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Bridge. afterwards in a bridge of about 180 feet span, which was erected on the Tees at Yarm. In 1802 or 1803, an elegant iron bridge, of 181 feet span, and 16 rise, was erected at Staines. Its general form resembled that of the bridge at Wearmouth, but the mode of connexion of the parts was somewhat different. In a short time after its completion, it began to sink, and some of the tranverse pieces broke, in consequence of the change of form. Upon examination it was found that one of the abutments had given way and when this was repaired and made firmer, the other failed. The abutment was pushed outwards horizontally, without any material derange ment of its form or direction; a circumstance which could not have happened if its weight had been sufficiently great but the architect seems to have trusted to the firmness of the iron, and the excel lence of the workmanship, and to have neglected the calculation of the lateral thrust, which it is of so much importance to determine.

Mr Rennie has executed several iron bridges with success in Lincolnshire; one at Boston, over the Witham, of which the span is 86 feet, and the rise 5 only but the abutments being well constructed, it has stood securely, notwithstanding the fracture of some of the cross pieces of the frames, which had been weakened by the unequal contraction of the metal in cooling. At Bristol, Messrs Jessop erected two iron bridges, of 100 feet span, rising 15; each of them contains 150 tons of grey iron; and the ex. pense of each was about L.4000. The construction appears to be simple and judicious. (Plate XLII. fig. 11.) Mr Telford has been employed in the construction of several aqueduct bridges on a considerable scale. One of these was cast by Messrs Reynolds, and completed in 1796, near Wellington in Shropshire: it is 180 feet long, and 20 feet above the water of the river, being supported on iron pillars. Another, still larger, was cast by Mr Hazledine, for carrying the Ellesmere canal over the river Dee, at Pontcysylte, in the neighbourhood of Llangollen. It is supported, 126 feet above the surface of the river, by 20 stone pillars, and is 1020 feet in length, and 12 feet wide. (Plate XLII. fig. 12.)

In France, a light iron bridge, for foot passengers only, was thrown across the Seine, opposite to the gate of the Louvre, in 1803. It is supported by stone piers, which are too narrow to withstand the effect of an accident happening to any part of the fabric, and leaving the lateral thrust uncompensated: nor is there any immediate reason to apprehend that any inconvenience should arise from this deficiency of strength; since it is highly improbable than any partial failure should occur, in such a situation, supposing the bridge originally well constructed. (Plate XLIII. fig. 1.)

But all these works have been far exceeded, in extent and importance, by the three new bridges, lately built and now building over the Thames. The

Vauxhall Bridge was completed and opened in August 1816: it consists of nine arches of cast iron, each of 78 feet span, and between 11 and 12 feet rise. The breadth of the roadway is 36 feet clear. The architect was Mr Walker. The form of the arches considerably resembles that of Messrs Jessop's bridges at Bristol; but it is somewhat lighter and

more elegant, and it has the advantage of a greater Bridge. solidity in the blocks supporting the principal part of the pressure. (Plate XLIII. fig. 2, 3.)

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This advantage characterizes also very strongly the masterly design of Mr Rennie for the structure about to be erected at the bottom of Queen Street, Cheapside, opposite to Guildhall, under the name of the Southwark Bridge. It exhibits an excellent specimen of firmness of mutual abutment in the parts constituting the chief strength of the arch, which has been shown in this essay to be so essential to the security of the work, and which the architect has probably been in great measure induced to adopt from his practical experience of the comparative merits of different arrangements. A plan of the bridge was in February last made public in the Repertory of Arts; a work which amply deserves the encouragement of all those who wish to promote the diffusion of useful information: and the magnitude of the object is such, as to justify our entering into some details of calculation respecting the pressure and strength of the different parts of the fabric, founded on a particular account of their weights and dimensions, which has not yet been made public. (Plate XLIII. fig. 4, 5, 6.)

An act of Parliament for the erection of this bridge was passed in 1811; but it was not begun till 1814; the act having directed that no operations should be commenced, until L. 300,000, out of the required L. 400,000, should be raised by subscription. The subscribers are allowed to receive ten per cent. annually on their shares, and the remainder of the receipts is to be laid by, and to accumulate, until it shall become sufficient to pay off to the proprietors the double amount of their subscriptions, and after this time the bridge is to remain open, without any toll. A considerable part of the iron work is already cast, by Messrs Walkers of Rotherham. The middle arch is to be 240 feet in span, the side arches 210 feet each. The abutment is of firm masonry, connected by dowels, to prevent its sliding; and resting on gratings of timber, supported by obliqué piles. The piers stand on foundations nine or ten feet below the present bed of the river, in order to provide against any alterations which may hereafter take place in its channel, from the operation of vari ous causes and they are abundantly secured by a flooring of timber, resting on a great number of piles.

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Whole weight

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Springing plate

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Abutment

1523 0 13 10 11,000 0 Span 240 feet. Rise 24. Depth of the blocks or plates at the crown 6 feet; at the pier. 8 feet.

It is evident from the inspection of this statement of the weights, that their distribution is by no means capable of being accurately expressed by any one formula; but it will be amply sufficient for the determination of the thrust, to employ the approximation founded on the supposition of a parabolic curve (Prop. T.); and if we afterwards wished to find the effect of any local deviation from the assumed law of the weight, we might have recourse to the mode of calculation exemplified in the answer to the fifth Question. But, in fact, that answer may of itself be considered as sufficient to show, that the effect of a variation of a few tons, from the load appropriate to each part, would be wholly unimportant.

We must, therefore, begin by finding the weight of a portion of the arch corresponding to a quarter of the span; and the whole angle, of which the tangent is

24 120

= .2, being 11° 18', its sine is .1961; and the angle, of which the sine is .09805, being 337.5 678.5'

5o 37, we have to compute the weight of

1

or

of the angular extent, beginning from the mid2.01' dle of the arch. And this will be 48 18+ 88% + 95 18+ (87) X .7345 = 297 tons. Now, the weight of the covering-plates, cornice, palisades, roadway, and pavement, are distributed throughout the length, without sensible inequality, making 879 tons; from which the part immediately above the piers might be deducted; but it will be safer to retain the whole weight, especially as something must be allowed for the greater extent of the upper surface of the wedges. We shall, therefore, have, for the interior quarter, 297 + 439.5=736.5 tons, and for the exterior 1523 — 736.5 = 786.5, the difference being 50 tons; one-sixth of which, added to 736.5, gives us 744.8 for the reduced weight, which is to the lateral thrust as the rise to the half span. But for the rise we must take 23 feet, since the middle of the blocks next to the piers is a foot more remote from the intrados than that of the blocks at the crown. And the true half span, measured from the

120

same point, will be 4 x greater than that of the

312

intrados, amounting to 121.6. We have, therefore, 23:121.6745.8:3942 tons, for m the lateral thrust. 50 6

And for 1 ax, 736.5 — =728.2; whence,

2

I

1 12

1

ax2+ bx*; but ax for the whole arch is 728.2,

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than 1 in 4, if it were intended to stand on the piles without friction; but in reality it rises only 66 inches in 624, or nearly 1 in 9; so that there is an angular difference of 1 in 7 between the direction of the piles and that of the thrust, which is probably a deviation of no practical importance.

It remains to be inquired how far the series of masses of solid iron, constituting the most essential part of the arch, is well calculated to withstand the utmost changes of temperature that can possibly occur to it in the severest seasons (Prop. K.) For this purpose, we may take the mean depth a= 7 feet, 4h 99 h being 23; then 1 + = = 14.14, and 1 + a 7 16hh 9199 15aa 735 tual compression or extension of such a structure is to the mean change which takes place in the direction of the chord, as 14.14 to 12.52, or as 1.129 to 1; and if, in a long and severe frost, the temperature varied from 52° to 20°, since the general dimensions would contract about

=12.52: consequently the greatest ac

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Bridge. about 10,000,000 feet, this change would produce a resistance equivalent to the weight of a column of the same substance 2258 feet high: that is, to about three tons for each square inch, diminishing gradually towards the middle of the blocks, and converted on the other side into an opposite resist. ance so that this force would be added to the general pressure below in case of contraction, and above in case of extension. Now, the lateral thrust is derived from a pressure equivalent to a column about 329 feet high, of materials weighing 1523 tons, while the blocks themselves weigh 357; that is, to a column equal in section to the blocks, and 1400 feet high it will, therefore, amount to about two tons on each square inch: consequently such a change of temperature, as has been supposed, will cause the extreme parts of the abutments to bear a pressure of five tons, where, in the ordinary circumstances, they have only to support two.

The ingenious architect proposes to diminish this contingent inconvenience, by causing the blocks to bear somewhat more strongly on the abutments at the middle than at the sides, so as to allow some little latitude of elevation and depression, in the nature of a joint: and, no doubt, this expedient will prevent the great inequality of pressure which might otherwise arise from the alternations of heat and cold. But it cannot be denied that there must be some waste of strength in such an arrangement, the extreme parts of the abutments, and of the blocks near them, contributing very little to the general resistance; and when we consider the very accurate adjustment of the equilibrium throughout the whole structure, we shall be convinced that there is no necessity for any thing like so great a depth of the solid blocks, especially near the abutments; and that the security would be amply sufficient if, with the same weight of metal, they were made wider in a transverse direction, preserving only the form of the exterior ones on each side, if it were thought more agreeable to the eye. In carpentry, where there is often a transverse strain, and where stiffness is frequently required, we generally gain immensely by throwing much of the substance of our beams into the depth; but in a bridge perfectly well balanced, there is no advantage whatever from depth of the blocks we only want enough to secure us against accidental errors of construction, and against partial loads from extraneous weights; and it is not probable that either of these causes, in such a bridge, would ever bring the curve of equilibrium six inches, or even three, from its natural situation near the middle of the blocks.

sides a foot pavement of seven feet on each side. The arches and piers are built of large blocks of granite, with short counterarches over each pier. The haunches are filled up, as is usual in the most modern bridges, by spandrils, or longitudinal walls of brick, covered with flat stones, and extending over about half the span of the arch; the remainder being merely covered with earth or gravel, which is also continued over the stones covering the spandrils. The hollow spaces between the walls are carefully closed above, and provided with outlets below, in order to secure them from becoming receptacles of water, which would be injurious to the durability of the structure. The mean specific gravity of the materials is such, that a cubic yard of the granite weighs exactly two tons, of the brick work one ton, and of the earth a ton and an eighth. Hence, the weight of the whole may be obtained from the annexed statement. (Plate XLIV. fig. 1, 2, 3.)

Contents of the materials in half an arch of Waterloo Bridge, from the middle of the pier to the crown, beginning from the springing of the arch.

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From this statement, and from a consideration of plate, we may infer that the half arch, terminated the arrangement of the materials, exhibited in the

where the middle line of the arch-stones enters the pier, is equivalent in weight to about 34,000 cubic feet of granite; its inner half containing in round have 14,333 for the reduced weight of the quarter numbers 13,000, and its outer 21,000, whence we arch (Prop. T.). The extreme ordinate will be about 21 feet; the middle of the blocks being somewhat more than 16 feet above the springing of the arch, and the key-stone being four feet six inches deep; consequently. the horizontal thrust will be expressed by 14,333 × 60

We cannot conclude our inquiries into this subject with a more striking example, than by applying the principles of the theory to the magnificent edifice which is now nearly finished, by the same judicious and experienced architect, and which is destined to weighing 3033 tons. bear the triumphant appellation of Waterloo Bridge; a work not less pre-eminent among the bridges of all ages and countries, than the event which it will commemorate is unrivalled in the annals of ancient or modern history. It consists of nine elliptical arches, each of 120 feet span, and 35 feet rise. The piers are 20 feet thick, the road 28 feet wide, be

1

2

40,952 cubic feet,

21

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x=30, a= 389, and feet; while the radius of curvature of the ellipsis at 60 × 60 the crown is 35

=103 feet. It is obvious,

Bridge,

Brisson.

Brisson.

joints in the neighbourhood of D will be incapable Bridge of resisting the pressure in the direction of the curve CD, and must tend to turn on their internal terminations as centres, and to open externally. (Prop. Y.)

Bridge therefore, that the curve of equilibrium will pass everywhere extremely near to the middle of the blocks, and there can be no apprehension of any deficiency in the equilibrium. It is true that, as it approaches to the piers, it acquires an obliquity of a few degrees to the joints; but the disposition to slide would be abundantly obviated by the friction alone, even if the joints were not secured by other precautions.

In building the arches, the stones were rammed together with very considerable force, so that, upon the removal of the centres, none of the arches sunk more than an inch and a half. In short, the accuracy of the whole execution seems to have vied with the beauty of the design, and with the skill of the arrangement, to render the Bridge of Waterloo a monument, of which the metropolis of the British Empire will have abundant reason to be proud, for a long series of successive ages.

EXPLANATION OF THE PLATES.

Plate XLII. fig. 1. If AB represent the distance of any two particles of matter, and BC, DE, FG the repulsive forces at the distances AB, AD, AF respectively, and BC, DH, FI, the corresponding cohesive forces, then GI must be ultimately to EH as FB to BD. (Sect. I. Prop. A.)

Fig. 2. The block will support twice as great a pressure applied at A as at B. (Prop. B.)

ABC

Fig. 3. It is obvious that ABC-ADE CFG, HI being HK, and HG=HA; and the difference ABFHA is always equal to DB x KH. (Prop. C.)

Fig. 4. It is evident that AB is to CD as AE to CE, or as z + a to z. (Prop. E.) It is also obvious that as z or CE is to CD, so is EF to FG. (Prop. F.)

Fig. 5. Supposing the arch AB to be so loaded in the neighbourhood of C as to require the curve of equilibrium to assume the form ADCEB, "the

Fig. 6. A, B, C, Different steps in the fall of a weak arch. (Prop. Y.)

Fig. 7. Elevation and plan of Mess. Telford and Douglas's proposed iron-bridge over the Thames. (Sect. V.)

Fig. 8. Elevation of Mr Darby's iron Bridge at Colebrook Dale. (Sect. VI.)

Fig. 9. Elevation of Mr Burdon's Bridge at Wearmouth. (Sect. VI.)

Fig. 10. Elevation of Mr Telford's Bridge at Buildwas. (Sect. VI.)

Fig. 11. Elevation of Messrs Jessop's Bridges at Bristol. (Sect. VI.)

Fig. 12. Elevation of Mr Telford's Aqueduct Bridge at Pontcysylte. (Sect. VI.)

Plate XLIII. Fig. 1. Elevation of the Bridge of the Louvre at Paris. (Sect. VI.)

Fig. 2. Elevation of Vauxhall Bridge. (Sect. VI.) Fig. 3. Middle arch of Vauxhall Bridge. (Sect. VI.) Fig. 4. Middle arch of Southwark Bridge. (Sect. VI.)

Fig. 5. Elevation of Southwark Bridge. (Sect. VI.) Fig. 6. Plan of Southwark Bridge. (Sect. VI.) Fig. 7. Elevation of London Bridge in its present state. (Sect. IV.)

Fig. 8. Plan of London Bridge, with its sterlings. (Sect. IV.)

Fig. 9. London Bridge, as proposed by Mr Dance to be altered.

Plate XLIV. Fig. 1. Elevation of Waterloo Bridge (Sect. VI.)

Fig. 2. Plan of Waterloo Bridge. (Sect. VI.) Fig. 3. Section of an arch of Waterloo Bridge, showing the foundations of the piers, and the spandril walls of brick; together with the centre supporting it. The dotted line represents the direction of the curve of equilibrium. (Sect. VI.)

(0. R.)

BRISSON (MATHURIN JAMES), a zoologist and natural philosopher, born at Fontenay le Comte, 3d April 1723, the son of Mathurin Brisson and Louisa Gabrielle Jourdain.

He was originally intended for the church, but he had acquired at an early age a taste for natural history, which was particularly encouraged by the advantage that he enjoyed of passing his holidays with the justly celebrated Réaumur, who had an estate near Fontenay. At the age of twenty-four, he had made great progress in his theological studies, and. had fully qualified himself for the rank of a subdeacon; but his courage failed him at the time appointed for taking orders, and he then determined to confine himself to the study of physical sciences. Réaumur had the direction of the Chemical Laboratory of the Academy of Sciences, and had given up the salary attached to it to several young men in succession, whom he appointed as his assistants, and of whom Pitot and Nollet became afterwards the most

distinguished. He now chose Brisson for the situation, which served him, as it had done his predecessors, rather as a step in his advancement with respect to general science, than in enabling him to pursue any objects more immediately chemical; and he followed his passion in attaching himself, almost exclusively, to natural history. The collection of Réaumur furnished him with ample materials for his studies, and with the principal subjects described in his works on the Animal Kingdom. The first of these was published in 1756, containing quadrupeds and cetaceous animals. It consists of simple descriptions of the different species, together with synonyms in various languages, more in the nature of a prodromus than of a complete history. His Ornithologie appeared in 1760, forming six volumes, and containing a number of well-executed plates. But upon Réaumur's death, the collection having been added to the Royal Cabinet, Messrs Buffon and Daubenton, the Directors of that Cabinet, not affording him all

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