Correspondence about Shrinkage


About

At the end of Chapter 7, The Forms of Tissues, in the 2nd edition of On Growth and Form is a “note on shrinkage” which does not appear in the 1st edition.

During the writing of his 2nd edition, D’Arcy pays a visit to Emil Hatschek to see his gelatine shrinkage-figures. He details what he found in a letter to Dorothy Wrinch, dated 27th September 1924 (ms24476):

Shrinkage1
Letter to Wrinch (page 1)
Shrinkage2
Letter to Wrinch (page 2)
Shrinkage3
Letter to Wrinch (page 3)
Shrinkage4
Letter to Wrinch (page 4)

D’Arcy observes that Hatschek’s shrunken gelatine cube looks very similar to a figure in his book (Fig. 134 in 1st edition, Fig. 212 in 2nd edition), that of Plateau’s experiment of a wire cube dipped in soap solution, and he is inclined to believe that the gelatine cube, when shrinking, is trying to form this very figure. He also observes that Hatschek’s squat cylinder of gelatine shrinks to a form which closely resembles another figure in his book (Fig. 65 in 1st edition, Fig. 108 in 2nd edition), that of Plateau’s experiment of a cylinder of oil which has had some oil removed. From this, D’Arcy asserts that curved surfaces formed by the shrinking gelatine as it dries resemble the minimal area surfaces which are given by Plateau’s experiments.

D’Arcy asks Wrinch to help him understand the intermediate stages as the gelatine shape transforms to the equilibrium figure (assumed immediately by the soap-films in Plateau’s experiment), choosing her to help him because she is interested in conformal series of curves.

No mathematics actually makes it into this “note on shrinkage”, perhaps because D’Arcy could not comprehend the maths that Wrinch sent him in response to his letter. In a reply, he deems her paper “too deep” (ms24476).

Shark vertebrae
Fig. 218 from On Growth and Form

Hatschek’s gelatine figures are of particular interest to D’Arcy, especially the squat cylinder which assumes precisely the form of a typical vertebra of a shark, or that of any other cartilaginous fish. The above picture of shark vertebrae, taken from page 564 of On Growth and Form, can clearly be seen to resemble D’Arcy’s sketch of the shrunken squat cylinder of gelatine, on the second page of his letter to Wrinch, also pictured above.

Correspondents

Dorothy Wrinch

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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School of Mathematics and Statistics
University of St Andrews, Scotland

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