476

HISTORY OF ENGINEERING.

Rook I.

It is evident, that the strength of thearched part of the bridge will be as thelength c d of the side of one of these wedges ;as is the excess of n c, the upper or backpart of the wedge, above k d, so will it beincreased as ct/is lengthened. The heightof (/ and D the highest point in bde, andthe highest point of the bridge above thehorizontal line A F, limit the lengtheningof c d, the side of the wedge. Thesewedges act upon one another by theirown gravity and the gravity of the matter over them. The sides c d, tik, &c., of thewedges being accurately directed to the centre of the circle, occasioned him to consider thewhole of the arched part of the bridge equally strong, as one piece of cast-iron, of the sameform, dimensions, and weight; and that if tho iron work above the arched part of thebridge be firmly connected together, and with the arched part, the whole may be consideredas one piece of cast-iron, of the same dimensions and weight.

Mr. Playfair , Professor of Mathematics at Edinburgh , in his consideration of this ques-tion, remarked, that iron bridges admit of being constructed more exactly on the principlesof equilibrium than stone bridges, but that the equilibrium may be more safely dispensedwith in the former than in the latter ; as the frames of iron in the form of truncatedwedges may be made of any depth, so that the whole mass from the interior to the exteriorcurve of the bridge may consist of such wedges, and every single ounce of matter may con-tribute to support itself. In bridges of stone, on the contrary, the depth of the wedges orkey-stone is necessarily limited to a few feet. AR the superincumbent load, being merelydead weight, the exact distribution of which, according to the law required by the equi-librium, is extremely difficult, or rather impossible to be attained. The truth of the secondassertion, that an exact equilibrium of the parts may more safely be dispensed with inbridges of iron than in bridges of stone, depends partly on this that the materials whichcompose the former are much lighter for their strength than those which compose thelatter, iron being hardly three times heavier than stone, and more than an hundred times asstrong. It depends also on this other circumstance, that the whole mass being connected,especially if it consist of truncated wedges, extending from the interior to the exterior curveof the bridge, even though an exact equilibrium does not take place, every part of the masscontributes its share to the support of the whole.

The whole bridge, if we except the road over it, the parapet, and the framework, thatimmediately support them, is to be regarded as a system of wedges, resting against twoimmovable abutments, each of which wedges, whether the whole be in perfect equilibriumor not, contribute to its own support. This holds in the strictest sense in this instance, asthe bridge consists of 63 wedge-form frames of iron, each 10 feet thick at its lowerextremity, with the inclined sides all converging to the same point. This is withoutdoubt a most advantageous construction.

Mr. J Robeson, Professor of Natural Philosophy at Edinburgh , observed that in thisquestion was involved several others, and that taking the whole structure together, hethought that it must not be considered as in the condition of an arch of masonry, each partacting merely by its weight, and the whole maintaining its form by being equilibrated ; andobserved, I see, however, that the ingenious inventors have had this very much in theirthoughts, because the profile is plainly divisible into several arch frames of different radii,all having a common tangent at the crown. The undermost may be considered as themain arch, which the superior ones are only intended to relieve, while they stiffen it, anticonnect it with the road-way. But in this way of considering the structure, it is very farfrom being fit for supporting itself by mere equilibrium. The main arch is abundantlyable to do this, if alone, because a catenusea of the same span and base will not deviatefrom one of its circles 3 inches in any part. But when the upper arches are taken in, theroad at and towards the haunches is vastly too great. I do not think, however, that thisgreat want of equilibrium will make the bridge unable for its load, because the crown isstill by far the weakest part, the total strength at the haunches being vastly greater thanis necessary. I think the bridge abundantly strong, if united in a proper manner, but Ithink that it is rather in the condition of a frame of iron consisting of two pieces, leaningon each other in the middle. I think that our mathematical theories of arch vaulting areextremely defective, and that their defects arise from the very anxiety of the mathematiciansto make them perfect. The joints are supposed to be without cement, perfectly polished,and therefore everywhere perpendicular to the curve or soffite of the arch ; and the mutualpressure is supposed to be everywhere perpendicular to those joints. But the mutualfriction of the parts and the connection of straps or of joggles introduces a force which hasno place in those theories. It enables a load on one part to act on a far distant part trans-versely with the energy of a lever. By attending carefully to the way that old arches tail,