Correspondence about Shrinkage


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):

Letter to Wrinch (page 1)
Letter to Wrinch (page 2)
Letter to Wrinch (page 3)
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.


Dorothy Wrinch



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

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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.
School of Mathematics and Statistics
University of St Andrews, Scotland

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