On Growth and Form

GROWTH AND FORM




 CAMBRIDGE UNIVERSITY PRESS

 C. F. CLAY, MANAGER

 London: FETTER LANE, E.C.

 Edinburgh: 100 PRINCES STREET

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 _All rights reserved_




 ON GROWTH AND FORM

 BY

 D’ARCY WENTWORTH THOMPSON


 Cambridge:
 at the University Press
 1917




“The reasonings about the wonderful and intricate operations of nature
are so full of uncertainty, that, as the Wise-man truly observes,
_hardly do we guess aright at the things that are upon earth, and with
labour do we find the things that are before us_.” Stephen Hales,
_Vegetable Staticks_ (1727), p. 318, 1738.




PREFATORY NOTE


This book of mine has little need of preface, for indeed it is
“all preface” from beginning to end. I have written it as an easy
introduction to the study of organic Form, by methods which are the
common-places of physical science, which are by no means novel in their
application to natural history, but which nevertheless naturalists are
little accustomed to employ.

It is not the biologist with an inkling of mathematics, but the
skilled and learned mathematician who must ultimately deal with such
problems as are merely sketched and adumbrated here. I pretend to no
mathematical skill, but I have made what use I could of what tools I
had; I have dealt with simple cases, and the mathematical methods which
I have introduced are of the easiest and simplest kind. Elementary
as they are, my book has not been written without the help—the
indispensable help—of many friends. Like Mr Pope translating Homer,
when I felt myself deficient I sought assistance! And the experience
which Johnson attributed to Pope has been mine also, that men of
learning did not refuse to help me.

My debts are many, and I will not try to proclaim them all: but I beg
to record my particular obligations to Professor Claxton Fidler, Sir
George Greenhill, Sir Joseph Larmor, and Professor A. McKenzie; to a
much younger but very helpful friend, Mr John Marshall, Scholar of
Trinity; lastly, and (if I may say so) most of all, to my colleague
Professor William Peddie, whose advice has made many useful additions
to my book and whose criticism has spared me many a fault and blunder.

I am under obligations also to the authors and publishers of many books
from which illustrations have been borrowed, and especially to the
following:―

To the Controller of H.M. Stationery Office, for leave to reproduce a
number of figures, chiefly of Foraminifera and of Radiolaria, from the
Reports of the Challenger Expedition. {vi}

To the Council of the Royal Society of Edinburgh, and to that of the
Zoological Society of London:—the former for letting me reprint from
their _Transactions_ the greater part of the text and illustrations of
my concluding chapter, the latter for the use of a number of figures
for my chapter on Horns.

To Professor E. B. Wilson, for his well-known and all but indispensable
figures of the cell (figs. 42–51, 53); to M. A. Prenant, for other
figures (41, 48) in the same chapter; to Sir Donald MacAlister and Mr
Edwin Arnold for certain figures (335–7), and to Sir Edward Schäfer
and Messrs Longmans for another (334), illustrating the minute
trabecular structure of bone. To Mr Gerhard Heilmann, of Copenhagen,
for his beautiful diagrams (figs. 388–93, 401, 402) included in my
last chapter. To Professor Claxton Fidler and to Messrs Griffin, for
letting me use, with more or less modification or simplification,
a number of illustrations (figs. 339–346) from Professor Fidler’s
_Textbook of Bridge Construction_. To Messrs Blackwood and Sons, for
several cuts (figs. 127–9, 131, 173) from Professor Alleyne Nicholson’s
_Palaeontology_; to Mr Heinemann, for certain figures (57, 122,
123, 205) from Dr Stéphane Leduc’s _Mechanism of Life_; to Mr A. M.
Worthington and to Messrs Longmans, for figures (71, 75) from _A Study
of Splashes_, and to Mr C. R. Darling and to Messrs E. and S. Spon
for those (fig. 85) from Mr Darling’s _Liquid Drops and Globules_.
To Messrs Macmillan and Co. for two figures (304, 305) from Zittel’s
_Palaeontology_, to the Oxford University Press for a diagram (fig.
28) from Mr J. W. Jenkinson’s _Experimental Embryology_; and to the
Cambridge University Press for a number of figures from Professor
Henry Woods’s _Invertebrate Palaeontology_, for one (fig. 210) from Dr
Willey’s _Zoological Results_, and for another (fig. 321) from “Thomson
and Tait.”

Many more, and by much the greater part of my diagrams, I owe to the
untiring help of Dr Doris L. Mackinnon, D.Sc., and of Miss Helen
Ogilvie, M.A., B.Sc., of this College.

 D’ARCY WENTWORTH THOMPSON.

 UNIVERSITY COLLEGE, DUNDEE.

 _December, 1916._




CONTENTS


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