GROWTH AND FORM
CAMBRIDGE UNIVERSITY PRESS
C. F. CLAY, MANAGER
London: FETTER LANE, E.C.
Edinburgh: 100 PRINCES STREET
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Bombay, Calcutta and Madras: MACMILLAN AND Co., LTD.
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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
CHAP. PAGE
I. INTRODUCTORY 1
II. ON MAGNITUDE 16
III. THE RATE OF GROWTH 50
IV. ON THE INTERNAL FORM AND STRUCTURE OF THE CELL 156
V. THE FORMS OF CELLS 201
VI. A NOTE ON ADSORPTION 277
VII. THE FORMS OF TISSUES, OR CELL-AGGREGATES 293
VIII. THE SAME (_continued_) 346
IX. ON CONCRETIONS, SPICULES, AND SPICULAR SKELETONS 411
X. A PARENTHETIC NOTE ON GEODETICS 488
XI. THE LOGARITHMIC SPIRAL 493
XII. THE SPIRAL SHELLS OF THE FORAMINIFERA 587
XIII. THE SHAPES OF HORNS, AND OF TEETH OR TUSKS: WITH
A NOTE ON TORSION 612
XIV. ON LEAF-ARRANGEMENT, OR PHYLLOTAXIS 635
XV. ON THE SHAPES OF EGGS, AND OF CERTAIN OTHER HOLLOW
STRUCTURES 652
XVI. ON FORM AND MECHANICAL EFFICIENCY 670
XVII. ON THE THEORY OF TRANSFORMATIONS, OR THE COMPARISON
OF RELATED FORMS 719
EPILOGUE 778
INDEX 780
LIST OF ILLUSTRATIONS
1. Nerve-cells, from larger and smaller animals (Minot, after Irving
Hardesty) . . . 37
2. Relative magnitudes of some minute organisms (Zsigmondy) . . . 39
3. Curves of growth in man (Quetelet and Bowditch) . . . 61
4, 5. Mean annual increments of stature and weight in man (_do._)
. . . 66, 69
6. The ratio, throughout life, of female weight to male (_do._)
. . . 71
7–9. Curves of growth of child, before and after birth (His and
Rüssow) . . . 74–6
10. Curve of growth of bamboo (Ostwald, after Kraus) . . . 77
11. Coefficients of variability in human stature (Boas and Wissler)
. . . 80
12. Growth in weight of mouse (Wolfgang Ostwald) . . . 83
13. _Do._ of silkworm (Luciani and Lo Monaco) . . . 84
14. _Do._ of tadpole (Ostwald, after Schaper) . . . 85
15. Larval eels, or _Leptocephali_, and young elver (Joh. Schmidt)
. . . 86
16. Growth in length of _Spirogyra_ (Hofmeister) . . . 87
17. Pulsations of growth in _Crocus_ (Bose) . . . 88
18. Relative growth of brain, heart and body of man (Quetelet) . . . 90
19. Ratio of stature to span of arms (_do._) . . . 94
20. Rates of growth near the tip of a bean-root (Sachs) . . . 96
21, 22. The weight-length ratio of the plaice, and its annual periodic
changes . . . 99, 100
23. Variability of tail-forceps in earwigs (Bateson) . . . 104
24. Variability of body-length in plaice . . . 105
25. Rate of growth in plants in relation to temperature (Sachs)
. . . 109
26. _Do._ in maize, observed (Köppen), and calculated curves . . . 112
27. _Do._ in roots of peas (Miss I. Leitch) . . . 113
28, 29. Rate of growth of frog in relation to temperature (Jenkinson,
after O. Hertwig), and calculated curves of _do._ . . . 115, 6
30. Seasonal fluctuation of rate of growth in man (Daffner) . . . 119
31. _Do._ in the rate of growth of trees (C. E. Hall) . . . 120
32. Long-period fluctuation in the rate of growth of Arizona trees (A.
E. Douglass) . . . 122
33, 34. The varying form of brine-shrimps (_Artemia_), in relation to
salinity (Abonyi) . . . 128, 9
35–39. Curves of regenerative growth in tadpoles’ tails (M. L. Durbin)
. . . 140–145
40. Relation between amount of tail removed, amount restored, and time
required for restoration (M. M. Ellis) . . . 148
41. Caryokinesis in trout’s egg (Prenant, after Prof. P. Bouin)
. . . 169
42–51. Diagrams of mitotic cell-division (Prof. E. B. Wilson)
. . . 171–5
52. Chromosomes in course of splitting and separation (Hatschek and
Flemming) . . . 180
53. Annular chromosomes of mole-cricket (Wilson, after vom Rath)
. . . 181
54–56. Diagrams illustrating a hypothetic field of force in
caryokinesis (Prof. W. Peddie) . . . 182–4
57. An artificial figure of caryokinesis (Leduc) . . . 186
58. A segmented egg of _Cerebratulus_ (Prenant, after Coe) . . . 189
59. Diagram of a field of force with two like poles . . . 189
60. A budding yeast-cell . . . 213
61. The roulettes of the conic sections . . . 218
62. Mode of development of an unduloid from a cylindrical tube
. . . 220
63–65. Cylindrical, unduloid, nodoid and catenoid oil-globules
(Plateau) . . . 222, 3
66. Diagram of the nodoid, or elastic curve . . . 224
67. Diagram of a cylinder capped by the corresponding portion of a
sphere . . . 226
68. A liquid cylinder breaking up into spheres . . . 227
69. The same phenomenon in a protoplasmic cell of _Trianea_ . . . 234
70. Some phases of a splash (A. M. Worthington) . . . 235
71. A breaking wave (_do._) . . . 236
72. The calycles of some campanularian zoophytes . . . 237
73. A flagellate monad, _Distigma proteus_ (Saville Kent) . . . 246
74. _Noctiluca miliaris_, diagrammatic . . . 246
75. Various species of _Vorticella_ (Saville Kent and others) . . . 247
76. Various species of _Salpingoeca_ (_do._) . . . 248
77. Species of _Tintinnus_, _Dinobryon_ and _Codonella_ (_do._)
. . . 248
78. The tube or cup of _Vaginicola_ . . . 248
79. The same of _Folliculina_ . . . 249
80. _Trachelophyllum_ (Wreszniowski) . . . 249
81. _Trichodina pediculus_ . . . 252
82. _Dinenymplia gracilis_ (Leidy) . . . 253
83. A “collar-cell” of _Codosiga_ . . . 254
84. Various species of _Lagena_ (Brady) . . . 256
85. Hanging drops, to illustrate the unduloid form (C. R. Darling)
. . . 257
86. Diagram of a fluted cylinder . . . 260
87. _Nodosaria scalaris_ (Brady) . . . 262
88. Fluted and pleated gonangia of certain Campanularians (Allman)
. . . 262
89. Various species of _Nodosaria_, _Sagrina_ and _Rheophax_ (Brady)
. . . 263
90. _Trypanosoma tineae_ and _Spirochaeta anodontae_, to shew
undulating membranes (Minchin and Fantham) . . . 266
91. Some species of _Trichomastix_ and _Trichomonas_ (Kofoid) . . . 267
92. _Herpetomonas_ assuming the undulatory membrane of a Trypanosome
(D. L. Mackinnon) . . . 268
93. Diagram of a human blood-corpuscle . . . 271
94. Sperm-cells of decapod crustacea, _Inachus_ and _Galathea_
(Koltzoff) . . . 273
95. The same, in saline solutions of varying density (_do._) . . . 274
96. A sperm-cell of _Dromia_ (_do._) . . . 275
97. Chondriosomes in cells of kidney and pancreas (Barratt and
Mathews) . . . 285
98. Adsorptive concentration of potassium salts in various plant-cells
(Macallum) . . . 290
99–101. Equilibrium of surface-tension in a floating drop . . . 294, 5
102. Plateau’s “bourrelet” in plant-cells; diagrammatic (Berthold)
. . . 298
103. Parenchyma of maize, shewing the same phenomenon . . . 298
104, 5. Diagrams of the partition-wall between two soap-bubbles
. . . 299, 300
106. Diagram of a partition in a conical cell . . . 300
107. Chains of cells in _Nostoc_, _Anabaena_ and other low algae
. . . 300
108. Diagram of a symmetrically divided soap-bubble . . . 301
109. Arrangement of partitions in dividing spores of _Pellia_
(Campbell) . . . 302
110. Cells of _Dictyota_ (Reinke) . . . 303
111, 2. Terminal and other cells of _Chara_, and young antheridium of
_do._ . . . 303
113. Diagram of cell-walls and partitions under various conditions of
tension . . . 304
114, 5. The partition-surfaces of three interconnected bubbles
. . . 307, 8
116. Diagram of four interconnected cells or bubbles . . . 309
117. Various configurations of four cells in a frog’s egg (Rauber)
. . . 311
118. Another diagram of two conjoined soap-bubbles . . . 313
119. A froth of bubbles, shewing its outer or “epidermal” layer
. . . 314
120. A tetrahedron, or tetrahedral system, shewing its centre of
symmetry . . . 317
121. A group of hexagonal cells (Bonanni) . . . 319
122, 3. Artificial cellular tissues (Leduc) . . . 320
124. Epidermis of _Girardia_ (Goebel) . . . 321
125. Soap-froth, and the same under compression (Rhumbler) . . . 322
126. Epidermal cells of _Elodea canadensis_ (Berthold) . . . 322
127. _Lithostrotion Martini_ (Nicholson) . . . 325
128. _Cyathophyllum hexagonum_ (Nicholson, after Zittel) . . . 325
129. _Arachnophyllum pentagonum_ (Nicholson) . . . 326
130. _Heliolites_ (Woods) . . . 326
131. Confluent septa in _Thamnastraea_ and _Comoseris_ (Nicholson,
after Zittel) . . . 327
132. Geometrical construction of a bee’s cell . . . 330
133. Stellate cells in the pith of a rush; diagrammatic . . . 335
134. Diagram of soap-films formed in a cubical wire skeleton (Plateau)
. . . 337
135. Polar furrows in systems of four soap-bubbles (Robert) . . . 341
136–8. Diagrams illustrating the division of a cube by partitions of
minimal area . . . 347–50
139. Cells from hairs of _Sphacelaria_ (Berthold) . . . 351
140. The bisection of an isosceles triangle by minimal partitions
. . . 353
141. The similar partitioning of spheroidal and conical cells . . . 353
142. S-shaped partitions from cells of algae and mosses (Reinke and
others) . . . 355
143. Diagrammatic explanation of the S-shaped partitions . . . 356
144. Development of _Erythrotrichia_ (Berthold) . . . 359
145. Periclinal, anticlinal and radial partitioning of a quadrant
. . . 359
146. Construction for the minimal partitioning of a quadrant . . . 361
147. Another diagram of anticlinal and periclinal partitions . . . 362
148. Mode of segmentation of an artificially flattened frog’s egg
(Roux) . . . 363
149. The bisection, by minimal partitions, of a prism of small angle
. . . 364
150. Comparative diagram of the various modes of bisection of a
prismatic sector . . . 365
151. Diagram of the further growth of the two halves of a quadrantal
cell . . . 367
152. Diagram of the origin of an epidermic layer of cells . . . 370
153. A discoidal cell dividing into octants . . . 371
154. A germinating spore of _Riccia_ (after Campbell), to shew the
manner of space-partitioning in the cellular tissue . . . 372
155, 6. Theoretical arrangement of successive partitions in a
discoidal cell . . . 373
157. Sections of a moss-embryo (Kienitz-Gerloff) . . . 374
158. Various possible arrangements of partitions in groups of four to
eight cells . . . 375
159. Three modes of partitioning in a system of six cells . . . 376
160, 1. Segmenting eggs of _Trochus_ (Robert), and of _Cynthia_
(Conklin) . . . 377
162. Section of the apical cone of _Salvinia_ (Pringsheim) . . . 377
163, 4. Segmenting eggs of _Pyrosoma_ (Korotneff), and of _Echinus_
(Driesch) . . . 377
165. Segmenting egg of a cephalopod (Watase) . . . 378
166, 7. Eggs segmenting under pressure: of _Echinus_ and _Nereis_
(Driesch), and of a frog (Roux) . . . 378
168. Various arrangements of a group of eight cells on the surface of
a frog’s egg (Rauber) . . . 381
169. Diagram of the partitions and interfacial contacts in a system of
eight cells . . . 383
170. Various modes of aggregation of eight oil-drops (Roux) . . . 384
171. Forms, or species, of _Asterolampra_ (Greville) . . . 386
172. Diagrammatic section of an alcyonarian polype . . . 387
173, 4. Sections of _Heterophyllia_ (Nicholson and Martin Duncan)
. . . 388, 9
175. Diagrammatic section of a ctenophore (_Eucharis_) . . . 391
176, 7. Diagrams of the construction of a Pluteus larva . . . 392, 3
178, 9. Diagrams of the development of stomata, in _Sedum_ and in the
hyacinth . . . 394
180. Various spores and pollen-grains (Berthold and others) . . . 396
181. Spore of _Anthoceros_ (Campbell) . . . 397
182, 4, 9. Diagrammatic modes of division of a cell under certain
conditions of asymmetry . . . 400–5
183. Development of the embryo of _Sphagnum_ (Campbell) . . . 402
185. The gemma of a moss (_do._) . . . 403
186. The antheridium of _Riccia_ (_do._) . . . 404
187. Section of growing shoot of _Selaginella_, diagrammatic . . . 404
188. An embryo of _Jungermannia_ (Kienitz-Gerloff) . . . 404
190. Development of the sporangium of _Osmunda_ (Bower) . . . 406
191. Embryos of _Phascum_ and of _Adiantum_ (Kienitz-Gerloff) . . . 408
192. A section of _Girardia_ (Goebel) . . . 408
193. An antheridium of _Pteris_ (Strasburger) . . . 409
194. Spicules of _Siphonogorgia_ and _Anthogorgia_ (Studer) . . . 413
195–7. Calcospherites, deposited in white of egg (Harting) . . . 421, 2
198. Sections of the shell of _Mya_ (Carpenter) . . . 422
199. Concretions, or spicules, artificially deposited in cartilage
(Harting) . . . 423
200. Further illustrations of alcyonarian spicules: _Eunicea_ (Studer)
. . . 424
201–3. Associated, aggregated and composite calcospherites (Harting)
. . . 425, 6
204. Harting’s “conostats” . . . 427
205. Liesegang’s rings (Leduc) . . . 428
206. Relay-crystals of common salt (Bowman) . . . 429
207. Wheel-like crystals in a colloid medium (_do._) . . . 429
208. A concentrically striated calcospherite or spherocrystal
(Harting) . . . 432
209. Otoliths of plaice, shewing “age-rings” (Wallace) . . . 432
210. Spicules, or calcospherites, of _Astrosclera_ (Lister) . . . 436
211. 2. C- and S-shaped spicules of sponges and holothurians (Sollas
and Théel) . . . 442
213. An amphidisc of _Hyalonema_ . . . 442
214–7. Spicules of calcareous, tetractinellid and hexactinellid
sponges, and of various holothurians (Haeckel, Schultze, Sollas and
Théel) . . . 445–452
218. Diagram of a solid body confined by surface-energy to a liquid
boundary-film . . . 460
219. _Astrorhiza limicola_ and _arenaria_ (Brady) . . . 464
220. A nuclear “_reticulum plasmatique_” (Carnoy) . . . 468
221. A spherical radiolarian, _Aulonia hexagona_ (Haeckel) . . . 469
222. _Actinomma arcadophorum_ (_do._) . . . 469
223. _Ethmosphaera conosiphonia_ (_do._) . . . 470
224. Portions of shells of _Cenosphaera favosa_ and _vesparia_ (_do._)
. . . 470
225. _Aulastrum triceros_ (_do._) . . . 471
226. Part of the skeleton of _Cannorhaphis_ (_do._) . . . 472
227. A Nassellarian skeleton, _Callimitra carolotae_ (_do._) . . . 472
228, 9. Portions of _Dictyocha stapedia_ (_do._) . . . 474
230. Diagram to illustrate the conformation of _Callimitra_ . . . 476
231. Skeletons of various radiolarians (Haeckel) . . . 479
232. Diagrammatic structure of the skeleton of _Dorataspis_ (_do._)
. . . 481
233, 4. _Phatnaspis cristata_ (Haeckel), and a diagram of the same
. . . 483
235. _Phractaspis prototypus_ (Haeckel) . . . 484
236. Annular and spiral thickenings in the walls of plant-cells
. . . 488
237. A radiograph of the shell of _Nautilus_ (Green and Gardiner)
. . . 494
238. A spiral foraminifer, _Globigerina_ (Brady) . . . 495
239–42. Diagrams to illustrate the development or growth of a
logarithmic spiral . . . 407–501
243. A helicoid and a scorpioid cyme . . . 502
244. An Archimedean spiral . . . 503
245–7. More diagrams of the development of a logarithmic spiral
. . . 505, 6
248–57. Various diagrams illustrating the mathematical theory of
gnomons . . . 508–13
258. A shell of _Haliotis_, to shew how each increment of the shell
constitutes a gnomon to the preexisting structure . . . 514
259, 60. Spiral foraminifera, _Pulvinulina_ and _Cristellaria_, to
illustrate the same principle . . . 514, 5
261. Another diagram of a logarithmic spiral . . . 517
262. A diagram of the logarithmic spiral of _Nautilus_ (Moseley)
. . . 519
263, 4. Opercula of _Turbo_ and of _Nerita_ (Moseley) . . . 521, 2
265. A section of the shell of _Melo ethiopicus_ . . . 525
266. Shells of _Harpa_ and _Dolium_, to illustrate generating curves
and gene . . . 526
267. D’Orbigny’s Helicometer . . . 529
268. Section of a nautiloid shell, to shew the “protoconch” . . . 531
269–73. Diagrams of logarithmic spirals, of various angles . . . 532–5
274, 6, 7. Constructions for determining the angle of a logarithmic
spiral . . . 537, 8
275. An ammonite, to shew its corrugated surface pattern . . . 537
278–80. Illustrations of the “angle of retardation” . . . 542–4
281. A shell of _Macroscaphites_, to shew change of curvature . . . 550
282. Construction for determining the length of the coiled spire
. . . 551
283. Section of the shell of _Triton corrugatus_ (Woodward) . . . 554
284. _Lamellaria perspicua_ and _Sigaretus haliotoides_ (_do._)
. . . 555
285, 6. Sections of the shells of _Terebra maculata_ and _Trochus
niloticus_ . . . 559, 60
287–9. Diagrams illustrating the lines of growth on a lamellibranch
shell . . . 563–5
290. _Caprinella adversa_ (Woodward) . . . 567
291. Section of the shell of _Productus_ (Woods) . . . 567
292. The “skeletal loop” of _Terebratula_ (_do._) . . . 568
293, 4. The spiral arms of _Spirifer_ and of _Atrypa_ (_do._) . . . 569
295–7. Shells of _Cleodora_, _Hyalaea_ and other pteropods (Boas)
. . . 570, 1
298, 9. Coordinate diagrams of the shell-outline in certain pteropods
. . . 572, 3
300. Development of the shell of _Hyalaea tridentata_ (Tesch) . . . 573
301. Pteropod shells, of _Cleodora_ and _Hyalaea_, viewed from the
side (Boas) . . . 575
302, 3. Diagrams of septa in a conical shell . . . 579
304. A section of _Nautilus_, shewing the logarithmic spirals of the
septa to which the shell-spiral is the evolute . . . 581
305. Cast of the interior of the shell of _Nautilus_, to shew the
contours of the septa at their junction with the shell-wall . . . 582
306. _Ammonites Sowerbyi_, to shew septal outlines (Zittel, after
Steinmann and Döderlein) . . . 584
307. Suture-line of _Pinacoceras_ (Zittel, after Hauer) . . . 584
308. Shells of _Hastigerina_, to shew the “mouth” (Brady) . . . 588
309. _Nummulina antiquior_ (V. von Möller) . . . 591
310. _Cornuspira foliacea_ and _Operculina complanata_ (Brady)
. . . 594
311. _Miliolina pulchella_ and _linnaeana_ (Brady) . . . 596
312, 3. _Cyclammina cancellata_ (_do._), and diagrammatic figure of
the same . . . 596, 7
314. _Orbulina universa_ (Brady) . . . 598
315. _Cristellaria reniformis_ (_do._) . . . 600
316. _Discorbina bertheloti_ (_do._) . . . 603
317. _Textularia trochus_ and _concava_ (_do._) . . . 604
318. Diagrammatic figure of a ram’s horns (Sir V. Brooke) . . . 615
319. Head of an Arabian wild goat (Sclater) . . . 616
320. Head of _Ovis Ammon_, shewing St Venant’s curves . . . 621
321. St Venant’s diagram of a triangular prism under torsion (Thomson
and Tait) . . . 623
322. Diagram of the same phenomenon in a ram’s horn . . . 623
323. Antlers of a Swedish elk (Lönnberg) . . . 629
324. Head and antlers of _Cervus duvauceli_ (Lydekker) . . . 630
325, 6. Diagrams of spiral phyllotaxis (P. G. Tait) . . . 644, 5
327. Further diagrams of phyllotaxis, to shew how various spiral
appearances may arise out of one and the same angular leaf-divergence
. . . 648
328. Diagrammatic outlines of various sea-urchins . . . 664
329, 30. Diagrams of the angle of branching in blood-vessels (Hess)
. . . 667, 8
331, 2. Diagrams illustrating the flexure of a beam . . . 674, 8
333. An example of the mode of arrangement of bast-fibres in a
plant-stem (Schwendener) . . . 680
334. Section of the head of a femur, to shew its trabecular structure
(Schäfer, after Robinson) . . . 681
335. Comparative diagrams of a crane-head and the head of a femur
(Culmann and H. Meyer) . . . 682
336. Diagram of stress-lines in the human foot (Sir D. MacAlister,
after H. Meyer) . . . 684
337. Trabecular structure of the _os calcis_ (_do._) . . . 685
338. Diagram of shearing-stress in a loaded pillar . . . 686
339. Diagrams of tied arch, and bowstring girder (Fidler) . . . 693
340, 1. Diagrams of a bridge: shewing proposed span, the corresponding
stress-diagram and reciprocal plan of construction (_do._) . . . 696
342. A loaded bracket and its reciprocal construction-diagram
(Culmann) . . . 697
343, 4. A cantilever bridge, with its reciprocal diagrams (Fidler)
. . . 698
345. A two-armed cantilever of the Forth Bridge (_do._) . . . 700
346. A two-armed cantilever with load distributed over two pier-heads,
as in the quadrupedal skeleton . . . 700
347–9. Stress-diagrams. or diagrams of bending moments, in the
backbones of the horse, of a Dinosaur, and of _Titanotherium_
. . . 701–4
350. The skeleton of _Stegosaurus_ . . . 707
351. Bending-moments in a beam with fixed ends, to illustrate the
mechanics of chevron-bones . . . 709
352, 3. Coordinate diagrams of a circle, and its deformation into an
ellipse . . . 729
354. Comparison, by means of Cartesian coordinates, of the
cannon-bones of various ruminant animals . . . 729
355, 6. Logarithmic coordinates, and the circle of Fig. 352 inscribed
therein . . . 729, 31
357, 8. Diagrams of oblique and radial coordinates . . . 731
359. Lanceolate, ovate and cordate leaves, compared by the help of
radial coordinates . . . 732
360. A leaf of _Begonia daedalea_ . . . 733
361. A network of logarithmic spiral coordinates . . . 735
362, 3. Feet of ox, sheep and giraffe, compared by means of Cartesian
coordinates . . . 738, 40
364, 6. “Proportional diagrams” of human physiognomy (Albert Dürer)
. . . 740, 2
365. Median and lateral toes of a tapir, compared by means of
rectangular and oblique coordinates . . . 741
367, 8. A comparison of the copepods _Oithona_ and _Sapphirina_
. . . 742
369. The carapaces of certain crabs, _Geryon_, _Corystes_ and others,
compared by means of rectilinear and curvilinear coordinates . . . 744
370. A comparison of certain amphipods, _Harpinia_, _Stegocephalus_
and _Hyperia_ . . . 746
371. The calycles of certain campanularian zoophytes, inscribed in
corresponding Cartesian networks . . . 747
372. The calycles of certain species of _Aglaophenia_, similarly
compared by means of curvilinear coordinates . . . 748
373, 4. The fishes _Argyropelecus_ and _Sternoptyx_, compared by means
of rectangular and oblique coordinate systems . . . 748
375, 6. _Scarus_ and _Pomacanthus_, similarly compared by means of
rectangular and coaxial systems . . . 749
377–80. A comparison of the fishes _Polyprion_, _Pseudopriacanthus_,
_Scorpaena_ and _Antigonia_ . . . 750
381, 2. A similar comparison of _Diodon_ and _Orthagoriscus_ . . . 751
383. The same of various crocodiles: _C. porosus_, _C. americanus_ and
_Notosuchus terrestris_ . . . 753
384. The pelvic girdles of _Stegosaurus_ and _Camptosaurus_ . . . 754
385, 6. The shoulder-girdles of _Cryptocleidus_ and of _Ichthyosaurus_
. . . 755
387. The skulls of _Dimorphodon_ and of _Pteranodon_ . . . 756
388–92. The pelves of _Archaeopteryx_ and of _Apatornis_ compared, and
a method illustrated whereby intermediate configurations may be found
by interpolation (G. Heilmann) . . . 757–9
393. The same pelves, together with three of the intermediate or
interpolated forms . . . 760
394, 5. Comparison of the skulls of two extinct rhinoceroses,
_Hyrachyus_ and _Aceratherium_ (Osborn) . . . 761
396. Occipital views of various extinct rhinoceroses (_do._) . . . 762
397–400. Comparison with each other, and with the skull of
_Hyrachyus_, of the skulls of _Titanotherium_, tapir, horse and rabbit
. . . 763, 4
401, 2. Coordinate diagrams of the skulls of _Eohippus_ and of
_Equus_, with various actual and hypothetical intermediate types
(Heilmann) . . . 765–7
403. A comparison of various human scapulae (Dwight) . . . 769
404. A human skull, inscribed in Cartesian coordinates . . . 770
405. The same coordinates on a new projection, adapted to the skull of
the chimpanzee . . . 770
406. Chimpanzee’s skull, inscribed in the network of Fig. 405 . . . 771
407, 8. Corresponding diagrams of a baboon’s skull, and of a dog’s
. . . 771, 3
“Cum formarum naturalium et corporalium esse non consistat nisi in
unione ad materiam, ejusdem agentis esse videtur eas producere cujus
est materiam transmutare. Secundo, quia cum hujusmodi formae non
excedant virtutem et ordinem et facultatem principiorum agentium in
natura, nulla videtur necessitas eorum originem in principia reducere
altiora.” Aquinas, _De Pot. Q._ iii, a, 11. (Quoted in _Brit. Assoc.
Address_, _Section D_, 1911.)
“...I would that all other natural phenomena might similarly be
deduced from mechanical principles. For many things move me to suspect
that everything depends upon certain forces, in virtue of which the
particles of bodies, through forces not yet understood, are either
impelled together so as to cohere in regular figures, or are repelled
and recede from one another.” Newton, in Preface to the _Principia_.
(Quoted by Mr W. Spottiswoode, _Brit. Assoc. Presidential Address_,
1878.)
“When Science shall have subjected all natural phenomena to the laws
of Theoretical Mechanics, when she shall be able to predict the result
of every combination as unerringly as Hamilton predicted conical
refraction, or Adams revealed to us the existence of Neptune,—that we
cannot say. That day may never come, and it is certainly far in the dim
future. We may not anticipate it, we may not even call it possible. But
none the less are we bound to look to that day, and to labour for it
as the crowning triumph of Science:—when Theoretical Mechanics shall
be recognised as the key to every physical enigma, the chart for every
traveller through the dark Infinite of Nature.” J. H. Jellett, in
_Brit. Assoc. Address_, _Section A_, 1874.
{1}
CHAPTER I
INTRODUCTORY
Of the chemistry of his day and generation, Kant declared that it
was “a science, but not science,”—“eine Wissenschaft, aber nicht
Wissenschaft”; for that the criterion of physical science lay in its
relation to mathematics. And a hundred years later Du Bois Reymond,
profound student of the many sciences on which physiology is based,
recalled and reiterated the old saying, declaring that chemistry would
only reach the rank of science, in the high and strict sense, when it
should be found possible to explain chemical reactions in the light of
their causal relation to the velocities, tensions and conditions of
equilibrium of the component molecules; that, in short, the chemistry
of the future must deal with molecular mechanics, by the methods and
in the strict language of mathematics, as the astronomy of Newton
and Laplace dealt with the stars in their courses. We know how great
a step has been made towards this distant and once hopeless goal,
as Kant defined it, since van’t Hoff laid the firm foundations of a
mathematical chemistry, and earned his proud epitaph, _Physicam chemiae
adiunxit_[1].
We need not wait for the full realisation of Kant’s desire, in order
to apply to the natural sciences the principle which he urged. Though
chemistry fall short of its ultimate goal in mathematical mechanics,
nevertheless physiology is vastly strengthened and enlarged by making
use of the chemistry, as of the physics, of the age. Little by little
it draws nearer to our conception of a true science, with each branch
of physical science which it {2} brings into relation with itself:
with every physical law and every mathematical theorem which it learns
to take into its employ. Between the physiology of Haller, fine as it
was, and that of Helmholtz, Ludwig, Claude Bernard, there was all the
difference in the world.
As soon as we adventure on the paths of the physicist, we learn to
_weigh_ and to _measure_, to deal with time and space and mass and
their related concepts, and to find more and more our knowledge
expressed and our needs satisfied through the concept of _number_, as
in the dreams and visions of Plato and Pythagoras; for modern chemistry
would have gladdened the hearts of those great philosophic dreamers.
But the zoologist or morphologist has been slow, where the physiologist
has long been eager, to invoke the aid of the physical or mathematical
sciences; and the reasons for this difference lie deep, and in part
are rooted in old traditions. The zoologist has scarce begun to dream
of defining, in mathematical language, even the simpler organic
forms. When he finds a simple geometrical construction, for instance
in the honey-comb, he would fain refer it to psychical instinct or
design rather than to the operation of physical forces; when he sees
in snail, or nautilus, or tiny foraminiferal or radiolarian shell, a
close approach to the perfect sphere or spiral, he is prone, of old
habit, to believe that it is after all something more than a spiral or
a sphere, and that in this “something more” there lies what neither
physics nor mathematics can explain. In short he is deeply reluctant
to compare the living with the dead, or to explain by geometry or by
dynamics the things which have their part in the mystery of life.
Moreover he is little inclined to feel the need of such explanations
or of such extension of his field of thought. He is not without some
justification if he feels that in admiration of nature’s handiwork he
has an horizon open before his eyes as wide as any man requires. He
has the help of many fascinating theories within the bounds of his own
science, which, though a little lacking in precision, serve the purpose
of ordering his thoughts and of suggesting new objects of enquiry.
His art of classification becomes a ceaseless and an endless search
after the blood-relationships of things living, and the pedigrees of
things {3} dead and gone. The facts of embryology become for him, as
Wolff, von Baer and Fritz Müller proclaimed, a record not only of the
life-history of the individual but of the annals of its race. The facts
of geographical distribution or even of the migration of birds lead
on and on to speculations regarding lost continents, sunken islands,
or bridges across ancient seas. Every nesting bird, every ant-hill
or spider’s web displays its psychological problems of instinct or
intelligence. Above all, in things both great and small, the naturalist
is rightfully impressed, and finally engrossed, by the peculiar beauty
which is manifested in apparent fitness or “adaptation,”—the flower for
the bee, the berry for the bird.
Time out of mind, it has been by way of the “final cause,” by the
teleological concept of “end,” of “purpose,” or of “design,” in one or
another of its many forms (for its moods are many), that men have been
chiefly wont to explain the phenomena of the living world; and it will
be so while men have eyes to see and ears to hear withal. With Galen,
as with Aristotle, it was the physician’s way; with John Ray, as with
Aristotle, it was the naturalist’s way; with Kant, as with Aristotle,
it was the philosopher’s way. It was the old Hebrew way, and has its
splendid setting in the story that God made “every plant of the field
before it was in the earth, and every herb of the field before it
grew.” It is a common way, and a great way; for it brings with it a
glimpse of a great vision, and it lies deep as the love of nature in
the hearts of men.
Half overshadowing the “efficient” or physical cause, the argument of
the final cause appears in eighteenth century physics, in the hands of
such men as Euler[2] and Maupertuis, to whom Leibniz[3] had passed it
on. Half overshadowed by the mechanical concept, it runs through Claude
Bernard’s _Leçons sur les {4} phénomènes de la Vie_[4], and abides in
much of modern physiology[5]. Inherited from Hegel, it dominated Oken’s
_Naturphilosophie_ and lingered among his later disciples, who were
wont to liken the course of organic evolution not to the straggling
branches of a tree, but to the building of a temple, divinely planned,
and the crowning of it with its polished minarets[6].
It is retained, somewhat crudely, in modern embryology, by those
who see in the early processes of growth a significance “rather
prospective than retrospective,” such that the embryonic phenomena
must be “referred directly to their usefulness in building the body
of the future animal[7]”:—which is no more, and no less, than to say,
with Aristotle, that the organism is the τέλος, or final cause, of
its own processes of generation and development. It is writ large in
that Entelechy[8] which Driesch rediscovered, and which he made known
to many who had neither learned of it from Aristotle, nor studied it
with Leibniz, nor laughed at it with Voltaire. And, though it is in a
very curious way, we are told that teleology was “refounded, reformed
or rehabilitated[9]” by Darwin’s theory of natural selection, whereby
“every variety of form and colour was urgently and absolutely called
upon to produce its title to existence either as an active useful
agent, or as a survival” of such active usefulness in the past. But
in this last, and very important case, we have reached a “teleology”
without a τέλος, {5} as men like Butler and Janet have been prompt to
shew: a teleology in which the final cause becomes little more, if
anything, than the mere expression or resultant of a process of sifting
out of the good from the bad, or of the better from the worse, in short
of a process of mechanism[10]. The apparent manifestations of “purpose”
or adaptation become part of a mechanical philosophy, according to
which “chaque chose finit toujours par s’accommoder à son milieu[11].”
In short, by a road which resembles but is not the same as Maupertuis’s
road, we find our way to the very world in which we are living, and
find that if it be not, it is ever tending to become, “the best of all
possible worlds[12].”
But the use of the teleological principle is but one way, not the
whole or the only way, by which we may seek to learn how things came to
be, and to take their places in the harmonious complexity of the world.
To seek not for ends but for “antecedents” is the way of the physicist,
who finds “causes” in what he has learned to recognise as fundamental
properties, or inseparable concomitants, or unchanging laws, of matter
and of energy. In Aristotle’s parable, the house is there that men
may live in it; but it is also there because the builders have laid
one stone upon another: and it is as a _mechanism_, or a mechanical
construction, that the physicist looks upon the world. Like warp and
woof, mechanism and teleology are interwoven together, and we must not
cleave to the one and despise the other; for their union is “rooted in
the very nature of totality[13].”
Nevertheless, when philosophy bids us hearken and obey the lessons both
of mechanical and of teleological interpretation, the precept is hard
to follow: so that oftentimes it has come to pass, just as in Bacon’s
day, that a leaning to the side of the final cause “hath intercepted
the severe and diligent inquiry of all {6} real and physical causes,”
and has brought it about that “the search of the physical cause
hath been neglected and passed in silence.” So long and so far as
“fortuitous variation[14]” and the “survival of the fittest” remain
engrained as fundamental and satisfactory hypotheses in the philosophy
of biology, so long will these “satisfactory and specious causes”
tend to stay “severe and diligent inquiry,” “to the great arrest and
prejudice of future discovery.”
The difficulties which surround the concept of active or “real”
causation, in Bacon’s sense of the word, difficulties of which Hume and
Locke and Aristotle were little aware, need scarcely hinder us in our
physical enquiry. As students of mathematical and of empirical physics,
we are content to deal with those antecedents, or concomitants, of our
phenomena, without which the phenomenon does not occur,—with causes,
in short, which, _aliae ex aliis aptae et necessitate nexae_, are no
more, and no less, than conditions _sine quâ non_. Our purpose is still
adequately fulfilled: inasmuch as we are still enabled to correlate,
and to equate, our particular phenomena with more and ever more of the
physical phenomena around, and so to weave a web of connection and
interdependence which shall serve our turn, though the metaphysician
withhold from that interdependence the title of causality. We come in
touch with what the schoolmen called a _ratio cognoscendi_, though
the true _ratio efficiendi_ is still enwrapped in many mysteries. And
so handled, the quest of physical causes merges with another great
Aristotelian theme,—the search for relations between things apparently
disconnected, and for “similitude in things to common view unlike.”
Newton did not shew the cause of the apple falling, but he shewed a
similitude between the apple and the stars.
Moreover, the naturalist and the physicist will continue to speak
of “causes,” just as of old, though it may be with some mental
reservations: for, as a French philosopher said, in a kindred
difficulty: “ce sont là des manières de s’exprimer, {7} et si elles
sont interdites il faut renoncer à parler de ces choses.”
The search for differences or essential contrasts between the phenomena
of organic and inorganic, of animate and inanimate things has occupied
many mens’ minds, while the search for community of principles, or
essential similitudes, has been followed by few; and the contrasts are
apt to loom too large, great as they may be. M. Dunan, discussing the
“Problème de la Vie[15]” in an essay which M. Bergson greatly commends,
declares: “Les lois physico-chimiques sont aveugles et brutales; là
où elles règnent seules, au lieu d’un ordre et d’un concert, il ne
peut y avoir qu’incohérence et chaos.” But the physicist proclaims
aloud that the physical phenomena which meet us by the way have their
manifestations of form, not less beautiful and scarce less varied than
those which move us to admiration among living things. The waves of the
sea, the little ripples on the shore, the sweeping curve of the sandy
bay between its headlands, the outline of the hills, the shape of the
clouds, all these are so many riddles of form, so many problems of
morphology, and all of them the physicist can more or less easily read
and adequately solve: solving them by reference to their antecedent
phenomena, in the material system of mechanical forces to which they
belong, and to which we interpret them as being due. They have also,
doubtless, their _immanent_ teleological significance; but it is on
another plane of thought from the physicist’s that we contemplate their
intrinsic harmony and perfection, and “see that they are good.”
Nor is it otherwise with the material forms of living things. Cell
and tissue, shell and bone, leaf and flower, are so many portions
of matter, and it is in obedience to the laws of physics that their
particles have been moved, moulded and conformed[16]. {8} They are no
exception to the rule that Θεὸς ἀεὶ γεωμετρεῖ. Their problems of form
are in the first instance mathematical problems, and their problems
of growth are essentially physical problems; and the morphologist is,
_ipso facto_, a student of physical science.
Apart from the physico-chemical problems of modern physiology, the road
of physico-mathematical or dynamical investigation in morphology has
had few to follow it; but the pathway is old. The way of the old Ionian
physicians, of Anaxagoras[17], of Empedocles and his disciples in the
days before Aristotle, lay just by that highwayside. It was Galileo’s
and Borelli’s way. It was little trodden for long afterwards, but once
in a while Swammerdam and Réaumur looked that way. And of later years,
Moseley and Meyer, Berthold, Errera and Roux have been among the little
band of travellers. We need not wonder if the way be hard to follow,
and if these wayfarers have yet gathered little. A harvest has been
reaped by others, and the gleaning of the grapes is slow.
It behoves us always to remember that in physics it has taken great
men to discover simple things. They are very great names indeed that
we couple with the explanation of the path of a stone, the droop of
a chain, the tints of a bubble, the shadows in a cup. It is but the
slightest adumbration of a dynamical morphology that we can hope to
have, until the physicist and the mathematician shall have made these
problems of ours their own, or till a new Boscovich shall have written
for the naturalist the new _Theoria Philosophiae Naturalis_.
How far, even then, mathematics will _suffice_ to describe, and physics
to explain, the fabric of the body no man can foresee. It may be that
all the laws of energy, and all the properties of matter, and all the
chemistry of all the colloids are as powerless to explain the body as
they are impotent to comprehend the soul. For my part, I think it is
not so. Of how it is that the soul informs the body, physical science
teaches me nothing: consciousness is not explained to my comprehension
by all the nerve-paths and “neurones” of the physiologist; nor do I
ask of physics how goodness shines in one man’s face, and evil betrays
itself in another. But of the construction and growth and working {9}
of the body, as of all that is of the earth earthy, physical science
is, in my humble opinion, our only teacher and guide[18].
Often and often it happens that our physical knowledge is inadequate
to explain the mechanical working of the organism; the phenomena are
superlatively complex, the procedure is involved and entangled, and the
investigation has occupied but a few short lives of men. When physical
science falls short of explaining the order which reigns throughout
these manifold phenomena,—an order more characteristic in its totality
than any of its phenomena in themselves,—men hasten to invoke a
guiding principle, an entelechy, or call it what you will. But all the
while, so far as I am aware, no physical law, any more than that of
gravity itself, not even among the puzzles of chemical “stereometry,”
or of physiological “surface-action” or “osmosis,” is known to be
_transgressed_ by the bodily mechanism.
Some physicists declare, as Maxwell did, that atoms or molecules more
complicated by far than the chemist’s hypotheses demand are requisite
to explain the phenomena of life. If what is implied be an explanation
of psychical phenomena, let the point be granted at once; we may go
yet further, and decline, with Maxwell, to believe that anything of
the nature of _physical_ complexity, however exalted, could ever
suffice. Other physicists, like Auerbach[19], or Larmor[20], or
Joly[21], assure us that our laws of thermodynamics do not suffice, or
are “inappropriate,” to explain the maintenance or (in Joly’s phrase)
the “accelerative absorption” {10} of the bodily energies, and the
long battle against the cold and darkness which is death. With these
weighty problems I am not for the moment concerned. My sole purpose is
to correlate with mathematical statement and physical law certain of
the simpler outward phenomena of organic growth and structure or form:
while all the while regarding, _ex hypothesi_, for the purposes of this
correlation, the fabric of the organism as a material and mechanical
configuration.
Physical science and philosophy stand side by side, and one upholds the
other. Without something of the strength of physics, philosophy would
be weak; and without something of philosophy’s wealth, physical science
would be poor. “Rien ne retirera du tissu de la science les fils d’or
que la main du philosophe y a introduits[22].” But there are fields
where each, for a while at least, must work alone; and where physical
science reaches its limitations, physical science itself must help us
to discover. Meanwhile the appropriate and legitimate postulate of the
physicist, in approaching the physical problems of the body, is that
with these physical phenomena no alien influence interferes. But the
postulate, though it is certainly legitimate, and though it is the
proper and necessary prelude to scientific enquiry, may some day be
proven to be untrue; and its disproof will not be to the physicist’s
confusion, but will come as his reward. In dealing with forms which are
so concomitant with life that they are seemingly controlled by life, it
is in no spirit of arrogant assertiveness that the physicist begins his
argument, after the fashion of a most illustrious exemplar, with the
old formulary of scholastic challenge,—_An Vita sit? Dico quod non._
――――――――――
The terms Form and Growth, which make up the title of this little
book, are to be understood, as I need hardly say, in their relation
to the science of organisms. We want to see how, in some cases at
least, the forms of living things, and of the parts of living things,
can be explained by physical considerations, and to realise that, in
general, no organic forms exist save such as are in conformity with
ordinary physical laws. And while growth is a somewhat vague word for a
complex matter, which may {11} depend on various things, from simple
imbibition of water to the complicated results of the chemistry of
nutrition, it deserves to be studied in relation to form, whether it
proceed by simple increase of size without obvious alteration of form,
or whether it so proceed as to bring about a gradual change of form and
the slow development of a more or less complicated structure.
In the Newtonian language of elementary physics, force is recognised by
its action in producing or in changing motion, or in preventing change
of motion or in maintaining rest. When we deal with matter in the
concrete, force does not, strictly speaking, enter into the question,
for force, unlike matter, has no independent objective existence. It is
energy in its various forms, known or unknown, that acts upon matter.
But when we abstract our thoughts from the material to its form, or
from the thing moved to its motions, when we deal with the subjective
conceptions of form, or movement, or the movements that change of form
implies, then force is the appropriate term for our conception of the
causes by which these forms and changes of form are brought about. When
we use the term force, we use it, as the physicist always does, for
the sake of brevity, using a symbol for the magnitude and direction of
an action in reference to the symbol or diagram of a material thing.
It is a term as subjective and symbolic as form itself, and so is
appropriately to be used in connection therewith.
The form, then, of any portion of matter, whether it be living or dead,
and the changes of form that are apparent in its movements and in its
growth, may in all cases alike be described as due to the action of
force. In short, the form of an object is a “diagram of forces,” in
this sense, at least, that from it we can judge of or deduce the forces
that are acting or have acted upon it: in this strict and particular
sense, it is a diagram,—in the case of a solid, of the forces that
_have_ been impressed upon it when its conformation was produced,
together with those that enable it to retain its conformation; in the
case of a liquid (or of a gas) of the forces that are for the moment
acting on it to restrain or balance its own inherent mobility. In an
organism, great or small, it is not merely the nature of the _motions_
of the living substance that we must interpret in terms of force
(according to kinetics), but also {12} the _conformation_ of the
organism itself, whose permanence or equilibrium is explained by the
interaction or balance of forces, as described in statics.
If we look at the living cell of an Amoeba or a Spirogyra, we see
a something which exhibits certain active movements, and a certain
fluctuating, or more or less lasting, form; and its form at a given
moment, just like its motions, is to be investigated by the help of
physical methods, and explained by the invocation of the mathematical
conception of force.
Now the state, including the shape or form, of a portion of matter,
is the resultant of a number of forces, which represent or symbolise
the manifestations of various kinds of energy; and it is obvious,
accordingly, that a great part of physical science must be understood
or taken for granted as the necessary preliminary to the discussion
on which we are engaged. But we may at least try to indicate, very
briefly, the nature of the principal forces and the principal
properties of matter with which our subject obliges us to deal. Let
us imagine, for instance, the case of a so-called “simple” organism,
such as _Amoeba_; and if our short list of its physical properties and
conditions be helpful to our further discussion, we need not consider
how far it be complete or adequate from the wider physical point of
view[23].
This portion of matter, then, is kept together by the intermolecular
force of cohesion; in the movements of its particles relatively to
one another, and in its own movements relative to adjacent matter, it
meets with the opposing force of friction. It is acted on by gravity,
and this force tends (though slightly, owing to the Amoeba’s small
mass, and to the small difference between its density and that of the
surrounding fluid), to flatten it down upon the solid substance on
which it may be creeping. Our Amoeba tends, in the next place, to be
deformed by any pressure from outside, even though slight, which may be
applied to it, and this circumstance shews it to consist of matter in a
fluid, or at least semi-fluid, state: which state is further indicated
when we observe streaming or current motions in its interior. {13}
Like other fluid bodies, its surface, whatsoever other substance, gas,
liquid or solid, it be in contact with, and in varying degree according
to the nature of that adjacent substance, is the seat of molecular
force exhibiting itself as a surface-tension, from the action of which
many important consequences follow, which greatly affect the form of
the fluid surface.
While the protoplasm of the Amoeba reacts to the slightest pressure,
and tends to “flow,” and while we therefore speak of it as a fluid,
it is evidently far less mobile than such a fluid, for instance, as
water, but is rather like treacle in its slow creeping movements as
it changes its shape in response to force. Such fluids are said to
have a high viscosity, and this viscosity obviously acts in the way of
retarding change of form, or in other words of retarding the effects
of any disturbing action of force. When the viscous fluid is capable
of being drawn out into fine threads, a property in which we know that
the material of some Amoebae differs greatly from that of others, we
say that the fluid is also _viscid_, or exhibits viscidity. Again, not
by virtue of our Amoeba being liquid, but at the same time in vastly
greater measure than if it were a solid (though far less rapidly than
if it were a gas), a process of molecular diffusion is constantly going
on within its substance, by which its particles interchange their
places within the mass, while surrounding fluids, gases and solids in
solution diffuse into and out of it. In so far as the outer wall of
the cell is different in character from the interior, whether it be
a mere pellicle as in Amoeba or a firm cell-wall as in Protococcus,
the diffusion which takes place _through_ this wall is sometimes
distinguished under the term _osmosis_.
Within the cell, chemical forces are at work, and so also in all
probability (to judge by analogy) are electrical forces; and the
organism reacts also to forces from without, that have their origin
in chemical, electrical and thermal influences. The processes of
diffusion and of chemical activity within the cell result, by the
drawing in of water, salts, and food-material with or without chemical
transformation into protoplasm, in growth, and this complex phenomenon
we shall usually, without discussing its nature and origin, describe
and picture as a _force_. Indeed we shall manifestly be inclined to use
the term growth in two senses, {14} just indeed as we do in the case
of attraction or gravitation, on the one hand as a _process_, and on
the other hand as a _force_.
In the phenomena of cell-division, in the attractions or repulsions of
the parts of the dividing nucleus and in the “caryokinetic” figures
that appear in connection with it, we seem to see in operation forces
and the effects of forces, that have, to say the least of it, a close
analogy with known physical phenomena; and to this matter we shall
afterwards recur. But though they resemble known physical phenomena,
their nature is still the subject of much discussion, and neither the
forms produced nor the forces at work can yet be satisfactorily and
simply explained. We may readily admit, then, that besides phenomena
which are obviously physical in their nature, there are actions
visible as well as invisible taking place within living cells which
our knowledge does not permit us to ascribe with certainty to any
known physical force; and it may or may not be that these phenomena
will yield in time to the methods of physical investigation. Whether
or no, it is plain that we have no clear rule or guide as to what
is “vital” and what is not; the whole assemblage of so-called vital
phenomena, or properties of the organism, cannot be clearly classified
into those that are physical in origin and those that are _sui generis_
and peculiar to living things. All we can do meanwhile is to analyse,
bit by bit, those parts of the whole to which the ordinary laws of the
physical forces more or less obviously and clearly and indubitably
apply.
Morphology then is not only a study of material things and of the
forms of material things, but has its dynamical aspect, under which
we deal with the interpretation, in terms of force, of the operations
of Energy. And here it is well worth while to remark that, in dealing
with the facts of embryology or the phenomena of inheritance, the
common language of the books seems to deal too much with the _material_
elements concerned, as the causes of development, of variation or of
hereditary transmission. Matter as such produces nothing, changes
nothing, does nothing; and however convenient it may afterwards be
to abbreviate our nomenclature and our descriptions, we must most
carefully realise in the outset that the spermatozoon, the nucleus,
{15} the chromosomes or the germ-plasm can never _act_ as matter alone,
but only as seats of energy and as centres of force. And this is but an
adaptation (in the light, or rather in the conventional symbolism, of
modern physical science) of the old saying of the philosopher: ἀρχὴ
γὰρ ἡ φύσις μᾶλλον τῆς ὕλης.
{16}