While trying to explain the biological world in terms of mathematics, D’Arcy considered the concept of the legs moving in the style of a pendulum, first discussed by the Weber brothers in Mechanik der menschl. Gehwerkzeuge, Gottingen, 1836. This model treats the leg as a simple pendulum, swinging with the help of gravity at a “pendulum rate”. However, mechanical differences such as the time spent with the foot on the ground and the leg's conical shape and jointing complicate the case, and make the rate hard to calculate or even define.
Upon reading through the proofs for the second edition, Bennett sent D’Arcy a letter saying that he disagreed with the model and giving several mathematical arguments in support (ms26130). The relevant section of the letter is shown below.
In a response, D’Arcy admitted that he had considered removing the section entirely, but confessed that he found it hard to remove large sections of his own writing (ms26131).
In the end, D’Arcy included the model on pages 3941 of Chapter Two, On Magnitude, with a footnote that “the pendulum theory is not the whole story, but only an important first approximation to a complex phenomenon.”
Introduction

Overview & D'Arcy's Life

On Growth and Form

Heilmann & Shufeldt

Maths of Transformations

Correspondence

D'Arcy and Mathematics

Coordinate Transformations

Logarithmic Spirals

Forms of Cells

Forms and Mechanical efficiency

Shrinkage

Wartime and D'Arcy

The Leg as a Pendulum

Recreational Maths

Fibonacci Sequence

CellAggregates

Claxton Fidler

Eric Harold Neville

John Marshall

Alfred North Whitehead

Charles Robert Darling

Peter Guthrie Tait

William Peddie

Geoffrey Thomas Bennett

Dorothy Wrinch



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