THE PRINCIPLES OF BRIDGES.

TRACT I.

38

to ob. Lastly, make od = v /oc i + o«/%and of = v^oe 1 + oj l ,and oh = ^/og 2 + c/< ! , &c ; then shall the line or curvedrawn through all the points b? d, f, fi, k, &c, be the topof the wall, so as the whole fabric may be balanced, or kept •in equilibrio, by the mutual weights and pressures of thestones, having smooth or polished sides, and at liberty todescend along them.

Note .—When the given interior curve ace &c, is a circle,all the radii of curvature will be equal to each other, andwill all have the same centre o. But in other curves, havingvarious degrees of curvature, the radii and centres of curva-ture will be all different.

EXAMPLES.

Suppose the interiorcurve to be a Semicircle.

And suppose the spanor diameter lm to be m84 feet, the height orpitch oa 42 feet, and thethickness at the crown

ab 6 feet, which is the 14th part of the span.ob so, that Ob' 1 be equal to ob 1 — oa 1 , or ob — ob 2 — oa*= 23’2379, and through b draw mbn parallel to the baselm ; from the centre o draw a number of radii ohen &c,Cutting the circle in as many points g, and the line mn inas many points h\ on the perpendicular ln set off all thedistances l/> equal to the several distances oh, cut on the

Then take

radii by the directrix mn ; then transfer the distances op tothe same radii produced to h, namely taking oh = op; thenshall the points h be so many points of the exterior curve,through all which points the bounding line being drawn witha steady hand, it will be as is seen in the figure to this ex-ample, which is accurately constructed and drawn by ascale to the dimensions above given, and which will extend