A bridge is a mode of conveyance from one part of space to another, the intermediate part being either impassable, or difficult, or otherwise of an inconvenient access. The strength must be in proportion to the weight which is to be supported; the extent or width of the passage being likewise taken into consideration. This passage may be of a considerable distance, and the weight to be supported inconsiderable; for example a spider is the greatest weight to be supported; and she can spin as much matter from her bowels as will answer her purpose, and can find supports upon which she can make the extremities of her bridge to rest. But not to take up time to mention the ingenuity (or under whatever name it may be designed) of insects, birds, or quadrupeds, who discover admirable instances of art suitable to their nature, and uses fitted for their situation, our chief intention is to investigate the different exertions of the rational part of the creation, and their manner of accommodating themselves to answer their necessary exigencies, particularly at present confining ourselves to the formation of bridges of different kinds. The most simple part of these, we cannot doubt, were in use from the beginning of time. When any passage exceeded the step or stretch of a man's legs, we cannot imagine, but his natural invention would lead him to apply a stone, if of sufficient length to answer his purpose; but if not, a piece of wood, or trunk of a tree, would be employed in the same way to render the passage more easy for himself.

History does not inform us that this useful art was carried to any great extent, in the ages of the antediluvians; but we can scarcely imagine but they were acquainted with it, so far as we have mentioned, and even to a greater degree. Can we suppose that such geniuses as discovered the method of founding and working in iron and brass, and the formation and use of musical instruments, would be wanting in discovering methods so intimately connected with their own own advantage? We have no accounts handed down to us, that they occupied houses composed of different apartments, and of different stories or flats; yet we find the infinitely wise and merciful Governor of the universe, when admonishing Noah respecting the building of an ark for his safety, speak to him of different rooms and stories, of which it was to consist, in terms with which Noah was well acquainted. As the Almighty always accommodates himself to the capacities of his creatures, if Noah had not been acquainted with these terms, can we doubt that the Almighty would not have furnished his favourite servant with a perspective view of these rooms and stories as he did to Moses, when giving him instructions to raise and construct a fabric of which he formerly never had obtained a view? But this amounts to no more than that it might be, and therefore we will not dwell upon it.

Of what took place after the flood, we have no remains of antiquity, for many years, of this art being cultivated to any extent; although it is surprising, that upon viewing the beautiful and superb dome of the heavens, and the variegated arch that at times made its appearance, that an imitation of neither of these was not earlier attempted. Among the eastern nations, and after them the Egyptians, who have left us so many monuments of grandeur and art, very little of the arch is to be found in any degree of elegance. In some of the late researches into their antiquities, a zodiac painted in lively colours, and some vaultings cut in a rock, have been discovered; but what is formed of different stones is but of a rude composition; yet being of the more early period, we cannot but conclude, that they gave the idea to the Greeks, who improved it in a more elegant style.

It is probable that the Chinese, even at an earlier period, arrived at a degree of perfection and elegance in this art, which neither the Greeks nor the Romans ever reached. We, who boast, and not without some reason, of the elegance and extent to which we have carried it, have not outdone them. We find that they have constructed a bridge of one arch, the span 400 cubits, in the ordinary computation 600 feet, from one mountain to another; the height of this arch is likewise given of 500 cubits or 750 feet. It is universally allowed, that if Noah was not the founder of that monarchy, it was some of his grand-children, at a very early period; their form of government resembles the patriarchal, which is in favour of Noah's being their founder, and that they cultivate these arts, of which he instructed them in the rudiments: but this is not a place for discussion of this subject.

But to return to the Greeks and Romans, of whose history we know more than we do of the other: Although we have admitted the Egyptians to have struck out the plan, yet, in point of elegance, in combining the parts of the arch, we will not deny the Greeks to have the first share. On account of an effigy, having Janus upon the one side, and a bridge on the opposite, some have ascribed the honour of the art to him; he might indeed, on account of his improvements of the art, shewn himself deserving of having, along with his effigy, the distinguished art he had excelled in, engraved on the metal, as a memorial of his merit. Whether the bridge improved by Janus were over land or water we are not informed; but certain it is, that necessity, which is the mother of invention, could not fail to form schemes for conveyance over water. We find boats, or some species of ships, used at a pretty early period; and we are surprized not to find them more early than we have account of. A boat or ship is an inverted arch turned down into the water. Of a bridge of this kind, we find Darius avail himself in passing the Hellespont, or the Bosphorus, for we find different historians of different opinions which of them he passed, and the word Propontis answers to either; although we rather agree with those that make the passage at the Dardanelles, or in that strait. This mode of passage is still in use, and found very convenient; but we can scarcely suppose that Darius, and his officers, and court, never heard of a bridge before that idea struck them, in the execution of which they happily succeeded. It is highly probable that they were acquainted with, and had formed bridges in their own country, and that want of materials to make a solid wall, induced them and others to construct arches, for the purpose of aqueducts, of which there is so much occasion in Persia, on account of the scarcity of water; and as they knew not the mode of conveying their water in pipes.

Among the Romans we find arches of different kinds, and particularly triumphal arches, although these were not always formed of lasting materials; but their aqueducts were, of which the remains of several are found in France, Spain, and others of their ancient territories. Caesar formed a bridge over the Rhine, Trajan over the Danube; with many others, the particular mention of which would not much amuse our readers: at the same time we hope it will not be disagreeable to give a short account of Trajan's bridge, in the words of Dion Cassius. "Trajan built a bridge over the Danube, which in truth one cannot sufficiently admire; for though all the works of Trajan are very magnificent, yet this far exceeds all the others. The piers were 20 in number, of square stone; each of them 150 feet high above the foundation, 60 feet in breadth, and distant from one another 170 feet. Though the expense of this work must have been exceeding great, yet it becomes more extraordinary by the river's being very rapid, and its bottom of a soft nature; where the bridge was built was the narrowest part of the river thereabout, for in other parts of the river it was double or treble this breadth; and although on this account it became so much the deeper, and more rapid, yet no other place was so suitable for this undertaking. The arches were afterwards broken down by Adrian; but the piers are still remaining, which seems as it were to testify, that there is nothing which human ingenuity is not able to effect." From this account, the whole length of this bridge is 4770 feet, that is 500 feet less than an English mile. The architect of this great work is said to be Apollodorus of Damascus, who, it is likewise said, left a description of the work; but how much it is to be regretted that it is nowhere found on record!

Among the moderns, the French and German engineers, and perhaps the Italians, ought not to be neglected. Of those who have written on the subject, we we may name Belidor, of whom it is said, that he had the best information, from his acquaintance and knowledge of the chief works of France and Germany, as well as from his experience as an engineer. His directions as to an arch or bridge are shortly thus; that the piers ought to be one-fifth part of the opening, and not less than one-sixth; that the arch stones ought to be one thirty-fourth part of the opening: In general, that the pier ought to be of that strength, that it will support its arch as an abutment, which by practice he finds one-fifth part of the opening to be sufficient; but gives as a rule, one-sixth part, and two feet more: that is, an arch of 36 feet, one-sixth is $6 + 2 = 8$, the thickness of the pier. And where the arch is 72 or more, he deduces three inches for every six feet above 48; therefore the pier of 72 would be 14, that is two feet more than the one sixth-part; but with the above allowance the pier is only 13; when the width is 96 or above, he allows the one sixth part of the opening as quite sufficient: this he seems only to deduce from observation, without adducing a reason; now why a wide arch should be supported by more slender piers, in proportion, does not appear quite consistent with his principles; that the pier must be of such strength as to serve for an abutment to the arch thrown upon it, independent of the other arches, which when thrown, are allowed to be a counterpoise to the prelure. Although we do not see why it is applicable to his principles, we will afterwards have occasion to show, that it tends to corroborate the principles we mean to advance.

We find another experienced engineer, Mr Gautier, who only differs from Belidor, in so far as we observe, as to the length of the arch-stones. Gautier directs, that if the arch is 24 feet, the arch-stone ought to be 2 feet; if 45, 3 feet; if 60, 4 feet; if 75, 5 feet; if 96, 6 feet; if the stone is of a durable nature: if soft, of greater dimensions. Belidor gives the general rule, one twenty-fourth part of the opening: this must certainly be considered under some limitation; for, if the arch is only 12 feet, the arch-stone would be only six inches, which, we think, will be thought too light; and arches over doors and windows would not be three inches; but although he mentions no limitation, we suppose, if a 24 feet arch is allowed 2 feet of an arch-stone, the rule may with safety be followed; and that a six foot stone, of a durable nature, may be an arch-stone, although the span was 150 or 200 feet.

Under whatever names later engineers have acted, we find Belidor has in general been followed; both by Mr Mylne and others. Peter of Colechurch, a priest, architect of London bridge, has given his pier a much greater strength, being more than half the opening; the piers being from 25 to 34 feet, 18 in number; the width of the river only 900 feet, over which this bridge extends.

An ample reparation is made for these inconveniences in Westminster bridge; the piers more slender; a more easy passage for the water, the piers being only 17 feet. The breadth of the river 1223 feet. The arches are all semicircular, and spring from about two feet above low-water mark; they consist of 13 large arches and two smaller; the middle arch is 76 feet span, and the other arches decrease on each side by four feet. The passage for carriages is not of an easy ascent, having 30 feet of rise in 611.5 feet; it is supplied with plinth stones for foot passengers on each side; the ledges adorned with balustrades, and semi-octagonal towers, which form the recesses of the foot-way; the whole width is 44 feet. The whole is allowed to be elegant and well executed.

We now take a view of Blackfriars bridge (fig. 12. Plate CXXX.), which presents us with something novel, is agreeable to the eye, and no precaution is neglected that could contribute to its strength, or give addition to its elegance. Its arches are of the elliptic form, at least nearly so. Upon examination of the figure of which we are possessed, the middle arch is a span of 100 feet, the flat part of the arch is described with a radius of about 57 feet; and the lesser circles on each side 35 or 36 nearly; this small arch is continued below its diameter, till its chord become 16 feet nearly, and its versed sine 5 feet, which gives it the degree of novelty alluded to; and which is far from being disagreeable to the eye. The shoulders are compactly filled with rubble-work; the bed of each row tending to the centre of the arch. To the height the arch can be raised without a supporting frame, an inverted semicircle is drawn, the convexity of the arch resting upon this rubble-work, which is formed of Kentish rag, but other hard stone will equally answer the purpose, as this cannot be everywhere procured. This inverted arch answers two material uses; it prevents this rubble being raised by any lateral pressure; and which we think the most material is, that it makes these parts of the arch, which form the greatest lateral pressure, to abut upon one another; of consequence there is little or no lateral pressure upon the pier. But we shall refer our observations upon this as well as the preceding arches, till we have given some account of other bridges; as we wish to make the article conducive to the information of our readers, and at the same time methodical.

The bridge of the greatest extent in England, is that built over the Trent at Burton; its length is 1545 feet, supported by 34 arches.

The most stupendous bridge in Europe, is that built over the Tawe in Glamorganshire, consisting only of one arch, the segment of a circle whose diameter is 175 feet; the chord of the segment or span of the arch is 140 feet; the height 35, and abutments 32 feet; the architect of this stupendous arch was William Edward, a country mason; it was executed in the year 1756.

We have likewise an account of the famous bridge the Rialto at Venice, the design of Michael Angelo. On account of its flatness and extent, being 98½ feet span, it is reckoned a master-piece of art. It was built in the year 1591. Its height is only 23 feet above the water, but we find it now outdone by a country mason in Britain.

The next species of bridge to be noticed is a rafted bridge; this species of bridge is formed of bundles of rafters, which being covered with boards and planks, form a passage over marshy ground. Bridges formed of casks, bottles, or sometimes bullocks bladders blown up, and attached to one another, have been used upon occasions by armies. They have been named scogafri. The materials are carried along with the army in their march, which when joined, form Bridge form a ready passage over rivers, or other obstructions by water; which they term a portable bridge: materials of the above kind being light, and many of them, as barrels, being useful for other purposes. Bridges may be used of them to a very great extent.

Draw-bridges differ only in form and materials, being made of wood, and turning at one end upon hinges, or, when opening in the middle, at both ends, for the purpose of allowing ships to pass up and down a river; in this case the passage over the middle arch is formed by a draw-bridge; the manner of raising them being so universally known, it would be superfluous to describe.

A Flying bridge, is a bridge formed of one or more boats joined together, and covered with planks in the manner of flooring, surrounded with a rail or balustrade; according to its breadth it has one or more masts to support a rope at a proper height; one end turns round a windlass, the other end of the rope is fastened to an anchor in the middle of the water; the rope is kept from sinking in the water, by resting on small boats at proper distances, that float and support the rope. The bridge is then wrought by one or more rudders, from side to side of the river; the rope is lengthened or shortened by the windlass, according to the breadth of the river. Some of these bridges are formed with an upper and lower deck, for conveying cavalry and infantry at the same time, or a greater number of infantry; it being well understood by military gentlemen, that the greater number that can be conveyed over at once, they can the sooner form into defensible corps, and support one another till their strength is augmented that they can act on the offensive.

In Plate CXXIX, we have represented a flying bridge of this kind. Fig. 1. is the perspective view of the course of a river and its banks; \(a, b, c, d\) two long boats, or batteaux, which support the bridge; GH, KL, two masts joined at their tops by two transverse beams, and a central arch supported in a vertical position, by two pairs of shrouds, and two chains LN, HR. M, a horse, or cross-piece, upon which the cable MF ef rests; the use of this cable is to react upon the working of the rudders, and prevent the bridge from being carried down by the current of the water. E is the windlass formerly mentioned; \(a, b\), the rudders. AB, CD, two portions of bridges of boats, fastened to the banks on each side of the river, and between which the bridge traverses. \(e, f\), Chains supported by small floats, sometimes five or six of them placed at proper distances; the number to be used will be regulated according to the length of the cable; one of them is placed at the anchor, so as the cable may swing above the surface of the water as near as the depth of the river will permit.

Fig. 2. is a plan of the same bridge; \(a, b, c, d\), the two boats that support it. K, G, the two masts. KFG, the transverse piece, over which the cable passes; E, the windlass about which the cable is wound; \(a, b\), the rudders; o, a boat; c, one of the floaters that support the chain; N, N, pumps for extracting the water out of the boat; P, P, captains.

Fig. 3. A lateral elevation of the bridge, A, c, one of the boats; b, the rudder; E, the windlass; M, the horse; GH, one of the masts; E, N, H, F, the cable.

In this view the balustrade along the side of the bridge is in full view.

Fig. 4. is an elevation of the hinder part of the bridge or stern. \(a, b\), The two boats; GH, KL, the two masts; HL, the upper transverse beam; p, q, the lower transverse beam, over which the cable passes, and occasionally slides from the one mast to the other; and must on that account be kept well greased; p k, g g, shrouds extending from the sides of the bridge to the top of the masts; M, the cross-piece, over which the cable passes to the windlass.

Besides these temporary bridges of boats already mentioned, there are permanent bridges formed of boats, as at Rouen, Beaucaire, and Seville. Those of Rouen and Seville are the most noted; that at Rouen was constructed to supply the stone bridge built by the Romans, said to have been a stately fabric. The boats are very firm, well moored with strong chains, and kept in proper repair. It is almost 300 yards in length, paved with stones as a street. A bridge of boats has the advantage of other bridges, if well moored, for as the water rises, whether by rains or tides, they keep afloat. This bridge is represented by some as a wonder of the present age; others say, it is far surpassed by that of Seville; but when we reflect upon that constructed by Darius over the straits of the Dardanelles; and on that by Caesar over the Rhine, we cannot view either of them with so much surprize.

We find some of a different construction, called floating bridges; which we think should rather be called sliding bridges; they are so constructed that the one lies above the other, when not in use. When intended to be used, by drawing of ropes turned over pulleys, the upper one moves forward, till it passes over the other, when they are joined in one, and form the intended passage. It will readily occur to our readers, that these must be much limited as to their length, both on account of their weight, and the strength of the rope that would be necessary, both to pull them over, and return them to their place; they can only be of use in passing a moat, in besieged places, or such as are of inconvenient access and little frequented.

We cannot omit taking notice of some natural bridges, in particular two very remarkable ones; the one in Virginia, described by Mr Jefferson in his State of Virginia. It commences at the ascent of a hill, which seems to have been cloven asunder, by some convulsion of nature; the fissure at the bridge is by some measurements said to be 270 feet; by others only 205; width at bottom 45 feet, at top 90, which gives the length of the bridge; the thickness at the summit of the arch is 40 feet; considerable part is of earth, upon which grow many large trees; the residue is of the same materials with the hill on both sides, which is a solid lime-stone rock, and forms the arch, which is of a semi-elliptical form, very flat; the height of this arch above the water (the whole being 205 and 40 the thickness) is 165 feet; the breadth at the middle is about 60 feet. It has no ledges, but what is formed on some parts by the rock, but even at these few can stand upon their feet to look down; but go on hands and feet to peep over. On the contrary the view from below is most delightful, and enchanting. The fissure continuing narrow, and straight, both above and below; and of such height that Bridge that it exhibits a prospect, for about five miles; gives a short but very pleasing view of Blue ridge on the one side, and North mountain on the other; the stream that passes below it is called Cedar creek, and falls into James river. The bridge is in the county of Rockbridge, to which it has given the name. We have no account of the time when it was produced. It has, however, formed a passage between two mountains otherwise impassable but at a great distance from it.

The other is in the province of Angaraez in S. America, described by Don Ulloa. It is from 16 to 22 feet wide; 111 feet deep, of breadth one and one-third of a mile, and is not sensibly greater at top than at bottom. Don Ulloa thinks it has been effected by the wearing of the water, which runs below it; if so, it would have worn down plain and smooth; or most to that side on its descent, where the rock was of softer materials; but he informs us that the cavities on the one side, where equally hard, tally with protuberances of the other, that if they met they would fit in all their indentures, so as to leave no space void; from which we are rather inclined to conclude, that it has been formed by some violent convulsion of nature.

In comparing the two, although we find in the bridge in Virginia, the same quality of rock on both sides, and with the bridge itself, we do not find the protuberances on the one side answering to cavities on the other; if any such have been, the protuberances must have been effaced by time.

Before we proceed to make observations on the different forms already described, and the principles of their construction; we will lay down a theory founded upon approved philosophical principles; and we will endeavour to simplify our expression, so as to be understood by the mechanic, and, we hope, not despised by the philosopher.

The bridges we have described, are formed of arches of different curves; those of the circle and ellipse are the most prevalent. These are formed of certain materials, so joined together, as to retain the curvilinear form of the original curve from which it is taken, whether circle, ellipse, or other curve; and as it is only a part of the curve, and composed of different materials, the extremities of the arch must have some sufficient support, to retain the materials in the form of the intended curve. Although authors that have treated upon this subject, have not agreed upon fixed principles to ascertain the strength of these abutments or supports; yet all agree, that they must be sufficient to sustain the impressing force.

It is an universal principle in nature, that all bodies, on or near the surface of the earth, tend by the laws of gravity towards its centre, unless prevented by some force, that has the power to resist them, or change their direction. If we attend particularly to one body, having all its parts tending equally to the centre of the earth, and supported in that position, it will retain its position. If we suppose another body to press upon it, so as to change that position it has on its support or force away its support, in whole, or in such part, that a greater part of the body has a tendency to the centre, more than it has to its support; it will fall toward the earth in a direction to its centre.

Let A, B, fig. 5. Plate CXXIX. be two supports, suppose one foot square, of height 5 feet, or any other height less or more, standing perpendicular; and let a piece of the same dimensions, wood or stone, of three feet in length, be placed across in equilibrium; the perpendicular support is not pressed by this weight, but in the perpendicular direction; if a second piece of five feet is laid upon the other, in the same way, projecting two feet over on each side, they will still remain in equilibrium, and so on till the two bodies upon the two uprights meet one another, as in the figure, the planks or logs DD meet in E, without affecting the supports, except in the perpendicular direction; the equilibrium being preserved, no force imposed will make the supports give way, that will not separate the particles of matter, or break its texture; neither will any weight push it over, that is not greater than the perpendicular pressure: for action and reaction are equal, acting in contrary directions. The force, then, that it will support before it yield, to press upon its support, is equal to the number of square feet that rests on the surface, and turns upon the angular point F. Now suppose this operation continued the whole length of the bridge, and the whole level blocks in contact with one another, received by the abutments, or land-tops, the bridge will support any weight that the strength of these blocks could sustain, and the abutments react upon; this would be a bridge formed of the Egyptian arches, not very elegant, but of great strength, as each block is supported at one foot distance; and the upper ones in contact with one another, only react by their own strength, at one foot distance without support; and by the reaction of the land abutments, cannot yield to give any lateral pressure upon the pier.

Let us now suppose a semicircle or any other arch described, the superfluous matter is carried off, and the arch remains in strength and beauty. Now instead of balancing the blocks by counterpoise on each side of the support, let this be taken off, and applied as weights above the pier, being equal in weight to those that form the arch, the equilibrium is still preserved, without any lateral pressure. This may be illustrated by a very simple experiment. Let A, B, C, D, fig. 6. be four blocks; the first A, a square, which represents the base; the second B, a pentagon, inscribed in a circle of the same radius about which the square is described, placed with one of its angles to the perpendicular edge of the square, a perpendicular or plumb falls within the base, it is therefore firmly supported; let the hexagon C, be placed upon one of the sides of the pentagon, the two angles likewise coinciding; in this the perpendicular falls over the base, it will therefore be no longer firmly supported, but will fall, and if attached to the pentagon, would carry a part of it along with it, except prevented by friction and consistency of the texture of the materials. In this situation let it be retained, till a pentagon is placed on the opposite side of the hexagon; the plumb-line or perpendicular, as it now stands, falls within the base, and will be again supported so as to carry an additional block raised upon it, or require a considerable force to pull it over to that side, to which the hexagon was inclined to fall. The conclusion we would draw from the above, is that if the column or pier is of such dimensions at top, where the spring of the arch rises, that a weight of such materials as the arch is composed of can be raised, not exceeding the height of the vertex or crown of the arch, as will counterpoise that part of the arch, that produces the lateral pressure; then a

Vol. IV. Part II. Bridge. pier of such dimension is of sufficient strength to support such an arch, till the other arches are thrown, and the whole made to abut upon columns that will counterpoise the whole with any incumbent weight proposed.

The manner we would recommend to apply the arches to their pier, and to one another is, that they abut upon one another, as in fig. 7, 8, and 9. In fig. 10, Plate CXXX., we take a semicircular arch of 75 feet span; our arch-stone we think of a sufficient strength at three feet length; our pier six feet, equal to the two arch-stones. As every arch can be raised to a certain height, without the support of the centre arch; allowed, to the 30th degree or one-third of the distance to the crown of the arch. We have divided the quadrant or half of the arch into 8 equal parts; and where more than half of the arch-stone falls over the perpendicular, we consider as the height, not to be exceeded without support: the weight of matter upon the pier to this height, we compare with the weight of matter from that contained in the arch-stones; or, rather, what breadth of pier will contain a quantity of matter that will counterpoise the weight of the arch-stones, of an arch of given span, and length of arch-stones to the crown of the arch.

In investigations of this kind, we find recourse is had to trigonometrical calculations, and to algebraic and fluxionary equations. Foreign writers, as Belidor, give us rules, collected from such contrivances as suited their taste; and most of the algebraic and fluxionary equations that we have investigated, take their data from some bridge, the construction of which pleases them, and bring their result agreeable thereto; and with some degree of confidence tell us that they are right, as it has agreed to the construction of so able an engineer. If we allow ourselves to follow this method, we can never expect to make improvements.

A late writer (Atwood) has treated learnedly, and we think judiciously, upon this subject; he considers each of the arch-stones, as a wedge abutting upon one another, and the whole upon the land-stool, or upon the pier of the particular arch, and is resisted by a force or prelure, with a force which he expresses by a line placed at right angles to an arch-stone, at that part of the arch which would begin to rest upon the centre arch, which here he calls BS, but says, that the length of the line or the point S is not determined: this, we hope, will be found to be determined in the result of our theory.

We hope our readers will excuse us in departing from the method of investigation formerly mentioned; and, in following that plain geometrical method, which every mechanic is able to understand, and judge of; and which, at the same time, we flatter ourselves the learned will not find cause to challenge.

The thickness of our pier we have taken is, A b, fig. 10, six feet; each division of our arch is equal to two feet on the outside, and tending to the centre of the circle as a wedge: the inside measures 1.8 feet; the mean is 1.9 x 3; the length of the stone is 5.7 feet of surface; we suppose it taken three feet into the arch, equal 17.1 solid feet, in each of our divisions; the scale half an inch to 10 feet. The solid measure, on the whole, is easily found; 3 the 30° is at a, but the arch will rise without the support of the centre arch to c. Now, the number of divisions from a, to the centre of the arch, is 22.2; 17.1 solid feet each, is 374.75 solid feet; our pier of six feet contains to the height a, the surface A b d a; at a mean, taken as in the table, a is 72.75, being each two feet, is 145.5 superficial feet, X 3, the alluded depth is 436.5 solid feet, being fully in equilibrium with the arch-stones; but, as the arch will rise to c, there is an additional weight of 229.5 solid feet, which will be allowed more than a counterpoise to the pressure of the arch, without any aid from the pier, which has only the perpendicular prelure to support. The counterpoise is, therefore, by this ascertained, which will support this arch till the other arches are raised; which, as they all abut upon one another, the land-stool must be made of such strength as to counterpoise the whole; which is ascertained upon the same principles, and leaves no stress upon the piers but the perpendicular prelure alone. This pier is scarce one-twelfth part of the opening, by which, the river having to free a passage, will affect the bridge by prelure but very little: but this will fall in our way to consider afterwards. Fig. 7, is a perspective view of one arch of a bridge, on this construction, with part of an adjoining arch on each side.

When the situation of the river, or other circumstances, or when a segment of a circle is made choice of for the ease of the passage, or economy in the use of materials and mason work; or the base of the arch, or surface of the pier, will not admit of mason work to bear upon the spring of the arch, of such weight as to produce a sufficient counterpoise to the arch-stones that produce the lateral prelure, the pier must be made of greater breadth, as, if much flatter than fig. 8, the pier, in that case, ought to have been of the breadth as represented by the dotted line ab, ab; but this is ascertained in projecting the plan. Fig. 8, is a perspective view of one arch, with its adjoining arch, and part of the abutment on the land side, which will be considered afterwards. At the same time, as the fall of an arch is attended with very great loss, both in money, time, and loss of materials; which might prove hurtful to many ingenious undertakers of such works; by way of precaution, if they shall doubt that the slenderness of our pier will support the arch till the others are thrown, for none can doubt them afterwards, beams may be made to abut upon one another, and upon each pier, as in fig. 8.: this is no loss of time or materials, as it will supply, in part, the supports of the centre arches, upon which the arch of the bridge is raised; and it is a precaution used, upon a smaller scale, when in front-walls of houses; the whole is often supported upon arcades of shop-doors and windows, many of their piers not exceeding nine or ten inches: a cross-bar or piece of wood is laid across, to prevent their yielding or losing the perpendicular, till the whole is completed. Now, the prelure upon the arch is not so great, as most writers have assigned to it; that is, the whole incumbent weight of all the materials above it, together with that of passage. The art of masonry is such, that the beds or rows of stones to bound one with another, that each makes a prelure on its contiguous part, so as to form an arch of themselves. We see in well-built walls a vast excavation made Bridge made in the lower part, or in the middle of the wall, and the upper part of the building not affected. In like manner, the arches being all raised to the height that they can be, without support of the centre arch, they are completed and filled up to the level of the keystone, but not higher. The arch is properly secured, if the principles of equilibration, in filling up, are properly attended to; but if one side is overloaded either in filling up, or in building, it must twist the arch, and if not instantly to break it, must tend to an uncertainty as to its durability. For although some have concluded, they say, from a result of their calculation, that the mathematical theory of equilibrated arches is of little value to the engineer; we do not hesitate to assert, that, if preserving the equilibrium, both in raising the arch, and filling up the haunches, is not attended to, we would not assert it to be in favour of its durability; and we know of no principles in philosophy that will support the opinion, that these can be neglected with propriety; neither do we think such a practice will be readily adopted by a skilful engineer.

Among the various writers upon bridges, some prefer the circular arch, both for strength and elegance. Others contend, that it is exceeded in both by the elliptic arch. Others will give the preference to the catenarian arch; and we are told, that the excellency lies on the side of the parabolic curve. We do not think it incumbent on us to combat each of these, neither do we think our readers would thank us for so doing. It may, however, be expected that we should not pass them entirely unnoticed. In the first place, then, we are of opinion, that the arch that bears most equably throughout the whole, one part upon another, has the best claim to strength. Our reason is, which we illustrate thus, let AB, AC, be placed as in fig. II. Suppose a weight placed upon them in such manner as to press equally upon the point A, the two bodies AB, AC, will in that point support the greatest weight: if the same weight is laid in the middle, between A and C, or A and B, they will each yield to the pressure; for the weight is not equally divided between them. But if these bodies are so placed, that in every position on which a weight can be applied to them, that the weight being equally supported by both, this being the case with the circle (fig. 7.) inclines us to give it the preference as to strength. As to elegance, we know, that regularity is a qualification that suits every taste; and here the circle cannot be outvied. It is not, however, without its disadvantages; with regard to expediency, the semicircular arch is sometimes too high for the situation of some bridges. In this case, the elliptic arch (fig. 9.), formed upon the greater axis, offers itself in point of expediency, and refuses to yield in point of elegance. It is bold enough to assert, that if strength of materials forms its composition, and be properly abutted, it will not yield, in point of strength, in any exigence to which it may be opposed. In point of economy, it claims a preference to the semicircular arch; for our part, we are inclined to own the reasonableness of its claim, and to give it the preference to the segment of a circle (fig. 8.), which might perhaps be preferred in point of expediency, as it can be rendered as flat as the ellipse; but its flatness we rather consider as a disadvantage, as in the rise of the water, it is apt to choke its course and overturn it; whereas, the ellipse being nearly formed of two segments of circles of different radii, the smaller arches at its extremity rise more in the perpendicular, and give more scope to the current of the water; and likewise, it does not require a stronger pier than a semicircle of the same diameter. The segment, on the other hand, if flat, requires a stronger pier, and therefore tends more to choke the current of the river, which ought always to be avoided when it can be done.

In the catenarian arch, as every one will observe, when a chain or rope is fixed at each end, and allowed to fall down in the middle, the curvature is not equal throughout; and we therefore cannot think it entitled to equal claim with the circle or ellipse. The same objection may, with equal propriety, be made to the parabola. This curve, near its vertex, has nearly the property of a circle; but every one who knows a parabola, is convinced how much it deviates from it afterwards; although everywhere it retains the property of its own curve.

We now take a review of the different bridges we have mentioned, and make some observations upon them. In general, we remark, that all the writers upon this art have formed the abutments of each particular arch, to be placed in the pier below the spring of the arch; on which account many have constructed their piers of greater strength than necessary. The first we mentioned, was that by the Roman emperor Trajan, over the Danube: the arches being broken down by the emperor to impede the passage of his invaders, we cannot, with certainty, compute the lateral pressure upon the piers; but their height being 150 feet from the foundation, must have considerable strength to react upon an arch of 170 feet span; which would act upon this column as upon a lever of 150 feet length. We find this pier is 60 feet of thickness, more than one-third of the opening; one-fifth would have been 34 feet: we cannot think this architect has acted without principles; but it is unnecessary for us to conjecture what those were. If we had been informed of the figure of the arch, we might have come near; it probably was a semicircle, and if so, perhaps 20 feet thick of pier, even at that height, might have been of sufficient strength.

The next we have mentioned, are those formed upon the principles, or rather by the rules, given by Bedlidor; for, although he has not condescended to lay down his principles, it does not appear that he has proceeded without principles. Upon investigating what must be the breadth of a pier that will form an abutment to an arch of 75 feet span, we have formerly stated that this arch can be raised to c (fig. 10.), without applying the centre arch: from the centre of this arch-stone we raised a perpendicular pe, and from the lower part of the arch-stone drew the line fg parallel to it: this line fg we supposed to cut the centre of the pier in g. Suppose him to have allowed a part of the pier equal to the length of his arch-stone, which we have in this figure taken three feet, one twenty-fourth of the opening nearly, viz. h h, Ak, for the perpendicular support of the arch-stones to c. We find h g measures five and a half feet, we therefore extend h g to l, which is 11 feet, and A l 14 feet for the breadth Bridge. of the pier: in place of taking the whole width of the bridge, we take only three feet as formerly. The number of equal divisions from c to the vertex or middle of the keystone, is 204; each of the equal divisions at three breadth contains 17.1 solid feet, as by our former measure, which multiplied by 204 = 350.55 solid feet. The pier, 14 feet breadth by six in height, viz. the height he supposes his pier, and three deep, is 252 solid feet: the solid building c f g m being supported in the perpendicular, he considers as a part of his abutment, of which f g measures 26 feet, by c f 3, and by 3 in depth, is 234 + 252 = 486 solid feet, to counterpoise 350.55 solid feet, which he considers more than sufficient. Suppose then the pier is 13 feet, at the above height it contains 234 feet + 234 as before = 468 feet, which to account for accidents, and from his practice and observation gives his rule, which we suppose is fully accounted for. If the height of the pier is more than six feet, he would add to the breadth of his pier in proportion, which he does not take notice of, but affirms, that when the span is above 80, that one-sixth of the opening is sufficient in strength to resist every exigence; but if the arch is a segment, the same rule we have given will find the breadth of the pier, but would give it more than 14 feet. Belidor confines his rule to the semicircular arches. We have already mentioned what we think a proper limitation to his rule for taking the 24th part of the arch for the length of his arch-stone.

London bridge was executed in stone, under the direction of Peter of Colechurch, a priest; it was 33 years in building, being begun by King Henry in 1176, and finished by King John in 1209. The piers are 18 in number, from 25 to 34 feet thick. In what manner this priest executed so great an undertaking at that time, and in these days of ignorance, we are not informed; he has, however, given it superabundant strength of pier, and choked up the course of the river, from 900 feet to 194: but as this objection is about to be removed, we need say no more about it.

Westminster bridge is generally allowed to be an elegant and noble fabric. The height of the pier is only eight feet from the bed of the river; the thicknesses, for a sufficient counterpoise to the arch, could not exceed 14 feet: the architect, Mr. Labley, has given it 17: his arches are semicircular, the middle 16 feet span; his ascent one-twentieth part of the half width of the river, which is here 1223 feet, one-half is 621.15, the rise 30½ feet in that extent.

The next we notice is Blackfriars (fig. 12.), executed by Mr Mylne, whose ingenuity and ability as an engineer are universally acknowledged. The middle arch is a span of 100 feet, of the elliptic form; by which, with other advantages, the passage is rendered more commodious, the ascent being more easy; the quickness of the rise of the arches of the small circles, with the flatness of the large circle, are particularly well adapted to give a more easy passage to the river, rising either from a tide or other accidental causes, renders the choice of the elliptic arch here very judicious: we are likewise much pleased with the ingenuity of the inverted arch; it effectually prevents any rising of the rubble work that fills the interstices between the arches, by any pressure whatever; as it abuts upon the arch-stones at E, it presses their joints upon one another, in a more effectual manner than perhaps could be accomplished by any other method; but the effect produced by it, and in which we think its excellency mostly consists, is, that it makes the arches, at that point, where they produce the greatest lateral pressure, to abut upon one another, and thus take off the lateral pressure upon the pier. It does not a little surprise us, that Mr Mylne did not avail himself of this, by which his pier would have been at least one-half thinner: in place of this, he has made it at the extremity of the greater axis, A a, B b, 19 feet, and increased it in a circular form to 22 feet; experience having proved, that when the resisting force is placed in the pier, one-fifth of the opening is more than sufficient for the resisting force; why he, after taking off the resisting force, should contract the course of the river from 100 feet to 70, when 19 feet, as has been shewn, by many experiments in practice, was more than sufficient, although he had not taken off this resistance, by making the two arches abut upon one another. The depth of the water, at ordinary tides, is not less than 16 feet, and by the principles of hydrostatics, the pressing force of a solid foot of water, at that depth, is equal to 8500 lb. × 30 the number of feet contracted, is 255,000 lb. or 113.8 tons upon the found of his pier, more than necessary, and which he might have avoided. We hope we shall be excused for these remarks, as a work of this kind is executed for general use, and to point out what might escape the most eminent, and far superior to what we can pretend to; we must likewise point out, under the same apology, and at the same time apologize for our own ignorance, in not understanding the signification of the word joggle, as here applied; we understand the Scots phrase to joggle, which is loose and infirm in position, when a man is bedding a stone, if it is too heavy for trial by his arms, he stands upon it with his feet; if he do not find it firm, he says it is not firm, it joggles in such a position, and we think the Teutonic favours this Scoticism. Now, how a phrase that signifies infirm, should be used to give firmness, may be owing to our ignorance of that language that gives it such a signification; but this does not at all derogate from the method. It is, beyond doubt, that each stone is so bound with another by it, that they are rendered as one stone; and that one cannot be forced from its place without carrying the whole along with it, or pulling the stone afoul, which no weight that can come upon a bridge would do.

That the above may be the better understood, we have given a drawing of the middle arch, and part of the adjoining arches: AB, fig. 12. is the length of the greater axis of the ellipse, and span of the arch 100 feet; C the centre of the ellipse; c the centre of the circle, that describes the flat part of the arch; f, f, represent the two foci, or in this, the centres of the lesser circles; D, D the inverted arches abutting upon the arch-stones E, E; V the vertex or crown of the arch; F, F the thickness of the pier at the bed of the river; A a B b the thickness of the pier at the extremity of the greater axis. We have put on the bolting in one of the arches, done with the Kentish ragstone; the bolts about a cubic foot sunk half-way into each stone; the stones in the pier are bolted with firm oak. BRIDGE

oak, of a solid foot, dovetailed into each stone, which renders the whole pier firm as if one stone.

What has been said on the breadth of piers, renders any observations on the bridge over the Trent at Burton, or the single arch over the Tave in Glamorganshire, unnecessary; the abutments of the last being on land, the method of obtaining their strength will be pointed out when we speak of the abutments of iron bridges, of which there are now several in England.

The first, as described in the Philosophical Magazine, over the Severn near Coalbrookdale in Shropshire, was built by Mr Abraham Darley; the iron work was cast at Coalbrookdale in 1779. It consists of one arch of 100 feet six inches of span; rises to the height of 45 feet; consists of ribs, each cast in two pieces, secured at the crown by a cast iron key-plate; and connected horizontally and vertically, by cast iron braces formed with dovetails, and forelocks; the ribs are covered with cast iron plates; the railing is of iron; the weight of the whole is 38½ tons. The iron work executed by Messrs Wilkinson and Darley, iron-masters, of which they have great credit, being the first instance of that material being applied in the bridge way. In 1801 it appeared as perfect as when put up, except what was owing to the failure in the stone abutments, which had occasioned some cracks in some of the small pieces.

The second bridge of this kind was built over the same river at Buildwas, at the expense of the county of Salop, agreeable to a plan under the direction of Mr Telford surveyor of the public works in that county; the iron work was cast at Coalbrookdale in 1795, and 1796; it consists of an arch of 132 feet span; the rise of the arch 27 feet from the spring to the foreshift. The situation of the road here rendered it necessary to be kept low; the outside ribs are made to go up as high as the tops of the railing, and are connected with the ribs that bear the covering plates by bars of iron cast with deep flanges close to each other, and form an arch of themselves; so that the bridge is made upon the whole, compact and firm; the weight of the whole is 173 tons 18½ cwt. Some smaller arches and an aqueduct at Longdon, have been made under Mr Telford's direction in the same county.

The next upon a large scale made of iron, is that over the river Wear at Monk-Wearmouth, in the county of Durham. This bridge, fig. 13, is the segment of a circle, whose radius is 443 or 444 feet; the span of the arch, or length of the bridge, is 236 feet; the height of its vertex above the spring of the arch is 34 feet; and height above the surface of the water 60 feet, so that vessels of considerable burden may pass below it without interruption. The width of the bridge or breadth of the road-way is 32 feet; it is formed of five ribs, placed about five feet distant from one another; each rib consists of 125 blocks of cast iron, five feet in height, and two feet broad at the middle; the lines drawn from this to the centre of curvature determine the length of the block above and below, and a circle described with the radius of curvature gives the convexity of the upper part of the block, and the concavity in the lower, agreeable to the curvature of the whole arch of the bridge; the parts of the block are represented in fig. 14, upon a large scale.

In each of the three longitudinal parts of the block there is a square groove one inch deep, into which is fitted a bar of wrought iron of the same dimensions with the groove, into which it is inserted marked b, b, b, by which the blocks are joined together to form the rib. These ribs are connected laterally by a hollow bar of cast iron, fig. 15, about four inches diameter, and five feet long, with flanges, through which iron bolts are made to pass it, and the sides of the ribs fixed with screws or forelocks; two of the blocks are joined by the bars of wrought iron, and connected with a bar of another rib by the iron hollow bar, as represented in fig. 16. All the ribs joined together and connected in the same manner as in fig. 16, complete the arch of the bridge. To support the beams that form the road-way, circular pieces are formed of cast iron, to abut upon one another at their horizontal diameter, the beams that form the road-way resting upon the circular pieces at the vertical diameter, which gives a firmness to these supports, that no weight coming upon the bridge can injure. The beams or planks are then covered with plates of iron, and such materials as are reckoned to be best adapted to form the road, and prevent water passing through to the injury of the bridge; we have therefore no doubt of the strength of the circular supports, and this figure is always pleasing to the eye; but perhaps in point of economy the form of a support we have given in fig. 13, and added a short description, might be sufficiently strong, and we think contains less metal, which will produce a saving. As we have at the end of this paragraph given a description of the parts agreeable to the figure, we only add, that it was constructed under the direction, and chiefly at the expense of Rowland Burdon, Esq. then M. P. for that county; it was cast at the manufactory of Messrs Walker of Rotherham in Yorkshire, and does honour to the projector and iron-masters; it is nearly double the span of that at Buildwas, and more than double the middle arch of Blackfriars Bridge. We have seen what is called a perspective drawing of this bridge, but as it is in many instances faulty, and in some instances ridiculous, we would not wish such a piece to appear in our work; in the background drawing, the houses vanish in the direction quite opposite to the point of sight, and the view which is allowed to be from below, the eye is made to see quite through between the arch, and the road-way at both ends of the bridge, although at the height of 60 feet, and distance of 236. Our drawing we describe thus: A, fig. 14, is one of the blocks; b, b, b, are bars of wrought iron sunk into their grooves; B, fig. 15, is the hollow cross bar which joins the ribs in the manner as represented fig. 16, which shews two pieces joined, and bolted by the wrought iron bars, and the bolts represented at 1, 2, 3, and the two ribs joined by B, B, B, in which manner the whole bridge is connected; the front of the ribs in length is represented on fig. 9, by a, a, a, a, the other ribs by the different lines, which appear in the perspective; E is an arch through which a road passes, and stretches along behind the three houses by the side of the hill. The blocks placed in a vertical position, in the same manner as in the front of the bridge, are to be considered as curvilinear; but the great extent of the radius could not be conveniently applied, and at that small distance would differ little from a right line when viewed separately. Fig. 17, is the support we proposed in point of Bridge of economy to supply the place of the circles, the flanches resting and coinciding with the curvature of the arch, and all abutting with one another form a covering arch, by which the blocks perhaps might be thought of sufficient strength, although somewhat less than five feet in height, the uprights, of such height along, as the beams of the road-way might rest at the distance of five feet, or thereby, from one another.

Our only doubt of the durability of iron bridges is, that the water being blown in by storms, rests on the flats of the iron, and tends to corrode it and waste its parts; and what will be of the worst consequence, find its way into the joints. Perhaps if between these, thin plates of lead were placed, the two pieces might have their joints closed, by abutting upon the lead, and the same precaution being taken with the wrought iron, where inserted into the grooves of the cast metal, the water would be prevented from entering, or settling in the interstice.

Two other bridges we find described, for both of which patents are obtained, the one by Mr Jordan for a suspending bridge, enrolled in December 1796, the patent obtained, and description January 1797, which exhibits the principle of the invention with its advantages, and a perspective drawing. It consists of two suspending ribs, one on each side of the bridge, which are to extend over the whole breadth of the river: if this distance is thought to be too great for one stretch, it is proposed to raise two other ribs on the opposite side, to meet and abut upon one another; on this account a pier is required, upon which the two abutting ends may rest, and as it bears only the perpendicular pressure, it may be so thin, as to make little obstruction to the current of the river. The suspending arch being erected, is to be understood to be of such strength as to bear the bridge suspended to it from the arch; bars descend on each side to which cross beams or bars of iron are fixed on each side of the bridge at proper distances; along these others are extended in a direction across the river, and covered in such a way as to form a passage for carriages and passengers of every description. It has this particular advantage, that it admits of a draw-bridge.

The advantages proposed by the patentee are: That the span may be greater by this than by other constructions, and that the distances between the abutments and intermediate pier, may be greater than heretofore, or if more piers are requisite, between pier and pier: more particularly, 1. A bridge of this construction requires less time to execute, it not being subject to the interruption of tides. 2. That it is done at less expense. 3. The ascent easier. 4. They are not so liable to decay. 5. They may be repaired with more certainty and facility, and at less expense. 6. They will not be subject to the accidents which have destroyed others. 7. They may be erected at any extent, in regard to length and width. 8. They can be secured as to form one entire piece. 9. They can be preserved in their parts from decays of an accidental nature, and assisted in their durability, by the application of different preservatives. 10. And lastly, It is clearly evident on inspection of the figure, that bridges of this construction, whatever their length be, are in no respect subject to the continual accidents which arise to bridges on the common construction, from currents, Bridge tides, swells, inundations, &c. &c.

In this bridge, there is much ingenuity displayed; and very considerable advantages attached to the use of it; as it is a level, the passage over it is easy; it being well adapted for a draw-bridge where requisite, renders it worthy of attention, and in several situations it might be advisable to adopt it; but at the same time, we are not certain, that so many advantages would accrue from the use of it, as is proposed by the patentee; for instance the suspending arch must be raised by scaffolding as well as other arches; and this scaffolding, we apprehend, must be preserved till the whole of the bridge is finished. On the other hand, if piers are to be raised, they may be slender, having only the perpendicular weight to sustain, and will on that account be little interruption to the course of the river.

The other patent is obtained by Mr John Nash, architect, Dover-street, London, for his invention of an iron bridge, Feb. 7, 1797, on a new and improved construction. What the patentee here proposes, is that in forming the arches and piers for a bridge, in place of archstones, that boxes of cast iron, or plate iron, be formed to the size and figure of the arch stone; and that these boxes be cast with a bottom, or that the bottom may be put in before using. The piers are raised by like boxes, the first row of boxes being laid for the found of the bridge, and fixed to the bed of the river by piles driven into the ground; the boxes are then filled with clay, sand, and mixed with lime, stone of any kind, small or great, brick, with or without lime; being thus filled, another row of boxes is placed, and bedded as if stone; filled up in the same manner till prepared for throwing the arch. The arch-boxes being prepared as already mentioned, are placed in the same manner as arch-stones are placed in an arch; and being filled as before directed, the arch is completed and formed of solid materials caled with iron; and that iron may not abut on iron, he proposes plates of lead laid between each box, and in this manner the bridge is finished, formed one solid mass caled with iron.

In some parts of this, and other countries, the situation is such, that neither stone nor lime can be procured, but at an enormous expense; in such a situation the invention would be meritorious; as a bridge could be erected forming a convenient passage, the boxes being filled with such earthy or stony materials as the place could supply, and if filled with small or round stones, the interstices might be filled with mortar, to render them solid. In some places so situated, that although stone is to be got in quantity and quality sufficient, yet lime cannot easily be procured, the invention might succeed; but we suppose that when both stone and lime can be procured, few would think of caing it with iron, which is less durable than stone, when constantly exposed to the air, in wet and dry. A body of solid iron is very different from a thin plate, exposed on both sides to materials different from itself.

We come now to the description of the greatest undertaking of this kind, that ever graced the British annals, or was accomplished in Europe or the world, that we have accounts of, except in China, as formerly mentioned. The London Bridge, which, though clumfly clumsily executed, and with no great judgment, has performed its service faithfully for near 600 years; but on account of the advance in trade, and necessary improvements, it must now be superseeded by this noble fabric, that will even dazzle the eyes of the enlightened world.

This interesting project has so far engaged the attention of the legislature, that a select committee has been appointed of such members as were no ways concerned in any of the plans brought forward; they have made three valuable reports, that respecting this bridge being contained in the third report, viz. the rebuilding of London bridge, by which colliers, and coasting vessels, and all vessels of light burdens, are to be admitted to pass the new London bridge, and to ship and discharge goods immediately at wharfs, and warehouses, to be constructed along the banks of the river, and opposite to the centre of the city; for which purpose this new bridge is to be formed of cast iron 65 feet high, clear above high water, with inclined planes connecting it with the present streets, and such other improvements as may grow out of this alteration. The bed of the river is to be deepened, so as to admit ships of 200 tons lying afloat at low water; and that no encroachment may be made on the property of those connected with the shore, it is proposed to contract the course of the river to 600 feet, according to Mr Jeffon's report, by which room will be procured for the inclined plane, or wharfs, and warehouses. The plan of the bridge is projected by Messrs Telford and Douglas; the span 600 feet, equal to the width of the river when contracted, which is now accomplished, and we understand the plan is far advanced in the execution; but a plan of so great extent must be subject to many unavoidable interruptions.

A short account of the plan of the bridge will not be unacceptable to our readers, as it will enable them to form a more perfect judgment of this magnificent structure. The whole is of cast iron, which is less liable to corrode than hammered iron; the ribs are cast in as large portions, as can conveniently be moulded; they are connected together by crois and diagonal tie-braces, in such a manner, that any of the pieces of the ribs or braces can be taken out, and replaced, without injuring the whole, or interrupting the passage, thus the bridge can be kept in repair with ease, and convenience; all the frames are so connected vertically and horizontally, from the soffit of the arch to the road-way, that the whole will act as one solid frame; and are so disposed from the middle of the arch, to the abutment, as to give a greater width to the bridge at entrance from the shore, from the different inclined planes, which enter to the bridge from three different directions, by which the public will be accommodated by three different bridges, as to entrance and egress.

The inclined planes which afford entrance to the bridge from the shore, and streets, will give ample room for warehouses, vaults, and other conveniences for depositing the goods, before they can be put on board, or after they are unshipped, till they can be conveniently carried off by the proprietors.

We come now, as proposed, to ascertain the strength of an abutment that will support, or counteract the pressure of any number of arches, abutting upon one another, in the manner we have proposed. Throw up the contents of the number of feet in all the arch-stones, from the one end of the bridge to the other; divide this between the two abutments, and find what base is necessary to contain a number of feet equal to the half, upon each pier from the spring of the arch to the height of the road-way, with one-fourth or one third added, for allowance made for superincumbent weight upon the bridge, or any default in equilibration or otherwise, care being always taken to secure a proper found to abutments. To find the abutments of iron bridges, being of so great extent as those now raised, or may be raised; take a base that will contain a weight of stone, equal to half the weight of the bridge from the spring to the road-way with what is thought necessary to add for extra weight upon the bridge; here it is still more necessary to attend to a proper found, and further it may be necessary in large arches of stone, or an iron arch, to bolt the stones together according to Mr Mylne's method; as the great pressure is laid upon them before the cement has fastened the stones, this may be the cause of the failure in the abutment in the Shropshire bridges; and also of others. Such magnificent structures are worthy of every attention.

We have already treated, and we hope with satisfaction to our readers, of the principles upon which this theory is founded. We shall now adduce some undeniable instances, from the practice of modern and ancient architects. First, upon a small scale, we find vaults thrown, of 8, 10, or more feet, of arches abutting upon one another, upon thin walls; some not exceeding 10 inches, and 6 feet in height; and arches from 18 to 20 feet, the supporting wall from which the arch springs not exceeding 14 inches, the arches below the semicircle, the main abutments being of sufficient strength. Upon a larger scale, in the Gothic architecture, it has universally been practised to support the arches by abutments on the outside of the wall, but not without exception, and where this exception has been made, we find the arch equally well secured, and with much superior grandeur and elegance. In that superb structure of Gothic architecture, St Giles's Church, commonly known by the name of the High Church, Edinburgh, the steeple stands upon four columns, not stronger in proportion to its weight than the five feet pier we propose for an arch of 75 feet span; this centre part of the building is supported by the parts to the east and west, and by arcades, forming aisles in the other direction, none of them exceeding half its height or thereby; it rises above them with its majestic head, adorned with an imperial crown; and for supporting the flatly arches that form this crown, no outside abutments are prepared; in this, the exception above referred to consits; it seems as if by the art intended for the support of our theory. The weight is laid upon the shoulder at the spring of the arch, but with too much elegance as if it were only intended to form an ornamental part of the proposed figure; and under the appearance of an ornament concealing its real use. Some of the arch-stones likewise are projected outward, in the horizontal direction, ornamented at their extremity, and, at the same time that they enrich the crown with an additional ornament, they are a counterpoise to the arch at that place. To complete the deception, Bridge. ception, to adorn the proposed figure throughout, and to finish a well proportioned and elegant crown, the summit is put upon it, at the same time securing the key-stone, which without this precaution would by the side pressure have sprung upwards, and have brought the whole arches to ruin.

That these arches are as well protected by the weight placed at the spring of the arch, as any that are supported by abutments, we need only as a proof produce their stability, in resisting, notwithstanding its great height and exposure in situation, the boisterous effects of the elements, and the concussion arising from the vibration of large bells, suspended in it, and so frequently rung.

From the principles formerly laid down, and the authority now adduced in support of our theory, we hope that it has received ample confirmation. And we venture to conclude, that we have pointed out a method to every mason, and engineer, how in drawing his plan, he may be able to ascertain the weight to be laid on the shoulder of his arch, to counterpoise the weight, according to the intended span, and what thicknesses he has occasion to make his pier, without encumbering it, not only with useless matter, but what is materially injurious to the strength of his bridge, by choking the current, and causing it act with ten times more force upon it, than it otherways would do, as we have formerly shown.

We cannot pass the instance of ancient architecture last mentioned, without observing what attention has been paid to the principles of equilibration; and, although the architects have not communicated the principles upon which they executed their plans, they give evident proofs of their having followed some regular theory. Can we suppose that the projector of St Giles's church, Westminster abbey, and innumerable others, could have produced such elegant and well-proportioned structures accidentally, without a well regulated principle to act upon, or that the projector of this imperial crown we have been describing, had not thoroughly digested all its parts and ornaments, before it began to be erected. The ancient architects have, however, thought proper to leave to posterity to collect their principles from the works that have been executed. The moderns are actuated with more liberality of sentiment, in laying down their principles, as well as executing their projects, many of which will do honour to the age, and leave posterity both principles and examples to follow, and improve upon.

After having treated upon the rise and progress of bridges, from what we know, from the most early periods; it may appear somewhat awkward that the foundation is neglected, and the manner of preparing; but when it is considered that this must be regulated by the superstructure, to be raised upon it; that although it must be the first part, with which we begin, it must be the last in the plan; and in founding a bridge there is indeed much to be considered; and as we propose to offer some methods for founding, which so far as we know have not appeared, we will be attentive to lay them before our readers, under the article FOUNDATION.

We have described bridges of different materials, but have mentioned none of wood; this will come properly to offer itself under the article CENTRE, in which we intend to offer some concise and simple construction, and some forms of wooden bridges, that in point of elegance and strength, may not only vie with, but supercede the use of iron bridges in many instances.

Table referred to in fig. 10.

| No. | Extent | Sum. | Arith. Mean | |-----|--------|------|------------| | 1 | 6 | 12.4 | 6.2 | | 2 | 6.4 | 15.2 | 6.6 | | 3 | 6.8 | 13.8 | 6.9 | | 4 | 7 | 14.5 | 7.25 | | 5 | 7.5 | 15.5 | 7.75 | | 6 | 8 | 16.8 | 8.4 | | 7 | 8.8 | 18.3 | 9.15 | | 8 | 9.5 | 19.5 | 9.75 | | 9 | 10 | 21.5 | 10.75 | | 10 | 11.5 | | |

Deficiency of 2 feet between 8.9 divisions, .10 Between 9 and 10, .015 Sum, .025 Mean, .0125

.0125 X mean of extent 10.5 = .13125 By the depth 3 Solid content, .39375

Deficiency of 2 feet between 10 and 11, .05 Between 11 and 12, .06 Between 12 and 13, .7 Mean, .06

38.25 X 2 = 76.5 Surface, 3 Depth, 229.5 Solid feet.

Sum of Mean. Extent 38.25 Mean 12.75 X .06 = .885 Superficial, 3 Depth. 2.655 Solid.

Explanation From the spring of the arch (fig. 10.), parallel lines are drawn from the divisions of the arch, to the perpendicular db, being each two feet at the outer part of the arch-stone. These divisions are marked in the figure 1, 2, 3, &c.; the measures of each of these lines are inserted in column 2d; the first and second are added together as marked in column 1st, their sum is inserted in column 3d, the half or arithmetical mean in column 4th. In the same manner the 2d and 3d, the 3d and 4th, &c. The sum of the means when added make 72.75, being each 2 feet distant, 145.5 superficial feet, × 3 in depth is 436.5 solid feet; but as these parallel divisions decrease in breadth as they ascend from the spring of the arch, the mean deficiency in solid measure, as above, in the work, .39375, being deducted from the 436.5, leaves the remainder 436.1 solid feet. Between the 10th and 13th division the deficiency is greater, as above, amounting to 2.655 solid feet, to be deducted from 229.5; there remains 226.845 solid feet, which, added to 436.1 is 662.045, the resisting force, to counteract the lateral pressure of the arch-stones 374.75, reckoned from a; but reckoned from c, which the counterpoise is raised to, there being only 20½ divisions, the lateral pressure only amounts to 347.55 solid feet, little more than one half of the opposing force. The arch then must be sufficiently secured without any addition to the pier, more than furnishing a base for this weight.

We have chosen to express both forces by solid feet, in place of weight, as the weight will differ according to the quality of the stone; whereas the solid foot is applicable to every quality of stone of which an arch is raised, stones from the same quarry being nearly of the same specific gravity, and of consequence a solid foot will be as nearly of the same weight. If from different quarries, the weight of a solid foot of each can be easily ascertained. The above table, and work of means and deficiency, we might have expressed in algebraic and fluxionary equations, the small increment of deficiency being the fluxions. We should have had the appearance of being more learned, but whether we should have been more useful to the generality of our readers, we leave them to judge; but we think it becoming in every learned man, to express himself so, as to be universally understood, otherwise we think his learning is misapplied, if not suspicious.

Gunnerie, the two pieces of timber which go between the two transoms of a gun-carriage, on which the bed rests.

Musick, a term for that part of a stringed instrument over which the strings are stretched. The bridge of a violin is about nine inch and a quarter high, and near an inch and a half long.

Bridge-Town, the capital of the island of Barbadoes, situated in W. Long. 61°. N. Lat. 13°. It stands in the inmost part of Carlisle bay. This originally was a most unwholesome situation, and was chosen entirely for its convenience for trade; but is now deemed to be as healthy as any place in the island. The town itself would make a figure in any European kingdom. It is said to contain 1500 houses, and some contend that it is the finest the British possess in America.

The houses in general are well built and finished, and their rents as high as such houses would let for in London. The wharfs and quays are well defended from the sea, and very convenient. The harbour is secured from the north-east wind, which is the constant trade-wind there; and Carlisle bay is capable of containing 500 ships, and is formed by Needham and Pelican points. But what renders Bridge-town the finest and most desirable town in the West Indies, is its security against any attacks from foreign enemies. It is defended on the westward by James-fort, which mounts 18 guns. Near this is Willoughby's fort, which is built upon a tongue of land running into the sea, and mounts 12 guns. Needham's fort has three batteries, and is mounted with 20 guns; and St Anne's fort, which is the strongest in the island, stands more within land. In short, according to Mr Douglas, there is all along the lee-shore, a breastwork and trench, in which, at proper places, were 29 forts and batteries, having 368 cannon mounted, while the windward shore is secured by high rocks, steep cliffs, and foul ground. Such was the state of the fortifications in 1717; but since that time they have been much strengthened. Bridgetown is destitute of few elegancies or conveniences of life that any city of Europe can afford. The church of St Michael exceeds many English cathedrals in beauty, largeness, and conveniency; and has a fine organ, bells, and clock. Here also is a free-school for the instruction of poor boys, an hospital, and a college. The latter was erected by the society for propagating the Christian religion, in pursuance of the will of Colonel Christopher Codrington, who left about 2000l. a-year for its endowment, for maintaining professors and scholars to study and practise divinity, surgery, and physic. See CODRINGTON.