BRIDGE. 



It will be readily admitted, by thofe who attend to thefe 

 fubjcfts, thai whatever properties may be fhewn to relate to 

 a geometrical or lineal arch, confidered without thicknefs, 

 and of its fuperiiicumbciit plane, may be eafily and fafcly 

 tranbferred to a real arch of folid materials, and the heavy 

 matter fullalned by it ; for it is maniftll that a folid arch 

 may be conceived citlicr to be generated by the motion of a 

 linear arch, a^J its plane in a dircftion pei-pendiciihir to that 

 plane, or t J be made up of an indefinite number of fuch 

 tqual li icur arches and corrcfpondint; planes : and in either 

 caff, what is Ihewn to obtain with retpeft tothe former, may 

 without helitation be applied to the latter. This the reader 

 will keep in mind. 



The firll hint of a principle which we recoiled, is contained 

 in Dr. Hooke's affertion, that the figure into which a chain 

 or rope, perfedlly flexible, will arrange itfelf when fufpcndcJ 

 from two hooks, is, when inverted, the proper form for an 

 arch compofed of (loncs ofuniform weight. Tlie realon af- 

 figned for this principle is, thai wlicn the flexible felloon of 

 heavA- bodies becomes inverted, ftill touching one another in 

 the fame points, the force with which they prefs on each other 

 in this lali cafe, is equal and oppofitc to the forces with which 

 they draw cacli other in the cafe of fufpenfion. The curve 

 formed by a rope, or flexible chain, of extremely fniall links, 

 when thus fufpended, is well known to oiu- geometricians by 

 the name of the catenarian curve ; by the French it is called /.; 

 cba'mcltc. If a curve of this kind be difpofed in fuch a manner 

 that its vertex (hall be uppermoft ; and if a multitude of globes 

 be fo arranged that their centres (hall be in the circumference 

 of this curve, they will all remain motionlefs and in equili- 

 brium : much more will this equilibrium fubfift, if, inlUad 

 of globes, we fubllitute thin vouffbirs, having flat fides, 

 which touch each other in diredions perpendicular to the 

 curve. In the former cafe, the equilibrium will be deftroyed 

 very eafily, jull as a globe refting on a plane lurface is eafily 

 put into motion ; in the latter, the equilibrium cannot be de- 

 ftroyed without confiderable force, juft as when a heavy body 

 is placed upright on a broad flat bale, it will not only ftand, 

 but will require confiderable force to pufh it over. 



Since the catenarian curve is readi^- defcribed mecha- 

 nically, it is no wonder that this principle of Dr. Hooke's 

 ftiould be very generally received ; but many of thofe who 

 adopted it, forgot that it could not be extenfively applied, 

 without certain moJifications : thefe modifications, it will be 

 feen farther on, caufe this principle to coincide txafily w ith 

 the true theory of equilibration. As to the contrary, it is 

 manifeft, from what we have already faid, that it is only the 

 form of a very ficnder arch rib ofuniform thicknefs, and un- 

 fit for the purpofc of a bridge ; which requires a confiderable 

 mafs of mafonry to lie upon the arch and fill up the Ipace to 

 the roadway, thus completely deftroying the equilibrium at 

 firil eftablilhed in the arch itfelf. It would be pofiible, in- 

 deed, to coiiftruft a catenarian curve of equilibration, having 

 a horizontal line for the extrados, but then the tliicknefs of 

 the mafs above the crown of the arch mull be enormous ; 

 thus, for a catenarian of lOO feet in fpan, and 40 feet high, 

 the diftance from the top of the arch to the horizontal ex- 

 trados mud have been nearly 37 feet to cnfure an equilibrium. 

 For thefe reafons the catenarian curve has been very feldom 

 ufcd in the erection of bridges. 



Another principle, which was firft alTumed about the end 

 of the 17th century, is, that every perpendicular column of 

 mafonry above the arch is merely kept from Aiding down 

 the arch by the next adjoining column. It is very obvious, 

 at firft fight, that this principle is not confident with nature ; 

 it has therefore found but few advocates. When analytical 

 expreffions are deduced for the curvature of arches con« 



ftrufled on this principle, it is worth obfcrving, that they co- 

 incide exaflly with thofe which would flow from the fuppofi- 

 tion that the arch was in equilibrio, in confequence of havinga 

 .luid, with a horizontal furface, preffing upon every part of it. 



A third principle is drawn from the confideration of the 

 arcli Hones being frullums, or parts of wedges. This prin- 

 ciple, we believe, originated in France, and has been prefented 

 in various forms by De la Hire, Bclidor, Varignon, Parent, 

 and other French philofophers, and lately by our ingenious 

 countryman Mr. Atwood. 



In the method now alluded to, it is confidered what 

 weight, in or upon a wedge, is balanced by forces afting 

 againft the fides ; or what force fuch a wedge exerts both 

 horizontally and perpendicularly to its fides ; and thence it 

 is computed what muft be the pofition andfhape of the con- 

 tiguous wedges of given weights ; or what muft be their 

 weights to a given fliape and pofition, fo as juft to exert 

 the adequate degree ofrefiftance required by the firft wedge ; 

 and fo on, from wedge to wedge, till the whole is balanced. 

 A mere arch conftrufted in this way, would remain in equi- 

 librio as long as the conftituent vouflbirs had liberty to fiide, 

 without friftion, down the refpedlive inclined planes on which 

 they lay. This method is, indeed, liable to many objections. 

 Firii, this theory requires, that either the denfity or the mag- 

 nitude of the refpettive vouflbirs, from the crown to the foot 

 of the arch, fhould keep conftantly increafing in proportion to 

 the differences of t!ie tangents of the fevcral angles, which 

 the joints of the voufToirs make with the vertical axe of the 

 curve. Now, if the architeft fhould with to change the 

 denfity of his materials in the required proportion, we knowr 

 not what materials he could ufe ; for the denfity muft al- 

 ways be very great towards the fpring of the arch ; and, in 

 many cafes, it muft be infinitely great. If, on the other 

 hand, the magnitudes of the vouifoirs were gradually in- 

 creafed, it would be neceflary that thofe at the fpring, and 

 confequently the abutments, fliould be immenfely great, and 

 often infinite-, befidcs, that the wedges muft be cut to dif- 

 ferent oblique angles, very difficult in execution, and totally 

 unfafe when eredted, as the acute angles would be in conftant 

 danger of flufhing off. Here too, in real praftice, there 

 would be a total want of balance, on account of the mafs of 

 mafonry and rubble work, which fills the fpace between the 

 arch and the road-way. But even this is not all ; the arch 

 ftones cannot be made, nor indeed ought they, to aft as the 

 true mathematical wedge, the properties of which were em- 

 ployed in attempting to etlablifh the equilibrium. The 

 wedge of thcie theorifts is fuppofed to have its butting fides 

 perfectly polilhcd, and to have its weight or other force on 

 its back balanced by proper equivalent forces afting perpen- 

 dicidarly againft thofe fides. Now this is fo far from being 

 the cafe in the praftice of bridge-building, that architefts 

 contrive to have the butting fides of their wedges fo rough 

 as to oceation a great deal of friftion between them ; and to 

 increafe the adhefion of thefe fides the more, they introduce 

 between them the beft and ftrongeft cement they can pro- 

 cure. By thefe means, fo far from the arch ftones being 

 kept in their places only by forces perpendicular to their 

 butting fides ; and having liberty to Aide along thofe fides, as 

 in the wedge theory, they are abfolutely prevented from the 

 poffibility of fo Aiding, and in a great meafure kept in their 

 places in the arch, by forces that aft even perpendicular to 

 thofe which the wedge theory requires. On thefe accounts, 

 then, we conceive that, however fpecious and plaufible this 

 theory may appear on paper, it ought not to be admitted, 

 fince it is manifeftly inapplicable to any cafe which can ever 

 occur in real praftice. 



On the contrary, the theory which we have adopted, or that 



given 



