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similar to that composing the catenary,suspended to any point F in the curve,and producing by its weight the same ten-sion at that point in the direction of gravity,as that of the curve at the same point inthe direction of its tangent, is a propermeasure of the tension of the chain at thatpoint; in like manner the length of a simi-lar chain C R may be taken as a propermeasure of the constant tension at the ver-tex C.

8. Problem. Wherein it is required toinvestigate the relations between the differ-ent parts of the catenary ; which relationsare commonly called the equations of thecurve.

Let ACB be a catenary whose vertexis C, and axis CD ; and conceive the vari-able ordinate HF to move from the pointC, always parallel to itself, and suppose hf