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THE PRINCIPLES OF BRIDGES.

TRACT I.

these lines are perpendicular to the actions of the forces, ofpressure and push, of the arch pieces, the same proportionsamong these, as before deduced, still take place, and holdgood; viz. that the weights are in proportion as the parts ofthe line b dflik, arid the oblicpie push as the correspondinglines ob, od, of, &c, of which ob is as the horizontal thrust.

It has also been supposed, that the joints are cut or drawnperpendicular to the inner curve at every point, or that allthe angles at it, c, E, &c, are right-angles. But neither isthis necessary in the theory; for the system of balancingwill be still the same, whatever those angles may be, whetherall alike or all various, as these differences will only causean alteration in the weight or length of the arch-pieces,which still will be represented in their proportions by theparts of the line bdfhk. And indeed we often see this kindof oblique joints employed in the small arches in the com-mon practice of architecture and building, as over windows,doors, gateways, &c. But yet such a practice is not to hoadmitted into the larger kind of arches, employed in bridges,

<kc, as being both

ungraceful

and troublesome, as well as

weakening the fabrick.

It is manifest, from all the theories, that the balancing ofthe arch is not restricted to any particular kind of curve orshape,for either the under or upper curve; as the arch maybe balanced with any particular curves we please. It alsofollows very evidently, that the same angles or directions oftlie joints may be employed to balance a great variety of

arches, and indeed anythis fig.; where,jf the wedges>t, b, c , d, &c,form a balancedarch, by beingtaken in the re-quired propor-tion to eachother,viz,asthedifferences ofthe

sort of an arch whatever: as

in