Chap. XXV.

ON STONE BRIDGES.

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tympanums, as in one of the bridges of Pavia, and there may be cases in which they maybe used with advantage: taste should proscribe none, for each has its merit when properlyapplied.

On the Width of Arches of Bridges . — Although the width of the arches depends generallyon the particular circumstances of the place where the bridge is to be built, a few obser-vations may assist us relative to this point. Small arches principally suit tranquil rivers,whose waters do not rise to a great height, whence it is generally easy to lay the foundations,and no fears need arise with regard to multiplying the points of support: great arches onthe contrary are adapted for torrents, in which it is generally difficult to obtain foundations,and which, carrying down rocks and trees, damage the piers and springing of the arches,which in such cases consequently should be placed above the surface of the waters. Ingreat rivers large arches are preferable, above all where strong eddies frequently occur ; butthe cost which the foundation of the piers would entail must greatly influence the decisionon this subject: due consideration must also be given to the nature of the materialsemployed, which require to be of greater solidity for large than for small bridges, also tothe size of the craft navigating the river, for which a commodious passage must be left.With regard to the relative openings of the arches, these two plans may be adopted, eitherto make them equal to each other, or to diminish them progressively from the centre tothe abutments. If all the arches be equal, a level line may be preserved and the samecentres used; but then the height of the approaches must be augmented, and consequentlyit is necessary to enlarge the embankments, thereby raising them above the houses in thevicinity : another inconvenience arises from the want of fall to drain off the rain water,which, if allowed to remain long on the bridge, penetrates by degrees down to the coveringof the extrados, and injures it: much inclination cannot be given to the channels whichconvey the water to the gullies by which it is ejected into the river, whether the watersflow off at the extremities of the bridge, or by the openings practised through the archesthemselves. If the diameters of the arches are unequal, these latter inconveniences dis-appear ; each side of the pavement of the bridge may then have a fall, which, however,must not exceed 3 in 100: the difficulties occasioned by lofty embankments are at thesame time overcome. It is possible, however, to unite the advantages of these twomethods, by giving to all the arches the same opening, but placing the springing atlevels decreasing from the middle to the extremities of the bridge : it is necessary to leavethe arches of a sufficient height that in floods, trees, &c., which the river carries down, maypass freely under them.

Of the Breadth of Bridges -The breadth which should be given to bridges depends

solely on their situation, and must be regulated by the importance of the road on whichthey have been constructed, or the population of the town to which they belong ; and it isessential not to make the breadth too considerable, because it uselessly increases theexpense. If the bridge be constructed in the country for a road in its vicinity, it willbe sufficient to give it a width of from 12 to 15 feet, if not very long ; for a road of thesecond class, the width should be from 18 to 22 feet, which will be sufficient for the passageat one time of two carriages and foot passengers : for a road of the first class it should be from25 to 35 feet in width. In the interior of cities the width may vary from 30 to 60 feet,with relation to the population and commercial activity, but it should seldom exceed thislatter limit, though the Pont Neuf at Paris , which is without doubt one of the mostfrequented bridges in existence, is 72 feet in width between the parapets.

Arches used in the Construction of Bridges, when semicircular, should have their centre atthe level of the top of the foundations, or that of low water; circumstances sometimesrequire it to be elevated above when it is raised on piers.

Flat Arches with three Centres, or two. — The form of these arches is not entirely deter-mined either by the span or the height; it is possible to describe on two given diametersan infinity of different curves ; the sole condition to which the curve of flat arches issubject is, that the tangent at the summit be horizontal, and those at the springing bevertical. As a semi-ellipsis satisfies these tw'o conditions, it appears natural to select thiscurve, which, decreasing regularly from the springing to the summit, is peculiarly agree-able to the eye : but it has the inconvenience of requiring a different template for eachvoussoir composing the arch ; neither does it allow so much water-way as the curves ofwhich we are about to treat, unless the difference in the two diameters of the arch be madevery considerable.

Instead of the semi-ellipsis, curves are generally employed, formed by arcs of a circle,since they enable the engineer to determine with ease the length and the radii of thesearcs, and thus to give the most convenient form to the arch : two conditions must, how-ever, be fulfilled : —

1st, That the outline of the first arc of the curve, setting out from the springing, shouldcontain that of an ellipsis, constructed on the two diameters of the flat arch, in order toobtain for the latter greater water-way than it would have if the ellipsis were employed.

2nd, That the radius of the arc at the summit should not surpass a certain limit; for the