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taken to be, exactly, the ordinary catenary, andsolved accordingly.

The bridge, fig. 3 and 4, PI. 8, derives thegreater part of its strength from the floor cables,which, without the others, are, it appears, page313, capable of sustaining any strain to whichthey may fairly become subject, from the pas-sage of troops of any arm. The floor cablesK K, though stretched nearly into a right line,are urged more or less into the catenary curva-ture by the weight of the cables and floor ap-plied as a force to the centre of gravity, ormiddle of the bridge, and the strains upon themmay therefore be determined accordingly.

Suspension bridges present so many advan-tages and facilities to the military engineer, thatit may here be proper to investigate the equa-tions of the catenary,* from which to deduce

* Let A D, fig. 7, PI. 8, be a rope or chain perfectly flexible,and of uniform thickness and density, suspended at the pointsA and B, and A C B the curve which it forms, when acted onsolely by the force of gravity. Let C be the lowest point, orthe point where the direction of the curve is horizontal. ThroughC draw C M vertical, and from any point, P, draw PM perpen-dicular to C M. Now if we suppose the part C P to becomerigid, after it has assumed the form of equilibrium, it willevidently he supported in the same manner, and the tensionsat C and P will be the same as before: and as C P is kept atrest by three forces, the tensions at P and C in the directions

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