14 .

THE PRINCIPLES OF BRIDGES.

TRACT I

thrust at the angle d, is proportional to the line ch ; and thepart of the vertical force or iveight on the angle d, whichproduces the oblique force dc, is proportional to the part ofthe vertical line dh.

In like manner, the oblique force cb, acting at c, in the di-rection cb, resolves into the two bn, hc ; therefore the hori-zontal force or thrust at the angle c, is expressed by the linech, the very same as it was before for the angle d ; and thevertical pressure at c, arising from the weights on both dand c, is denoted by the vertical line bn.

Also, the oblique force ac, acting at the angle b, in thedirection ba, resolves into the two uh, hc ; therefore againthe horizontal thrust at the angle b, is represented by the linech, the very same as it was at the points c and d ; and thevertical pressure at b, arising from the weights on b, c, andd, is expressed by the part of the vertical line an.

Thus also, the oblique force ce, in direction de, resolvesinto the two ch, He, being the same horizontal force withthe vertical He; and the oblique force c f, in direction ef, re-solves into the two ch, i if; and the oblique force eg, in di-rection fg, resolves into the two ch, ng ; and the obliqueforce eg, in directipn fg, resolves into the two ch, ii£'; andso on continually, the horizontal force at every point beingexpressed by the same constant line ch ; and the verticalpressures on the angles by the parts of the verticals, viz, anthe whole vertical pressure at b, from the weights on theangles b, c, d : and bn the whole pressure on c from theweights on c and d; and dh the part of the weight on dcausing the oblique force dc ; and ne the other part of theweight on d causing the oblique pressure de ; and 11/ thewhole vertical pressure at e from the weights on d and e;and h g the whole vertical pressure on f arising from theweights laid on d, e and f. And so on.

So that, on the whole,

an denotes the whole weight on the points from d to a. ;and h g the whole weight on the points from d to g ;and ag the whole weight on all the points on both sides;