D'Arcy Thompson and Mathematics
Alice Gowenlock and Indre Tuminauskaite
Correspondence about Form and Mechanical Efficiency
Claxton Fidler (1841-1917) was a British Engineer, most recognised for his book on Bridge Construction published in 1887. He proved to be a considerable influence on a large part of On Growth and Form, particularly on the section on Mechanical Efficiency, and therefore indirectly influenced engineers around the world.
In his correspondence with Thompson, Fidler discussed, in detail, the comparisons between the bone skeleton and the framework of a steel bridge and states that the structure of an animal skeleton is most comparable to the main girder of a double-armed Cantilever Bridge (such as the Forth Bridge). The analogy of the bridge stems from the idea that both structures rely on an alternately rigid and flexible system.
Thompson was particularly interested in fish and Fidler believed a better comparison for a fish was to a steamer - with the key function being propulsion. An interesting point that Fidler highlighted is the importance of similarity of function, more so than similarity of form -- however Thompson decided not to develop this idea in his book.
D'Arcy incorporated a great amount of Fidler's engineering knowledge into On Growth and Form. Fidler is credited in the preface of the book for his large contribution.
Fidler's correspondence with D'Arcy on Mechanical Efficiency can be seen at THIS LINK, with key notes provided.