My attention was first directed to a consideration of suspension bridges, and of the catenary curve on which their theory depends, when the plan for making such a communication across the Menai Straits was submitted to the Commissioners appointed by Parliament to improve the communication by roads and bridges through Wales. It then appeared to me, that the proposed depth of curvature, was not sufficient for ensuring such a degree of strength and permanence as would be consistent with the due execution of a great national work. This opinion I advanced as a Member of the Commission. But wishing to take on myself the full responsibility for such increased expense, as must of necessity be occasioned by enlarging the curvature, I also printed some approximations, hastily deduced, in the Quarterly Journal of Science; and derived from them a confirmation of the opinion that had been given. The interval between the points of support and the road-way of the Menai Bridge has in consequence been augmented to fifty feet; and it now possesses that full measure of strength, which experience has established as requisite and sufficient for works of iron not perfectly at rest. Since bridges of suspension are obviously adapted to very general use, I have flattered myself with the hope of doing something serviceable to the public, by expanding into tables the formulæ from which my approximations were derived; adding to them other formulæ and tables for the catenary of equal strength. A curve not merely of speculative curiosity, but of practical use, where a wide horizontal extent may chance to be combined with natural facilities for obtaining a correspondent height for the attachments.
The Catenary Curve: A Guide To Mandibular Arch Form