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certain quantity, which varies directly as the square of itslength, and inversely as the product of the central staticaldeflection, (that is, the amount of deflection which would takeplace if all the load were placed at the centre of the beam,)and with the square of the velocity with which the load passesover the bridge.

In a bridge, therefore, constructed with a single beam, thereare two counteracting forces, which, by mutually neutralizingeach other, prevent the beam of which it consists from yield-ing ; this constitutes what is called the rigidity of the timber,'vhich thus opposes an obstacle to its bending,and which isincreased in the direct proportion of thesquareof thedepth,andinversely as its length within certain limits, provided it is notloaded to more than a third of its calculated capability, whichis taken into consideration in the above formula. This formof bridge merely rests upon its abutments, or piers, pressingvertically upon them. It exerts no force tending to over-turn or push against them in an oblique direction. In thisconsists its superiority over bridges which are constructedsolely on the principle of compression, such as arched bridgesin general, or bridges formed completely on the principles oftension, as in the case of suspended bridges, in both of whichit is necessary to introduce some countervailing weight orpressure, so as to resist the tendency which both those des-criptions of bridges have of oversetting their supports. Thisadds greatly to their complicated nature, and consequentlyto rhe difficulty of their construction, involving, as it does,nice calculation, founded upon careful observation andexperiment.

It may be said, if such advantages are gained by formingbridges in this simple manner, why not have adhered to theirprinciple all along, instead of adopting difficult and intricateplans of construction, which give rise to great additional ex-pense, besides making the subject so much more involved andUncertain ? but on the other hand, it must be remarked, that•udependently of the short duration of timber in comparison°f stone, iron, &e., where large spans have to be crossed, itcannot always be obtained of sufficient dimensions, as respectslength and depth, and besides, in some localities, a supply ofSuch timbers is not always to be obtained ; and even in those'vltere a great quantity was at one period to be found, thev ery fact of a large consumption leads to a deficiency in theCourse of time, and trees of a later growth and smaller scant-ling would necessarily come to be used ; and further, in con-"exion with the application of beams to large spans, it mustbe borne in mind, that where the distance between the sup-ports becomes greater, the dimensions require to be aug-mented, and that when the size is increased in an arithmeticalProportim the weight is added in a much greater ratio.Under tiiese circumstances, it may easily be conceived, thatbeam or girder bridges could only be employed within certaincircumscribed limits ; now, however, that tire Britannia Tubeba* originated the system of building up hollow beams, by' v hich their strength may be made sufficient for the workrequired of them, without adding so enormously to their"eight, we may expect to see wooden-bridges, formed of hollowbeams, taking the place of rib and arched timber bridges, and’"deed, in some instances superseding both stone and iron,88 bein" calculated for much larger spans than have hitherto* J een attempted, and capable of being constructed at a com-paratively small cost.

But to go back to the history of wooden bridges, we willf n id that where rivers were broad, and their channels deep,lt Would be impossible to cross them by single beams of tim-ber. j n guc ), c . lge s, a timber framing or scaffolding would

formed in the bed of the river, by driving piles, or a pier^Ight be formed of stones, or other materials. On these,

beams of timber would be placed, with one extremity restingon the pier, and the other on the bank of the river, or onan abutment raised at the water’s edge, and upon severalpiers in the water, as the case might be. Where the dis-tance between the supports were too great for the dimensionsof the timber forming the roadway, the main beams werepropped up by struts projecting from the sides of the piersor piles, which were sometimes made to meet, in the centre, orif that was not practicable on account of the distance betweentiie supports, they could eacli be made to sustain the beam,and a cross-piece on which their ends should abut be placedbetween them, and fastened to the underside of the beam,these struts, or stays, were then multiplied and disposed invarious ways, until at length a rib or arch of timber wasformed to support the roadway, while the spandrels werefilled up with struts and ties to resist the compression.

The ribs of bridges constructed in this manner were com-posed of frames, the lower portion of which form segmentsof circles, frequently made up of several pieces of woodplaced-immediately one over the other, and joggled together,so arranged, however, that their ends should break joint.To these circular arcs, or polygonal frames, upright pieceswere attached either by bolts, mortises, or iron straps, bywhich the weight of beams supporting the roadway wassustained at intervals, and so disposed as that each partmight, as far as possible, conduce to the strength of thewhole.

The spnndrils, or spaces between the lower rib and the road-way, were differently arranged, according to circumstances ;in some there were perpendicular braces, and in others pen-dant pieces were made to radiate towards the centre of thecircle, or polygon, of which the ribs were composed. Again ;instead of forming the lower bar of the polygon, &c., bylayers of timber bound closely together, it was, in some cases,constructed of two rails placed at some distance from eachother, and fastened to radiating pendants, the intermediatespaces being filled up by abutting pieces placed regularlyacross, so as to keep all the parts of the ribs in their properplaces. Besides this, toft'ee-bridges may be mentioned,which consist of two or more frames composed of top andbottom rails, either horizontal or slightly cambered, and thespaces between them filled in with diagonal pieces, crossingone another at an angle of 45°, or some other suitable angle;these pieces are bolted to one another at every crossing, asalso to longitudinal walings, and the top and bottom rail;bridges of this description are easily constructed, exceedinglycheap, and have been found to answer extremely well forlarge spans. In addition to those enumerated, there are alarge class of timber-bridges formed on the tension principle,by framing king and queen-posts to the main beam on whichthe roadway is supported, and bolting to them an upper rail,at the same time filling in the intermediate spaces with tiesand truss-bars.

The Pons Sublicius was the first bridge ever built acrossthe Tiber . It was at first constructed of timber in thereign of Ancus Martins. It was put together without eitherbolts or ties, so that it could readily be taken asunder; andwas built for the purpose of connecting together the Aven-tine and Janiculuin hills.

The bridge built over the Danube by Trajan is almost oneof the oldest timber-bridges of which we have a detailedaccount. It was supported on twenty stone piers, which were150 feet high and 6 feet broad ; on these were framed timber-arches, each 170 feet span, and formed of three concentrictimber-rings bound together by radiating pendants ; these,together with the arches, supported the longitudinal beamson which the flooring-joists were placed across the bridge.