The Leg as a Pendulum


About

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.

Pendulumletter1

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.”

Pendulum1
Simple Pendulum
Pendulum2
More complex model of the leg as a pendulum

Correspondents

Geoffrey Thomas Bennett

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

   

Cell-Aggregates

   

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


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Cammy Sriram and Edward Smith © July 2019
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University of St Andrews, Scotland

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