The length of an arc of a flexible rope or chain suspended in the catenary y = c cosh x/c is s = c sinh x/c when measured from the vertex, but the practical determination of s is troublesome, owing to the difficulty in finding the parameter c from the transcendental equation when the coordinates of the point of suspension are given. The importance of a formula such as Huygens' approximation to the length of a circular arc s = 2B+⅓(2B−A), where A is the chord of the arc and B that of half the arc, is due to the fact that one can scale directly these lengths by rectilinear measurements without requiring to find the central angle or to make any subsidiary calculations. Formulae of this nature applicable to the parabola, or to curves whose arcs might be replaced by parabolic arcs, would be useful in the design of structural works dealing with ropes or chains. In such cases, as the dip is frequently less than one-eighth of the space, the catenary may be replaced by a parabola.