or outer surface of the areh at Re.'. If some resistance, of an abutment or pier, be not opposed at this last point to the pressure, the whole of which acts there, the areh will be overthrown. If it be supported there by a pier, the line of resistance passes into the pier, and assumes a new character and direction; that direction having a general tendency towards the back or outer surface of the pier. If, by reason of the comparatively small height of the pier, the line cf resistance does not anywhere reach the back of the pier, but intersects its base, the pier will stand. But if the height be

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