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the timbers sufficiently strong to withstand either tensionor compression.

There are several other principles of constructing the ribsof centering ; one of these may be that of a large truss,spanning the whole opening, having its vertex supportingthe summit of the arch, and its rafters, or principal braces,supporting other subordinate trusses which resist the pressureof the arch at other intermediate points.

Of this kind is that of the bridge of Orleans, by M. Hupeau,one of the boldest centres ever executed in Europe . Anotherprinciple is that of two independent trusses, one supportingthe sides or haunches of the arch, and the other the crown.Of this construction was the centering of the nave and tran-septs of St. Peter’s church, at Rome , by Michael Angelo, andtwo centres by Pitot. Another principle of centering is thatof inscribed equilateral polygons; that is, the exterior beams,supporting the curve, are of equal lengths, and joined toge-ther in the form of a polygon : another polygon is formedwithin this, having its angles in the middle of the sides of theformer, and so on, alternately, until there are as many poly-gons inscribed as will make the centering sufficiently strongor stiff. This mode of centering may be of two kinds : one,when the angles are fixed at their junction to the sides of thelast polygon with bolts ; bridles, or double truss-pieces, beingput over the angles to prevent a transverse strain at the sec-tion of the timbers where the two pieces meet, and to supportthe curve above. The other kind is, when the polygons actindependently of each other; these polygons are brought intoaction by bridles, which support the curve, and act upon theangular points of each other’s polygon. Of this kind werethe centering of the bridges of Cravant, Nogent, Mayence ,and Neuilly , constructed by Perronet. Though these center-ings have been executed to very large spans, the last men-tioned being 120 feet, their equilibrium is by no means sosecure as when the angles of the inner polygon are fastenedto that immediately preceding, as is evident from the infor-mation given of the erection of these bridges, by the ingeniousarchitect who has favoured the world with a treatise on thissubject.

Another principle of centering is that of Westminster andBlackfriars bridges, London . They consist of a series oftrusses, each supporting a point in the arch, the principalbraces having their lower extremities abutting below, at eachend of the centering, on the striking-plates, and at the upperend, upon apron-pieces, which are bolted to the curve thatsupports bridgings for binding the pieces which compose themtogether at their junction. There is one disadvantage underwhich this mode labours; that is, the frequent intersection ofthe principal braces with each other: they must either behalved one upon the other, otherwise they must be discon-tinued, and made in various lengths. Both these modesdiminish their lateral strength, and consequently make themmuch more liable to buckle than when whole; but of the two,that of halving is to be preferred ; as by the braces being inone length, there can be no sagging occasioned by interme-diate joggles, and the braces may be rendered sufficientlysecure, laterally, by running straps longitudinally acrossthe notched part on each side, bolting these straps to thebraces.

Lastly, another mode of centering may be that of a numberof quadrilateral frames abutting on each other, having theirjoints radiating to a centre, in the manner of the wedge-stonesof an arch in masonry. These frames should all be resolvedinto triangles by one or two diagonals, according to the kindof strain, keeping in view that a piece, which is a tie in onediagonal, is, in the other diagonal of the same quadrilateral,a strutt; but if the kind of strain on any frame be not well

ascertained, it would be better to place two diagonals, baL®upon each other. The frames are to be secured with keysbolts, and by this precaution each frame will be renderquite immovable.

The general principle of construction is a series of ti'is 0gles, of which every two are connected by a common side.

Plate I., Figure 1. Let a b c d e f g be the curve of ^arch which requires a centre; let the points A, b, C, &c. ^connected so as to form the equilateral polygon, a b C d E Fand join AC, c E, and E G ; the timbers thus disposed ' v *form three triangles, which may be looked upon as. so nia ,solids, revolvable about the angular points a, c, e, g > ® Lpose now, that these are to be in equilibrium, the sinajforce on either side would throw it down, and there!without other connecting timbers, it would be unfit forpurpose of a centre. . j,

Figure 2. Let abcdefg be the curve of an arch tvi® ^requires a centre ; first, form the equilateral polygon, A 13E e G, with the timbers A B, b C, C d, &c., and fix the tintac, c e, eg, as before, which will form three triang ^movable round a, c, e, g ; let the timbers b d and x> ^fastened, and thus the whole will be immutable; so th*^supported at the points a and G, and a force applied a* aother of the angles b, c, d, or f, the timbers will be all •state of tension, or in a state of compression, and the ^ , gmay be looked upon as a solid body; for suppose the tn aa b c to be supported at the points A and b, the point c > c pthe other two sides, b c, c A, will be fixed; and because ® ^is a triangle, and the points B and C are fixed, theand consequently the sides C D and d b ; in like manner, gc d e is a triangle, and the points c and d fixed, the P 01 ,^will also be fixed, and therefore the sides d e and E c. ^ fi ,same may be shown, in like manner, for the points v anSuppose, then, two equal and opposite forces applied ilt ^points A and G, in the plane of the figure, the fig ul ’ e ijjieneither be extended out, nor compressed together. i, epieces A h, h b, and gi,if, are of no other use than t0 , t jjgthe centre stand firmly on its base. This disposition 0 ^timbers will cause them to occupy the least possible sp“ ^p

If the timbers are fixed at the points k, l, tn,Figure 2, the same immutability of figure may be a ^ t j,estrated; for, suppose the points a and h to be ™ %e ^ tb epoint k will also be fixed ; the points a and k being ’ jng" ' ><* H . v ii

point b of the triangle A k b ; again, the points B ana a llfixed, the point l will also be fixed: in the same niann^ g( j

HAGUj tllG pUUllf v VV All ulOU Uv 11AGU • 111 lliG

the remaining points, C, m, D, n, e, o, f, p, G, i, will be P^j l0 )c

to be stationary in respect of the points a, ii ; and the jn

figure being kept in equilibrio by any three forces, »° ^ t jje

the plane of the figure, at any three angles, the action a

forces will only tend to compress or extend the time

direction of their length. . g juf >1

In the construction of this truss, the triangular P ar i (b e

’ — j; an a i

be constructed all in the same plane, as in Figure

pieces b d and d f may be halved upon the pieces e r»le G; but the utmost care must be taken to secure thepieces concurring at each of the angles, by bolting )0 u!straps, as no dependence can be put in any such join!' tb eiron: but perhaps the best method of any is to h® ^ ft

:tS

thickness of the pieces A c, C e, e g, at tiie points ^and also the pieces a b, b c ; cd,de; e f, f g ; _ ®t 3 . ; p c >

B, d, f : then bolting the ends a and C of the pieces ^ fthe ends C and e of the pieces d C and D e, and t1 ,

- ■ fixing 0 trl)g 9,

of the pieces f e and f g, and then -

side of th e

and G

braces bd, d f, that is, fixing b d upon one siuo t0and another upon the other side of the truss, opP 0 ®^ p,also fixing d f upon one side, and another opposite j e gThe disposition of the timbers forming only a