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tity y, and through H draw HG parallelto the axis CD, intersecting the curve ACBin G, and through G draw the ordinateGF and the construction is done.

CASE iv.

When x and y are the two given quan-tities.

From CE, any assumed tension at thevertex, construct the indefinite catenaryACB as in Case I., and on its axis CD layoff CL equal to the given quantity x, andthrough L, perpendicular to CL, draw LMequal to the other given quantity y. ThroughC and M draw the straight line CM, cut-ting the curve ACB in G, and through Gdraw the ordinate GF. Take any point N,between C and G, in the curve ACB, andthrough C and N draw the indefinitestraight line CNO ; join FN, and throughL, parallel to FN, draw LP cutting CO inP, then will P be a point in the requiredcatenary. In the same manner any num-ber of points in the required catenary may