The Leg as a Pendulum


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 39-41 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.”

Simple Pendulum
More complex model of the leg as a pendulum


Geoffrey Thomas Bennett



Overview & D'Arcy's Life


On Growth and Form


Heilmann & Shufeldt


Maths of Transformations




D'Arcy and Mathematics


Coordinate Transformations


Logarithmic Spirals


Forms of Cells


Forms and Mechanical efficiency




Wartime and D'Arcy


The Leg as a Pendulum


Recreational Maths


Fibonacci Sequence




All Correspondence Links

Claxton Fidler


Eric Harold Neville


John Marshall


Alfred North Whitehead


Charles Robert Darling


Peter Guthrie Tait


William Peddie


Geoffrey Thomas Bennett


Dorothy Wrinch


Main Index Biographies Index

The support of The Strathmartine Trust towards this website is gratefully acknowledged    

Cammy Sriram and Edward Smith © July 2019
Creative Commons LicenceExcept where otherwise indicated, the text in this work by Cammy Sriram and Edd Smith is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

University of St Andrews, Scotland

The URL of this page is: