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Plate I. TO CONSTRUCT A CATENARY, THE THICKNESS OF ITTFig. 28. (that is, the area of its section) being at

EVERY POINT AS THE TENSION AT THAT POINT.

Make EC =c —any given quantity andconstruct the logarithmic curve * KCH,whose axis is NEF and subtangent CE.Through C draw the indefinite right lineCM parallel to the axis EF, and through Edraw EM making any angle with EC, andcutting CM in M. With the centre E anddistance EM, describe an arc cutting ECproduced in L, and through L draw LPparallel to NEF, cutting the logarithmiccurve in P. Through P draw the indefiniteright line PB at right angles to LP, cuttingMC produced in D, and the axis of thelogarithmic curve in N. With the centreE and distance CE, describe the arc CRcutting EM in R. Make DA and DB eachequal to the circular arc CR, then shall C,

# See page 1i.