54

To draw a line at right angles to the tangent tothe intrados VFO at any point a.

From the point a, draw the vertical line ag equal to Fig. 2CA, the radius of curvature at the vertex and the anci S 'horizontal line gi. Continue ab, the thickness of thearch, at right angles to the extrados at b, cutting gi inL Take in ag, ac equal VA, and draw the horizontalline cb, cutting ai in b. With the radius ab and centrea, cut ag in d, and draw the horizontal line de, cuttingia in e. Draw the vertical line ik equal to ae. Joinha, which is the line required.

TO FIND THE INTRADOS WHEN THIS CATENARY BECOMESA STRAIGHT LINE, OR THE ARCUATION AND FLEXIBI-LITY CEASES; THE LINES TS, DE, DRAWN AT RIGHTANGLES TO THE EXTRADOS, BEING PARALLEL.

When a horizontal line. Let AD be the hori- pj g> 2zontal line. With the centre A, and any radius AI inthe vertical line AGO, cut AD in T. Draw TS atright angles to AD and IH horizontal, cutting theextrados of the arch at the point H. Make TS equalHF, the thickness of this catenary at right angles toit at H. In like manner find any other points E, andQ. Through YSEQ draw the curve VSEQ, the in-trados required, which is a logarithmic curve whose'subtangent equals the radius of curvature of the cate-nary AHU at the vertex A, from which it is derived.

The logarithmic curve may be drawn above or belowthe horizontal line AD.

extrados, and the joints at right angles to the intrados, whichhypothesis is happily favourable to the strength of the material,t0 *he stability of the arch, and conformable to the necessities ofpractice.

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