Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the 'catenary of equal strength'. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports. The 'catenary of equal strength' is the form of a cable whose cross-sectional area is made proportional to the tension at each point, so that the tensile stress is uniform throughout. In this paper I provide a sketch of the lives and achievements of Gilbert and Telford, and of their interaction over the Menai Bridge. There follows a commentary on Gilbert's 1826 paper, and on his two related publications; and a brief sketch of the earlier history of the catenary. I then describe the development of the suspension bridge up to the present time. Finally, I discuss relations between mathematical analysts and practical engineers. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.