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the principles of bridges.

TRACT I.

PROP. VI.

It is proposed to determine the nature and properties of abalanced arch, as derived from the property of the wedge, orby considering the voussoirs or arch-stones as Jrusiruips ofwedges.

the upper skies of them forming the exterior or outer curvobdfhk, and their butting sides making the joints ab, cd., ef,gh, ik, &c, which joints produced, meet in the point o, ofthe vertical line oab. Through any point b, in that line,draw the horizontal line bdfhk, or perpendicular to the ver-tical line oab, and cutting the directions of the joints in therespective or corresponding points b, d, f, h, k, &c.

Now every wedge in the balanced arch, supposing its sidespolished, must lie kept in equilibrio, in its place, by the inn-,tual action of three forces, viz, by its own weight acting ina direction perpendicular to the horizon, and by the thrustor pressure of the two adjacent wedges, one on each side, indirections perpendicular to their sides, or to the joints: So,for instance, the wedge ad is balanced, or kept in equilibrio,by its own weight acting in the vertical direction bo, and bytwo forces acting perpendicularly to ab and cn; and thestone cf, by its weight in the vertical direction, and by twqforces perpendicular to cd and ef. ; also the stone eh, by itsweight acting vertically, and by two forces perpendicular toand gh ; also the stone gk, by its weight vertically, and

Let acegi &c, be theinner or lower curve ofan arch, formed of thevoussoirs, or wedge pieces,the vertical sections ofwhich are the quadrila-terals AD, CF, EH, GK, &C,considered as so many ele-mentary parts of the arch,

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