Catenary

Catenary (Lat. catena, a chain) is the curve taken up by a chain when supported at its ends. The ordinary catenary in mathematics would be the shape assumed if the chain were perfectly flexible, inextensible, and of uniform character throughout; i.e. any inch length having the same mass. This special curve is, therefore, chiefly of theoretical interest, as it never occurs in practice. If the weight of the chain is distributed so that equally-spaced vertical lines intercept equal weights of the chain, the curve is parabolic. Thus the lowest part of an ordinary catenary is parabolic, and in all cases where we have a nearly flat catenary, as with telegraph-wires, we may advantageously assume that the curve is parabolic. Also it follows that in the case of a suspension brielge, where a uniform roadway is supported by vertical rods at equal intervals, the chains from which it hangs will assume the parabolic form, instantly disturbed, however, by the local addition of any load to the roadway. The stress at the supports of a catenary of given length becomes greater as the supports are taken farther apart. Hence the objection to making telegraph wires too taut.