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Full text of "Elements of Physical Biology"

ELEMENTS 

OF 

PHYSICAL BIOLOGY 



BT 
ALFRED J. LOTKA, M.A., D.Sc. 




"Voil& un homme qui a fait son miens pour _enniwer 
deux ou trois cents de ses concitoyens; mais son intention 
6tait bonne: il n'y a pas de quoi dftniire PersepolM. 

Yoltovre 




BALTIMORE 

WILLIAMS & WLKINS COMPANY 
1925 



Composed and Printed at the 
WAVERLf PRESS 

BT THE VYlLLIAMS & WlLKINS 

Baltimore, Md., U. S. A. 



T 



COPTEIQHT 1925 

WILLIAMS & WILKINS COMPANY 

Made in United States of America 
Published February, 1925 

ALL BIGHTS KESERVIpD 



v^ 



DEDICATED 
TO THE MEMORY 

OF 
JOHN HENBY POYNTING 



PREFACE 

The preface is that part of a book which is written last, placed 
first, and read least. As I approach my concluding task I am moved 
to reflect why a preface should be written at all. This question, if 
followed into all the intricacies of which it holds potentiality, should 
apparently result in a composition new in literature, a Preface to the 
Preface. Such precedent should not be lightly established, for it 
suggests a vista of future degenerations after the pattern of Josiah 
Royce's infinite succession of maps, each containing within Itself its 
own replica on a reduced scale. But without going to such lengths 
as this, the philosophy of the preface may perhaps briefly be sum- 
marized to this effect, that It is the author's subjective introduction , 
to the more objective matter that should follow. Here he may, if 
this is deemed of any interest, say something regarding the circum- 
stances that gave origin to the w-ork, and the conditions under which 
it came into being. He may express his feelings as to its alleged pur- 
pose, and may follow custom by giving voice to pious wishes as to the 
function which the product of his presumptive mind may fulfill in an 
Universe in which no event, however trivial be it no more than the 
addition of one more book to the groaning library shelves is with- 
out distant reverberations. 

As to origin, the first plan of the work was laid about 1902, in the 
author's student days In Leipzig. The development of the topic is 
recorded, in outline, in various publications, of which the first 
appeared in 1907 in the American Journal of Science. Eeference to 
this and to its various sequels will be found in pertinent places in 
the text that follows. The last stage of the work, arrangement of 
the matter in collected form, and filling in the flesh about the skele- 
ton framework elaborated in the journal literature, was carried out 
at the Johns Hopkins University upon the invitation of the Depart- 
ment of Biometry and Vital Statistics. For the courtesies so 
extended to him the author wishes here to express his thanks, as 
well as for the interest shown in the progress of the work by Dr. 
Raymond Pearl and the members of the Department, notably Drs. 
W. T. Howard, L. J. Reed and J. R. Miner. Outside the walls of 



VU1 PREFACE 

this University I think with very particular appreciation of the 
never-failing succor in times of mathematical trouble, which I 
found at the hands of Prof. F. R. Sharpe of Cornell University; also 
of the patient assistance, upon more than one occasion, from Prof. 
W. B. Fite of Columbia University. And I gratefully recall en- 
couragement received from Dr. G. K. Burgess, Director of the Bureau 
of Standards, especially in the earlier stages of the work, when 
encouragement was most needed. 

Acknowledgment has been made in the text for numerous quota- 
tions. The somewhat extended excerpts from certain articles pub- 
lished in the Scientific Monthly call for special notice here, and I 
wish to express my thanks both to the author, Prof. G. W. Martin, 
and to the Editor of the Monthly, for permission to quote thus at 
length from its pages. I am similarly indebted to the Editor of 
Harpers Magazine for permission to reproduce here certain portions 
of an article from my pen, entitled "Biassed Evolution", which 
originally appeared in the May issue (1924) of that publication. 

Toward the publishers, Messrs. Williams and Wilkins and in 
particular Mr. C. C. Thomas, I have every occasion to entertain 
feelings of the most cordial appreciation. Through their courteous 
attentions the business of bookmaking was made a pleasure. 

My greatest debt is acknowledged in the dedication. Whatever 
merits this book possesses may well be credited to the influence 
and teaching of Poynting. There is little danger that its faults 
shall be charged to his account. 

As to the topic of the work it seems unnecessary to say many words 
here, inasmuch as a delineation of this has been made the subject of a 
special chapter on The Program of Physical Biology. Only this 
explanation it may be well to offer here, that, as proposed in Chapter 
V } the term Physical Biology has been employed to denote the broad 
application of physical principles and methods in the contemplation 
of biological systems, whereas Biophysics, in common parlance, 
relates rather to the special field of certain physical aspects of the 
life processes of the individual. With this terminology, Physical 
Biology would comprehend Biophysics within its scope. 

The writer cannot in reason expect to have produced a work 
without blemish. Even an approach to such absolute perfection is 
the rare privilege of a few. He would, however, be unjustified in 
addressing the reading public at all if he did not entertain the hope 



PEEFACE IX 

that, despite shortcomings, these pages may bring to the reader 
new assets, here and there a new piece for his mental furniture, now 
and again a new perspective, a new comprehensive outlook over a 
body of facts and relations in themselves perhaps familiar. 

The work has been largely one of systematization, and of develop- 
ment of method. Factual material has been introduced essentially 
for the purpose of illustrating the point of view to be set forth. There 
seems therefore hardly any occasion for apologetic explanations that 
anything of the nature of completeness in the presentation of perti- 
nent facts was in nowise armed at. Indeed, it must be obvious upon 
most casual reflection that such completeness, in a subject of the 
amplitude of that here taken in view, could be achieved only in a 
cyclopedic work of several tiers of volumes. 

Considerable care has been taken to cite in detail the sources con- 
sulted. It was felt that, on account of the wide dispersal of these 
citations over a broad field of scientific literature, few readers could 
be expected to be familiar with all the branches of pertinent library 
lore, and for this reason a collation of such references should have a 
value of its own, even apart from the text. At the same time the 
compilation of anything like a complete bibliography could not be 
undertaken on the present occasion. 

It is hoped that the mathematical mien of certain pages will not 
deter biologists and others, who may be disposed to look askance at 
symbols of the art, from acquiring an interest in other portions of the 
book. Biometricians will, presumably, not shrink on this score; to 
them, and to physicists, (whom I should greatly wish to number among 
my readers) I may perhaps confess that I have striven to infuse the 
mathematical spirit also into those pages on which symbols do not 
present themselves to the eye. For this I offer no apology. 

For the sake of space economy recapitulary paragraphs have, as a 
rule, not been given a place in the text. An exception has however 
been made in Chapters XX, XXXIII and XXIV, the last of 
which, in particular resumes and amplifies somewhat certain phases 
of the topics discussed in earlier chapters. The reader who may 
wish briefly to review the substance of his reading as he proceeds, 
should find suitable assistance in the rather detailed Analytical 
Synopsis of Chapters that has been placed immediately after the 
Table of Contents. And finally, a bird's eye survey of the general 



X PREFACE 

field covered in this work can be obtained by consulting the Tabular 
Synopsis at the end. 

Here, then, I make my exit from the prefatory stage and commend 
my work to the tender mercies of the reader; not without some trepi- 
dation, for I recall how Voltaire said of one: "II fit une philosophic 
comrne on fait un bon roman; tout parut vraiseniblable, et rien ne 
fut vrai;" and there comes to mind the language still plainer of du 
Maupassant "Depuis qu'ils ont appris a lire et a ecrire, la betise 
latente se degage." I trust that the reader's response to these pages 
may not be too fervent an Amen to the prayer of The Sceptical 
Chymisi "It is to be hoped that these men, finding that they can 
not longer write impertinently and absurdly .... will be 
reduced either to write nothing, or books that may teach us something 
. , . . ; and so, ceasing to trouble the world with riddles or im- 
pertineneies, we shall either by their books receive an advantage, or 
by their silence escape an inconvenience." 

ALFEED J. LOTSA. 

Johns Hopkins University, May, 1924- 



CONTENTS 
PART I. GENERAL PRINCIPLES 

CHAPTER I 
Regarding definitions 3 

CHAPTER II 

Evolution Defined : The History of a System in the Course of Irreversible 
Transformation 20 

CHAPTER III 
The Statistical Meaning of Irreversibility 30 

CHAPTER IV 
Evolution Conceived as a Redistribution 41 

CHAPTER V 
The Program of Physical Biology 49 

PART n. KINETICS 

CHAPTER VI 

The Fundamental Equations of the Kinetics of Evolving Systems. Gen- 
eral Case 57 

CHAPTER VII 
Special Case : Single Dependent Variable 64 

CHAPTER VIII 
Special Cases : Two and Three Dependent Variables 77 

CHAPTER IX 
Analysis of the Growth Function 100 

CHAPTER X 
Further Analysis of the Growth Function 128 

PART III. STATICS 

CHAPTER XI 
General Principles of Equilibrium 143 

CHAPTER XII 

Chemical Equilibrium, as an Example of Evolution under a Known Law. . 152 

xi 



Xll CONTENTS 

CHAPTER XIII 
Inter-species Equilibrium. . , 161 

CHAPTER XIV 
Inter-species Equilibrium : Aquatic Life. 171 

CHAPTER XV 
The Stage of the Life Drama 185 

CHAPTER XVI 
The Circulation of the Elements. The Water Cycle 209' 

CHAPTER XVII 
The Carbon Dioxide Cycle 218 

CHAPTER XVIII 
The Nitrogen Cycle 229 

CHAPTER XIX 
The Phosphorus Cycle 246 

CHAPTER XX 
Cycles : Conclusion and Summary 252 

CHAPTER XXI 
Moving Equilibria. . . 259 

CHAPTER XXII 
Displacement of Equilibrium 280 

CHAPTER XXIII 
The Parameters of State 300 

PART IV. DYNAMICS 

CHAPTER XXIV 
The Energy Transformers of Nature 325 

CHAPTER XXV 
The Helation of the Transformer to Available Sources 336 

CHAPTER XXVI 
The Correlating Apparatus 362 

CHAPTER XXVII 
Extension of the Sensuous World Picture 371 

CHAPTER XXVIII 
The Adjusters. 381 



CONTENTS Xlll 

CHAPTER XXIX 
Consciousness 388 

CHAPTER XXX 
The Function of Consciousness 394 

CHAPTER XXXI 
The Origin of Consciousness in the Living Organism 402 

CHAPTER XXXII 
Energy Relations of Consciousness 406 

CHAPTER XXXIII 
Review of the Correlating Apparatus 410 

CHAPTER XXXIV 

Conclusions ] Retrospect and Prospect 417 

Synoptic chart of physical biology 435 



LIST OF ILLUSTRATIONS 

FIG. 1. Graph of model process illustrating the statistical meaning of 
irreversibility. Reproduced from A. J. Lotka, Two Models in Statis- 
tical Mechanics, Am. Math. Monthly, vol. 31, 1924, p. 122 31 

FIG. 2. Graph of second model process illustrating the statistical meaning 
of irreversibility. Reproduced from A. J. Lotka, Two Models in 
Statistical Mechanics, Am. Math. Monthly, vol. 31, 1924, p. 124 33 

FIG. 3. Frequency diagram for the deviations from the mean appearing in 
figure 2. Reproduced from A. J. Lotka, Two Models in Statistical 
Mechanics, Am. Math. Monthly, vol. 31, 1924, p. 125 34 

FIG 4. The law of population growth for the United States according to 
Pearl and Reed 68 

FIG. 5. Growth of a population of Drosophila (fruit flies) undsr controlled 
experimental conditions, according to Pearl and Parker. 69 

FIG. 6. Growth of a bacterial colony (B. dendroides). according to 
H. G. Thornton 71 

FIG. 7. Growth of rat according to H. H. Donaldson and T. B. Robertson. 73 

FIG. 8. Growth of sunflower seedlings according to H. S. Reed and R. H. 
Holland; computed curve by L. J. Reed 74 

FIG. 9. Growth of sunflower seedlings. The same data as in figure 8, but 
plotted in logarithmic diagram 75 

FIG. 10. Presumptive curve of growth of endemic malaria according to 
the Ross Equation. Reproduced from A. J. Lotka, Am. Jour. Hy- 
giene, January Supplement, 1923 84 

FIG. 11. Course of parasitic invasion of insect species according to W. R. 
Thompson 85 

FIG. 12. Increasing diffusion-in-time of successive generations in the 
progeny of a population element 86 

FIG. 13. Course of parasitic invasion of insect species, according to Lotka; 
elementary treatment 90 

FIG. 14. Course of parasitic invasion of insect species, according to Lotka; 
more exact treatment 91 

FIG. 15. Some historical human survival curves, exhibiting an evolution- 
ary trend toward longer average duration of life 103 

FiGi 16. Survival curves for the State of Massachusetts, for the three 
decades 1890-1900-1910. After Glover 104 

FIG. 17. Survival curves for different countries. After Glover 105 

FIG. 18. Survival curve plotted on logarithmic scale. II. S. 1910 107 

FIG. 19. Logarithmic survival curves for man, Drosophila, and Proales de- 
cipiens. Plotted according to centiles of life-span. After R. Pearl. . 109 

FIG. 20. Diagrams to illustrate proof of stability of normal age distribu- 
tion. Reproduced from A. J. Lotka, Proc. Natl. Acad. Sci., vol. 8, 
1922, p. 339 , 113 

xv 



^ LIST OP ILLUSTRATIONS 

FIG. 21. "Stable" age distribution, as exemplified by the population of 
England and Wales in the decade 1871-1880 ........................... 114 

FIG, 22. Diagram of relation between birth rate per head 6 and death rate 
per head d in population with stable age distribution ................ 117 

FIG. 23. Diagrammatic illustration of influence of random and of selective 
slaughtering upon survival curve of biological species .............. 120 

FIG. 24. Growth of favored type in mixed population of two phenotypes 
After J. B. S. Haldane ............................................. 124 

FIG. 25. Effect of selection on population comprising two phenotypes with 
Mendelian inheritance. After J. B. S. Haldane ..................... 126 

FIG. 26. Feed consumed, and increase in live weight of steers at several 
ages. After Moulton, Trowbridge and Haigh ....................... 133 

io. 27. Some fundamental types of equilibrium, in a system with two 
dependent variables ............................ j 4 g 

FIG 28. Map of integral curves for the Ross malaria equations.' Repro- 
1923 A ' J " L tka ' Am ' JoUr- Hygiene > Jan uary Supplement, 

FIG 29 Model of surface corresponding to figure 28 '."Reproduced from 
ff^ A ?' JoUr ' H yg iene > January Supplement, 1923 ......... 150 

G. dO. Age distribution in population of molecules of two substances in 
monomolecular chemical equilibrium. Reproduced from A. J. Lotka, 
Am. Jour. Science, 1907, p. 208 ....... 155 

n contents " of '' 



* of srasshoppe 



FIG 34. Seasonal food habits of the Meadow" Lark.' After H.c'.B^ant 
* ' ' 



^ 



of 
FIG. 39. Key to figure 38 .............................................. 177 



205 



LIST OF ILLUSTRATIONS 

FIG. 45. Periodic classification of the elements, showing division into 
petrogenic elements and metallogenic elements. After H. S. 

Washington ^ 7 

FIG. 46. Circulation of the elements in nature. The water cycle 215 

FIG. 47. Circulation of the elements in nature. The carbon cycle 226 

FIG. 48. Circulation of the elements in nature. The nitrogen cycle 230 

OQTJ 

FIG. 49. Organic nitrogen circulation * 0i 

FIG. 50. The rise of the saltpeter industry 235 

FIG. 51. The rise of the fixed nitrogen industry 24 

FIG. 52. Circulation of the elements in nature. The phosphorus cycle. . . 247 

FIG. 53. The Soxhlet extraction apparatus 253 

FIG. 54. Circulation of the elements in nature. The sodium chloride 

cycle ; m 

FIG. 55. Uranium and its products of radioactive disintegration 263 

FIG. 56. Equilibrium polygon for Radon (radium emanation) in contact 

with its disintegration products 266 

FIG. 57. Relative abundance of the elements. Diagram according to 
W. D. Harkins, based on analysis of meteorites. (Jour. Am. Chem. 

Soc., 1916, p. 863) 271 

FIG. 58. Equilibrium polygon for the human species and some of the spe- 
cies on which it depends for its food supply 277 

FIG. 59. The Yellow Shark and some of his relatives, as an example of 

possibly orthogenetic development 296 

FIG. 60. Law of urban concentration 308 

FIG. 61. Relation between rate of reproduction in Drosophila (fruit fly) 

and density of mated population. After Pearl and Parker 309 

FIG. 82. Relation between mean length of life and population density in 

Drosophila. After Pearl and Parker 310 

FIG. 63. Hyperbolic curves obtained by plotting as ordinates the number 
of genera 1, 2, 3, . . . n species, and as abscissae the number n of such 

species. After J. G. Willis 314 

FIG. 64. Relation between number and size of genera of all flowering 

plants, plotted logarithmically. After J. C. Willis 315 

FIG. 65. Relation between number and size of Rubiaceae, plotted logarith- 
mically. After J. C. Willis 315 

FIG. 66. Relation between number and size of genera of chrysomelid bee- 
tles, plotted logarithmically. After J. C. Willis 316 

FIG. 67. Solubility of carbon dioxide in water, expressed in volumes of COj 
measured at normal temperature and pressure, per volume of water. 

After G. W. Martin 318 

FIG. 68. The mill-wheel of life 334 

FIG. 69. Mechanical walking beetle, exhibiting the several characteristic 

elements of the correlating apparatus 341 

FIG. 70. The evolution of man's means of transportation 367 

FIG. 71. Growth of American Railways 369 

FIG. 72. How the future enters into the determination of the motion of the 
walking mechanical beetle, thus imitating purposive action (tele- 
ology) 382 



LIST OF TABLES 

Table 1. The program of physical biology 53 

Table 2. Growth of the population of the United States 67 

Table 3. Growth of bacterial colony. After H. G. Thornton 70 

Table 4. Growth of sunflower seedlings. After H. S. Reed and R. H. 

Holland 74 

Table 5. Course of parasitic invasion of insect species, according to W. R. 

Thompson 86 

Table 6. Tabular survey of different modes of interdependence of biologi- 
cal species 98 

Table 7. Example of normal age distribution 113 

Table 8. Relation between birth rate per head b and death rate per head d 

in a population with normal age distribution 117 

Table 9. Growth of steers, and feed consumed 134 

Table 10. Survey of methods of marine biological census 178 

Table 11. Principal components of the earth's surface crust 185 

Table 12. Distribution of gases in the atmosphere at different levels 188 

Table 13. Constituents of the atmosphere, at earth's surface and in toto . . 190 

Table 14. Composition of the Ocean 191 

Table 15. Comparison of air and aquatic atmosphere 192 

Table 16. Composition of lithosphere 194 

Table 17. Composition of human body 197 

Table 18. Composition of living organisms. After H. F. Osborne 198 

Table 19. Comparison of composition of blood serum and sea water 201 

Table 20. Moisture contents of foods 211 

Table 21. Discharge of the World's rivers 214 

Table 22. Progress of by-product coke ovens in the United States 233 

Table 23. Growth of the saltpeter industry 237 

Table 24. Uses of saltpeter 237 

Table 25. Meteoric rise of the nitrogen fixation industry 242 

Table 26. Supply of plant foods in the soil 257 

Table 27. Rate of participation of the elements in the cycle of nature. . . 258 
Table 28. Radioactive equilibrium of radium in contact with its disinte- 
gration products 265 

Table 29. Radioactive equilibrium of radon (radium emanation) in con- 
tact with its disintegration products 268 

Table 30. Geological time table. After C. Schuchert 269 

Table 31. World's production of population and its accessories. After 

R. Pearl 278 

Table 32. Association of high blood pressure with over-weight 295 

Table 33. Distance travelled in one hour by different modes of conveyance 368 
Table 34. Man's correlating apparatus, native and artificial contrasted. . 411 

Table 35. Man's correlating apparatus (continued). The Adjusters 413 

Table 36. Classification of the sciences 423 



ANALYTICAL SYNOPSIS OF CHAPTERS 
PART I. GENERAL PRINCIPLE 

Chapter I. Regarding Definitions. Definitions are arbitrary, 3 But are 
governed by considerations of expediency, 3 The problem of expediency in 
framing definitions is not always a simple one, 3 Pseudo-problems arising 
from failure to recognize the arbitrary character of definitions: Hunting the 
Jabberwock, 4 Subjective discontinuities introduced by the senses, 5 
Examples: Colors, e.g. blue, green; light and heat waves; distinction between 
animals and plants; between biological species; between living and non-living 
matter, 5 To such abrupt subjective divisions there may correspond no objec- 
tive discontinuity in nature, 5 Definitions in Biology, 5 Vitalism versus 
Mechanism; merely a question of terms, 7 Herbert Spencer's "proximate 
definition" of life, 7 Inadequacy of Spencer's definition, 7 Sir Edward 
Schaefer's standpoint, 8 Line of division recedes with increasing knowledge 
8 Alleged characteristics of living matter: Growth from within 8 Chemical 
growth as distinguished from physical growth of crystals, 10 Growth from 
unsaturated solution, as distinguished from growth of crystals from super- 
saturated solution, 10 "Selective" growth, 10 Reproduction, 11 Vital 
Force, 13 Physical chemistry of structured systems, 13 Geometrical element 
lacking in physical chemistry of today, 13 Systems ordinarily considered are 
either structureless or of simple structure, 14 This absence of structural 
features in physico-chemical systems is due to subjective, not objective rea- 
sons, 14 Due in part to convenient arbitrary restrictions, 15 Relation 
between growth, environment and structure, 15 The laws of chemical dy- 
namics in structured systems will be the laws that govern the evolution of a 
system comprising living organisms, 16 Application to Biology: The organ- 
ism as a structured physico-chemical system, 16 The travelling environment, 
milieu inte"rieur, 17 Increasing independence of organism of its remote en- 
vironment, 18 The policy of resignation: Abandoning the attempt to define 
life, 18 Parallels in the history of science : Abandonment of the attempt to 
prove Euclid's twelfth postulate led to new systems of geometry, 18 Aban- 
donment of attempts to build perpetual motion machines was equivalent to 
recognizing the law of conservation of energy, 18 Abandonment of the at- 
tempt to detect the earth's motion through the ether is the foundation of the 
modern theory of relativity, 18 The ideal definition is quantitative, 19 
Desirability of establishing a quantitative definition and conception of evo- 
lution, 19. 

Chapter II. Evolution Defined. Definition should conform as far as possi- 
ble to common usage of the term, 20 Analysis of common conception of evolu- 
tion, 20 Evolution is history, but not all history is evolution, 20 Systems in 
purely periodic motion would not be said to evolve. They repeat in endless 

xxi 



XXil ANALYTICAL SYNOPSIS OF CHAPTERS 

succession the same series of events. In an evolving system each day is unlike 
any other day, 21 Evolution not a mere changeful sequence, 21 Abortive 
attempts to formulate the direction of evolution, 21 These attempt defini- 
tion in terms of a single component, 22 Such definitions are foredoomed to 
failure, a successful definition must be framed in terms of the evolving system 
as a whole, 22 Evolution is the history of a system in the course of irreversible 
transformation, 24 Scope of this definition: What it excludes; what it 
includes 24 The line of division depends on the nature and extent of our 
knowledge regarding the system, 25 This is in harmony with the fact that 
problems of evolution are largely problems of probability, 25 All real trans- 
formations are irreversible, hence all real history is evolution, 26 What 
then is gained by the definition? 26 It indicates the direction of evolution as 
the direction of irreversible transformations, the direction of increasing 
entropy, 26 Example of pendulum. Irreversible feature introduced by fric- 
tional force, 27 Inertia-free or completely damped systems, 28 Accelerations 
vanish with velocities, 29 Velocities are single-valued functions of configura- 
tion, 29. 

Chapter III. The Statistical Meaning of Irreversibility., Apparent irrever- 
sibility (progressiveness in time) of certain theoretically periodic processes, 
30 Their periodicity, with eventual return to initial state, never observed in 
practice, 30 Explanation of this discrepancy: Macroscopic model illustrative 
of irreversibility of gaseous diffusion, 30 Return to initial state possible, but 
exceedingly rare (highly improbable), 31 The model is competent to illustrate 
also the highly improbable event of return to initial state, 32 Dynamical 
theory indicates not only occasional but periodic return to initial state, 32 A 
second model illustrates this also, 32 Evolution aspassage from less probable to 
more probable states, 35 Inadequacy of this "principle" : it is indefinite in fail- 
ing to specify the characteristic with respect to which probability is reckoned; 
and it is incomplete in failing to draw attention to certain energy relations, 
35 Irreversibility is relative, depending upon the means naturally available 
or arbitrarily permitted to operate upon the system, 35 Significance of this 
m organic world: Macroscopic irreversibility of diffusion processes in nature, 
36 Need of a method of mathematical analysis to deal with cases intermedi- 
ate, in specified degree, between the following two extremes: (a) Wholly in- 
discriminate (pure chance) operation upon material in bulk, (b) Wholly 
determinate operation, with nothing left to chance, upon materials discrimi- 
nated and acted upon in detail, piece by piece, and circumstance by circum- 
stance, _36--This method must take account of degree of perfection of the 
mechanical and psychic equipment by which each organism reacts upon its 
environment, 37-Senses as a means of overcoming chance, 37-PhysicaI sig- 
nificance of our subjective sense of forward direction in time, which finds no 
expression in the differential equations of pure dynamics, 37-This subjective 
tune sense may be related to the influence of initial conditions in dynamics, 
38-But the direction of evolution seems related rather to that directedness in 

Zdltl 18 f + r Ct T tiC f aperi dic r S6emingly a P eriodic ?**, 38- 
Inadequacy of thermodynamic method, 39-The linking of evolution with the 



ANALYTICAL SYNOPSIS OF CHAPTERS XX111 

concepts of thermodynamics and statistical mechanics is instructive as sug- 
gesting a conception of the direction of evolution, the direction of increasing 
entropy, increasing probability, 39 This point of view, however, is inadequate 
for application to concrete cases of organic evolution, because data are fur- 
nished in terms unsuited to the methods of thermodynamics, 39 Neither are 
existing methods of statistical mechanics, as applied to molecules and the 
like, helpful; the instrument is ill adapted to the scale of the object, 39 New 
method needed, that shall accept its problems in terms of biological data, as 
thermodynamics accepts its problems in terms of physical data; a General 
Theory of State, an "Allgemeine Zustandslehre " 39. 

Chapter IV. Evolution Conceived as a Redistribution. Evolution viewed 
as a redistribution of matter among the components of a system, 41 System 
described by statement of mass of each component, and indication of value of 
certain parameters, 41 Analytical expression of history of system given by 
relations or equations established between the variables and parameters de- 
nning the state of the system, 41 Fundamental equations usually simplest 
in form of differential equations, 42 Particular form of equations of evolv- 
ing systems, 42 General form of equations of evolving system, 43 Equations 
as applied to life-bearing system, 43 Definition of the components arbitrary 
but conclusions relate to the components as defined, 44 Relation of evolu- 
tion, as here conceived, to the problem of the origin of species, 44 Inter-group 
and intra-group evolution, 44 Analytical indication of intra-group evolution, 
45 Fundamental equations resemble in form the equations for an inertia-free 
or completely damped system, 47 Fundamental equations, as here given, 
may not cover all cases, but are at any rate of very wide scope, 47 Equations 
interpreted to include possible lag or lead effects, 47 Singular implications of 
lag and lead effects; possible relation to phenomena of memory and will, 48 
Appearance of lag and lead effects in equations may, however, be spurious, 48. 

Chapter V. The Program of Physical Biology. Systematization and 
division of subject, 49 General mechanics of evolution, 49 Macro-mechanics 
and micro-mechanics, 50 Statistical mechanics as the connecting link, 50 
Stoichiometry, the study of mass relations (material transformations), 50 
Energetics or Dynamics, the study of the energy transformations, 50 Kinetics 
and Statics, 51 Equilibrium and steady states, 51 Moving equilibria, 51 
Displacement of equilibrium; Le Chatelier's principle, 52 Sociological 
analogues of forces and "quasi-dynamics" (economics), 52 The term Physical 
Biology to be used to cover the territory indicated in this chapter, 52 Methods 
of obtaining data, 52 Chart of Program of Physical Biology, 53 Methods of 
elaborating data, 54. 

PART II. KINETICS 

Chapter VI. The Fundamental Equations of Kinetics of Evolving Systems. 
General case, 57 Some implications of the fundamental equations in their 
general form, 57 Equations of constraint, 58 Elimination of variables. 
Introduction of constants A, 58 Evolution with parameters P, Q and A 
constant, 58 Equilibria or steady states, 59 Number and character of 



XXIV ANALYTICAL SYNOPSIS OF CHAPTEES 

equilibria. Example: Fly population, 59 Fundamental equations trans- 
formed by introduction of excess of actual masses over equilibrium masses in 
place of the former, 60 Expansion in Taylor's series, and solution in exponen- 
tial series, 60 Characteristic equation for exponential coefficients, 60 Sig- 
nificance of sign and character of roots X of characteristic equation, 61 Sta- 
bility of equilibrium, 61 Mode of approach to equilibrium: Aperiodic and 
periodic (oscillatory) type, 61 Analytical confirmation and extension of a 
passage in Herbert Spencer's First Principles, 61 Zero or negative roots of the 
equilibrium equation: Unfit species, 62. 

Chapter VII. Fundamental Equations of Kinetics (Continued). Special 
Case: Single Dependent Variable. Law of population growth, 64 Popula- 
tion of United States, 66 Stability of equilibrium, 67 Experimental popula- 
tions, 69 Diminishing population, 70 Growth of individual organism, 71 
Autocatakinesis, 76. 

Chapter VTII. Fundamental Equations of Kinetics (Continued). Special 
Cases: Two and Three Dependent Variables. Interdependence of species, 
77 Several types of interdependence, 77 Analytical characteristics of those 
types, 78 Effect of these characteristics upon the nature of the solution of the 
equation of Kinetics for two variables, 79 Concrete examples, 5 Martini's 
equation for immunizing diseases, 79 A special case noted by Watson, 81 
The Ross malaria equations, 81 Example in parasitology, 83 Thompson's 
treatment of the case, 83-Objections to this, 87-Treatment of case by general 
equation of kinetics, 88-Nature of the solution: it represents a periodic or 
oscillatory process, 90-Comparison with observed facts according to L O 
Howard^ 90 Annihilation of one species by another, 92-Case of three depen- 
dent variables, 94-Relation of this to a practical problem in sea fisheries, 95- 
Replaceable and irreplaceable components, 95-Limiting factors, 97-Lie- 
big s law, 97 Chart of types of interdependence of biological species 98 
* 2!r K ' A * dysis of the Growth Unction. The form of thi function 
A+ ? T l aggregates 100-Demographic functions, 101-Survival 

M?^ 

'^ i T r , mal Ege diataibu *^ HO-Demogra P hic relations in 
normal population, 115-Rate of increase per generation, 118-Effect of 
selects slaughtering 119-Intelligence as a discriminating agency 20 
(With MendeH J B. S 



Chapter X. Further Analysis of the Growth Function. Adjustment of the 



e teful 

produce, 132- 



nrnHnna 1QO T?~i j.- j ' -^ vvu^o uiv, muuiaiS ICept tor 

p^ss^s^it^s^ 

Sr P S-^;-- -:s-i; 



ANALYTICAL SYNOPSIS OF CHAPTEBS XXV 

from standpoint of domestic species is high efficiency from human standpoint, 
135 Network of chains of interrelated species, 136 Transformation factors 
and their economic significance, 137. 

PART ill STATICS 

Chapter XI. General Principles of Equilibrium. Equilibria and station- 
ary states, 143 Scope of Statics, 143 Kinetic, dynamic, and energetic defini- 
tion of equilibrium, 143 Our chief interest here in stationary states not true 
equilibria, 145 General equilibrium condition, 145 Different types of equi- 
libria, 146 Illustration: Malaria equilibrium according to Ross, 147 Metas- 
table equilibrium, 151 Exceptional cases, 151. 

Chapter XII. Chemical Equilibrium, as an Example of Evolution under a 
Known Law. Case of simple balanced reaction, 152 Relation between 
"birth" rate and "death" rate of molecules, 153 The survival factor p (a) 
and life curve of molecules, 153 Reaction constant as a a force of mortality, 
154 Chemical reaction as a case of survival of the fittest, 154 Analogy of 
chemical reaction to course of events in population of mixed biological species, 
155 Presumptive mechanism of chemical reaction (Baly), 155 The fuga- 
ceous transitional state intermediate between chemical compounds (Schonbein), 
156 Laws of thermodynamics, as determinants of the end state in an equi- 
librium reaction, are, in this case, the Law of Evolution of the system, 157- 
Natural laws conveniently expressed as maximum or minimum principles, 157- 
Law of organic evolution may be expected to take this form, 158 Law of 
chemical evolution is framed in terms of the system as a whole ; law of organic 
evolution must undoubtedly also be thus framed, 158 Law of equilibrium 
expressed in form of a minimum principle, 158. 

Chapter XIII. Inter-Species Equilibrium. Equilibrium condition in more 
particular form, 161 Numerical illustration, 162 Economic relationship of 
coefficients appearing in equilibrium condition, 163 Sources of information 
regarding biological equilibrium : Biological surveys, 164 Analysis of stomach, 
contents, 166 Intra-species equilibrium (with Mendelian inheritance), 170. 
Chapter XIV. Inter-species Equilibrium: Aquatic Life. Special occasion 
for demological studies of aquatic population, 171 Fishes as natural dragnets, 
171 Aquatic food chains in relation to human food, 2 Importance of aqui- 
culture for the future, 172 Loss of fertilizer through modern methods of 
sewage disposal, 172 Partial restoration of such material to human food sup- 
ply through fisheries, 173 Different methods of census of marine population : 
dragnet; bottom samplers; recatching of marked catches; centrifuge; dilution 
culture, 173 The nannoplankton, 173 Work of Petersen in Kattegatt, 174 
Quantitative estimates of principal groups of the marine population of Katte- 
gatt, and their interrelation, 175 Summary of methods of marine biological 
census (Table), 176 Food chains, 176 Necessity of occupying ourselves with 
the more remote links of our food chain, 177 "Feeding our foods, " a species 
of symbiosis, 180 Agriculture and aquiculture, as mining and as manufactur- 
ing industries, 180 Resources but recently tapped, and others still untouched, 
180 Food chains in aquatic species, 180 Wastefulness of long food chains, 



XXVI ANALYTICAL SYNOPSIS OF CHAPTEES 

181 Economic value of shell fisheries owing to simple food chain coverting 
vegetation directly into human food (oysters, etc.); 181 Primary, secondary 
and tertiarv foods, 171 Cycles and the circulation of the elements in Nature. 
183. ' 

Chapter XV. The Stage of the Life Drama. The tripartite world, 185 
Atmosphere, 185 How the earth holds her atmosphere, 185 Cosmic losses 
from the atmosphere negligible, 188 Cosmic accessions to the atmosphere, 
192Hydrosphere, 192 Aquatic atmosphere, 193 Lithosphere, 193 Cosmic 
accessions to lithosphere, 195 Composition of earth's crust, 195 Relation to 
composition of organism, 197 Similarity in composition of sea water and 
blood serum, 201 Significance of this as regards aquatic origin of terrestrial 
fauna, 202 Chemical correlation in soil and in organism, 204 Accessibility 
of valuable earth constituents, 206 Accessibility not in any direct relation to 
abundance, 206 H. S. Washington's classification of petrogenic (rock-form- 
ing) and metallogenic (ore-forming) elements of the periodic table, 207 
Dissipating and concentrating processes in Nature, 208. 

Chapter XVI. The Circulation of the Elements : The Water Cycle. Circu- 
lation of elements vaguely realized by ancients, 209 Water requirements of 
human body, 210Water requirements of plants; rainfall as limiting factor, 
211 Sources of supply, 213 Quantitative estimates of several items in water 
cycle, 213 Water cycle diagram, 215 Fraction of total water circulation tak- 
ing part in life cycle, 216. 

Chapter XVII. The Carbon Dioxide Cycle. Combustion as an essential 
feature of the life process, 218 Analogy of flame arising from spark and life 
arising from germ, 218 Rarity of ignition except from pre-existing flame anal- 
ogous to apparent impossibility of life originating except from preexisting life, 
218 Oxygen as an inorganic food, 219 Plant nature of man in his attitude 
toward this inorganic food, 219-The carbon cycle, 220-Carbon as the organic 
element, 220 Source and gate of entry into the organic carbon cycle, 220 
Some estimates of quantities involved in the carbon cycle, 220 Interrelation 
of green plants and animals, 221 Carbonization of dead vegetable matter and 
its significance for the industrial civilization of the present era, 221The pres- 
ent an atypical epoch: man living on his capital, 222-Attempts to establish 
the balance sheet of the earth's carbon economy, 222 Absorption of C0 2 in 
weathering of rocks, 223-Formation of CO 2 by burning of coal, 224-The ocean 
as an equalizer regulating the C0 2 content of the air, 224-Unccrtainty as to 
net loss or gam of total C0 2 in atmosphere, 225 The oxygen cycle, 225-Oriin 
of atmospheric carbon dioxide and oxygen, 225-Carbon cycle diagram 226- 
Loss of oxygen from the atmosphere, 228. 

Chapter XVIII. The Nitrogen Cycle. Natural demand and supply 229- 
Seemmg abundance of nitrogen illusory, 229-Nitrogen cycle diagram,' 230- 
Cate of entry into nitrogen cycle, 232-Leak of nitrogen out of circulation 
2ipLoss of nitrogen in combustion, distillation and coking of coal 233-Sk- 
mficance and rapid increase of by-product recovery type of coke ovens, 233- 
Other losses of combined nitrogen, 234-Accessory sources of combined nitro- 
nSJ f ^' 234 r Human ^erference in nitrogen cycle, 236-Ex- 
ploitation of guano deposits, 236-CMlean nitre beds, 236-Consumption of 



ANALYTICAL SYNOPSIS OF CHAPTERS XXV11 

saltpeter as fertilizer and otherwise, 237 Origin of nitre beds, 238 Industrial 
nitrogen fixation processes, 239 Birkeland and Eyde nitric acid process. 
Cyanamide process. Haber ammonia process. Biicher cyanide process, 
239 Combination of Haber process with Solvay soda process, 239 Ostwald 
oxidation process, 241 Meteoric rise of nitrogen fixation industry, 241 Its 
ethnological significance, 241 Economic and energetic significance of concen- 
tration, e.g. of supply of combined nitrogen, 243 Localized sources of concen- 
trated supplies as centers of attraction in man's economic activities, 244 
Total circulation tends to increase, 245. 

Chapter XIX. The Phosphorus Cycle, Immobile elements, 246 Natural 
phosphorus supply of soils, 246 Phosphorus cycle diagram, 247 Leakage of 
phosphorus from circulation, 248 Phosphate rock and the migration of phos- 
phorus, 248 The role of fish and birds in the phosphorus cycle, 249 Soil losses 
of phosphorus, 250 Phosphate slag as fertilizer, 251. 

Chapter XX. Cycles: Conclusion and Summary. Circulation of chlorine 
and the alkalis, 252 The sea and the sun as a Soxhlet extractor, 252 Sodium 
chloride cycle diagram, 254 Differential behavior of sodium and potassium 
in the process of extraction, 255 Comparative rarity of potash in soils, 255 
Effect of World War on potash market, 256 Circulation of sulphur, 256 
Circulation of iron, 256 Summary of cycles, 257 Supply of plant food in soil, 
257 Rate of participation of elements in cycles of nature, 258. 

Chapter XXI. Moving Equilibria. Principle of continuity, 259 Equation 
of slowly moving equilibrium; first approximation, 259 Higher approxima- 
tions, 260 Special case : pace set by slowest member in a chain, 261 Radio- 
active equilibrium, 261 Equilibrium polygon, 266 Extinction of unadapted 
species, 266 Example of inaccuracy of first approximation, 268 Radioactive 
chains as cosmic clocks, 268 Geological time table, 269 Origin of elements 
and ultimate genesis of organisms, 269 Relative abundance of the elements, 
271 Terminal stages of the earth's evolution: Geophysics and geochemistry, 
273 Joly's theory of periodic melting of the earth's crust, 275 Organic 
moving equilibria, 276 Equilibrium polygon, 277. 

Chapter XXII. Displacement of Equilibrium. Perfectly general case of 
influence of change in parameters will not here be considered, 280 Principle 
of Le Chatelier, 281 Some common misstatements of the principle, 282 
Early essayed application to biology, 283 Conditions of validity of the prin- 
ciple, 284 Extension of scope of rigorous applicability, 286 Area and rent, 
288 Discussion of displacement of equilibrium independently of Le Chatelier's 
principle, 289 Case I: Displacement of equilibrium between food and feeding 
species, 289 Case II: Change of circulation through moving cycles, 292 
Some significant cases of instability, 294 Vicious circles, 294 Cumulative 
cycles simulating orthogenesis, 296 Benign cycles, 297. 

Chapter XXIII. The Parameters of State. Topographic parameters, 300 
Intensity factor of energy, 303 Simpliest examples of topographic par- 
ameters : volume, area, 301 Complexity of topography in organic evolution, 
301 Simplification of problem by "substituting ideal upon which it is possible 
to operate, for intractable reality", 302 Empirical study of biogeography and 
ecology, 302 Conjugate parameters, 303 The intensity law in organic and 



xxviii ANALYTICAL SYNOPSIS OF CHAPTERS 

economic systems, 303-Rent as a measure or index of population pressure 
304 But population pressure exists independently of rent, e.g., in species 
other than man, 304-Distant analogy of law of population pressure to gas law, 
305-Law of urban concentration, 306-Biological background of population 
pressure, 307 Influence of population density on rate of reproduction (Pearl 
and Parker), 308 Influence of population density on duration of life (Pearl 
and Parker), 309 Topographic parameters during period of diffusion, 311 
Willis' theory of Age and Area, 311 Climatic parameters, 317 Their labora- 
tory investigation (Pearl and Parker), 319 Parameters of state and the 
analytical condition for equilibrium, 319 Thermodynamic analogy, 320 
Inversion of typical problem of thermodynamics, 321 Systems of Quasi- 
Dynamics, 321. 

PART IV. DYNAMICS 

Chapter XXIV. The Energy Transformers of Nature. The fundamental 
equations of Kinetics do not exhibit any explicit reference to dynamical or 
energetic relations, 325 But certain of the components S are energy trans- 
formers, 325 Fundamental characteristics of energy transformers, 325 
Cyclic working; output and efficiency, 326 Thermodynamic law of maximum 
output, 326 Reversible and irreversible processes, 327 Composite and 
coupled transformers, 327 Accumulators, 328 Chemical accumulators, 328 
Growth, 328 Law of growth, 328 Anabions and catabions, 329 Systems of 
transformers, 329 Plant and animal as coupled transformer, 330 The World 
Engine, 331 Share of sun's energy that falls to different constituents of world, 
331 Share falling to organic circulation, 331 Relation of transformer cycle to 
circulation of the elements, 334 Influence of limiting factors upon working of 
world engine, 334 Evolution of the World Engine, 335. 

Chapter XXV. Relation of the Transformer to Available Sources. Distrib- 
uted and localized sources of energy, 336 Random and aimed collisions, 337 
Negative correlation, 337 The correlating apparatus, 338 Component ele- 
ments of correlating apparatus: Depictors, Receptors, Elaborators, Adjus- 
ters, 339 Receptor-effector circuit begins and ends in environment, 340 
Significance of this, 340 Correlating apparatus not peculiar to living organ- 
isms, 340 Mechanical imitations of living beings (automatons) 341 Chess 
as a conventional model of the battlefield of life, 343 The biological contest 
considered in the light of the chess analogy, 343 Topographic map, centers of 
mobility and centers of influence as the elements of the game, 343 Zones of 
influence, 344 Collisions or encounters, 344 Zones of mobility, 345 Analyt- 
ical statement of problem of organic conflict, 345 The behavior schedxile, 
346 Specific productivity, 347 Effect of change in zone pattern, (Intra- 
species evolution), 348 Biologic relation of economic value, 350 Effect of 
change in behavior schedule, 350 Rigid or automaton type and elastic or 
free-choice type of behavior schedule, 350 Relation between ideal and 
actual organism, 352 Effect of small departure from perfect adjustment, 
353 Relation of economic value to physical energy, 354 Economic conver- 
sion factors of energy, 355 General or aggregate effect of individual 



ANALYTICAL SYNOPSIS OF CHAPTERS XXIX 

struggles for energy capture, 356 The law of evolution adumbrated as a law 
of maximum energy flux, 357- Statistical mechanics of a system of organ- 
isms, 358 Mean free path, 358 Frequency of collision and capture, 359 
Influence of size of organism, 359 Curves of pursuit, 360 Random motion 
under a bias, 360 Use of models, 360. 

Chapter XXVI. The Correlating Apparatus, 362 Receptors, 363- Artificial 
receptors, 364 Significance of these in evolution of modern man, 364 Effec- 
tors, 366 Artificial effectors; industrial evolution, 367 Singular effects of in- 
dustrial evolution, 368. 

Chapter XXVII. Extension of the Sensuous World Picture. The Elabora- 
tors, 371 The scientific world picture : Systems of coordinates, 372 The ego 
as a coordinate reference frame, 372 The ego immaterial, 373 Interpenetra- 
tion of the egos, 374 Where is Mind?, 375 Fundamental premises and implicit 
assumptions, 376 Difficulty of shaking off preconceived premises, 377 Ob- 
stacle which this raises to understanding, 377 The communicators, 378 
Orthogenesis in human evolution, 378 Orthogenesis does not suspend selec- 
tion, 380 Importance of curiosity in evolution, 380. 

Chapter XXVIII. The Adjusters. Mechanistic and teleological inter- 
pretation of adjusters, 381 Significance of the future in the operation of ad- 
justors, 382 The future that may be and the future that will be, 382 The 
doubtful cases, 383 Final causes or purposes not usually postulated when 
sufficient account can be given of events in terms of efficient causes (e.g., in 
terms of mechanistic explanation), 384 Adaptive adjustment of tastes, 385 
Spencer's hedonistic principle, 386 Genuine utility for social service, 386. 

Chapter XXIX. Consciousness. Relation of consciousness to physical 
conditions, 388 Conditional relations, 388 A fundamental hypothesis ad- 
mitted, 389 Consciousness is closely bound up with life processes and struc- 
tures, 390 Consciousness dependent on metabolism. The personal element, 
391 Consciousness possibly a general property of matter, 392. 

Chapter XXX. The Function of Consciousness. The contents of conscious- 
ness determined by past and present bodily states, 394 Operative relations of 
consciousness to physical conditions, 394 Not only knowledge but motive 
required in the working of the human organism, 394 Motivation in lower 
organisms appears fatalistic (simple tropisms), 395 Purposive action, 395 
Dynamic psychology, instinctive drives to action, 396 Individual traits. In- 
stinct of workmanship and self-expression, 396 Influence of special aptitudes, 
399 The industrial and the personal problem of satisfying instincts, 400. 

Chapter XXXI. The Origin of Consciousness in Living Organisms. Why 
has nature resorted to consciousness as means for effecting adaptive reactions 
of organisms? 402 The problem of psycho-physical parallelism, 402 The 
double aspect theory of consciousness, 403 Physical analogies, 403 Physico- 
chemical theory of consciousness as a state related to the transitional state of 
molecules in chemical reaction, 403 Argument of simplicity of structure 
may be invoked in favor of this theory, 404 Origin of consciousness, 404 
Some elementary forms of consciousness perhaps a general property of all 
matter, 404 In that case not consciousness has been evolved, but only a par- 
ticular type of consciousness, a consciousness integrated around an ego, 404. 



XXX ANALYTICAL SYNOPSIS OF CHAPTEBS 

Chapter XXXII, Energy Relations of Consciousness. Seeming conflict 
between directive power of consciousness and determinate character of physi- 
cal events, 406 Possible explanations : First alternative possible inaccuracy 
of laws of dynamics, 406 Second alternative singular orbits with indetermi- 
nate motion, 407 Conception of Clerk Maxwell and of J. Boussinesq, 407 
Third alternative possible influence of factors eliminated from equations of 
dynamics, 408. 

Chapter XXXIII. Review of the Correlating Apparatus. Tabular synopsis 
and classification of Depictors or Informants, 410 Epictors or Transformants, 
411 Adjusters, 412 Internal adjusters, 412 Tabular synopsis of adjusters, 
413 External adjustors, 414 Anatomical and physiological adjustment of 
social activities, 414 Economic adjustment of social activities, 415 Disad- 
vantages of latter form of adjustment, 415 Its advantages or necessity in the 
human community, 415. 

Chapter XXXIV. Conclusion; Retrospect and Prospect, The life struggle 
in the modern community, 417 New character of this struggle : competition is 
principally within the species, 417 Organization of motives lags behind indus- 
trial organization, 418 Philosophy as a necessary part of scientific enquiry, 
418 Classification of Sciences in relation to Self and External World, 419 
Bertrand Russell's viewpoint regarding object and subject, 420 This leads to 
a natural division and classification of the sciences, 421 The ego as at once a 
Knower and a Wilier; hence the reaction of knowledge upon the emotions, 421, 
424 The poetry of science, 425 Significance of emotional reaction of knowl- 
edge for our future evolution, 425 Evolution of the Self may have overshot 
the mark, 426 Man's opportunity to influence the destiny of his species by 
his own initiative, 427 Desirability of concerted action, 427 Of constructive 
optimism, 428 Evolutionary value of nurture and tradition, 428 Fallacy 
of cynical deprecation of potency of nurture, 429 Extension of Spencer's 
hedonistic principle, 430 How it explains the appearance of design in nature, 
430 Such design can be neither proved nor disproved, and may therefore be 
made an article of faith, 430 Man may embrace the World Purpose for his 
own, 430 Survival value of such attitude, 430 Orthogenesis in field of ethics, 
430 Once more the reaction of knowledge upon the emotion, 432 Evolution 
is not achieved by struggling against cosmic forces, but by adaptation to them 
(Claude Bernard, Sir Charles Sherrington), 433 He that survives must be in 
some measure a collaborator with Nature, 433 Evolution towards fusion of 
personal will with natural law, 433. 



I 

GENERAL PRINCIPLES 



CHAPTER I 
REGARDING DEFINITIONS 

Truth comes out of error more readily than out of confusion. 

Bacon. 

A definition is a purely arbitrary thing. If I choose to define a 
triangle as a plane figure bounded by four sides and having four 
angles; and if, also, I define a quadrilateral as a plane figure bounded 
by three sides and having three angles, I shall run into no logical 
conflicts; my geometry need in no wise depart from that of Euclid; 
I shall need to make no changes in existing works on geometry, 
beyond that of substituting throughout the word triangle for the 
word quadrilateral, and vice versa. 

But while a definition is in this sense, from the point of view of 
logic, a purely arbitrary thing, while my definition of a triangle as a 
four-sided figure may be admissible, it is by no means expedient. 

Thus the definition of terms, which naturally forms one of the first 
steps in the systematic treatment of any subject, may present no 
particular problems of logic, but it does present certain problems of 
expediency. 

In the geometrical example cited, the unusual definitions given, 
though quite permissible, are inexpedient for simple etymological 
reasons. Such a choice of terms would be misleading, and, instead of 
assisting the memory, would impose upon it an unnecessary burden. 
In this case the application of the principle of expediency is obvious 
to the point of being grotesque, the example having purposely been 
chosen to illustrate the principle in drastic fashion. 

But the framing of definitions at times involves more subtle con- 
siderations of expediency, so subtle in fact, that they may be over- 
looked, or misunderstood, and a problem which is, in truth, a problem 
of definition, falsely masquerades as a problem of fact. Certain 
pseudo-problems of science have owed their origin to a failure to 
realize this circumstance. 1 

1 On the other hand, some very fundamental advances of science are, upon 
critical examination, found to rest essentially upon the establishment of a 

3 



4 ELEMENTS OF PHYSICAL BIOLOGY 

The writer of the book of Genesis shows good judgment. Our 
legendary forebear, the originator of the first biological system of 
nomenclature, sees each creature first, and thereupon names it. 
We have not always been equally wise. Sometimes we have tried to 
invert the method; we have found or made a name, and then gaily 
set forth on an expedition to discover the thing that should answer 
to that name; we have hunted the Jabberwock. Forgetful of the 
wisdom of Mephistopheles : 

Derm eben wo Gedanken fehlen 

Da stellt ein Wort zur rechten Zeit sich ein 

we have given way to an inherent bias of the human ,mind described 
in characteristic fashion by H. G. Wells 2 : 

. . . . when we have a name we are predisposed and sometimes 
it is a very vicious predisposition to imagine forthwith something answering 

to the name If I say Wodget or Crump, you find yourself passing 

over the fact that these are nothings, .... and trying to think what 
sort of a thing a Wodget or a Crump may be. You find yourself insensibly, by 
subtle associations of sound and ideas, giving these blank terms attributes. 8 

So the biologist of the past generation, finding in his native 
vocabulary the words animal and plant, forthwith proceeded in an 
effort to establish precise distinctions between animals and plants, 
never giving any thought, it would seem, to the fact that these names 
had already been parceled out generations ago, by "popular" 
consent, by unscientific persons without any regard to fine distinc- 
tions. There is clearly, here, the tacit assumption that because two 
distinct words are found in the vocabulary, therefore two correspond- 
ingly distinct things exist in nature. In point of fact, we know well 
enough (though we may not at all times have this knowledge clearly 
in the focus of our consciousness) that in nature many things form 
finely graded series, with extremes at the two ends, extremes to which 

judicious definition. A notable instance of this is the enunciation of the prin- 
ciple of the survival of the fittest, which is essentially of the nature of a defi- 
nition, since the fit is that which survives. Regarding the epistemological 
significance of definitions compare A. N. Whitehead and B. Russell, Principia 
Mathematica 1910, vol. 1, p. 12. 

* H. G. Wells, First and Last Things, 1908, p. 32. 

8 "Gewohnlich glaubt der Mensch, wenn er nur Worte 
Es mtisse sich dabei auch etwas denken lassen." 



REGARDING DEFINITIONS 5 

^ our vocabulary has lent more or less definitely associated names, but 

with no definite line of demarcation between. Examples of this are 

\ innumerable. We speak of objects as being red, orange, yellow, 

green, blue, violet, etc. There is nothing in nature to correspond to 
such staccato classification of colors: the visible spectrum runs con- 
tinuously from a wavelength of about 8 x 10 ~* mm. (extreme red) to 
about 4 X 10~ 4 mm. (extreme violet). Cases therefore must neces- 
sarily arise when we are in doubt whether to call a thing blue, or 
green, for example; and such doubt can be resolved, if at all, only 
by arbitrary definition. The question is not "what is green, and 
what is blue," but, at best, "what shall we agree to call green, and 
what blue." 

It lies in the nature of the mechanism by which we enter into 
possession of our knowledge, that problems of definition of this kind 

*- arise. We are equipped with two separate and distinct senses, the 

one responding to electromagnetic waves ranging from about 4 x 10 ~ 4 
to 8 x 10 ~ 4 mm., light waves; the other to somewhat longer waves 
otherwise of the same character, heat waves. Accordingly we have 
two separate terms in our language light and heat, to denote two 
phenomena which, objectively considered, are not separated by any 
line of division, but merge into one another by gradual transition. 
Here the question might be raised whether an electromagnetic wave of 
a length of 9 x 10 ~ 4 mm. is a light wave or a heat wave. The answer 
is obvious: Call it what you please, it is merely a question of arbitrary 
definition. We must beware of 

.... that false secondary power 
'* By which we multiply distinctions, then 

Deem that our puny boundaries are things 
That we perceive, and not that we have made. 

Wordsworth. 

Definitions in Biology. The attempt to establish a rigorous distinc- 
tion between "animals" and "plants" may be similarly regarded. 
Expediency demands that if these terms are appropriated for 
exact scientific use, their sense, when so used, shall, if possible, be 
reasonably near akin to the sense commonly associated with these 
words. The difficulties encountered in seeking to establish a satis- 
factory line of division between animals and plants were long regarded 
as difficulties in a problem of fact. It was thought that some biologi- 
* cal principle must be sought which divided animals from plants. 



6 ELEMENTS OF PHYSICAL BIOLOGY 

The truth is, of course, that we may define "animals" and "plants" 
any way we please- as for instance by reserving the term, plant for an 
organism possessing cellulose' but whether such definition is "cor- 
rect" or "satisfactory" is not a question of biological fact, it is a 
question of expediency. It is not a question whether there is any 
definable difference between animals as a class and plants as a class, 
nor what this difference is, but whether it is expedient to retain for 
purposes of strict scientific classification the popular terms "animals" 
and "plants," which were not originally founded upon any rigorous 
examination of facts; and if so, where we should, by definition, draw 
the line of separation. 

When the problem is viewed in this way the difficulty of distin- 
guishing between animals and plants vanishes. In the case of the 
higher forms of life it is easy to establish biological distinctions that 
do not conflict with the popularly drawn lines of division. In the 
case of certain lowly forms of life popular distinctions cannot exist, 
since these forms are not known to the public except through biologi- 
cal publications. And the biological line of demarcation we can, 
by definition, draw arbitarily where we choose, or, better perhaps, 
we may say that the terms "animal," "plant," do not correspond to 
any fundamental objective distinction and, though conveniently 
applied to certain common forms of living matter, are entirely 
unnecessary 4 and only introduce difficulties of definition and classifica- 
tion when applied to certain simple organisms. What difference does 
it make whether we call Volvox a plant or an animal? Whether it 
is a plant or an animal is merely a matter of definition, not a question 
of biological fact. 

Somewhat similar remarks apply to the narrower divisions into 
which the biologist divides the world of living organisms. Disputes 
as to what constitutes a species are fruitless. "A species is a thing 
described as such." This is simply a matter of definition. If on 
grounds of expediency one definition is preferable to another, it may 
be well to urge its general adoption. But its adoption or rejection will 
neither add nor subtract one jot from our stock of ascertained facts. 

It is necessary to guard against the error of disputing about mere 
words. Not always does this error strut about in such blatant form 
as in the example quoted by Fechner: S. Sachs, in a book published 

4 R. W. Glaser, Science, 1918, vol. 48, pp. 301-302: "We are justified at 
present in not classifying viruses either wit|i plants or animals." 



KEGARDING DEFINITIONS 7 

in 1850, takes the astronomers to task for their presumptuous specula- 
tions: "How do they know that the star they call Uranus is Uranus?" 

If any one should think that in our day it is no longer necessary to 
guard against errors of this kind (though less gross, perhaps), let 
him consider such a question as this: Is not the perennial debate 
between vitalism and mechanism a quibble about words? Is not the 
whole situation summed up accurately in the words of L. J. Briggs: 5 
"The mechanism of plant processes not at present explainable on a 
physico-chemical basis would be termed by the vitalistic school 
"vital," by the physico-chemical school "unknown"? 

And in searching for the essential characteristics of life, those that 
should finally and conclusively distinguish the living from the non- 
living, are we not just searching for the thing in nature that should 
correspond to a word in our vocabulary? Are we not hunting the 
Jabberwock? 

Definitions of Life. The difficulty of giving a precise meaning to 
the word life has been realized probably by everyone who has ever 
seriously attempted a definition. Herbert Spencer remarks: 

Classifications are subjective concepts, which have no absolute demarca- 
tions in Nature corresponding to them .... Consequently, when we 
attempt to define anything complex .... we can scarcely ever avoid 
including more than we intended, or leaving out something that should be 
taken in. Thus it happens that on seeking a definition of life, we have great 
difficulty in finding one that is neither more nor less than sufficient. 

Nevertheless he proceeds to establish his definition of life: "The 
continuous adjustment of internal relations to external relations." 8 
It cannot be said that Spencer has been very happy in this choice 
of a definition or that he has been at all successful in avoiding the very 
pitfalls which he himself so clearly points out. For obviously many 
purely mechanical systems fall under this definition. It would, for 
example, include a windmill provided with a device automatically 
turning its arms into the most favorable plane according to the 
direction of the wind. 7 Indeed, in a sense it is true of every physical 

6 L. J. Briggs, Jour. Washington Acad. Sci., 1917, vol. 7, p. 89; compare also 
E. M. East, Mankind at the Crossroads, 1923, p. 21. 

6 Herbert Spencer, Principles of Biology, section 30. 

7 Compare the following : "No one has yet succeeded in formulating a clean- 
cut definition of the limits of the reflex either at its lower or its higher extreme, 
and perhaps no one ever will; for the whole list of behavior types, from ma- 
chines to men, probably form a closely graded series." C. J. Herrick: The 
Evolution of Intelligence and Its Organs. Science, 1910, vol. 31, p. 18. 



8 ELEMENTS OF PHYSICAL BIOLOGY 

system that it "adjusts its internal relations to external relations." 
For this statement simply implies that there is a tendency for the 
establishment of equilibrium between a selected portion of a physical 
system, and the remainder, the environment. Thus, for example, if 
the system 2H 2 + 2 is left to itself hi a suitable vessel at 1480C. 8 

H 2 

and one atmosphere pressure, the ratio ^rp: which we may term an 

"internal relation" of the system, assumes the value 0.0002. If 
now the external conditions of temperature and pressure are changed 

"FT 
to 2929C. and one atmosphere pressure, the internal relation rrr-z 

adjusts itself to the new external condition and acquires the value 
0.11. 

With better judgment than Herbert Spencer, Sir Edward Schafer 9 
frankly evades the definition of life. He remarks : 

The ordinary dictionary definition of life is "the state of living." Dastre, 
following Claude Bernard, defines it as "the sum total of the phenomena com- 
mon to all living beings." Both these definitions are, however, of the same 
character as Sidney Smith's definition of an Archdeacon as "a person who 
performs archidiaconal functions." I am not myself proposing to grapple 
with a task that has proved too great for the intellectual giants of philosophy, 
and I have the less inclination to do so because recent advances in knowledge 
have suggested the probability that the dividing line between animate and 
inanimate matter is less sharp than it has hitherto been regarded, so that the 
difficulty of finding an inclusive definition is correspondingly increased. 

It is, indeed, an elementary historical fact that, as knowledge has 
advanced, the scope embraced in the term "vital" processes has 
continually decreased, since Wohler took the first cut out of it in 
1828 by the synthesis of a "vital product" (urea) in the laboratory; 
and the field of known physico-chemical processes going on in 
living organisms has correspondingly increased. For the rest, the 
most uncompromising vitalist does not deny that some, at least, of 
the processes going on in living matter are physico-chemical. Even 
so fundamentally biological a process as the stimulation of an ovum 
to development we have learnt to effect by purely physical means. 

Alleged Characteristics of Living Matter. On the other hand 
some of the features commonly ascribed to living matter as its peculiar 

8 W. Nernst, Theoretische Chemie, 1913, p. 713. 

9 E. A. Schaefer, Presidential Address at Dundee Meeting of Brit Assoc 
Adv. Sci. 1912. 



EEGAEDING DEFINITIONS 

and characteristic attributes seem Irrelevant to the point of triviality. 
"^his. remark applies particularly to the distinction sometimes claimed 
for living matter, that it grows "from within," as distinguished from 
crystals, which, in a suitable mother liquor, "grow from without." 
There may or may not be many and profound differences between 
a bacterial colony growing in a culture medium, on the one hand, 
and on the other hand a mass of crystals growing in a supersaturated 
solution. But whether the growth takes place from within or without 
is merely an accident of structure. If a droplet of chloroform is 
brought near to a glass particle coated with shellac, the drop flows 
around the particle, engulfs it, absorbs the shellac coating and 
finally rejects the "undigested" glass particle. 10 The droplet thus 
grows "from within." 

In point of fact "growth from within" is the rule and not the 
exception in chemical systems. For what do we mean by growth? 
We mean the increase of the mass of one component of a system at the 
expense of another. It is precisely the same thing as that which 
occupies the center of attention of the physical chemist, though he 
does not ordinarily call it growth. In fact, he does not find it neces- 
sary to give it any particular name, for, being accustomed to the use 

Ci'YYI 

of mathematical methods and symbols, he simply writes it -=- , rate 

Cit 

d /m\ 
of increase of mass with time, or, more often, T.\ I, rate of increase of 

concentration (mass/volume) with time. And in homogenous 
systems, at least, which (on account of their comparative ease of 
theoretical and experimental treatment) figure prominently in the 
physical chemistry of today, growth is necessarily from within. 

Some writers (J. Loeb, The Organism as a Whole, 1916, p. 28) 
have seen a characteristic feature, peculiar to living organisms, as 
distinguished, for example from crystals growing out of a solution, 

10 "Let it be clearly understood that this illustration is here quoted, not as 
an example of life-like analogies in the world of non-living matter; nor as a 
veiled suggestion that such a drop of chloroform represents even a modest 
degree of success in the artificial imitation of life; nor yet again as an argument 
that the conduct of amoeba can today be fully accounted for on a physico- 
chemical basis; this example was cited merely to show that "growth from 
within" cannot be claimed as a distinguishing characteristic of living matter. 
For further discussion of so-called simulacra vitae see McClendon, Physical 
Chemistry of Vital Phenomena; Burns and Paton, Biophysics, 1921, p. 403. 



10 ELEMENTS OF PHYSICAL BIOLOGY 

in the fact that the latter grow by a physical process, the former by 
chemical processes. Leaving aside the question as to whether there 
exists any fundamental distinction between physical and chemical 
processes, at most the point to which attention is drawn by these 
authors would class living organisms with chemical, as distinguished 
from physical systems, but would furnish no basis whatever for 
separating organisms in a class by themselves from other chemical 
systems. This is not saying that they are not in a class by them- 
selves, but only that the distinction suggested fails in effect. 

It has similarly been urged, as a distinction between the growth of 
a crystal and that of an organism, that the former will grow only in 
a supersaturated solution of its own substance, while the latter ex- 
tracts from an unsaturated solution the substance needed for its 
anabolism. 

This is really the same distinction in another form. It may 
distinguish the organism from the growing crystal, but leaves it m... 
one class with any chemically reacting system whatever, since in the 
case of the latter also there is "growth," i.e., formation of one or 
more products of reaction, in a system which need not be physically 
supersaturated in the narrow sense in which the crystallizing solution 
is. In a wider sense 11 the system may indeed be said to be super- 
saturated with regard to a chemical substance that is formed within 
it but in the same sense a system can probably be said to be super- 
saturated with regard to the substance of a bacterial colony growing 
therein. 

Neither can we subscribe to the view set forth by J. Loeb (The 
Organism as a Whole, 1906, p. 29), that the synthesis of specific 
materials from simple compounds of non-specific character distin- 
guishes living from non-living matter. In every chemical reaction 
specific materials are formed. In a mixture of hydrogen, chlorine, 
and nitrogen, the hydrogen and the chlorine unite, leaving the nitro- 
gen on one side unchanged. This is merely a brutally simple example 
of a universal fact. Chemical reaction is always selective. And if 
"complexity" is to be made the characteristic of life processes, then 
the question immediately arises, what degree of complexity is re- 
quired to place a given process in the category of life processes? 

"Namely in the sense that it is metastable, that is, its thermodynamic 
potential is not at a minimum. 



EEGARDING DEFINITIONS 11 

Reproduction. Another characteristic that has been cited by some 
as exclusively peculiar to living organisms is the power of reproducing 
their kind. "How, says Driesch in effect, can a mechanism provide 
for its own reconstitution? No machine known to us is able to con- 
struct another like itself, nor can it repair its own parts." 12 

Undue emphasis on this alleged distinction between living and non- 
living machines seems ill advised, for two reasons. In the first place, 
though it may be true that no man-made engine exists that performs 
the functions of self-repair and self-reproduction, no one has ever 
attempted, so far as I know, to demonstrate that no such engine can 
be built. Anyone who should be disposed to regard this objection 
as specious should reflect for a moment on the amazing development 
in technical arts within the last thirty or forty years. Half a century 
ago one might with equal justice have pronounced flight a funda- 
mental, essentially biological characteristic of birds, incapable of 
duplication by man-made engines. 

But in another, perhaps more significant respect, we must regard 
as misplaced the emphasis sometimes laid on the power of reproduc- 
tion in organisms, and its absence in human artefacts. It is based on 
an exaggerated conception of the part played by the parent in the 
making of the offspring. This probably has its origin in the instance 
of reproduction that to us is naturally of supreme interest, the repro- 
duction of man. As a mammal, the young human organism grows 
within the parent body, and seems to us to be in some way fashioned 
by the parent; this conception must be at the basis of The alleged ! 
distinction between organic reproduction and the incapacity of ; '. ; 
non-living engines to reproduce their kind, for without such con- 
ception the comparison would lack all parallel. Now, in point of 
fact, we need but call to mind the familiar hatching of a chick to 
realize that the part necessarily played by the parent in the formation 
of the young individual is really very restricted. The process in this 
case goes on, for the most part, in complete isolation from the parent. 13 

12 H. C. Warren, Jour. Philos., Psychol. and Scientific Method, vol. 13, 1916, 
p. 36. 

13 Compare E. G. Conklin, Heredity and Environment, 1918, pp. 99,45, 
109: "The hen does not produce the egg, but the egg produces the hen 

and also other eggs We know that the child comes from 

the germ cells and not from the highly differentiated bodies of the par- 
ents, and furthermore that these cells are not made by the parents' bodies but 



IZ ELEMENTS OF .PJtilKlUAJLi 

As for the initiation of cell division of the ovum, we now know that, 
in some cases at least, this can be effected by ordinary physical 
means. 

Recent development in experimental embryology suggest a more 
rational view of this process of self-reproduction of the living engine, 
a view which strips it of at least some of its mystery, and which 
certainly takes from it any force it might otherwise have had as a 
basis for distinction between living and non-living matter. If, after 
the first division of the ovum of a frog, the two cells are separated, 
each will under suitable conditions develop into a separate and com- 
plete, normal organism. These two organisms A and B are, in fact 
twin brothers or sisters. No one would for a moment entertain the 
thought that in this case A reproduces B, or vice versa. Now suppose 
that in some way, after the first division, A alone grows into a com- 
plete mature organism, while the single cell B remains attached to 
it, say for six months. At the end of this time it is separated, and 
stimulated to start its growth into a frog. We would ordinarily 
describe this state of affairs by saying that A reproduced B as 
offspring, that B was the child of A. In point of fact it is merely a 
delayed twin brother or sister of its elder brother or sister A. u A 
had little or nothing to do with the production of B; the latter grew, 
very much in the same way as A grew in its own time. That nature 
has evolved, in surviving races, this method of delayed development, 
so as to stretch out the totality of living organisms in a long chain, a 
succession in tune, is of course a fact of most fundamental importance, 
the significance of which will deserve our profound contemplation. 
One of its consequences has been to render possible a practically 
infinite number of organisms, built from a finite and quite restricted 
amount of matter, the same substance being used over and over 
again, for it is literally true that we live on our forefathers. Had all 

these cells have arisen by the division of antecedent germ cells 

Parents da not transmit their characters to their offspring, but these germ cells 
in the course of long development give rise to adult characters similar to those 
of the parent." 

14 The perhaps somewhat doubtfully authenticated cases of fetus in fetu, 
"those strange instances in which one might almost say that a man may be 
pregnant with his brother or sister," add a touch of realism to the discussion 
here presented. For further data on this singular subject see G. M. Gould 
and W. L. Pyle, Anomalies and Curiosities of Medicine, 1897, pp. 199 et seq. 
Compare also in this connection, the phenomenon of pedogenesis; see for 
example, G. H. Parker, Psyche, 1922, vol. 29, p. 127. , 



these organisms sought to grow simultaneously, their career would 
have been stopped by lack of material. , 

If anyone should object that these reflections leave out of account 
entirely the r61e of sex in reproduction, with all the complex phe- 
nomena of the fusion of gametes, the mingling of chromosomes, and 
biparental inheritance, the obvious reply is that these phenomena are 
now known to be less fundamental than they formerly appeared; that 
reproduction of an organism can very well take place without them; 
and that therefore they may at most serve to distinguish certain forms 
of life from non-living matter, but they cannot possibly be made the 
basis of a distinction between living matter in general and that which 
we commonly describe as non-h'ving. , 

Vital Force. If we have cause to hesitate in defining hie,_ still 
more is it the part of wisdom to be very conservative in the coming 
and use of such phrases as vital force, nerve energy, and the like. 
Shall we not do well to follow the biblical example, and wait, to name 
the animal, until it is physically present to our senses? Or, to pass 
from legend to the world of scientific fact, let us borrow, if we^ can, 
the method of the physicist: He discovers that a quantity f mv 
possesses certain important properties. Then, he proceeds to name 
it: Energy, in particular, kinetic energy. But biologists have been 
disposed sometimes to adopt the reverse procedure: they have 
named a vital force, a nerve energy, a mental energy, and what not, 
and now they entertain the pious hope that in due time they may 
discover these "things." That there is something radically at 
fault with such terms is evident from the fact that forces and energy 
are magnitudes, and "to define a magnitude and to say how it is 
measured are one and the same thing." 15 But who has ever told us 
how to measure vital force 18 and such like? 

Physical Chemistry of Structured Systems. In the physical 
chemistry of today structure, that is to say, geometrical configura- 
tion, plays a subordinate rdle. For obvious reasons the theory of 
chemical reaction in homogeneous, or in heterogeneous systems of 
comparatively simple form, is more approachable than that of systems 
which possess intricate structure, resulting in complicated mechanical 

18 Nature, September 25, 1922, p. 405. 

18 G. Bunge, in his Physiologic and Pathologic Chemistry, 1902, p. 1, re- 
marks : "I regard vital force as a convenient resting place where, to quote 
Kant, 'reason can repose on the pillow of obscure relations.'" Curiously 
enough this damning admission is made by an advocate of vitalism. 



14 ELEMENTS OF PHYSICAL BIOLOGY 

interactions of their parts, in accompaniment of chemical reaction. 
In technical practise, too, reactions in homogeneous systems (solu- 
tion, gas) are common, and where there is heterogeneous structure, 
this is usually of a form very simple as compared with the complex 
biological structures. 

But this comparative absence, from physico-chemical discussion, 
of reference to structure, to geometrical features, is not due to any 
inherent characteristic property of chemical systems, as contrasted 
with the structurally complex organic systems: the reason for the 
simplicity is to be found in ourselves. It is not a physical phenom- 
enon of the thing observed, but a psychological phenomenon in the 
observer. Physical chemistry is still a comparatively young science, 
and naturally the simpler phenomena have been sought out for first 
attention. This is not because complex physico-chemical structures 
do not exist, nor even because they are unimportant. On the con- 
trary, it is to be expected that the future will bring important develop- 
ments in this direction, as followed, for example by Sir William 
Bayliss in his work Interfacial Forces in Physiology, 

The rate of formation, the rate of growth, of a chemical substance, 
is a definite function of its environment. In a structureless system 
the nature and state of this environment is defined in comparatively 
simple terms (e.g., by stating the concentration of each of the reacting 
substances) . 

But in a system possessing structure, the environment of a given 
portion of the system depends on the structure, the topography of the 
system, which, in general, will be variable with the time. In particu- 
lar, the structure may be such that a given substance or complex of 
substances carries its own immediate environment around with it. 
The rate of formation (growth) of that substance will then depend 
largely upon the mechanical properties of those portions of the 
system which accompany this substance or complex in its travels 
through the system. 

The complete discussion of a system of this kind may well fall 
outside the scope of present day physical chemistry, not because it 
is inherently foreign to that branch of science, but because no case 
of this kind, sufficiently simple to invite discussion on a mathematical 
and physico-chemical basis, has clearly presented itself. 17 

^Compare W. M. Bayliss, Physiology, 1915, p. XI, "All that we are justi- 
fied in stating is that, up to the present, no physico-chemical system has beea-**l|| 



EBGARDING DEFINITIONS JLO 

Yet there is absolutely nothing in such a case that in principle 
places it outside the pale of physico-chemical science. It is largely 
as the result of intentional selection of simple conditions that the 
systems with which the chemist ordinarily deals (outside of biological 
chemistry) are comparatively structureless. 

We can, in fact, even now lay down certain general observations 
with regard to structured physico-chemical systems. 

Let us consider a system of this kind in which local conditions are 
subject to variation from point to point and from instant to instant. 
We fix our attention on some one component which requires for its 
growth certain definite conditions of its immediate environment. 
If this component is associated with a structure whose geometrical 
and mechanical properties secure and maintain for it a comparatively 
constant suitable environment amid the changing conditions of the 
system, then that component will grow. 

Furthermore, the several components will compete with greater or 
less success for the material available for their growth, in proportion 
as their structure is more or less perfectly adapted to secure and 
maintain for them a suitable environment. 

The chemical dynamics of such a system, that is to say, the laws 
governing the distribution of matter among its several components, 
may evidently assume a fundamentally different character from that 
to which we are accustomed from our study of ordinary structureless 
systems. For in these latter the arrangement and rearrangement of 
matter within the system depends chiefly on chemical coefficients 
(affinity coefficients), and scarcely at all on geometrical features. 
In structured systems, on the other hand, there is the possibility 
that geometrical and mechanical features may play the dominant 
role. This possibility will present itself particularly in those systems 
which receive a continuous or periodic supply of free energy, for 
instance in the form of illumination. Here the advantage will go to 
those structures that are adapted to direct available energy into such 
channels as lead to the maintenance of the environment required for their 
growth. 1 * But a little reflection shows that this is precisely the princi- 

met with having the same properties as those known as vital; in other words, 
none have, as yet, been prepared of similar complexity and internal 
coordination. 

18 It should be observed that nothing has been said of life in describing the 
system. The system may or may not comprise living organisms, the argument 



pie which governs survival in the struggle for existence among living 
organisms. Hence we may say: 

The laws of the chemical dynamics of a structured system of the kind^ 
described will be precisely those laws, or at least a very important section 
of those laws, which govern the evolution of a system comprising living 
organisms. 

For it is precisely structured systems of the kind considered above 
that are presented to us in living organisms growing in an "environ- 
ment." 

Application to Biology. The several organisms that make up the 
earth's living population, together with their environment, con- 
stitute one system, 19 which receives a d :1 y supply of available 
energy from the sun. 

Each Individual is composed of various chemical substances assem- 
bled into a definite structure and capable of growth, i.e., of accretion 
out of the environment by chemical reaction 1 provided a suitable 
medium or environment is offered. 

Moreover, each mobile organism carries with it a travelling en- 
vironment, suitable for the growth of its substance. It maintains 
this environment by virtue of the peculiar mechanical properties 
associated with its structure, whereby it is enabled to turn to this 
use, directly or indirectly, the available energy of the sun's light. 
And while the travelling environment may not be absolutely constant, 

remains the same. This suggests that a term, such as life, so vague that it 
defies definition, is perhaps not likely to play an important part in any exact 
argument; -we may, indeed, find it wholly unnecessary. It may, in time, in the 
literature of exact science, meet with the fate of the word cause: a term of 
rare and at best incidental occurrence in records of exact investigations. 

19 This fact deserves emphasis. It is customary to discuss the "evolution 
of a species of organisms. 3 ' As we proceed we shall see many reasons why we 
should constantly take in view the evolution, as a whole, of the system [organ- 
ism plus environment]. It may appear at first sight as if this should prove a 
more complicated problem than the consideration of the evolution of a part 
only of the system. But it will become apparent, as we proceed, that the 
physical laws governing evolution in all probability take on a simpler form 
when referred to the system as a whole than to any portion thereof. 

It is not so much the organism or the species that evolves, but the entire 
system, species and environment. The two are inseparable. 

"The organism, as Uexkull teaches us, must be studied, not as a congeries 
of anatomical and physiological abstraction, but as a piece of machinery, at 
work among external conditions," 0, C. Glaser, Science, vol. 21, 1910, p. 303. 



it is more nearly so than the more remote portions of the system, 
and keeps within such limits of variation as are compatible with the 
survival of the organism or its species. A concrete illustration may 
help to make this point clear. Many aquatic forms of life are con- 
stantly bathed in a saline solution sea water. Their body fluids are 
accordingly in equilibrium with this environment. Variations in the 
salinity of their environment, if they exceed certain comparatively 
narrow bounds, are apt to be fatal to such organisms. 

The higher organisms have made themselves (largely) independent 
of their immediate environment. Their tissues are bathed from 
within by a fluid (the blood) which they carry around with them, a 
sort of "internal environment." 20 

The degree of perfection with which this constancy of the internal 
or traveling environment, independently of the external environment, 
is developed, increases as we ascend the biologic scale. This is 
lucidly set forth, for example, by Claude Bernard: 21 

Chez tous les 6tres vivants le milieu inte'rieur qui est un produit de 1'organ- 
isme, conserve les rapports ne'ce'ssaires d'Schange avec le milieu e'xte'rieur ; mais 
& mesure que 1'organisme devient plus parf ait, le milieu organique se sp< cifie et 
s'isole en quelque sorte de plus en plus du milieu ambiant. 

It is the peculiar structure and the mechanical properties of the 
organism that enable it to secure and maintain the required environ- 
ment (including the milieu interieur). The higher animals, in 
particular, are provided with an intricate apparatus, comprising many 
members, for securing food (internal environment) as well as for 
warding off hostile influences. 

20 "Etant donne* que 1'eau de mer a un contact si intime avec les organismes 
de la mer et que non seulement elle les entoure de ses flots, mais qu'elle traverse 
leurs branchies et impregne en partie les corps des inverte"bre"s, il semble assez 
justind de la placer dans la m&ne cate"gorie que les autres liquides physio- 
logiques." S. Palitzsch, Comptes Rendus de Carlsberg, vol. 10, part 1, 1911, 
p. 93. Compare also the following: 

"Not only do the body fluids of the lower forms of marine life correspond 
exactly with sea water in their composition, but there are at least strong 
indications that the fluids of the highest animals are really descended from 
sea water .... the same substances are present in both cases, and 
in both cases sodium chloride largely predominates." L. J. Henderson, The 
Fitness of the Environment, 1913, pp. 187-188. See also ibid., pp. 116 and 153; 
H. F. Osborn, The Evolution and Origin of Life, 1917, p. 37 ; D'Arcy W. Thomp- 
son, Growth and Form, 1917, p. 127. 

21 Introduction a l'6tude de la me'decine expe"rimentelle, 1885, p. 110. 



The increasing independence, as we ascend the biological; ~ jale, 
which the organism displays toward its more remote environment, is 
thus accompanied by a parallel increase in the perfection of the 
apparatus by which this independence is earned. Here again we 
may quote Claude Bernard : 22 

A mesure que 1'ori s'eleve dans l'e"chelle des etres, ces appareils deviennent 
plus parfaits et plus eomplique's; ils tendent & affranchir completement 
1'organisme des influences et des changements survenus dans le milieu ex- 
te"rieur. Chez les animaux inverte'bre's, au contraire, cette independence vis- 
a-vis du milieu exte"rieur n' est que relative. 

The Policy of Resignation : Its Parallel in Other Sciences. What- 
ever may be our ultimate conclusions, we may do well to adopt 
at least as a temporary expedient the policy of resignation; with 
Sir Edward Schafer we may abandon the attempt to define life. 
Perhaps, in doing this, we are following historical precedents : Geome- 
ters have had to resign themselves to the fact that Euclid's 
parallel axiom cannot be proved. But as the reward of this 
resignation came the new geometries of Bolyai, Lobatchewski and 
Riernann. Enlightened inventors have abandoned the attempt to 
build a perpetual motion machine; but again, resignation is rewarded 
with the recognition of a fundamental law, the law of conservation 
of energy. Physicists, following Einstein, have abandoned, for the 
time being at any rate, the attempt to determine experimentally the 
earth's absolute motion through space. The reward has been the 
theory of relativity, one of the greatest events in the history of 
science. 

The whole development of science, especially in recent years, is 
a record of tearing down barriers between separate fields of knowledge 
and investigation. Little harm, and perhaps much gain, can come 
from a frank avowal that we are unable to state clearly the difference ;' 
between living and non-living matter. This does not in any way ' 
commit us to the view that no such difference exists. l 

For the present, then, we shall adopt the position that the problem 
is essentially one of definition. The question is not so much "What is 
life," but rather, "What shall we agree to call life?" And the 
answer, for the present at any rate, seems to be that it is immaterial 
how we define life; that the progress of science and our understanding 
of natural phenomena is quite independent of such a definition. 

22 Ibid. 



We shall, wherever convenient, continue to employ the terms life, 
living organism, merely as a matter of convenience. This use of the 
terms does not imply or presuppose any precise distinction between 
living and non-living matter; it merely rests upon the fact that in 
most cases ordinarily met there is essentially universal agreement as 
to whether a portion of matter is to be classed in the first or in the 
second category. We will adopt the policy of Sir William Bayliss : 

If asked to define life I should be inclined to do as Poinsot, the mathe- 
matician did, as related by Claude Bernard: "If anyone asked me to define 
time, I should reply: Do you know what it is that you speak of? If he said 
Yes, I should say, Very well, let us talk about it. If he said No, I should say, 
Very well, let us talk about something else." 

The ideal definition is, undoubtedly, the quantitative definition, 
one that tells us how to measure the thing defined; or, at the least, 
one that furnishes a basis for the quantitative treatment of the sub- 
ject to which it relates. We have already spoken of evolution. 
Most of what follows will relate directly or indirectly to evolution. 
It will be well here, while discussing definitions, to establish a defini- 
tion, a conception, of evolution that shall, as far as may be, have the 
quantitative stamp. 



CHAPTER II 
EVOLUTION DEFINED 

Nature must be considered as a whole if she is to be understood in detail. 

Bunge. 

As has been abundantly made plain, the choice of a definition is 
a matter of expediency. In adopting, for special use in exact science, 
a term already in general use, we must seek, so far as possible, to 
embody in our definition the fundamental and essential features of 
the concept denoted by the term as used popularly and by the best 
workers, thinkers and writers. 1 In so far as there is divergence in 
the use of the term, it may be well to frame the definition broadly, 
so as to cover a wide range of phenomena and lead to a compre- 
hensive view of natural events, corresponding to the essential unity 
of nature. In this way we shall be most likely to see the facts of 
nature arraying themselves in a natural order, and to achieve that 
economy of thought which is secured by a well devised system of 
classification. Facts which naturally belong together will, then, be 
found together, in our system, in the same or in neighboring pigeon- 
holes. 

Now if we seek to analyze what is in our minds when we speak of 
the evolution of a given system, we find' and on this probably all are 
agreed that the fundamental, the central thought, is that of the 
history of the system. But the concepts of the history and of the 
evolution of a system, though related, are not identical if they 
were, one word would suffice to denote the single concept. The 
popular and also the scientific conception of evolution contains as an 
essential feature the element of progress, of development . We would 
not ordinarily class as evolution the history of such a system as a 
swinging pendulum, or a celestial body circling in its orbit, in so far 

1 Compare Bertrand Russell, Analysis of Mind, 1921, p. 197: "The use of the 
word comes first, and the meaning is to be distilled out of it by observation and 
analysis." "In each case the work consists chiefly in making explicit proc- 
esses which are instinctive," as J. W. N. Sullivan (Aspects of Science, 1923, 
p. 24) remarks apropos of certain other matters. 

20 



EVOLUTION DEFINED 21 

as these motions are purely periodic or cyclic. In the history of such 
systems the element of progression in time, of development, is lacking. 
They repeat in endless succession the same series of events. The 
hand of the clock, like a symbol of perpetual youth, goes through 
its daily double cycle, making no distinction between yesterday, today 
and tomorrow. It is the calendar that reminds us we grow older 
year by year, the calendar that turns a new and different leaf each 
o!ay. "The book of Nature is the book of Fate. She turns the 
gigantic pages leaf after leaf, never returning one. . . . . " 2 

But, to characterize the kind of history we speak of as evolution, 
it is not enough that each day be unlike every other; it is not merely 
that a system never passes twice through the same state; 3 not merely 
that a biological species never retraces its steps, 4 or that "when a 
race has lived its term it comes no more again." 5 

Evolution not a Mere "Changeful Sequence." Such a statement 
as those cited in the preceding paragraph alone is insufficient to dis- 
tinguish evolution as a progress from merely a changeful sequence', 
it is insufficient to define the direction of evolution. 6 For if the 
world's events taken in historical order A, B, C . . . are a 
changeful sequence, the same is also true of the inverted series 

. . . C, B, A, Mere unlikeness of two days is insufficient to 
tell us which is antecedent to the other. To determine this we 
must know something regarding the character of the unlikeness. 
In a vague way this character is indicated by the term progress, 
which, as already remarked, is closely associated, in popular 
conception, with evolution. And the more rigorous scientific dis- 
ciplines of biology, too, leave us with a not very clearly defined 
idea of progression as one of the fundamental characteristics of 
those changes which are embraced by the term evolution. Such 
phrases as "the passage from lower to higher forms" which are 
often used to describe the direction of evolution, are vague, and 

2 Emerson, Conduct of Life, Everyman's Library Edition, 1915, p. 157. Com- 
pare also Lee Wilson Dodd's lines: 

" . . . . Nor do the stars retrace 

their glistening snail marks of slow destiny." 

3 J. Perrin, Traite" de Chimie Physique, 1903, vol. 1, p. 142. 

4 Petronievics, Science Progress, 1919, p. 406. 
6 Emerson, Conduct of Life, p. 158. 

6 For this reason the characterization of the trend of evolution given by 
Petronievics, loc. cit., is inadequate. 



22 ELEMENTS OP PHYSICAL BIOLOGY 

undoubtedly contain an anthropomorphic element. 7 At best they 
give every opportunity for divergence of opinion as to what con- 
stitutes a "higher form." If, on the other hand it is stated that 
evolution proceeds from simpler to more complex forms, or from 
less specialized to more specialized forms, then the direction of 
evolution is but poorly defined, for the rule is at best one with 
many exceptions. It should be particularly noted that all these 
efforts to specify the direction of evolution attempt to do so in terms 
of a single component of the evolving system. Such definitions of 
the direction of evolution are foredoomed to failure. It is the system 
as a whole that evolves, and we can hope to establish a definition of 
the direction of evolution only in terms of the system as a whole. 
Evidently, we must seek a more precise indication of the direction 
of evolution if our definition is to be truly expedient. We must 
analyze further the contents of our mind when it contemplates the 
concept of evolution. We return to our examples of the pendulum, 
or of the earth in its orbit. When frictional resistances are neglibible, 
or are disregarded, the periodic series of events in the system may be 
history, but seems hardly worthy of the name evolution. In actual 
fact the motion of the pendulum bob gradually dies down, owing to 
friction and other dissipative forces. The motion is not strictly 
periodic. The pendulum does not, actually, count out similar 
seconds, unidentified, but marks, by its greater amplitude, an earlier 
vibration as distinguished from a later. So also, the earth in its 
motion is slightly delayed by frictional forces introduced by the tides; 
it slows down a little as the centuries pass. The strictly periodic proc- 
ess is changed into one in which successive days differ by a trifle 
in length. The process has a definite direction in time. We feel 
justified in speaking of the system as "evolving." Now the thing to 
mark is that what has imparted to the process its directed character 
is frictional resistance, dissipative forces, typical irreversible effects, 
to speak in the language of the physicist. 

7 "Evolution is thus almost synonymous with progress, though the latter 
term is usually confined to processes of development in the moral, as distin- 
guished from the physical world. Further, this idea, as Mr. Spencer remarks, 
has rather a subjective value in existence, as judged by our feelings" (Encycl' 
Brit., 9th edition, vol. 8, p. 751). Compare also Bertrand Russell Our Knowl- 
edge of the Eternal World, 1914, p. 12. "A process which led from amoeba to 
man appeared to the philosophers to be obviously a progress though whether 
the amoeba would agree with this opinion is not known." 



EVOLUTION DEFINED 23 

Again, consider a typical example of what we are all agreed to 
speak of as evolution: the history of the earth and its living in- 
habitants. The readjustments, the re-adaptations of life-forms 
which have here taken place, were undoubtedly due in part to changes 
in external conditions, such as climate, geographic distribution of 
land and sea, etc. In part, also, such changes have gone on and are 
going on before our eyes independently of any external changes, 
and under approximately constant conditions. Organic evolution 
being a slow process, it takes a certain time, when equilibrium or 
near-equilibrium is disturbed, for a new equilibrium or near-equi- 
librium to become established. There is therefore a tendency for 
internal readjustments or changes to lag behind the external changes 
by which they are conditioned. As a special case, if an external 
change is followed by constant external conditions, internal changes 
may continue to proceed under constant external conditions. 

Now such internal changes in a material system, which lag behind 
the determining external changes, or which go on under constant 
external conditions, are typically irreversible processes.* 

8 A. process is said to take place reversibly, if the direction of the change is 
reversed by a suitable alteration, however small, of the (generalized) force 
applied to produce the change. For example, if two equal weights are sus- 
pended from the ends of a string passed over a simple pulley, then, the weights 
being initially at rest, any weight however small, added on one side of the system 
will produce motion downward on that side, provided there is no friction at the 
pulley and no stiffness in the string. If, on the contrary, a weight, however 
small, is lifted off from the same side of the system, motion will be initiated 
in the opposite direction. Note that if there is friction at the pulley, these 
statements are no longer true. It will now require a weight of definite size, 
perhaps a decigram, or a milligram, to start or reverse the motion. 

In the first instance the change is reversible, in the second it is said to be 
irreversible. Note that in this example the circumstance that imparts to the 
process an irreversible character is the presence of friction, which causes the 
dissipation of energy, that is to say, its conversion into heat at the tempera- 
ture of the surroundings. 

Again, consider a vessel containing water at a temperature Ti in a room at 
temperature Tj. If TI is ever so slightly greater than T 2 , heat passes from the 
vessel to the surroundings, and vice versa. When, therefore, TI and T s are 
very nearly equal, the passage of heat from the vessel to the surroundings is 
essentially reversible. If there is a material difference between TI and T 8 , the 
heat transference is irreversible. For example, if the vessel is at 50C. and the 
room at 20C., heat will pass from the vessel to the room. And the direction 
of this heat transfer will remain unchanged if the temperature of the vessel is 



24 ELEMENTS OF PHYSICAL BIOLOGY 

We are thus led, from two slightly different points of view to the 
following definition of evolution: Evolution is the history of a system 
undergoing irreversible changes. 

Scope of Definition, It is worth while at this point to consider 
briefly what kind of history this definition excludes and what it 
includes. It has already been noted that we have excluded certain 
purely mechanical systems of periodic habit, such as the frictionless 
pendulum and the planet circling in its orbit through empty space, 
in absence of tidal effects. 9 It is not the case, however, that all 
purely mechanical systems are excluded, that is to say, all systems 
in which all energy is either kinetic or potential (configurational), 
all forces either inertia forces or positional forces. If our knowledge 
of such a system is statistical in character, if we know only averages 
of certain of the variables defining the state of the system, it may 
happen that certain changes therein appear to us irreversible, and 
would accordingly be classed, by our definition, among processes of 
evolution. 10 This leads to the seemingly embarrassing conclusion 
that a process is or is not a process of evolution, according to the 

reduced 1, 2 or even 10. Not until the vessel is cooled by more than 30 will 
the stream of heat be reversed. The passage of heat in such case, from a body 
at one temperature to another at essentially lower temperature, is irreversible 
in this sense, the sense in which the term is employed by the physicist in dis- 
cussions of this kind. 

In the case in which internal readjustments lag behind changes in external 
conditions, there is necessarily a finite difference between the applied (gener- 
alized) force, and the opposing resistance. Such processes are, therefore, of 
necessity, irreversible. 

From the examples given, it will be seen that during a reversible change a 
system is at all times (very nearly) in equilibrium. It can therefore be said 
that a reversible change is one in which the system passes through a con- 
tinuous succession of equilibria. In fact, the change is strictly reversible only 
if the difference in the applied (generalized) force and the resistance is infini- 
tesimal, and the change is infinitely slow. 

6 Such tidal effects act as brakes and destroy the exact periodicity of the 
motion. 

1S The irreversibility also of those changes occurring in a system whose 
internal adjustments lag behind changes in the applied forces, may be appar- 
ent, and may disappear when detailed knowledge of the individual parts of the 
system takes the place of statistical data. The reason for this is that when the 
reaction or readjustment is expressed in a statistical way, an average of indi- 
vidual reactions may show a lag, although each individual reaction itself may 
be immediate. 



EVOLUTION DEFINED 25 

nature and extent of our knowledge regarding the system. So, for 
example, the establishment of thermal equilibrium in a body of gas 
initially at non-uniform temperature is evolution if we merely know 
its total mass, composition, volume, pressure and initial temperature 
distribution. But should we be informed of the exact initial state 
of each molecule, then the process by which thermal equilibrium is 
established (if this does occur) would be classed, together with the 
journey of the earth in its orbit, among the cases excluded, as mere 
history, from our definition. 

This, upon reflection is neither as strange, nor as embarrassing as 
it may at first sight appear. For problems of evolution are in large 
measure problems of probabilities, statistical problems. Inciden- 
tally, this reflection disposes of the rather foolish objection sometimes 
raised against the theory of evolution, that it ascribes the course of 
events in an evolving system to chance. When we describe a phe- 
nomenon as being governed by chance, we do not, of course, mean 
that there are no definite causes (determining factors) at work; we 
merely state in these terms that the causes are complex and not 
known to us in detail. 

Practically there is no cause for embarrassment, since we never do 
know material systems in sufficient detail to compute their state at 
every instant from the initial state, except in terms of averages. 
In principle, however, it is necessary to make the admission that, in 
the last analysis, whether we class the history of a system as evolu- 
tion or not must depend on the extent and detail of our knowledge 
of that system. 11 

It will thus be seen that the line of division between reversible 
(purely mechanical) and irreversible (dissipative) processes is not 

11 To be quite exact, evolution, according to this, should be defined in terms 
of a point of view, say about as follows : 

Evolution is the history of a system, regarded as a progressive change or 
development, to which its unidirectional character is imparted by irreversible 
changes going on in the system. 

That a point of view is involved is also implied in the following definition 
given by Karl Pearson: 

"A causal description of the appearance of successive stages in the history 
of a system forms a theory of the evolution of that system. 

"If the theory be so satisfactory that it resumes in some simple statement 
the whole range of organic change, we term it the law of evolution," (Grammar 
of Science, 1900, p. 375). 



26 ELEMENTS OF PHYSICAL BIOLOGY 

so very sharply drawn. Furthermore, the cases excluded are, in 
point of fact, ideal cases. Real processes are always irreversible. 
Hence, after all, history, real history, is always evolution, and, though f . 

in principle the two concepts may be distinct, in practice they "-(' 
coincide in scope. 

What then is gained by our definition of evolution? 

This is the gain: Having analyzed the submerged implications of 
the term evolution as commonly used, so as to bring them into the 
focus of our consciousness, and having recognized that evolution, so 
understood, is the history of a system in the course of irreversible 
transformation; we at once recognize also that the law of evolution 
is the law of irreversible transformations; that the direction of evolu- 
tion (which, we saw, had baffled description or definition in ordinary 
biological terms), is the direction of irreversible transformations. ' . 
And this direction the physicist can define or describe in exact terms. Jl 
For an isolated system, it is the direction of increasing entropy. 12 
The law of evolution is, hi this sense, the second law of thermo- 
dynamics. 13 

12 More generally, it is the direction of decreasing thermo dynamic poten- 
tial, this potential being variously defined, according to the conditions of 
transformation. 

13 "The second law (of thermodynamics) is the law of evolution of the world 
accessible to our observation" (Chwolson, Lehrbuch der Physik, 1905, vol. iii, 
p. 499; Scientia, 1910, vol. iii, p. 51. 

the second law of the theory of energy is now generally 
regarded as essentially a statistical law. So viewed, the second law of energy 
becomes a principle stated wholly in terms of the theory of probability. It 

is the law that the physical world tends, in each of its parts, to pass from certain - -v 

less probable to certain more probable configurations of its moving particles. 
As thus stated the second principle .... becomes a law of evolution" 
(Josiah Royee, Science, 1914, vol. xxxix, p. 551.) 

"Tin systeme isole ne passe jamais deux f ois par le me'me e"tat. 
"Le second principe affirme un ordre nece"ssaire dans la succession de deux 
phenomenes, sans retour possible aux etats deja traverse's. C'est pourquoi 
j'ai cru expressif d' appeler ce principe un principe devolution. II se trouve 
qu'en proposant ce nom je suis fidele a la pens^e de Clausius, car le mot 
farpomft, d'oti ii a tire" entropie, signifie precisement Evolution." (J.Perrin, 
Trait6 de Chimie Physique, 1903, vol. 1, pp. 142-143.) 

"II est hautement improbable qu'un systeme isole" passe deux fois par le 
mgme e"tat; cela est d'autant plus improbable que la complication du systeme 
est plus grande, et pratiquement il serait insensS de se placer dans cette 
hypothec d'un retour a I'Stat initial." (J. Perrin, loc. cit., p. 146) . A 



EVOLUTION DEFINED 27 

Simple Mechanical Example. It will be desirable, at this point, 
to consider, by the aid of a simple example, the manner in which 
some of the facts considered in the preceding pages find expression 
in the analytical formulation of the behavior of mechanical systems. 
Take the example of the simple pendulum. For small vibrations the 
restoring force, tending to draw back the bob to its lowest position, 

3/ 

is easily shown to be mg -, where x is the horizontal displacement, 

6 

m the mass of the bob, and g the acceleration of gravity. This force 
is expended upon two items, first, in overcoming the inertia of the 
bob, and producing an acceleration a. The force so expended is 

cc 
measured by ma. Second, a part of the force mg - is expended in 

b 

overcoming the resistance of the air. If v is the velocity of the bob, 
this part of the force is measured (for ordinary velocities) by kv, 
where k is a constant depending on the shape of the bob, etc. We 
have then 

ma + kv = mg (1) 

/Jj* 

or, since the velocity v is the rate of change of x with time, i.e., =-> 

GlV 

fiir nD (i y 

and a is the rate of change of with time, i.e. a = = , 

at at ctt 

d?x dx x . . 



Now there are certain general characteristics to be observed in 
this equation, characteristics which are typical of the equations of 
motion of mechanical systems. The equation contains the first and 
second derivatives of x with regard to t and no higher derivatives, 

The first derivative is introduced by the frictional force, and dis- 
appears if this force is zero, Le., if the coefficient k in (2) is zero. 
The equation then takes the simpler form 



Now in this simplified form the equation has the following pecu- 
liarity: It is indifferent to the sign of t. For, in differentiating twice 
in succession with regard to t, the positive sign of the second deriva- 



28 ELEMENTS OP PHYSICAL BIOLOGY 

tive is restored. This is the analytical symptom, as it were, of the 
reversibility of the process. 14 It should be noted that this peculiarity 

disappears at once if the frictional term k ~ is present, for a single 

differentiation with regard to-* yields a result with sign opposite 
to that of differentiation with regard to t. The presence of a fric- 
tional force, therefore, imparts to the process an irreversible character, 
it establishes a distinction between t and-i; it singles out one direc- 
tion in time as a peculiar direction, the forward direction, the direc- 
tion of progression. 
Now, in point of fact, in the equations of motion of all real systems 

j 
the frictional term (viscosity term) k j or its equivalent is present, 

d?x 

though it may be small as compared with the inertia term *-^, 

The reversible system, in which this term is wholly absent (zero) 
is an ideal case, it represents a limit towards which real systems may 
approach; an abstraction. 

Inertia-Free or Completely Damped Systems. There is 
another such ideal limiting case, another abstraction, which is of 
much interest because certain important classes of real systems 
approach it very closely. This is the case in which the inertia term 

m is negligible, so that in the case of the pendulum, 
di- 

for example, the equation representing the history of the system 
reduces to 

, dx x /, N 

k = -mg r (4) 

at I 

The history of such inertia-free systems is typically of the irreversible 
kind. They have, furthermore, a property illustrated by certain 
features in the equation (4) above : 

dx 
It will be observed that if cc is zero, then --=- also is zero, or, as we 

may put it, the velocity vanishes with the displacement from equilib- 
rium. Moreover, differentiation of (4) gives 



di* I dt 



u Compare H. PoincarS, Thermo dynamique, 1908, p. 441. 



EVOLUTION DEFINED 29 

from which it is seen that the acceleration also vanishes with the 
velocity. 15 This implies that when the system is in its equilibrium 
position, it is also actually at r$si, unlike the pendulum, which swings 
twice through its equilibrium position in each vibration. The former 
property, the vanishing of the accelerations with the velocities, 
so that the equilibrium position is necessarily the position of rest, 
is characteristic of an important class of systems, including those 
with which we shall here be chiefly concerned. 

Another important characteristic of such systems, which is also 
exemplified by equation (4), is that the velocity is uniquely deter- 
mined for every value of x. This is not the case in the motion 
represented by (3). This latter equation gives, upon integration, 



--.C-* (6) 

dx 
so that for every value of x there are two possible values of . 

(M> 

W.e have, then, at the one extreme the "purely mechanical" system 
free from frictional (Viscosity) effects, and, in its most typical form, 
periodic in habit. 

As an intermediate link we have systems exhibiting both inertia 
and frictional effects. Their action may resemble that of a pendulum 
swinging in air; typically the history of such a system exhibits the 
phenomenon of damped oscillations, a periodicity over which there 
is superimposed the dying away of the motion. The damping is 
introduced by the frictional effects. 

At the other extreme we have inertia-free, or, as we might say, 
completely damped systems/ 6 typically irreversible in their history. 

The system and processes with which we shall largely be concerned 
here seem to belong essentially to this third type, as will be seen in 
the development of the theme. 

Compare E. Buckingham, Theory of Thermodynamics, 1900, p. 33. 
16 This does not, however, preclude the possibility of oscillations. More 
will be said on this point later. 



IISC Lib B'lore 

574 N25 



2544 



CHAPTER III 
THE STATISTICAL MEANING OF IRREVERSIBILITY 

Supposons que nous voulions placer un grain d'avoine au milieu d'un tas 
de hie": cella sera facile; supposons que nous voulions ensuite 1'y retrouver et 
1'en retirer; nous ne pourrons pas y parvenir. Tous les phe*nom6nes irr6ver- 
sibles, d'apres certains physiciens, seraient construits sur ce mo dele. 
JET. Poincari. 

One point, to which, allusion has been made incidentally, calls 
for comment. Many processes which, viewed in the gross, present 
the appearance of typically dissipative, irreversible phenomena, have 
long been suspected, and have in recent years been fully demon- 
strated to be, in fact, of the reversible type, "purely mechanical" 
processes, the details of which are merely hidden from our view 
owing to the diminutive dimensions (and correspondingly immense 
number) of the units at play. So, for example, consider the case 
of two vessels A and B at equal pressures, communicating by a tube 
that can be closed by means of a turncock. Let the vessel A con- 
tain 1 gram of nitrogen gas, and let B contain 1 gram of oxygen 
gas, the communication between A and B being closed. It is a 
matter of common knowledge that if the stopcock is now opened, the 
gas from the A will flow over into the vessel B and vice versa, and in 
a short time an equilibrium is reached in which each vessel con- 
tains 0.5 gram of each gas. Now, in point of fact, the molecules 
of the gas behave (approximately) like a number of elastic spheres, 
their equations of motion contain no dissipative term, but are of 
the type (3) (Chapter II). We should therefore expect the sys- 
tem to exhibit periodic motion, we should expect that after a cer- 
tain lapse of time the initial condition should return, and that all 
the nitrogen should once more be contained in the vesel A, all 
the oxygen in B. In actuality, such a thing is never observed. 
How is this discrepancy to be explained? 

Let us replace the two vessels and the gas molecules by some 
simple analogues of dimensions readily accessible to our senses, and 
let us., watch a process analogous to the diffusion of the gas from 
one vessel into the other. We provide ourselves with two boxes 

30 



STATISTICAL MEANING OF IRREVERSIBILITY 



31 



or urns. 1 In one of these, A we place 50 black balls; in the other 
B, we place 50 white balls. We shuffle both boxes thoroughly, and 
then draw blindly a ball from A, and one from B, and we return 
them to opposite urns. We continue this as long as desired. The 
more lightly drawn curve in figure 1 shows the graphic record of 
an actual series of drafts of this kind. The stair-case-like line 
shows how in successive drafts the number of black balls in box A 
gradually diminished until at last there remained about 25, one- 
half of the original number, in box A. But note that there are 
fluctuations, sometimes the box contains 26, 27, 28, then again 




3O 4O 

NUMBEff Cl 



90 



60 

(DOUBLE.) 

Fia. 1. GRAPH OF MODEL PROCESS ILLUSTRATING THE STATISTICAL MEANING 

OF IRREVERSTBILITY 

The more lightly drawn curve records the number of black tickets remaining 
in urn A after successive drafts. The heavier curve records the previous and 
ensuing history of 50 tickets found in urn A at the end of the fiftieth draft, 
(Reproduced from A. J. Lotka, Two Models in Statistical Mechanics, Am. 
Math. Monthly, vol. 31, 1924, p. 122.) 

27, 26, etc. of the original balls. It is nowise impossible that, if 
we continue the drafts for a long time, some time or other all the 
original 50 black balls will be back in box A; but it is highly im- 
probable that this should happen within any reasonable time. Curi- 
ously enough, the urn model is competent to illustrate also this 
highly improbable course of events. For this purpose, instead of 
starting with 50 black and 50 white balls, we start with the balls, 
or in this case more conveniently tickets, all white, and numbered 
from 1 to 50 in urn A, and from 51 to 100 in urn B. After a suit- 

1 A. J. Lotka, Am. Math. Monthly, March, 1924; Science, 1924, vol. 59, 
p. 532. 



32 ELEMENTS OP PHYSICAL BIOLOGY 

able number of drafts, say 50 double drafts, in which a record is 
kept of all the numbers drawn, the urns are opened, and the tickets 
in the second urn are now blackened. The drawing is then con- 
tinued, for, say, another 50 drafts, recording each time the numbers 
drawn. The numbers on the tickets enable us to trace the previ- 
ous history of the 50 black tickets, before they were blackened. In 
an experiment actually carried out it was found that these 50 black 
tickets were originally distributed essentially evenly in the two urns. 
The curve representing the first 50 drafts is an ascending curve, 
the system passed, during this stage of the process, from more prob- 
able to less probable states, as shown in the first, ascending por- 
tion of the more heavily drawn curve in figure 1. In the second 
series of fifty drafts the curve descends in normal fashion, with 
increasing probability of the successive states of the system. It 
may seem like a contradiction of terms that what amounts prac- 
tically to an infinitely improbable series of drafts should be cap- 
able of actual realization at will. But if the series of drafts de- 
scribed were extended to great length in both directions, say one 
million drafts before blackening the tickets, and one million after, 
it would be seen that the peak on the curve is indeed a very ex- 
ceptional feature. It is a perfectly safe bet that in two million 
drafts not more than one such peak, going up to 50 black balls in 
one urn, would be encountered. 

The model described exemplifies among others the fact that in 
an exceedingly long lapse of time it may some time occur that the 
system will return to its original state. This is quite in accord with 
the laws of mechanics; in fact, as already noted, these laws actually 
demand that every mechanical system of finite dimensions must,, 
ultimately return to its initial state, and must do this not onee 
only, but in everlasting reiteration at regular intervals: the mo- 
tion is periodic. This property also is capable of illustration by 
a simple model, such as the following: Twenty-six pendulums of 
periods T = 0.5, 0.6, . . . 2.9, 3.0 seconds are started simultane- 
ously to the left from their equilibrium position, and are then al- 
lowed to oscillate undisturbed. Count is then made, at the end of 
every tenth of a second, of the number of pendulums on the left 
of ^ the median. In this way the staircase curve figure 2 was ob- 
tained (computation here taking the place of actual observation). 
It will be seen that in the brief fragment of a period covered by the 



STATISTICAL MEANING OF IKREVEBSIBILITY 33 

record, this exhibits all the characteristics of a "passage from a 
less probable to a more probable distribution," though, in point of 
fact, we know that the system has a perfectly definite period of 
7385 years. The appearance of chance in this wholly determinate 
mechanical process is brought into still greater prominence if we 
plot the deviations, from the mean, of the number of pendulums 
on the left of the median position, at successive counts. We thus 
obtain the points indicated by small circles in figure 3. These 
group themselves very obviously about a typical Gaussian curve 
of random distribution, namely one having a standard deviation of 
y2L', this curve has been drawn in the diagram, and, as will be 
seen, the agreement is good, considering the smallness of the sample 




FIG. 2. GBAPH OF SECOND MODEL PEOCESS ILLUSTRATING THE STATISTICAL 
MEANING OF IEEEVEESIBILITY 

Number of pendulums found on left of median position at successive epochs. 
(Reproduced from A. J. Lotka, Two Models in Statistical Mechanics, Am. 
Math. Monthly, vol. 31, 1924, p. 124.) 

(412 observations, extending over 41.2 seconds, out of a total period 
of 7385 years). Thus for long stretches of time the periodicity of 
the motion of the system of pendulums is very effectively masked 
under an aspect of "chance." 

These simple models illustrate very clearly how the seeming con- 
flict between the periodicity of all mechanical motions and the ap- 
parently one-sided course of events, directed toward one definite 
end state, is resolved. The actual process of isothermal gaseous 
diffusion is, in fact, periodic, but with a period so long that humanly 
speaking, the return to the initial state never occurs at all. For all 
stretches of time that can have any real significance in human 
thought (and this includes the vast historical ranges of all geology 
and astronomy), it may therefore be said in a certain sense that evo- 



34 



ELEMENTS OF PHYSICAL BIOLOGY 



lution proceeds, in all but a vanisMngly small class of- exceptional 
cases, from less probable states (e.g., uneven distribution of the 50 
black balls in the two urns) to more probable states, tending ul- 
timately toward a most probable state. This statement cannot 
however be allowed to pass without a word of caution. It is mean- 




-/ft 



83 



FIG. 3. FREQUENCY DIAGRAM FOE THE DEVIATIONS FROM THE MEAN 
APPEARING IN FIGURE 2 

Abscissae represent deviations from the mean (13) in number of pendu- 
lums on left of median; ordinates represent corresponding frequencies, 
among the observations recorded in figure 2. (Reproduced from A. J. Lotka, 
Two Models in Statistical Mechanics, Am. Math. Monthly, vol. 31, 1924 t> 
125.) '*' 



STATISTICAL MEANING OF IEREVEESIBILITY 35 

ingless unless the characteristic with regard to which probability 
is reckoned is explicitly or implicitly indicated. Probability is es- 
sentially a matter of classification. An improbable event is one 
that is a member of a small class, and whether it is so or not depends, 
clearly, on our system of classification. For this reason the broad 
statement which has sometimes been made, 2 that the direction of 
evolution is from less probable to more probable states, is not only 
inadequate, but is really meaningless. It is indefinite In failing to 
specify with regard to what characteristic probability is to be reck- 
oned; and it is incomplete in failing to call attention to the fund- 
amentally important connection between the particular probabilities 
in question and available energy. 

Another point, which has not hitherto perhaps received its de- 
served attention is clearly brought out by the two models de- 
scribed, namely, that irreversibility is a relative term. For, ob- 
viously, if we use our visual discrimination in selecting the balls 
drawn from the boxes (instead of drawing blindly), we can easily 
bring it about that in short order all the black balls are back in 
box A. Thus a process may be reversible or not, according to the 
means that are naturally available or arbitrarily permitted in oper- 
ating upon the system under consideration; somewhat as the tri- 
section of an angle is or is not an impossible geometric construc- 
tion, according as we are or are not forbidden the use of instru- 
ments other than ruler and compass. In the case of molecular 
aggregates this fact has long been duly appreciated, having been 
first pointed out by Clerk Maxwell, who remarked that a demon 
capable of dealing with individual molecules would be able to cheat 
the second law of thermodynamics. But it seems to have been 
pretty generally overlooked that the relative character of irreversi- 
bility has an important significance in certain natural processes 
taking place on a macroscopic scale. In point of fact this is a mat- 
ter whose importance in the world of living organisms can hardly 
be rated too high. For there are certain diffusive processes going 
on in nature which, from the standpoint of thermodynamics, are 
not of the irreversible type; but which might as well be, so far as 
any benefit derived from their reversibility by the organism (and, 
in particular, by man) is concerned. If I should be the fortunate 

2 See for example, J. Royce, Science, 1914, vol. 34, p. 551. 



36 ELEMENTS OF PHYSICAL BIOLOGY 

possessor of a pound of gold dust, and some malicious person 
should take it and scatter it far and wide, so that it became hope- 
lessly diluted with dust and refuse, it would be a small comfort 
to me to know that it were merely mechanically commingled with 
such foreign matters, that it had not irreversibly undergone solu- 
tion or chemical transformation, and that therefore it could theo- 
retically be recovered without the expenditure of work. In prac- 
tice its recovery might entail the expenditure of far more energy 
than if the gold were present in reasonably concentrated solution. 
The point is that in practice I am restricted to operations in bulk 
upon reasonably large quantities, in reasonably concentrated form, 
otherwise the theoretical ideal of recovery without work is very 
far from being attained. And with this restriction placed upon my 
operations, certain processes acquire an irreversibility which they 
do not possess apart from that restriction. The illustration of the 
pound of gold has the advantage of simplicity and cogency. But 
if by any chance it has conveyed the impression that only in pecu- 
liar and far-fetched cases does this kind of irreversibility enter into 
play, then it is an unfortunate example indeed, for nothing could 
be farther from the truth. The fact is that nature abounds in 
just such dissipative processes as the scattering to the four winds, to 
utter inutility, of materials of the highest importance to life; and 
one of the central problems which the organism has to solve in the 
struggle for existence, is the reconcentration, into his immediate 
environment and into his body, of valuable materials that have 
become scattered by agencies beyond his control. It is not the 
least of the triumphs which have made man the lord of creation, 
that he has learnt, beyond all comparison more effectively than any 
of his competitors, to carry out this process of reconcentration to 
satisfy his needs. So a fleet of ships, year by year, bear a burden of 
saltpeter from Chile to all civilized countries, to balance the losses 
from our depleted fields. So, in his most recent technical achieve- 
ment, man has learnt to draw from the air a supply that will con- 
tinue unfailing, long after the Chilean nitre beds are exhausted. 

The fact is, in dealing with the physics of such macroscopically 
irreversible effects, it will ultimately be necessary to develop a 
method of mathematical analysis that shall be competent to dis- 
tinguish and handle not only the extremes the case of a primitive 
organism that can deal only in the gross, without intelligent or 



STATISTICAL MEANING OF IKREVEBSIBILITY 37 

other discrimination, with, the matter and situations presented to 
it; and an ideally perfect organism, that should expend just the 
minimum of effort, directed with absolute precision toward the 
attainment of its ends. A method must be devised that shall duly 
take account of, and use as a fundamental datum for its deduc- 
tions, the particular character, the particular degree of perfection 
of the mechanical and psychic equipment or organization by which 
each organism reacts more or less selectively upon its environment. 
We shall have occasion to refer to this matter again in greater 
detail in a~ later section. But here it is well to note that our two 
models are suggestive also with regard to this aspect of the subject. 
For it appears at first sight as if there were a fundamental differ- 
ence in character between the first and the second model, since it 
is essential for the operation of the urn model that the drawing be 
done blindly, so as to give chance a part in the process, as we would 
say; whereas the pendulum model we operate with our eyes open, 
apparently in full consciousness of what is going on. Chance 
seems to play no part here, the system is mechanically determinate. 

But there is a blindness which is not of the eye, and there is a 
vision that surpasses optical vision. The same struggle for ex- 
istence which has developed in man the organ of sight, to depict 
for him the external world, to furnish him with a map on which 
to base his plan of campaign, has also, in latter days, developed 
his internal vision, whereby he extends his world-picture beyond 
the powers of the bodily eye. It is immaterial by which process 
his map is drawn 'its function is the same; whether I peep into 
the urn and manipulate the drafts by the light of my eyes; or 
whether, in the light of my knowledge of mechanics, I adjust the pen- 
dulums to equal lengths and phases; or again, whether, in the more 
serious affairs of life I employ these same faculties to diverse ends, 
the effect is the same: In greater measure or less these organs and 
faculties emancipate me from the bonds of the fortuitous and make 
me a controller of events. Their function is to substitute choice for 
chance, to introduce aimed collisions in place of random encounters. 

Origin of Subjective Sense of Direction-in-Time. The failure of 
the differential equations of dynamics to discriminate between t 
and t raises the question as to the physical significance and 
origin of our subjective conviction of a fundamental difference 
between the forward and the backward direction in time, a con- 



38 ELEMENTS OP PHYSICAL BIOLOGY 

viction that is intimately bound up with the concept of evolution, 
for, whatever may ultimately be found to be the law of evolution, 
it is plain that no trend of any kind can be denned or even de- 
scribed without reference to a favored direction in time. 

One view which suggests itself is that this conviction is our sub- 
jective appreciation of the trend from less probable to more prob- 
able states recognized in statistical mechanics. But this does not 
seem very satisfying, for we somehow feel that our conviction must 
rest on something more fundamental than this somewhat accidental 
circumstance, which, as the models described clearly show, is funda- 
mentally incompetent to distinguish between the forward and the 
backward direction in time. For the pr ^in figure 1, for example, 
may indifferently be traversed from lefTto right or vice versa, it 
presents the same general character in either sense. 

Another alternative is to suppose that the differential equations 
of dynamics, as formulated by us today, are either an incorrect, or 
else an incomplete statement of facts. The latter view is, indeed, 
upon reflection, found to have a certain warrant. For the differ- 
ential equations of motion alone do not fully determine the actual 
course of events; this depends further on the value of certain ar- 
bitrary constants of integration; or, to speak in terms of physical 
entities, upon the initial velocities of the particle of which the sys- 
tem is composed. Strictly speaking it is only when the initial 
velocities are zero, that the equations of motion, considered in their 
totality, are indifferent to the substitution t' = t. From this 
point of view our sense of the forward direction in time would ap- 
pear as our subjective appreciation of the fact that, once a material 
system has been started on a certain course, with certain initial 
velocities, there then remains no further freedom; its history must 
continue to unfold in the direction determined by the initial veloc- 
ities. 

It seems, however, that it is not with this perfectly general type 
of irreversibility of the course of events that we are chiefly con- 
cerned in the study of evolution. The concept of evolution, ac- 
cording to the analysis which has been made of it in preceding 
pages, applies principally, if not exclusively, to systems that out- 
wardly at least affect the aperiodic habit, systems that do not 
return periodically to their initial state, but show a definite trend, 
whereby yesterday and tomorrow are never alike, and differ more- 



STATISTICAL MEANING OF IEEEVEESIBILITY 



39 



over in some definite and characteristic fashion, even though we 
may not be fully competent, at the present epoch of science, to 
specify exactly wherein lies the characteristic difference. 3 

Inadequacy of Thermo dynamic Method. Our reflections so far 
have linked the fundamental problem of the direction, the trend 
of evolution, with the disciplines of thermodynamics and statis- 
tical mechanics. From this point of view the direction of evolution 
is identified with the direction of the unfolding of irreversible proc- 
esses, the direction of increase of entropy (in thermodynamics) or 
of increasing probability (in statistical mechanics). 

A certain mental satisfaction may be derived from, this conclu- 
sion. It gives us, in principle at least, an answer to our question 
"Quo vadis?" But practically the answer is very inadequate. If 
the conclusions, the methods of thermodynamics, or of statistical 
mechanics, are to be applied to a concrete case, the data of the 
problem must be presented in a veiy particular form. So long as 
we deal with volumes, pressures, temperatures, etc., our thermo- 
dynamics serve us well. But the variables in terms of which we 
find it convenient to define the state of biological (life-bearing) 
systems are other than these. We may have little doubt that the 
principles of thermodynamics or of statistical mechanics do actu- 
ally control the processes occurring in systems in the course of 
organic evolution. But if we seek to make concrete application we 
find that the systems under consideration are far too complicated to 
yield fruitfully to thermodynamic reasoning; and such phases of 
statistical mechanics as relate to aggregation of atoms or mole- 
cules, seem no better adapted for the task. To attempt applica- 
tion of these methods to the prime problems of organic evolution 
is much like attempting to study the habits of an elephant by means 
of a microscope. It is not that the substance of the elephant is in- 
herently unfitted to be viewed with the microscope; the instrument 
is ill adapted to the scale of the object and the investigation. 

It would seem, then, that what is needed is an altogether new 
instrument; one that shall envisage the units of a biological popula- 
tion as the established statistical mechanics envisage molecules, 
atoms and electrons; that shall deal with such average effects as 

3 Perhaps the objective interpretation of our subjective sense of direction 
in time must be sought in quantum mechanics. Cf. A. J. Lotka, loc. cit., p, 
126, and, W. S. Franklin, Science, 1924, vol. 60, p. 258. 



40 ELEMENTS OF PHYSICAL BIOLOGY 

population density, population pressure, and the like, after the man- 
ner in which thermodynamics deal with the average effects of gas 
concentration, gas pressures, etc.; that shall accept its problems in 
terms of common biological data, as thermodynamics accepts prob- 
lems stated in terms of physical data; and that shall give the answer 
to the problem in the terms in which it was presented. What is 
needed, in brief, is something of the nature of what has been termed 
"Allgemeine Zustandslehre," 4 a general method or Theory of State. 
It is somewhat along these lines that the system now to be 
sketched is conceived. 

A term introduced by J. R. Rydberg, quoted by C. Benedicks, Zeitschr. f. 
phys. Chemie, 1922, vol. 100, p. 42. 



CHAPTER IV 
EVOLUTION CONCEIVED AS A REDISTRIBUTION 

Toutes ces choses ne peuvent se determiner surement que par des mesures 
precises que nous chercherons plus tard; mais auparavant il fallait au moins 
sentir ie besoin de les chercher. /. B. Biot. 

It now behooves us to establish, with respect to the problem of 
evolution, a viewpoint, a perspective, a method of approach, which 
has hitherto received its_ principal development and application 
outside the boundaries of biological science. Such prior develop- 
ment and applications, however extraneous to our chief line of 
interest here, may well serve us in our present interrogations, since 
we shall be in a position to profit by the precedents established in 
methods, in conclusions, and, most particularly, in habit of thought. 

This perspective is that which contemplates an evolving system 
as an aggregation of numbered or measured components of several 
specified kinds, and which observes and enregisters the history of 
that system as a record of progressive changes taking place in the 
distribution, among those components, of the material of which 
the system is built up. 

It is thus that physical chemistry views the progressive changes 
in a system comprising several chemical species, that is to say 
elements, compounds, phases, etc. It describes the system by 
enumerating these components, by stating their character and ex- 
tent (mass); and by further indicating the values of certain quan- 
tities or parameters, such as volume or pressure, temperature, etc., 
which, together with the masses of the components, are found 
experimentally to be both necessary and sufficient, for the purposes 
in view, to define the state of the system. With the instantaneous 
state of the system thus defined, physical chemistry investigates by 
observation and by deductive reasoning (theory) the history, the 
evolution of the system, and gives analytical expression to that 
history, by establishing relations, or equations, between the vari- 
ables denning these states (after the manner set forth above), and 
the time. 

It is commonly found that these fundamental equations assume 
the simplest, the most perspicuous form, when they are written 

41 



42 ELEMENTS OF PHYSICAL BIOLOGY 

relative to rates of change of the state of the system, rather than 
relative to this state itself. That is to say, it is found that the 
expressions for the rate of increase in mass, the velocity of growth, 
of the several components, are simpler, more primitive in form, than 
the expressions giving directly the mass of each component as a 
function of the time. In the language of the calculus, the differ- 
ential equations display a certain simplicity in form, and are there- 
fore, in the handling of the theory at least, taken as the starting 
point, from which the equations relating to the progressive states 
themselves, as functions of the time, are then derived by integration. 1 
So, for example, a simple system may be defined as comprising 
4 grarn-rnoleeules of hydrogen, 2 gram-molecules of oxygen, and 
100 gram-molecules of steam, at one atmosphere pressure, and at 
1800C. The fundamental relation expressing the law of evolu- 
tion, the historical pattern, of the system, is in this case given by 
the law of mass action: 



. 

/{^ (_-! } 

v dt v 3 v 2 

where v is the volume, mi is the mass of steam, m 2 the mass of hy- 
drogen, and m s , the mass of oxygen (all expressed in gram-mole- 
cules). The coefficients h, h, are functions of the temperature, 
or, for a given temperature, are characteristic constants of the re- 
action. 

We are not, here, interested in the particular form of the law 
of mass action. What does interest us is the general form of the 
equation (1). It states that the rate of increase in mass, the veloc- 
ity of growth of one component, steam (mass mi), is a function of 
the masses m*, nis, of the other components, as well as of the mass 
mi itself, and, besides, of the parameters v (volume) and T (tem- 
perature), the latter being contained in the coefficients fc x , /c 2 . This 
statement, in its more general form, is written, according to es- 
tablished notation 2 

1 In experimental observation usually (though not always) the reverse 
attitude is adopted. 

2 For the benefit of the non-mathematical reader it may here be explained 
that aquation (2) is merely a short-hand expression, so to speak, of the simple 

statement: The rate of increase of mass with time of the component Si is 

dt 

& junction of, or is determined by, the masses mi, m 2 , ma, of the components 
Si, S%, S s , as well as by the volume v and the temperature T. Precisely similar 
ia the construction to be placed on the equations (3). 



EVOLUTION CONCEIVED AS REDISTRIBUTION 43 

dni-i 

= F (nn, m z , m s ; v, T) (2) 

at 

Now it is this habit of thought, expressed in equation (2) , that 
is to be transplanted into the contemplation of problems of evolu- 
tion in general, and organic evolution in particular; this point of 
view, this perspective, which regards evolution as a process of re- 
distribution of matter among the several components of a system, 
under specified conditions. 3 

Having thus passed from the specific to the general from the 
case of physico-chemical systems to a general formulation -we now 
retrace our steps to the particular, but in a new direction. We 
now contemplate the kind of systems that form the object of study 
of the biological sciences. 

With the outlook gained in our preceding reflections we envisage 
the life-bearing system, in the progress of evolution, as an assembly 
of a number of components: Biological species; collections or ag- 
gregations of certain inorganic materials such as water, oxygen, 
carbon dioxide, nitrogen, free and in various combinations, phos- 
phorus, sulphur, etc. 

These components are placed in various relations of mutual in- 
teraction under specific conditions of area, topography, climate, etc. 
Under these conditions each may grow, decay, or maintain equi- 
librium. In general the rate of growth ~7T~of any one of these com- 
ponents will depend upon, will be a function of, the abundance 
in which it and each of the others is presented; this rate of 
growth will also be a function of the topography, 4 climate, etc. 
If these latter features are defined in terms of a set of parameters 
Pi P 2 . . . PJ, we may write, in the same sense as equation (2) 

3 Compare F. B. Jevons, "Evolution," Macmillan, 1902, Chapter VI, p. 72. 

4 Terrestial species have an essentially two-dimensional distribution, so 
that area functions here in a manner somewhat analogous to that in which 
volume enters into physico-chemical relations. Aquatic life, with its three- 
dimensional sphere of activity, is enacted in systems whose extension is 
described in terms of volume. More detailed topographic parameters may be 
required to define in sufficient completeness the configuration, the structure 
of these systems. The absence of such detail from the more familiar formu- 
lations of chemical dynamics is due to the purely accidental circumstance 
that the systems commonly dealt with in that branch of science are either 
homogeneous, or of comparatively simple heterogeneous structure. 



44 ELEMENTS OF PHYSICAL BIOLOGY 

~ = Fx (Z 1; Z,, . . . XnJ Pi, Pt, . . . Pi) 

CW 
j~v 

= Ft (Xi, Xz, . . . Xn', Pi, Pa, PI) (3) 

at 

j-y- 

= Fn (Xi, X^ . . . X R ; PI, Pj, . . . Pj) 
at 

In general there will be n such equations, one for each of the n 
components. 

The purport of these equations (3) remains uncertain so long as 
the components (e.g., biological species, etc.) Si Sz . . $ n are 
undefined. What definitions we may adopt for these is, in accord- 
ance with the principles discussed anteriorly, a matter for arbitrary 
disposition; though we may be guided in our choice by considera- 
tions of expediency. These may advise different policies from case 
to case, according to the particular phase of the problem taken in 
view. The conclusions reached will, of course, depend upon the 
particular definitions chosen. This is as it should be; the conclu- 
sions apply to the components as defined, and, in general, to no 
other. This seems clear enough, but if any further exposition is 
needed, it will be found In examples shortly to be considered. 

Intra-Group Evolution. While the precise definition of the com- 
ponents Si S 2 . . , SB may, and indeed must, be held over for 
determination as each separate phase of the general problem is 
singled out for treatment, yet there is one class of cases regarding 
which it is appropriate to set forth certain reflections at this 
juncture. 

It may have been observed that so far nothing has been said 
regarding one aspect of or/ganic evolution which, in the history of 
the subject in the past, and hi the minds and writings of its ex- 
ponents and students today, occupies a dominating position 
namely, the relation of evolution to the modification of species 
with the passage of time, and, in particular, to the origin of new 
species. 

Now a biological species, however defined, is not a homogenous 
group. It comprises portions (individuals) varying more or less 
widely with regard to numerous features, such as stature, weight, etc. 

If our description of the distribution of matter in the system is 
to be at all exhaustive, we shall need to know, not only the extent 



EVOLUTION CONCEIVED AS EEDISTEIBUTION 45 

(total mass) of each species, but also its constitution, as expressed 
by the frequency, the relative abundance, of each statistical type 
within the species. In the case of man, for example, we may wish 
to know the fraction F (56) of the total population whose height 
is comprised within the limits 58 and 57 inches at a given instant. 
And in observing the evolution of the system of which this popula- 
tion forms part, we shall be interested, not only in the growth 
(or decay) of the population as a whole, but also in the rate of 
change of the abundance (frequency) of each statistical type. This 
phase of the problem does not differ essentially, in character, firom 
that first considered : it is essentially a question of distribution and 
changes in distribution of mass in the system among its several 
cornponent; only now we have fixed our attention on a different 
set of components, components defined in a different way, on a 
finer scale. In the first instance we had taken in view the dis- 
tribution and changes in distribution of the matter of the system 
among the several major groups or species; now we are considering 
the distribution within each such group. This division of the gen- 
eral problem of organic evolution into two aspects has certain prac- 
tical advantages, and it will be convenient to have names to desig- 
nate the two separate aspects or domains of evolution. We shall 
accordingly speak of inter-group evolution on the one hand, when 
referring to changes in the distribution of the matter of the system 
among several component groups; and we shall speak of intra-group 
evolution when referring to changes in the distribution of matter 
within the group, among its statistical types, however defined. 

It is possible to set up equations relating to intra-group evolu- 
tion, similar in general character to those set forth above relative 
to inter-group evolution. However, this phase of the problem is 
probably treated more satisfactorily in other ways, of which some 
examples will arise in due course. 5 

It is nevertheless, desirable, to indicate in the system, of equa- 
tions (3) the incidence of intra-group evolution. 

Conveniently this may be done by writing the ith equation, for 
example, in more detailed form: 

= Fi (X 1} Z,, . . . X n ; Pi, P Sj . . . PI; Qi, Q, . . . Qk) (4) 

at 

5 See Chapter IX, p. 122; Chapter XIII, p. 170; Chapter XXV, pp. 348 et seq. 



46 ELEMENTS OF PHYSICAL BIOLOGY 

where Qi, Q 2) , . . Q k are parameters defining the character of 
several components (e.g., biological species) S; such definition may 
take the form of a set of characteristic frequency functions, or 
some other form. These parameters will, in general, be functions 
of the time, that is to say, each component may, in general, be 
variable in character through the occurrence of intra-group evolu- 
tion. Whether this variability is limited, or constrained to follow 
a certain course (orthogenesis), whether variations take place in 
continuously graded series or per saltum, or in any or all of these 
ways, are questions which will not be discussed at this point. At 
present all that need be said is that the origination of a new species 
in any of these ways falls within the scheme of our description of 
evolution as a change in the distribution of matter among the com- 
ponents of the system. 6 

It may be remarked, in passing, that in general a complete def- 
inition of the system may require an infinite number of parameters 
P and Q; this does not necessarily cause any undue complication 
in practise, since in many cases certain of the parameters P, Q either 
remain constant, or change so slowly that, in discussing changes in 
the variables X, we may treat these parameters as if they were 
constant. 

The parameters Q, defining the character of the species, are in 
general functions of the time, as has already been remarked. In 
this respect organic evolution exhibits a very important distinc- 
tion as compared with chemical evolution, i.e., the evolution of a 
system in the course of chemical transformation. In such a sys- 
tem the character of the components is usually fixed once for all. 
Water is H 2 for all time, unlike a species of organism which is 
subject to change in character. One important result of this is 
that, so far as we know, organic evolution is a process without end, 
for there seems to be no limit to the variety of forms of living mat- 
ter, as there is no limit to the variety of geometric configurations 
and mechanical systems that can be formed from a given portion 
of matter. Chemical evolution, on the contrary, terminates, under 
constant condition, in a definite equilibrium, determined once for 
all, by those conditions. 

8 This is not a new definition of evolution, it is a conception of evolu- 
tion wholly compatible with the definition that has been laid down in 
preceding pages. 



EVOLUTION CONCEIVED AS BEJHSTRIBTJTION 47 

It will be observed that the fundamental equations (3) resemble 
in form the equation (4) of Chapter II, which was given as a 
typical example of the equation for an inertia-free or completely 

JV 

damped system. The velocities -37 are single-valued functions F 

of the variables X. It is the single-valued character of the func- 
tions F that gives the system its stamp as an inertia-free or 
completely damped system; a system in the course of typically 
irreversible transformation. 

It is not maintained that these equations cover all cases that 
may be brought within the purview of the present study; nor shall 
we, in all cases, be tied down to the scope of these equations. They 
are, however, of very broad scope, and, upon reflection, will be 
found to cover at least a large and significant portion of the field 
of our interests here. 

To one point, however, it may be well to draw attention. To 
read these equations in their broadest interpretation we must be 
prepared to consider cases in which the phenomenon of lag or lead 
enters. Perhaps the terms lag and lead require explanation. In 
some cases the course of events today depends on certain features 
in the state of the world at a previous date. So, for example, the 
number of persons of age 50 in the year 1924 depends (among other 
things) on the birthrate in the year 1874. Or, to quote another 
instance, the number of new cases of scarlet fever today depends 
on the number of infections a week ago. There is thus a lag in 
the appearance of the observable effect in the system. In other 
cases there may be a lead. The price of land on Church Street 
today may suffer an increase or perhaps decrease because it be- 
comes known that in a year's time a railway station is to be built 
nearby. 

Since effects of this kind must be contemplated as a possibility, 
we must be prepared to read our equations in the following sense: 

The rate of increase ~T7~of the mass of the component Si at the 
at 

present instant, is a function of the masses X i} Xz, etc., at some 
other instant of time, say Xi at (t pi), X 2 at (t p 2 ), etc., where 
some of the p's may be negative (corresponding to a lead). 



48 ELEMENTS OF PHYSICAL BIOLOGY 

We must be prepared to consider our equations in this interpre- 
tation. Illustrative examples will not be offered here, as the math- 
ematical treatment of these cases is somewhat troublesome. The 
interested reader will find an illustration in the author's mono- 
graph on the Ross Malaria equations, Am. Jour. Hygiene, vol. 3, 
January Supplement, 1923. Only a reflection of general charac- 
ter shall find its place here. It is characteristic of systems whose 
history is defined by equations thus involving a lag, that, in general, 
the course of events at a v a instant is dependent upon the previ- 
ous history of the system over a certain finite range of time. The 
consequences of this feature are somewhat singular. If the world's 
events followed a system of equations of this kind, we might have two 
worlds, in every respect identical today, but each with a different 
past, and, in consequence each with a different future. And a similar 
reflection necessarily applies in the case of lead. 

This conclusion is perhaps not in harmony with a mechanistic 
conception of the universe. But the phenomena of memory and of 
will are of precisely such character as to introduce lags and leads 
into the world's equation, and we may be well advised to keep our 
minds open as to the possible effects of this circumstance upon the 
course of events. 

It should be observed, that the appearance of a lag or lead in 
our equation may be spurious. It may be due to a species of mathe- 
matical shorthand. It is easier to describe a person as having be- 
come infected with scarlet fever three days ago, than to describe 
precisely his present state today ensuant upon that infection. Hence 
we may prefer to, or, for lack of detailed knowledge we may be 
forced to write our equations in terms of (t p), although, if all 
the facts were known, we could, were we so disposed, write them in 
terms of t. And the same reflection applies to the appearance of 
a lead in our equations. Whether, with complete knowledge of all 
circumstances bearing on the situation, there should still remain 
a residuum of influences that could find expression only in terms 
of a lag or lead, this, perhaps, is fundamentally the nature of the 
problem of the influence of consciousness upon the course of the 
world's historv. 



CHAPTER V 
THE PROGRAM OF PHYSICAL BIOLOGY 

. . . . It will be the function of this new branch of science to investi- 
gate biological phenomena as regards their physical aspects, just as Physical 
Chomistry has treated the physical aspects of chemical phenomena. Because 
thiy field has not yet been systematically explored .... the individual 
data of Physical Biology appear, as yet, as more or less disconnected facts, or 
as regularities for which no proper place is found in the existing scheme of 
pre,Bent-day science; and the investigations of isolated problems in this field 
are as yet carried on as something of a scientific hobby by amateurs, with the 
result that they are guided by chance rather than by plan. . . . and are 
often totally lacking in any fundamental guiding principles or connecting 
theo.'y. As results gathered in this disconnected fashion accumulate, the need 
of their unification into a harmonious whole, into a distinct discipline of 
science, becomes more and more acutely felt. Such unification necessarily 
involves the working out of a viewpoint that shall make the several facts and 
relations fall in line naturally in an orderly system; in other words, what is 
needed is a labor of organisation. In the course of this, new and unforeseen 
problems will inevitably arise, and a fruitful field of scientific endeavor should 
thus be opened for the investigator. Porstmann. 

A first use to which we may with advantage put the results of 
the preceding analysis, is to systematise the subject here treated; 
there will thus be gained a general plan of work and a division of 
the topic into natural sections, upon which the arrangement of 
the succeeding chapters will, in the main, be based. 

Physical Biology, 1 as here conceived and discussed, is essentially 
a branch of the greater discipline of the General Mechanics oj Evolu- 
tion, the mechanics of systems undergoing irreversible changes in 
the distribution of matter among the several components of such 
system. 

1 In introducing the term Physical Biology the writer would suggest that the 
term Biophysics be employed (as hitherto) to denote that branch of science 
which treats of the physics of individual life processes, as exhibited in the indi- 
vidual organism (e.g., conduction of an impulse along nerve or muscle); and 
that the term Physical Biology be reserved to denote the broader field of the 
application of physical principles in the study of life-bearing systems as a 
whole. Physical biology would, in this terminology, include biophysics as a 
subordinate province. 

For a summary statement of what might be termed the program of bio- 
physics see A. Forbes, Science, 1920, vol. 52, p. 331. 

49 



50 ELEMENTS OF PHYSICAL BIOLOGY 

It so happens that many of the components that play an 
tant role In nature, both organic and inorganic, are built 
large numbers of individuals, themselves very small as compe The 
with the aggregations which they form. Accordingly the stud^ono- 
S3 r stenis of this kind can be taken up in two separate aspects, nam x- 3, 
first with the attention centered upon the phenomena displace- 
by the component aggregates in bulk; we may speak of this as hose 
Bulk Mechanics or Macro-Mechanics of the evolving system. A^al, 
secondly, the study of such systems may be conducted with f evi- 
attention centered primarily upon the phenomena displayed The 
the individuals of which the aggregates are composed. This brand's 
of the subject may suitably be termed the Micro-Mechanics^wo 
the evolving system. It is evident that between these two branc'ent 
or aspects of the general discipline there is an inherent relat-ilar 
arising from the fact that the bulk effects observed are of the na 
of a statistical manifestation or resultant of the detail workiiistic 
the micro-individuals. The study of this inherent connected of 
accordingly, the special concern of a separate branch which w^ads 
speak of as Statistical Mechanics, This terminology is i]P our 
coincident with accepted usage, but in part must be unde n the 
to refer to an expansion of the subject beyond the bounds h 
covered, whereby its scope shall be extended so as to inched in 
statistical treatment of the dynamical problems presented &the- 
gregates of living organisms; that is to say, aggregates of ? be- 
transf ormers possessing certain significant special properties sribe 

Each of the branches of the mechanics of evolution enur'SAce 
so far naturally splits up into two subdivisions, according v be 
devote our attention to the material changes or to the energy ch all 
involved. By an extension of prior usage in physical chemistr^n 
may employ the term Stoichiometry to denote that branch of " 
science which concerns itself with the material transformations., 
with the relations between the masses of the components. The 
discussion of this branch presents itself as the more elementary 
task, and will therefore be taken up first; after this has been dis- 
posed of we shall be better prepared to discuss the second aspect, 
the Energetics or Dynamics of Evolution. 

Taking now a survey of the Stoichiometry of systems in evolu- 
tionary transformation, we can hardly find a better guide, for 
the organization of this subject, than the fundamental equations 



PROGRAM OF PHYSICAL BIOLOGY 

^7 = F, (X, X,, . . . Xn; P, Q) 

at 

which we may speak of as the fundamental equations of the Kinetics 
of Evolution, since they furnish expressions for the velocities of trans- 
formation and exhibit the relations between these velocities and 
the masses of the several components, as well as the parameters 

P, Q. 

The very form of these equations suggests, as the first and most 
elementary problem, the treatment of the case of evolution under 
constant conditions, as defined by constant P's and Q's. This 
will, accordingly be the coarse here adopted, treating first the general 
case of n variables Xi, X 2 , . . . X n , and then some special cases 
in which the number of variables is restricted to 1, 2 and 3. 

The perfectly general case, of evolution under conditions of 
wholly unrestrained variability of the P's and Q's, is mathematically 
uninviting (though not wholly intractable), and is also of minor 
interest in practice. Little will therefore be said of this. Certain 
special types of changes in the P's and Q's (e.g., slow changes) will 
find a place in the next subdivision of the general subject, the Statics 
of evolving systems. This branch is, in a sense, a special division 
of the Kinetics of Evolution, namely that which concerns itself 
with systems in which the velocities of transformation are zero, 
so that there is Equilibrium, or, to be more exact, a Steady State. 
This, of course, implies, strictly speaking, constancy of the para- 
meters P, Q. But something very much like equilibrium presents 
itself in certain cases when these parameters change slowly. There 
may then arise what has been termed a Moving Equilibrium. In 
view of the important role which such moving equilibria play in 
nature, their discussion must form a part of the program of Physical 
Biology. 

A second special problem of evolution under changing conditions 
(changing parameters P) that lends itself to treatment with com- 
parative ease, is that which concerns itself with initial and end states 
(equilibria), as influenced by changing conditions, without demand- 
ing any information regarding the intermediate steps passed through 
by the evolving system. So, in physical chemistry, we may enquire 
what will be the effect, upon equilibrium, of a change in pressure 
or in temperature. Similar questions may be raised regarding 



52 ELEMENTS OP PHYSICAL BIOLOGY 

equilibria or steady states in life-bearing systems, and the matter 
calls for at least passing notice. This leads to the consideration of 
the Principle of Le Chatelier and, as a natural sequel of the train of 
thought thus started, to the examination of relations which may 
exist between certain of the parameters P, somewhat as, in physical 
chemistry, significant relations exist between pressure and volume, 
for example. It is found that some, at any rate, of the parameters 
P present analogy to the intensity and the capacity factors of an 
energy; out of this have arisen in the past sporadic efforts to es- 
tablish systems of social dynamics and the like, which, however, 
have been based upon an acceptance as identity of what is only 
analogy. Those who have followed this road have been led, not so 
much perhaps to erroneous conclusions, as to blind alleys, to barren 
fields. True progress can be expected only by retracing one's 
steps from such tentative excursions and striking out in a new 
direction; forsaking the way of quasi-dynamics, and breaking a 
trail toward a system of true dynamics, both of the individual 
(micro-dynamics) and of the system as a whole (macro-dynamics). 
Of intra-species evolution, as expressed in changes in the para- 
meters Q that define the character of the several species, little will 
be said here. The reasons and justification for this step-fatherly 
treatment of so important an aspect of our topic have been set 
forth in the preceding text. A discussion of at least one phase of 
intra-species evolution, falling under the head of dynamics, will, 
however, be presented when dealing with that phase of the subject; 
and we shall briefly note, in due course, some aspects of intra- 
species evolution, as discussed more particularly by J. B. S. 
Haldane. 

These, in broad outline, are some of the principal land-marks 
in the territory ultimately to be covered by Physical Biology, and to 
be given a preliminary survey here. In concentrated form the 
lay of the land, as set forth above, is sketched in the diagram or 
scheme table 1, which should be found helpful both in presenting to 
the eye the salient features of the field of investigation, and als'i in 
furnishing a logical basis for the systematic arrangement of the 
subject in the ensuing chapters. 

It remains, in this chapter, to enumerate the methods by which 
Physical Biology may be expected to develop. For the gathering 
of data two methods are available: observation in natural condi- 




1 



.2 -S 



Q, 

1H 
O 

" 



54 ELEMENTS OP PHYSICAL BIOLOGY 

tions, and observation under experimental (laboratory) conditions. 
Examples of both these methods will be noted. 

For the elaboration of data, the establishment of regularities 
(Jaws/, there is available in this field, as everywhere in science, the 
method of induction, aided, if need be, by statistical technique. 
In this volume, however, emphasis will be laid upon deductive 
methods of mathematical analysis, as applied either to data fur- 
nished by observation, or to "unknown" quantities, blanks, as it 
were, in our formulae, ready for numerical substitution whenever 
concrete data become available. 

The principal subdivisions of our topic, and the relations between 
them, as outlined above, are summarised graphically in table 1. 



KINETICS 



CHAPTER VI 

THE FUNDAMENTAL EQUATIONS OF KINETICS OF EVOLVING 

SYSTEMS 

L'emploi des signea mathe'matiques est chose naturelle toutes les fois qu'il 
s'agit de discuter des relations entre des grandeurs. A. Cournot. 

General Case. We now proceed to the systematic study of 
the subject in accordance with the general plan laid down in the 
preceding survey of the Program of Physical Biology. According 
to this schedule (table l)we approach first of all the section of Macro- 
mechanics (that is to say, the mechanics of evolving systems 
regarded as bujlt up of component species in the gross), without 
carrying the analysis down to the finer details of individual organ- 
isms. And, of the field of Macromechanics, we shall here take up 
the section of Stoichiometry, that is to say, we shall for the present 
confine our attention to the relations between the masses involved, 
leaving aside for a later section the associated energy changes. 
Of the general field of Stoichiometry the first division to be taken 
up, according to our schedule, is the Kinetics of Evolution, and we 
shall here begin with a brief consideration of the Fundamental 
Equations in their general form 

= Fi (* X tl . . . X K ; P, Q) (1) 

at 

One phase of the general problem before us must evidently be 
the study (by observation, experiment, or any other method 
available) of the character or form of the functions F which tell us 
how the growth of each component is dependent upon the other 
components and the parameters P and Q. It might be supposed, 
indeed, that until this phase of the problem had received considera- 
tion, the system of equations (1), would be at best a barren expres- 
sion of facts. But this is a misconception. Without knowing 
anything regarding the precise form of these functions, a good deal 
of information of considerable interest can be derived from these 
equations; and before proceeding to the consideration of concrete 

57 



58 ELEMENTS OF PHYSICAL BIOLOGY 

cases, in which something is known regarding the particular form of 
the functions F, it is proper, at this point, to extract from the fun- 
damental equations (1) all the information that we can. 

This requires a little mathematical manipulation of compara- 
tively simple character, 

The variables X, the masses of the several components of the 
system, are not, in general, wholly independent. They are subject 
to certain constraining relations. For example, for any self-con- 
tained system, we shall have an equation of the form 

X, X a + . , .+X n = SZ = A = const. (2) 



expressing the constancy of the total mass of the system; and a 
similar equation holds separately for every chemical element. 1 
These equations prohibit certain changes of mass in the system. 
They are analogous to equations introduced in mechanical problems^^,^ /- 
by the geometric constraints that limit possible displacements 
(as in the case of a ball rolling down an inclined surface, and pre- 
vented, by the resistance of the surface, from falling vertically). 
They are commonly spoken of as equations of constraint. 
Equations of constraint such as 

2Z = A = const. 

will in general enable us to eliminate certain of the variables X, 
expressing them in terms of the other X's and of certain constants A. 
If, by the aid of m such equations of constraint, m variables have 
been eliminated, the system of equations (1) can be reduced to a 
simpler one, of identical form, but containing only (n m) variables ^.. ( 
and the same number of equations. .-. { 

In all that follows we shall assume that this has been done, that 
we now read equations (1) in this sense : the n variables Xi X% . . . . 
X n are those left over after eliminating as many of the X's as the 
equations of constraint permit. The functions F will in general, 
after this elimination, contain constants A introduced by the equa- 
tions of constraint. 

We shall now, except where otherwise stated, restrict our con- 
siderations to the case in which the parameters P and Q and A 
are either constant, or change so slowly that we may disregard f f 

/"' 

1 Except in those rare cases in which radioactive or other atomic disintegra- /' 
ticms occur. / *_ 



FUNDAMENTAL EQUATIONS OF KINETICS 59 

their variation. This means that we restrict ourselves to the con- 
sideration of simple inter-group evolution under constant condi- 
tions. 

With this understanding, the first point we may observe about 
the system of equations (1) is that they define certain conditions of 
equilibrium, or, to be more precise, of steady states. For such a 

state ensues whenever all the velocities vanish, that is to say, 
according to (1) whenever 

Fi = F, = . . . = F n = (3) 

We thus have n equations between the n variables Xi, X Zi . . . 
X n , which, in general, determine certain values 




(4) 

such that when masses of the several components have these values, 
they persist in these values; the system is at rest, as regards changes 
in the distribution of matter among its components Si, S 2 , . . . S n . 

In general there will be a number of such possible equilibria, 
some of which will be stable, some unstable. The determination 
of their number and character is a technical point in the theory of 
equations, for the general treatment of which the reader must be 
referred to the pertinent literature (see, for example, Picard, Traite" 
d' Analyse, vol. 1, 1891, pp. 83, 123; vol. 2, 1893, pp. 183, 193, 196, 
footnote) . 

To give a touch of concreteness to the discussion at this stage a 
very simple example may be given to illustrate how several equili- 
bria may occur in a life-bearing system. A perfectly screened 
dwelling may be kept indefinitely free from flies. This is a condi- 
tion of equilibrium, but of unstable equilibrium; for if only a few 
flies gain access, presently these will breed, and the room will 
become inhabited by a population of flies whose number will depend 
on the amount of food present, on the measures taken to combat the 
pest, etc. Unless these measures are v,ery active, the flies will not 
be wholly exterminated, but the population will attain some approxi- 
mately steady number (for a given season) . There are, then, in this 
case, two possible equilibria; one with a zero population of flies, the 
other with some positive number of fly population. 



60 



ELEMENTS OF PHYSICAL BIOLOGY 



The equilibria in nature, involving countless species, are of course 
much more complicated in character, but the general principle is 
the same; and we must expect that in general a variety of different 
equilibria are possible, some unstable and some stable. 

For the further discussion of the equations (1) it is now desirable 
to express these relations, not in terms of the masses X } but in 
terms of the excess of each mass Xi over its corresponding equili- 
brium value, 

xi = Xi-d (5) 



The equation (1) then takes the form 



, 

~r- = / i 
at 



(6) 



the parameters P, Q being omitted, for the sake of brevity. Ex- 
panding the right hand member by Taylor's theorem we obtain 
the system of equations 



dt 



dt 



+ 



+ 



+ 



. -f 



dt 

A general solution of this system of equation is 



(7) 



(8) 



where the (?'s are constants, of which n are arbitrary, and Xi, X 2 
. . . X n are the n roots of the equation 2 for X 

Oil X 0,ii . . . dm 



- 2)(X) = 



(9) 



2 This equation is commonly spoken of as the characteristic equation. For 
greater detail see A. J. Lotka, Proc. Am. Acad. Sci., vol. 55, 1920, pp. 137-153. 



FUNDAMENTAL EQUATIONS OF EJNETIC3 61 

It is seen by inspection of the solution (8) that if all the X's are 
real and negative, x i} x 2 , . . , x n all approach zero as t increases 
toward infinity, since e~ m = 0. But according to (5)., as the 
re's approach zero, the X's approach their equilibrium valu_es C. 
In this case, obviously, equilibrium is stable, since, by allowing 
sufficient time to elapse, we can always make the system approach 
as near as we please to Xi = Ci, for all values of the subscript i. 
Precisely similar conclusions hold if some or all of the X's are com- 
plex, and the real parts of all the X's are negative. 

If all the roots X ar ( e real (and negative), 3 each term in the 
solution (8) diminishes continually and approaches zero asymptot- 
ically as t approaches infinity. 

If all the constants G are of the same sign, the sum. of the series 
also will, evidently have a similar type of approach to equilibrium. 

If some of the G's are positive, others negative, there may be a 
species of irregular oscillations, the mass X of the component rising 
sometimes above its equilibrium value (7, sometimes falling below 
it. Ultimately, however, the equilibrium is approached from one 
side only, s,ince ultimately tbe term containing the numerically 
smallest X will predominate over all other terms. 

If some of the roots X are complex, the solution will contain 
truly oscillatory terms, since the exponential function, for complex 
exponents, assumes the trigonometric form 

g ft _}_ i gi n ft) (10) 



In this case there will be regular oscillations about the equilibrium 
position; in general these oscillations will be damped, that is to say, 
their amplitude will diminish, so that equilibrium is approached 
more and more closely, but always with oscillation the equilibrium 
is approached from both sides at once, so to speak, the oscillations 
persisting forever, though on a diminishing and ultimately vanish- 
ing scajle. 

These conclusions are the analytical confirmation and extension 
of an inference drawn by Herbert Spencer 4 on qualitative grounds : 

3 The analytical condition that the real parts of all the roots X shall be nega- 
tive is given by Hurwitz, Math. Ann., vol. 46, 1895, p. 521. See also Blondel, 
Ann. de Physique, 1919, pp. 117, 153. It might be noted here that a necessary 
though by no means sufficient condition, evidently is that the absolute term 
in D (X), that is to say D (0), shall be positive when n is even, and negative 
when n is odd; for this absolute term is equal to the product of all the roots X. 

* Herbert Spencer, First Principles, Chapter 22, Section 173. 



62 ELEMENTS OF PHYSICAL BIOLOGY 

Every species of plant and animal is perpetually undergoing a rhythmical 
variation in number now from abundance of food and absence of enemies 
rising above its average, and then by a consequent scarcity of food and abun- 
dance of enemies being depressed below its average .... amid these 
oscillations produced by their conflict, lies that average number of the species 
at which its expansive tendency is in equilibrium with surrounding repressive 
tendencies. Nor can it be questioned that this balancing of the preservative 
and destructive forces which we see going on in every race must necessarily 
go on. Since increase of numbers cannot but continue until increase of mor- 
tality stops it: and decrease of number cannot but continue until it is either 
arrested by fertility or extinguishes the race entirely. 

It will be observed, however, that our analysis enables us to be 
considerably more specific in distinguishing several modes of ap- 
proach to equilibrium, and in indicating the particular conditions 
under which each occurs. A point that here deserves particular 
emphasis is that, in order to make these distinctions and indications, 
it is by no means necessary to have a complete knowledge, or even 
very extensive information regarding the functions F. Only the 
coefficients of the first (linear) terms in the Taylor expansion of 
these functions enters into the determinant D(X),, and only these 
need therefore be known to draw the requisite conclusions regarding 
the stability and mode of approach of equilibrium. Furthermore, 
Spencer's commentary relates specifically to the case of species 
related to each other in certain particular ways (food, enemies, 
etc.): the analysis here given is framed on perfectly general lines 
and covers any sort of interrelation, interdependence of the com- 
ponents Si, S . . . S n . Certain particular interrelations will 
be duly considered in the course of the further development of the 
theme. Here it may be well to draw attention once for all to the 
fact that there is nothing whatever to restrict the application of 
the principles and methods set forth to systems in organic evolu- 
tion. Indeed, a typical example to which these reflections apply 
is the case of a chain of elements in the course of radioactive trans- 
formation. 5 

It will be seen later, in considering a concrete example, that the 
equilibrium equation (12) may yield zero or negative roots for C. 
A zero root is simply interpreted; if the equilibrium to which it 
relates is a stable one, this means that the species in question will 

5 A. J. Lotka, Proc. Am. Acad. Sci., vol. 55, 1920, p. 148; Proc. Natl. Acad. 
Sci., vol. 7, 1921, p. 168; Phil. Mag., August, 1912, p. 353. 




FUNDAMENTAL EQUATIONS OF KINETICS 63 

become extinct 1 '. It is unfit, is unadapted ultimately 7 to survive 
under the existing conditions 8 (as defined by the parameters P, etc.). 

A negative value of C may also signify that the species is incapable 
of survival under the existing conditions. Masses cannot assume 
negative values. As soon as any component passes through zero 
it ceases to function in the system, whose history is henceforth 
represented by a new set of equations in which this component 
does not appear. 

These conclusions must in one respect be accepted with a certain 
caution. Since there may be several equilibria, a species may be 
incapable of existence in the neighborhood of one such equilibrium, 
but might nevertheless succeed in maintaining itself in the neighbor- 
hood of another equilibrium. Whether such cases occur in prac- 
tise may be left an open question. Our analysis suggests this 
possibility. 

e This conclusion does not apply, of course, if the equilibrium with X = O 
is unstable, as in the example of a fly population cited above. 

7 It maj*, however, persist for a time, and, it may be, for a long time. An 
instance in point is furnished, outside the field of organic evolution, by a 
chain of elements in radioactive transformation. Although here the ultimate 
equilibrium is one with a single survivor, namely the last link in the chain, yet 
for millions of years the several products exist side by side in constant ratio 
though in slowly diminishing amount. At the head of such a chain is always 
found a "parent substance" which is the longest-lived in the chain. This is 
not accident. It is easily shown that if at some prior period this substance 
was preceded by a more rapidly decaying pre-parent, this latter must have 
disappeared in the course of the ages. It is totally unfit, unadapted, even for 
a temporary equilibrium, under present conditions. (See A. J. Lotka, Phil. 
Mag., August, 1911, p. 354.) 

8 It should hardly be necessary to point out that adaptation is purely 
relative. 



CHAPTER VII 

FUNDAMENTAL EQUATIONS OF KINETICS (CONTINUED)- SPECIAL 
CASE: SINGLE DEPENDENT VARIABLE 

If arithmetic, mensuration and weighing be taken away from any art, that 

which remains will not be much Plato. 

Law of Population Growth. It will add concreteness to the pres- 
ent exposition to consider at this point a numerical illustration. 

The simplest possible example of numerical application of the 
equations set forth in the preceding pages will be one in which there 
is only a single variable X. The fundamental system of equations 
then reduces to a single equation 

f=F(JT) (1) 

at 

A. case in point arises when for any reason one particular biological 
species or group grows actively, while conditions otherwise remain 
substantial!}" constant. 

This seems to be essentially what has occurred in certain human 
populations. It is true that, in their growth, they have carried along 
with them a complicated industrial system or group, comprising both 
living and non-living elements. We may, however, look upon the 
number of the human population itself as a sort of single index or 
measure of the growth of the group as a whole. 1 

1 This is an example in which certain of the variables X are connected by 
equations of constraint. So, for example, the number of head of cattle Nc has 
for many years past, in the United States, been about six tenths of that of the 
human population, Nh so that we have an equation of constraint 



or, putting the average mass of cattle at 1000 pounds per head, that of a human 
being at 100 pounds (an average to include all ages) 



X e = 

Similar equations of constraint apply to the other species of domesticated 
animals and plants, so that the mass of each can be (approximately) expressed / 



in terms of the single variable Xh. 

64 



FUNDAMENTAL EQUATIONS OF KINETICS 65 

Applying to this case the equation (1) and the general method set 
forth in the preceding pages, we are led to consider first of all the equi- 
librium equation 

^ - F OT) = (2) 

at 

This equation, obviously, has a root at X = 0, for at least one 
female is required to start the growth of a population. Expanding 
by Taylor's theorem we shall therefore have for F a series lacking the 
absolute term, 2 thus 

= F (X) = aX + 6X> + cX 3 + . . . (3) 

dt 

Furthermore, the equation (2) will have at least one other root, 
since there must be some upper limit to the growth of the population. 
The simplest case satisfying this condition is that in which the right 
hand member of (3) terminates at the second degree term, i.e., 

^f = oZ + &Z (4) 

at 

The characteristic equation 3 for X is in this case simply 

A - a = (5) 

and the solution of (4) therefore is 
X = (?*' + Sue 20 ' 



Substituting this in (4) and equating coefficients of homologous 
terms we find 

Gn =-<?! (7) 

a 

<?m = -!<?'x (8) 

a 2 

so that (6) is a simple geometric series. Its sum is 



Z- f - (9) 

o a 

1 -- f>at - p at _ 1 



dX 

2 Otherwise would not vanish, with X 

dt 

3 Corresponding to equation (9), Chapter VI. 

4 The series (6) is divergent for large values of t if a is positive. But the 
expression (9) for the sum of (6) remains a solution of (4). 



66 ELEMENTS OF PHYSICAL BIOLOGY 

In formula (9) either Gi or the origin of time is arbitrary. A sim- 
plification can be effected by so adjusting the origin of time that 

(10) 
This fixes the value of the constant Gi 



(?:=-- (11) 



and the formula (9) becomes 



The equation (9) can also be written in another form. If we denote 
by X the value of X when t = o, and write x = X + 7, then (9) 

becomes 

a 

X = - - - (13) 

"'- 1 



Population of United States. Formula (12) has been applied by 
Pearl and Reed 6 to the population growth of the United States. 7 
The calculated curve for the number TV of the population fits the ob- 
served data over a long period of years (1790 to 1910) with remark- 

5 This result can also be obtained by direct integration of (4) in finite form. 
The process given above has here been followed to illustrate the general method 
of the solution (S), (9), of Chapter VI. 

6 P. F. Verhuist, Mem. Acad. Roy. Bruxelles, 1844, vol. 18, p. 1; 1846, vol. 
20, p. 1; R. Pearl and L. J. Reed, Proc. Natl. Acad. ScL, vol. 6, 1920, p. 275; 
Scientific Monthly, 1921, p. 194; R. Pearl, The Biology of Death, 1922, p. 250. 
The last-mentioned work, especially, should be consulted for a detailed dis- 
cussion. For a general treatment of the population problem see also particu- 
larity E. M. East, Mankind at the Crossroads, 1923 (Scribners). 

7 Measured, in this case, by the increase in the number N of persons. This 
Is evidently, in first approximation at any rate, proportional to the total 
mass X of the population. 



FUNDAMENTAL EQUATIONS OF KINETICS 



67 



able faithfulness, as will be seen from table 2 and the graph shown 
in figure 4. Numerically the formula (12) here takes the form 



N = 



197,273,000 



1+e- 



,-0. 03134 1' 



(14) 



and the time t' (in years) is dated from April 1, 1914 (t 1 , being negative 
for dates anterior to this). This epoch is one of peculiar interest. 
It represents the turning point when the population passed from a 
progressively increasing to a progressively diminishing rate of growth. 
Incidentally it is interesting to note that if the population of the 

TABLE 2 
Results of fitting United States population data 1790 to 1910 by equation (14) 



YEAH 


OBSBBVBD POPULATION 


CALCULATED POPU- 
LATION BY EQUATION 

(14) 


BBBOK 


1790 


3,929,000 


3,929,000 





1800 


5,308,000 


5,336,000 


+28,000 


1810 


7,240,000 


7,228,000 


-12,000 


1820 


9,638,000 


9,757,000 


+119,000 


1830 


12,866,000 


13,109,000 


+243,000 


1840 


17,069,000 


17,506,000 


+437,000 


1850 


23,192,000 


23,192,000 





1860 


31,443,000 


30,412,000 


-1,031,000 


1870 


38,558,000 


39,372,000 


+814,000 


1880 


50,156,000 


50,177,000 


+21,000 


1890 


62,948,000 


62,769,000 


-179,000 


1900 


75,995,000 


76,870,000 


+875,000 


1910 


91,972,000 


91,972,000 






United States continues to follow this growth curve in future years, 
it will reach a maximum of some 197 million souls, about double its 
present population, by the year 2060 or so. Such a forecast as this, 
based on a rather heroic extrapolation, and made in ignorance of the 
physical factors that impose the limit, must, of course, be accepted 
with reserve. 

Stability of Equilibrium. The equilibrium at X = 0, i.e., with 
total absence of human population, is evidently unstable, since A = a 
and a is an essentially positive quantity, its numerical value being, 
for the population of the United States, 0.0313395. The second 
equilibrium, corresponding to the saturation point, is evidently at 



88 



ELEMENTS OF PHYSICAL BIOLOGY 



X = r , and here it is easily found by the substitution x = X + 
that X = a, the equilibrium is stable. 




FIG. 4. THE LAW OF POPULATION GROWTH FOR THE UNITED STATES ACCORDING 
TO PEARL AND REED 

The lower S-shaped limb corresponds to the actual approach to equilib- 
rium from below. The upper limb represents the presumptive course of 
events for a diminishing population approaching equilibrium from above. 



FUNDAMENTAL EQUATIONS OF KINETICS 



Experimental Populations. Pearl has also fitted the same formula 
to the population of a number of countries, but the range covered by 
the available observation in these other cases is less extended, so that 
there is less opportunity for comparison with observed figures. Of 
particular interest is an application of the same formula, also by 
Pearl, to an experimental population of fruit flies (Drosophila). In 
this case practically the entire range of the S-shaped curve defined 
by equation (12) is realized, and a glance at the plot in figure 5 
shows that the agreement of the observed figures (represented by 
small circles) and the calculated curve is exceedingly satisfactory. 
Still closer is the agreement in the case of bacterial cultures studied 



aso 

ss-s 



125 
JOO 



GftOWH Of DKOSOPHILA 



z 



Days. 

FIG. 5. GROWTH OF A POPULATION OF DROSOPHILA (FRUIT FLIES) TJNDEB 
CONTROLLED EXPERIMENTAL CONDITIONS, ACCORDING TO PEARL AND 

PARKER 

by H. G. Thornton 8 (Annals of Appl. Biology, 1922, p. 265), whose 
observations are set forth in table 3 and are shown by the small 
circles in figure 6 ; the theoretical curve to fit these points, as com- 
puted here in the laboratory, is shown in the fully drawn line. As 
will be seen the agreement is excellent. This is due in part to the 
fact that the figures plotted represent the means of a number of 
individual cultures. 

A veiy particular interest attaches to this example, inasmuch as 
it forms, as it were, a connecting link between the law of growth of a 

8 Similar results have been obtained by A. G. McKendrick and M. 
Kesava Pai, Proc. Roy. Soc. Edin., vol. 31, 1911; for a study of the growth of 
yeast, see A. Slator, Trans. Chem. Soc., 1921, vol. 119, p. 126. 



70 



ELEMENTS OF PHYSICAL 



population, and the law of growth of the individual. A colony of 
unicellular organisms, regarded as a whole, is analogous to the body of 
a multicellular organism . Or, to put the matter the other way about, 
a man, for example, may be regarded as a population of cells. We 
need not, therefore, be greatly surprised, if the growth of the multi- 
cellular organism should be found to follow a law similar to that 
exhibited by populations. And in point of fact, as will be shown a 
little further on, this expectation is in not a few instances fulfilled. 



TABLE 3 



ifrowth of bacterial colony, according to H. G. Thornton (Ann. Appl, Biol., 

p. 865) 

For graph see figure 6 



AGE OF COLONY 


ABBA IN SQTTABH CENTIMBTEBB 


Observed 


Calculated* 


days 






0.0 


0.24 


0.2511 


0.5 




0.7208 


1.0 


2.78 


2.0324 


1.5 




5.4620 


2.0 


13.53 


13.0761 


2.5 




25.1961 


3.0 


36.30 


37.0479 


3.5 




44.2213 


4.0 


47.50 


47.3930 


4.5 




48.5974 


5.0 


49.40 


49.0231 



*According to the equation y = 



0.2524 



e +0.005125 

Diminishing Population. It may be noted here that in one respect 
the formula (12), while particularly simple in form, is of more 
restricted scope than (13). The former defines the characteristic S- 
shaped curve that appears in the graphs of actual populations shown 
in figure 4. But formula (13) gives a more complete definition of a 
curve composed of two limbs; one of these is the S-shaped curve 
already considered. The other is a steeply descending arc, shown in 
the upper portion of figure 4. This portion of the curve has not been 



4 



FUNDAMENTAL EQUATIONS OF KINETICS 



71 



realized in any recorded population. It represents the computed 
course of events if the population initially exceeds its equilibrium 

strength, i.e., if is positive. 
so 



43 




Pays. 

FIG. 6. GEOWTH OF A BACTEBIAL COLONY (B. DENDEOIDES) 
Observations by H. G. Thornton 

Growth of Individual Organism. Although, strictly speaking, the 
growth of the individual organism is a subject properly belonging to 
the field that has here been termed "micromechanics" (Chapter V), 
yet, in view of the very close analogy which has been found to exist, 
in certain cases, between the law of growth of a population, and that 
of the individual, it may be noted here that the formula (9) has also 



72 ELEMENTS OF PHYSICAL BIOLOGY 

been applied by T. B, Robertson 9 and by Wo. Ostwald 10 and others, 
to the growth of the individual organism. An example of such appli- 
cation Is shown in figure 1, which exhibits the growth day by day, of 
male white rats according to observations by H. H. Donaldson" 
and computations by T. B . Robertson. The fully drawn curve repre- 
sents the calculated values of the mass of the rats (in grams) at dif- 
ferent ages. The circles indicate selected observed values, namely, 
those which diverge most widely from the computed values. It 
will be seen that up to about the one hundredth day the agreement is 
good. Above this there is no agreement worthy of the name. 

Another example,, and one in which the computed curve fits the 
observed values with remarkable agreement, is the growth (in height) 
of sunflower plants as studied by H. S. Reed and R. H. Holland. 12 
The curve to fit these observations has been recomputed by the 
method of least squares by Dr. L. J. Reed, who has very kindly placed 
his results at the author's disposal. They are shown in figure 8. The 
observations on which they are based are shown in table 4. It will 
be seen that the fit is practically perfect through the whole range of 
observations. 

In practice we are not usually given the differential equation (4), 
but data corresponding to points on the integral curve (12). We 
then have the problem of determining from these points the charac- 
teristic constants of the curve. The detailed working out of theprob- 

9 Archiv liir die Entwiekelungsmeehanik der Organismen, 1907, vol. 25, 
p. 4; 190S, vol. 26, p. 108; The Chemical Basis of Growth and Senescence, 
publ. Lippincott, 1923. T. B. Robertson also quotes A. Monnier, Publications 
of Irist. of Botany, Univ. Geneva, 1905, which in turn refers to Chodat as hav- 
ing recognized the analogy of organic to autocatalytic growth. The idea is 
rather an obvious one, which probably has occurred to many. The earliest 
reference noted by the writer is L. Errera, Revue de 1'Univeriste de Bruxelles, 
1899-1900, May issue. Something very similar is found in Ostwald, Vorlesungen 
Ober Naturphilosophie, 1902, p. 342. These last-mentioned lectures were 
published in 1902. but were actually delivered somewhat prior to that date. 
The writer recalls that Ostwald referred to the matter in his lectures on Gen- 
eral Chemistry in 1902, and probably others will recall similar references on 
earlier occasions. 

10 Die Zeitlichen Eigenschaften der Entwickelungsvorgange, Leipzig, 1908. 

11 Boas Memorial Volume, 1906, p. 5; see also the same author's book 
The Rat, 1915. 

12 H. S. Reed and R. H. Holland, Proc. Natl. Acad. Sci., vol. 5, 1919, pp. 
135-144. 




FUNDAMENTAL EQUATIONS OP KINETICS 73 

lem may well be left to the reader, after pointing out the following 
interesting property of the curve (12). Taking reciprocals and 
writing A for a/b, we have 



_ _ 3 a _ /o) 

A" 

log (A% -1) = - o(f-* ) 



(15) 
(16) 



oo 




O SO 100 (SO ZOO ZSQ 3CO 

Ays. in days. 

FIG. 7. GROWTH OF RAT ACCORDING TO H. H. DONALDSON AND T. B. 

ROBERTSON 

Circles indicate only those observations that diverge most widely from the 
calculated curve. 

where t is the time corresponding to the point of inflection of the S- 
curve. Thus if we plot A 1 against t on logarithmic curve paper, 
we shall obtain a straight line diagram. This is shown in figure 9 for 
the same data (growth of sunflower) which have already been 



74 



ELEMENTS OP PHYSICAL BIOLOGY 



00 




y- 




Z6/.I 



O 7 H 2/ 28 35 -?2 +9 ?& 63 TO 77" &<f 

Age in days. 

FIG. 8. GHOWTH OP SUNFLOWER SEEDLINGS ACCORDING TO H. S. REED AND 
R. H. HOLLAND; COMPUTED CURVE BY L. J. REED 



TABLE 



Growth in height of sunflower plants (H. S. Reed and R. H. Holland;* computed 
values by L. J". Reed) 



MEAN HEIGHT 





Observed 


Computed 




cm. 


cm. 


7 


17.93 


21.89 


14 


36.36 


37.74 


21 


67.76 


62.08 


28 


98.10 


95.42 


35 


131.00 


134.56 


42 


169.50 


172.99 


49 


205.50 


204.64 


56 


228.30 


227.16 


63 


247.10 


241.56 


70 


250.50 


250.14 


77 


253.80 


255.05 


84 


254.50 


257.79 



Troc. Natl. Acad. Sci., vol. 5, 1919, p. 140. 



10.0 




7 



63 7O 77 84- SI 38 



Age. m day-s, 

FIG. 9. GEOWTH OF STJNFLOWEB SEEDLINGS 
The same data as in figure 8, but plotted in logarithmic diagram, with 

ordinates as indicated in the legend. 

75 



exhibited by another method in figure 8 . Taking now three equidis- 
tant points of time ^ t is and the corresponding ordinates &, 2, &, it 

is readily shown that 

ta-ft ^gLlLg; (17) 

' (t + &)-2& TM-& 

where 3/ denotes the geometric mean of 1 and | 3 and while m denotes 
their arithmetic mean. 

Thus the constant A can be determined from three suitably chosen 
points on the curve (after smoothing graphically if need be). The 
other constants then follow easily. 

Autocatakinesis. Both Robertson and Wo. Ostwald .draw atten- 
tion to the similarity between the law of growth (12) and the law of 
formation of a chemical substance by autocatalysis under certain con- 
ditions. The analogy is interesting, but must not be taken too 
seriously, inasmuch as in the one case the rate of growth is deter- 
mined by ordinary chemical influence, in the other (organic growth) 
by a complicated combination of factors both of chemical and of 
physical character. Rather more to the point seems to be the sug- 
gestion made above in connection with the law of growth of bacte- 
rial colonies, that, the body of a multicellular organism being a "popu- 
lation" of cells, it is not altogether surprising that it should be found to 
follow the law of growth of a population. 

A suggestion of terminology by Wo. Ostwald is worth noting. He 
proposes that growth of any kind, in which the substance or structure 
itself acts as nucleus for the formation about it of further quantities 
of the same substance or structure, be broadly termed autocata- 
kinetic growth, the narrower terms autocatalysis of autocatalytic 
growth being reserved for that particular kind of autocatakinesis 
which is chemical in character. This is a useful suggestion, as it 
leaves the term autocatakinesis quite neutral and free from any impli- 
cation or restrictions as to the mechanism by which the growth takes 
place. 



CHAPTER VIII 

FUNDAMENTAL EQUATIONS OF KINETICS (CONTINUED) SPECIAL 
CASES: TWO AND THREE DEPENDENT VARIABLES 

Life is a system of relations rather than a positive and independent ex- 
istence G. A. Sola. 

Interdependence of Species. The case of two dependent vari- 
ables, X\, Xz, which we now approach, is of interest as the simplest 
example exhibiting the relation between interdependent species. 
This relation can take on a variety of forms. Most fundamental, 
perhaps, is that form of interdependence (1) in which one species 
Si serves as food to another species S Z) so that, in this sense, Si 
becomes transformed into S 2} thus 

Si > $2 

All animal species, and many plants also, thus derive their sub- 
stance from other species on which they feed. And several dif- 
ferent types of this form of interdependence are observed. In 
the first type, (a) the organism $ 2 kills Si outright in the process 
of feeding upon it. We might term S 2 in such a case an episite 
of Si, in contradistinction from the second type, (&) in which 2 
lives on Si without killing it outright, being parasitic upon Si. 
The host is in most cases more or less injured by the parasite, and 
all pathogenic organisms fall into this class. For this reason quantita- 
tive epidemiology appears as one of the special branches of the general 
subject under consideration here. 

A third type (c) of interdependence, is that in which S 2 is sapro- 
phagous or saprophytic, feeding upon the cadavers of Si after death 
from other causes; or, /S 2 may live on waste products discharged by 
Si. In contrast to episites and parasites, saprophagous species are 
presumably beneficial rather than injurious to the host species, 
since they function as scavengers. Still another type, (d), of inter- 
dependence is that of symbiosis, in which Si and *S 2 live in partnership 
which, as a rule, is in some degree mutually beneficial. Man and 
his domesticated animals and plants are obvious examples of this 
type. 

77 



7S 



ELEMENTS OF PHYSICAL BIOLOGY 



In addition to these types (Id) to (Id), another large group of 
cases (2) are those in which two or more species compete for a common 
food supply. 

In their general form the fundamental equations of kinetics 

for the case of two dependent variables are 



dt 



dl 



-j- AuXi -r AitXz + . 
+ AtiXi -r AttKi T . 



(1) 



or, after the transformation (5), of Chapter VI 



= anXi -f- 

at 



dx s 
~dt 



= CsjXj + QssZs 4- . . . 



(2) 



We may note, first of all, as a general rule, the following observa- 
tions regarding the coefficients a in the several types of interdepen- 
dence enumerated above: 

la. S 2 lives on Si by killing Si outright (episitic type). In this 
case, evidently S 2 unfavorably influences the growth of Si } while, 
on the contrary, Si is advantageous to the growth of &, so that 



5 dZi 

Z 2 dt 



< 0, i.e., an < 



t 

~ > O, i.e., an > 
oXi at 



(3) 
(4) 



lb. 82 parasitic upon Si. Here a iz < 0, 021 > 0, as in case la. 

Ic. S 2 saprophytic upon Si, or living upon waste products of Si. 
Here we may expect that a iz ^ 0, a 2 i > 0. 

Id. S 2 feeds on Si, but at the same time cultivates it in symbiosis. 
Here a iz > 0, a 2 i > 0. 

The characteristic equation for two variables is 



X 



X 



= 



(5) 



FUNDAMENTAL EQUATIONS OF KINETICS 79 

or, In expanded form, 

X 2 (an + o^X + (andn 021^:2) = (6) 

X = I { (a u + a 22 ) =*= V(a u - a 22 ) 2 + 4a 2 iai 2 } (7 ) 

Certain general conclusions follow immediately. So, for example, 
if ai, ais are both of the same sign, as in the case of saprophytes 
and of symbiosis, the quantity under the radical is necessarily positive, 
and hence both roots for X are real. The oscillatory type of approach 
to equilibrium is here excluded. In the case of two species of the 
type (la) or (16), the episitic or parasitic type, on the contrary, 
the possibility of oscillations is indicated, under conditions where 
the equations (1) are applicable. 

CONCRETE EXAMPLES 

Martini's Equations for Immtinizing Diseases. Numerical appli- 
cations of the case of two dependent variables are not easily ob- 
tained. Of concrete examples in general terms (with unknown or 
very imperfectly known values of the constants involved) several 
are to be found in the literature. The simplest of these is a case 
for which the equations are given, without solution, by Martini 
in his Berechnungen und Beobachtungen zur Epidemiologie der Malaria 
(Gente, Hamburg, 1921, p. 70), namely, the case of the growth of 
an endemic disease of the type that confers acquired immunity 
upon persons who recover from it (e.g., measles, scarlet fever, etc.) 
Martini writes 

u = fraction of the population affected and infective 

i = fraction of the population not available for new infection (i.e., im- 
mune or already affected) 
(1 _ i ) = fraction of the population available for new infection 

p fraction of the population newly affected per unit of time 

q = fraction of the population of affected population that ceases to be so, 
per unit of time, by recovery or by death 

m = fraction of "unavailable" population that loses immunity or dies 
per unit of time 

a = infe.otivity (a proportionality factor) 

Martini puts the newly affected population, per unit of time, jointly 
proportional to the infective population u and to the population 
available for new infection, (1 i), so that 

p = a u(l t) 



80 ELEMENTS OF PHYSICAL BIOLOGY 

Then, obviously, 

= a u(l - - qu = (a - q}u - a ui 
di 

I- (9) 

= a u(l i) mi = a u mi a ui 
di j 

The characteristic equation for X here reduces, near the origin, 
simply to l 

| (a _ q ] _ A ) (m - X) = (10) 

and the solution, near the origin, is 

(7, ^- mt 4- . . 1 

(11) 




from which it is seen that the equilibrium near the origin is stable 
if and only if a < q 

There is a second equilibrium at 



in (a q) 



= I 



(12) 



Since, however, i can in reality assume only positive values, this 
equilibrium has a meaning only if a > q, i.e., just in the case in 
which the equilibrium at the origin is unstable. Hence we conclude 
that if a. < q the equilibrium at the origin is the only possible one, 
and is stable, so that the disease will die out. 

In the other alternative, a > q, the second equilibrium has a real 
meaning, and we can develop a solution in series 

- = ' Xlt ' X!t 1 

(13) 
i - I = (?' Sll e Xj *+ (?' 2 , 2 e X2t + . . . 

where X 3 , X 2 are given by 



q- 



1 A. J. Lotka, Nature, vol. Ill, 1923, p. 633. 



gi 

FUNDAMENTAL EQUATIONS OF KINETICS Oi 

We need not here consider the case (a - q) < 0, for, as pointed out 
above, in this case the second equilibrium is meaningless. But 
when a > q, it is seen from (14) that the real parts of the two 
roots will then in any case be negative, so that the equilibrium, if 
it exists at all, is stable. Furthermore, there will be two real and 
distinct, two real and coincident, or two complex roots, according as 

a- q 1 m ~> _ ft K) 

2. -1 - \i"J 

a" a 4 q < 

In the last-mentioned case equilibrium will be approached by a 
series of oscillations above and below the final state of equilibrium, 
so that a series of "epidemic" waves will appear, a feature which 
has an obvious interest in connection with the type of disease here 
discussed. 2 The oscillations thus occasioned by the factors duly 
taken into account in this elementary analysis may in practise be 
enhanced by factors here neglected, such as varying virulence of 
the disease, exhaustion of susceptible population, seasonal influences, 
etc. The last-mentioned, however, will in general tend to produce 
a separate series of waves whose period will have no relation to that 
of the oscillations derived above. 

For the special case = 1, Prof. G. N. Watson has given a complete 

solution, which may be consulted in the original. 3 It is to be noted 
that this case cannot, according to the analysis here presented, 
lead to oscillations, since the condition for oscillations according 
to (15) reduces to 

^" :o (16) 

and cannot be satisfied, as the square of a real quantity is necessarily 
positive. 

The Ross Malaria Equations. A system of equations has been 
established by Sir Ronald Ross 4 to represent, under certain 

2 Compare J. Brownlee, Investigation into the Periodicity of Infectious 
Diseases, Public Health, vol. 25, 1915, p. 125. 

3 G. N. Watson, Nature, vol. Ill, 1923, p. 808. 

4 Sir Ronald Ross, The Prevention of Malaria, second edition, 1911, p. 679. 
This volume also contains a bibliography. For a detaile ddiscussion of the 
Ross malaria equations see A. J. Lotka, Am. Jour. Hygiene, January 
Supplement, 1923. 



82 



ELEMENTS OF PHYSICAL BIOLOGY 



conditions, the course of events in the spread of malaria in a human 
population by the bites of certain breeds of mosquitoes infected 
with the malaria parasite. These equations are of the same form 
as Martini's equations discussed above, and inasmuch as Ross's 
malaria equations have been very fully treated by the writer in 
a separate monograph, 5 their detailed study may here be omitted. 
It will suffice to reproduce from this monograph one of the curves 
representing the course of events, the presumptive growth of malaria 
in a human population, as defined by the differential equations of 
Sir Ronald Ross. 




-4 

~ t 
years 

FIG. 10. CUHVE OF GROWTH OF ENDEMIC MALARIA ACCORDING TO SIB RONALD 

Ross's EQUATIONS 

The upper (S-shaped) curve relates to the particular case in which the 
initial malaria rates in the human and the mosquito population stand 
in the ratio which they have at equilibrium or are both small. The lower 
curve represents the course of events when the initial malaria rate is 4.2 per 
cent in the human population, and 1.4 per cent in the mosquito population. 
(The zero of the time scale is arbitrary.) Ordinates are malaria rates (human) 
expressed as fraction of unity. (Reproduced from A. J. Lotka, Am. Jour, of 
Hygiene, January Supplement, 1923.) 

5 A. J. Lotka, loc. cit. 



FUNDAMENTAL EQUATIONS OP KINETICS 83 

It will be observed (fig. 10) that the curve showi consists of two 
parts, the one an Srshaped limb which, in point of fact, is very 
nearly identical in type with the Verhulst-Pearl population curve. 
The second limb ascends very steeply, almost vertically, and finally 
bends to join the S-shaped limb. 

The meaning of these curves is as follows: If a small nucleus 
of malarial infection is introduced into a (constant) population 
of human beings and mosquitoes, both being previously free from 
such infection, then the growth of malaria in the human population 
will follow the course represented by the S-shaped limb. It will 
be seen that the process is a rather leisurely one, its essential comple- 
tion occupying about ten years, according to Ross's figures. (Strictly 
speaking it is never quite complete in a finite time.) Seasonal effects 
are here disregarded. 

On the other hand, if at the start there is already present a certain 
malarial rate in the human population, and also in the mosquito 
population, then, in the case here depicted, there is for a time a 
very rapid increase of malaria in the human population, until, in 
the brief space of about two months, the S-shaped curve is reached. 
After that the course of events is the same as in the first case. 

In practise, in temperate climes, we can expect only short sections 
of the S-shaped curve to be realized, owing to the interruptions 
of the seasons. No data are available for a numerical comparison 
of these results with observed conditions. Close agreement is not 
to be expected, as the Ross equations refer to a rather highly idealised 
case, a constant population both of men and mosquitoes. The 
latter could be even distantly approached only in the tropics. There 
is room here for further analysis along more realistic lines. It 
must be admitted that this may lead to considerable mathematical 
difficulties. The case of periodic seasonal influences is perhaps 
the one that promises to yield most readily to mathematical 
treatment. 

The Ross malaria equations are a typical example of equations 
affected with a lag, owing to the period of incubation. For a detailed 
discussion of this feature the reader must be referred to the author's 
monograph published by the American Journal of Hygiene. 

An Example in Parasitology. An interesting and practically 
significant case of inter-group evolution, of conflict between two 
species, has been made the subject of an analytical study by W. R. 



84 ELEMENTS OF PHYSICAL BIOLOGY 

Thompson. 6 He considers a host species^ numbering initially n in- 
dividuals, and a parasite species, initially p individuals. On a num- 
ber of simple assumptions, for which the reader must be referred to 
the original papers, he develops the following formula for the fraction 
a of the host population attacked, in the t ih generation, by parasites 



pa* 

a = 



(a* - a) 
n -p 
a 1 

where a is the ratio of the "reproductive power" of the parasite 
to that of the host, the reproductive power being measured by the 
number of eggs deposited per female. It is assumed that only 
one egg is deposited in each host. 
Putting 

a 1 = e rt (18) 

and 

X (19) 



P P 

Thompson's formula becomes, after a simple transformation, 

-^r-i (20) 

which will be recognized, once more, as the equation of the law 
of simple autocatakinetic growth. According to the value of a 
and K several different cases may arise, whose graphs are shown in 
figure 11. It should be observed that 

K = 1 according as a= 1 (21) 

r = according as a= 1 (22) 

< > 

In the special case that a = 1 the formula (20) becomes indeterminate 
and a is then given by 

P 



n-p(t-l) 
a hyperbolic relation (see fig. 11, the last diagram). 



(23) 



W. R. Thompson, Comptes Rendus Acad. Sci., vol. 174, 1922, pp. 201, 1443, 
vol. 175, p. 65. See also R. A. Wardle and P. Buckle, The Principles of Insect 
Control, Longmans, Green & Co., 1924. 



FUNDAMENTAL EQUATIONS OF KINETICS 



85 



Thompson gives a number of numerical examples exhibited 
in table 5 . From these examples and from this formulae he concludes 
that the invasion of the host species by the parasite may at first 




Fia. 11. COTJESE OF PAKASITIC INVASION OF INSECT SPECIES ACCOBDINQ TO 

W. R, THOMPSON 

proceed only very slowly, and that nevertheless, after a certain 
time, the increase may become very rapid. From a practical stand- 
point this is important to observe, since it implies that the first 
effect of "sowing" the parasite among a species of insect hosts, 



ELEMENTS OF PHYSICAL BIOLOGY 



with a view to destroying them, may be quite discouraging, and 
that this must not be taken as indicative of ultimate failure. This 

TABLE 5 

Percentage (IQOa) of host species attacked by parasite in t lh generation, according 
to W. R. Thompson 



p 


n 


a 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


10 


1,000 


1.5 


1.5 


2.28 


3.50 


5.40 


8.64 


14.2 


24.6 


50.0 


100.0 




10 


10,000 


1.5 


0.15 


0.23 


0.33 


0.51 


0.77 


1.16 


1.76 


2.7 


4.15 


6.5 


10 


100 


1.0 


10.0 


11.1 


12.5 


14.35 


16.6 


20.0 


25.0 


33.3 


50.0 


100.0 


10 


200 


1.0 


5.0 


5.25 


5.55 


5.88 


6.25 


6.66 


7.14 


7.7 


8.3 


9.1 


p 


n 


a 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


10 


10,000 


1.5 


9 6 


18.6 


34.2 


78.0 














10 


200 


1.0 


10.0 


11.1 


12.5 


14.3 


16.6 


20 


25 


33 


50 


100 



p= initial number of parasite species. 
7i=initial number of host species. 

parasite 



host 



a=ratio of reproductive powers 

The figures in the columns headed 1, 2, 3, etc., denote the values of 
100 a in the 1st, 2d, 3d, etc., generation. 



7i'm& in 



J>OO 




\ 



\ 



\ 



\ 



FIG. 12. INCREASING DIBTUSION-IN-TIME OF STJCCBSSIVH GENERATIONS IN 
THE PEOGENY OF A POPULATION ELEMENT 

observation is especially significant since in practise one must 
often be satisfied with the introduction of a relatively very small 
number of parasites. So, for example, in using the parasite species 



FUNDAMENTAL EQUATIONS OF KINETICS 87 

Liparis di&par, commonly about one thousand individuals have 
been sown. Supposing that there were one thousand million hosts, 
and that the parasite reproduced twice as fast as the host, it would 
require, according to Thompson's calculations, about 19 generations 
to exterminate the host; and then, even to the sixteenth generation, 
only 10 per cent or less of the host species would be attacked, 

Thompson's formula is open to certain objections. Its derivation 
seems to involve the assumption that each generation of the parasite 
is coextensive in time with the corresponding generation of the host. 
Furthermore, the use of a generation as a sort of time unit is un- 
satisfactory, because a generation is a very diffuse thing, spread 
out over varying lengths of time. This is easily seen by considering 
the progeny of a batch of individuals all born at the same time 
t 0. If we call this the th generation, and if fli, ao are respectively 
the lower and the upper limit of the reproductive period, then it 
is clear that the next generation, the first, will extend over the 
interval of time from a L to a 2 , the second from 2a^ to 2a 2 , the n th 
from nai to na z , an interval which will ultimately become very large 
as n increases, as shown by successive intercepts between the two 
sloping lines in figure 12. 

Less objectionable, perhaps, is the fact that Thompson's formula 
is expressed in terms of the "rate of multiplication per generation" 
of the two species. This term is not as clear as it might be. From 
the context it appears that it refers to the number of eggs deposited 
per female. This number is closely and simply related to the 
ratio 12 of the total births in two successive generations. If an 
individual of age a reproduces, on an average /3 (a) individuals per 
unit of time, the ratio R is evidently given by 



f* 

= j 

Jo 



(a)p(a)do 



The relation of this R to the rate of increase r per head of the popula- 
tion is not altogether obvious and cannot be expressed in simple 
form. For a population with fixed age distribution, it will be 
shown in Chapter IX that r is given by 



= e - r a p( a )p( a )fa 

|"SO / 

= I @(a)p(d)da r I a^(a} 
Jo Jo 



+ 



(25) 



88 ELEMENTS OF PHYSICAL BIOLOGY 

Hence 

Jra 
aj3(a)p(a)da + . . . (26) 

In view of the doubtful features in Thompson's formula which 
have been indicated above, it appears desirable to attack his problem 
in quantitative parasitology from another angle. We may do 
this by following the general method which has here been set forth 
and exemplified. 

Treatment of the Problem by the Method of Kinetics. Let 
NI be the number of the host population, &i its birthrate per 
head, (the deposition of an egg being counted a birth), and di its 
death rate per head from causes other than invasion by the 
parasite. Let kNiN* be the death rate per head due to invasion by the 
parasite, in the host population, the coefficient k being, in general, 
a function of both jVi and JV 2 , the latter symbol designating the 
number of the parasite population. 

The birth of a parasite is contingent upon the laying of an egg 
in a host, and the ultimate killing of the host thereby. To simplify 
matters we will consider the case in which only one egg is hatched 
from any invaded host. If an egg is hatched from every host 
killed by the invasion, then the total birthrate in the parasite popula- 
tion is evidently kNiN*. If only a fraction k' of the eggs hatch, 
then the total birthrate in the parasite population is evidently 
kk' NiN, which we will denote briefly by KNiN 2 . Lastly, let the 
deathrate per head among the parasites be d z . Then we have, 
evidently 



dt 

(27) 

dt ~ i 2 - - - 

where r x has been written for (b { d t ). 

Regarding the function k, we shall now make the very broad 
assumption that it can be expanded as power series in NI and N z , 
thus 

k = a. + &Ni + yN-t + . . . (28) 



FUNDAMENTAL EQUATIONS OP KINETICS 



It will be convenient first of all to consider an approximation. 7 
If the coefficients 3, 7, etc., are sufficiently small, we shall have, 
for values of A'i, X* not too large, essentially 



at 

(29) 



(30) 



Integrating, and putting 

k'a 

TI (^21 

a. 

we obtain 

d 2 Iog(x + p) + n \og(y + q) - h'ax - ay = M (33) 

where M is an arbitrary constant of integration. Expanding by 
Taylor's theorem we find 

M' (34) 



By giving successively different values to the arbitrary constant 
M r a family of closed curves is obtained for the plot of (34) in rec- 
tangular coordinates, as indicated in figure 13. In the neighborhood 
of the origin, where terms of higher than second degree are negligible, 
(34) reduces simply to 

(- -^ = constant (35) 

P~ <f 

and the integral curves are small ellipses. 

7 It will be observed that the "diagonal" terms in the linear part of (27), 
(29) are lacking, i.e., there is no linear term containing 2V 2 in the first equation 
of (27) and none containing NI in the second. This gives rise to an exceptional 
case to which the general solution given in Chapter VI is not applicable. 



90 



ELEMENTS OF PHYSICAL BIOLOGY 



The course of events represented by these curves is evidently 
a cyclic or periodic process, corresponding to a circulation around 
the closed curves. The period of oscillation, near the origin, 8 is 
given by 



T = 27r/Vr 1 d 2 



(36) 




FIG. 13. COURSE OF PARASITIC INVASION op INSECT SPECIES, ACCOEDINQ TO 
LOTKA; ELEMENTARY TREATMENT 

This finding accords well with the observation made by L. 0. Howard : 

With all very Injurious lepidopterous larvae .... we constantly see 
a great fluctuation in numbers, the parasite rapidly increasing immediately 
after the increase of the host species, overtaking it numerically, and. reducing 
it to the bottom of another ascending period of development. 

8 The purely periodic solutions have been discussed by the author in Proe. 
Natl. Acad. Sci., 1920, vol. 7, p. 410. The writer, however, at that time over- 
looked the existence also of the other types of solution, and also stated that 
the period of oscillation is independent of initial conditions. This is an error 
which he takes the present opportunity to correct. The expression given 
by him loc. cit. for the period of oscillation holds only in the neighborhood of 
x = y = 0. See also note 10 below. 



FU^TDAMEXTAL EQUATIONS OF KINETICS 



91 



The remarks of W. R. Thompson relative to this may also be 

quoted : 

Recent studies oa the utilization of entomophagous parasites seem to 
show that the role of these auxiliaries of man finds its maximum effective- 
n^== when the noxious insect has increased in numbers to the point of a 
ula-me, one or more of the factors of natural equilibrium having somehow 
failed ' to act as a check. The expansion of the noxious species then 
automatically produces an increase in the number of parasites; generation 




FIG. 14. COURSE OF PABASITIC INVASION OP INSECT SPECIES, ACCORDING TO 
LOTKA; MORE EXACT TREATMENT 

after generation this number increases at the expense of the host, until it first 
equals, and presently surpasses the number of the host species, and finally 
almost annihilates the host; but then comes a moment when the parasite pop- 
ulation, having grown to excess, largely disappears for the lack of food 
supply. 9 



9 L. O. Howard, Bureau of Entomology, Technical Series No. 5, 1897, p. 48. 
It will be noted that the analysis given by W. R. Thompson fails to give any 
indication of this oscillatory process. 



92 



ELEMENTS OF PHYSICAL BIOLOGY 



In this elementary discussion the terms of second and higher 
degree in A r i and JV 2 in equations (27) have been neglected, as in 
(29). When they are taken into account it is found that, in 
general, the system of closed curves in figure 13 is replaced by a 
spiral winding about the second equilibrium point (see fig, 14). 
The process is still oscillatory, but, in general, it is the nature of a 
damped oscillation. For detail of this more exact treatment the 
reader must be referred to the original literature. 10 

Annihilation of One Species by Another. The preceding example 
was suggested by W. H. Thompson's paper in the Comptes Rendus. 
Another case, leading to equations of the same form, had been 
previously treated by the writer, namely the following : 

A species S* feeds on a species Si, which, in turn feeds on some 
source presented in such large excess that the mass of this source 
may be considered constant during the period of time under consid- 
eration. Then we have the obvious relation 



(37) 



The first term in the right hand member, Mass of newly formed 
Si per unit of time, evidently must vanish with Xi } and we shall 
therefore write this term biXi, where 61 will, in general, be a func- 
tion of both Xi and X 2 . Similarly, and for the same reasons we 
shall write for the third term, excretory matter, etc., eliminated 
from Si per unit of time, diXi. Contracting these two terms into 
one we shall write for biXi diXi the single term riXi. The 
middle term, mass or Si destroyed per unit of time by 82, must 
evidently vanish with either Xi or X 2 separately. We shall ac- 
cordingly write this term kXiX 2 , so that the equation now appears 





Other dead 


Rate of in- 
crease of Xi 
per unit of 
time 


(Mass of newly 1 
= \ formed Si per > 
[unit of time J 


Mass of Si 
destroyed by 
2 per unit of 
time 


,_, 


or excretory 
matter elimi- 
nated from Si 
per unit of 




time 



at 



(38) 



10 H. Poincare, Journal de Mathem., 4th ser., vol. 1, p. 172. (See also E. 
Picard, Traite d' Analyse, vol. Ill, Chapter IX, p. 214); A. J. Lotka, Jour. 
Washington Acad. Sei., 1923, vol. 13, p. 152. 



FUNDAMENTAL EQUATIONS OF KINETICS 



93 



(39) 



For the species S which feeds on Si we have a corresponding 
relation 

'Mass of newly] 

formed 2 per Mass of S-. 
I unit of time I destroyed or 
I (derived from] eliminated per 
S\ as food in- unit of time 
.gested) j 

which, for reasons precisely analogous to those set forth above with 

reference to equation (38), we shall write 





at 



(40) 



It will be seen that these two equations are identical in form with 
those discussed in the preceding example, and it is therefore un- 
necessary to repeat the analysis there given. But one point invites 
attention, and will naturally lead us on presently to the consideration 
of a case in three dependent variables, which offers certain features 
of special interest. 

Let us leave aside all other considerations, and restrict our enquiry 
here to the following question : Is it possible, under the circumstances 
represented by our equations, for the hostile species $ 2 to exter- 
minate completely the species Si upon which it feeds? This would, 
of course bring in its train also the extermination of S z . 

To answer this question we note that 



Xi (n- 
X, 



dX, 



is satisfied by the particular solution 



i = for all values of 



(41) 



(42) 



Hence if we plot the integral curves of (41) in rectangular coordinates, 
the axis of X% is itself one of the integral curves. Now if r x , k, 
K, and c? 2 are single-valued functions of X i} and X z , as it is reasonable 
to suppose that they are, then any point in the XiX 2 plane is traversed 

by only one integral curve, since the derivative -=? is uniquely 

ClX 2 

determined by (41). It follows that no integral curve can cross 
the axis of X z and therefore Xi can never fall to the value zero, 



94 ELEMENTS OF PHYSICAL BIOLOGY 

it can be zero only if it had that value from the beginning. The 
food species cannot, therefore be exterminated by the predatory 
species, under the conditions to which our equations refer. 

This argument fails, however, at the origin, where the derivative 
dXi/dXz assumes the indeterminate form 0/0. But in the neigh- 
borhood of the origin, where second degree terms are negligible, we 
have, essentially, 

dXi Xi TI 
dXz Xy dz 

from which it is seen that in the positive quadrant the integral 
curves always slope downward from left to right near the origin. 
They cannot, therefore, in the positive quadrant, cross the axis 
of Xz at the origin, any more than at any other point, and the con- 
clusion is now fully established, that the species Sz cannot exterminate 
Si under the conditions here considered. 

A word of caution, however, is perhaps in order. Although 
8 2 cannot exterminate Si, it may so reduce the latter in numbers as to 
render it very vulnerable, and liable to extinction from those other 
influences which have deliberately been ignored in the development 
of the equations. 

Case of Three Dependable Variables. A singularly interesting 
conclusion is reached when we enquire what may be the effect 
of introducing, into the system discussed in the preceding section, 
a third species, which also serves as food for Sz, so that this now has 
two sources to draw upon, after the pattern 



One would perhaps naturally suppose that this alternative and 
additional source would in some measure protect Si from the attacks 
of Si. But we shall see presently that this is not necessarily the 
case, that, in fact, in certain circumstances, the introduction of the 
third species 83 may bring about the extermination of Si, from which, 
as we have seen, Si is naturally protected by the diminution of 
growth forced upon $2 when this species too greedily consumes its 
sole source of food. 



FUNDAMENTAL EQUATIONS OF KINETICS 95 

The equations for this case are similar to those for the preceding, 
except that we must add a third equation for the species $3 



~ = r,X s - hXzX* (44) 

at 

and add a term to the equation for S 2 to represent the consumption 
of the species 83 as food by S 2 , so that this equation becomes 

dX z 

: JK.X i.X.2 -j- 
at 



+ HX 3 - d 2 ) (45) 

We now have, near the axis of X s> 



_ . fAC\ 

J-tr V TJ"V~ ^ V*Q) 

and, if Xz is sufficiently large, the projection of the integral curves 
upon the XiX plane will slope upward from left to right in the 
positive quadrant. Such an integral curve may therefore cut 
through the X%X 3 plane, that is to say, the species Si may be reduced 
to zero. 
Similarly, near the axis of Xi 

_J = ! r J. (47) 

j~Y V K'Tf J ^ 

tt-A. 2 "- 2 ^Vwti. I ~~" ti2 



and hence an integral curve may cut through the XsXi, plane, thus 
reducing X 3 to zero. 

This observation is of practical interest. It has been pointed 
out that in sea fisheries the accompanying presence of a common 
fish may cause the extermination of a rarer species which, were 
it present alone, would be protected by its very scarcity, since this 
would make fishing unprofitable. But the more abundant fish 
continues to render a balance of profit from the trawling operations, 
and thus the rarer species, so long as any of it remains, is gathered 
in with the same net that is cast primarily for common species. 

Replaceable and Irreplaceable or Indispensable Components. The 
last two examples present an illustration of a point which calls 
for brief comment. So long as the species Sz has only one source 

jy 

of food, S i} it is to be observed that becomes negative as soon 

dt 



98 ELEMENTS OF PHYSICAL BIOLOGY 

as Xi is zero (see equation 40). In this sense Si is an essential 
component of the system, relatively to S, i.e., it is indispensable 
for the growth and even the mere continued existence of S. On 
the other hand, when two or more sources, such as Si and S s are 
provided, the vanishing of either Xi or X s singly does not bring 

j~y~ 

with it a negative value of . The components Si and $3 can 

more or less effectively replace, act as substitutes for, each other. 

When the feeding species ($ 2 in the example) is the human species, 
the facts indicated above find their expression in economic terms. 
It is an elementary fact of common knowledge that among the 
varied materials which the human race requires for its growth and 
sustenance are many that are more or less readily interchangeable. 
So, for example, a deficiency in the wheat crop may be in some 
degree met by increased supply of potatoes or other starchy food; 
or a deficiency in beef may be compensated by increased production 
in pork. On the other hand, there are certain requisites that are 
irreplaceable, and therefore absolutely essential. The most obvious 
example of such is our supply of oxygen. 

In terms of our general analysis these facts would be expressed 
somewhat as follows. If we survey the various components whose 
masses Xi,Xz . . . X n appear in the function FI 

= Fi (Xi, Xa, . . . -X" n ) 

at 

we may effect a classification by first of all dividing them into two 
classes, namely those that adversely affect the rate of growth of 
Xi, that is to say, those for which 

JL^< O 

dZj dt 
and those that promote the rate of growth of Xi, those for which 



dt 

Among the latter components, those favorable to the growth 
of X{, there is a special class distinguished by the following property : 

If X is the mass of a component of this special class, then 
dXi . 
~j7 is invariably negative as soon as X^ is zero, no matter what 



FUNDAMENTAL EQUATIONS OP KINETICS ~ 97 

may be the masses Xi, X , . . of the other components. Xk 
is indispensable for the growth and the sustenance of Xi] X& is 
an essential of irreplaceable component, relatively to Xi. 

The ground upon which we are here treading is evidently close 
to the biological basis of economics. A detailed analysis of -the 
relations involved belongs to the domain of the dynamics of life- 
bearing systems, and will in due course be considered in its natural 
place. 

Limiting Factors. In general the several components that promote 
the growth of the component of Si will be presented in varied abun- 
dance. If one essential component (or a group of components which 
jointly are essential) is presented in limited amount, any moderate 
increase or decrease in the ample supply of the other components 
will have little or no observable influence upon the rate" of growth 
Fi of Si. An essential component presented in limited supply thus 
acts as a check or brake, as a limiting factor, upon the growth of Si. 
The significance of such limiting factors seems to have been first 
pointed out by J. Liebig: 11 "Der Ertrag (des Bodens) ist von dem 
im minima in ihm enthaltenen Nahrstoff abhangig." And again : 

Fur die Wiederherstellung der Ertrage der durch die Cultur erschopften 
Felder durch Stallmistdiinguug ist die Zufuhr von alien den Nahrstoffen 
welche das Feld im tJberschuss enthalt, vollkommen gleichgiiltig, und es 
wirken nur diejenigen Bestandteile desselben gtinstig, durch. welche ein im 
Boden enstandener Mangel an einem oder zwei Nahrstoffen beseitigt wird. 

Limiting factors not only set certain bounds to the growth of the 
components to which they are thus related, but are competent 
also to give rise to the phenomenon of "moving equilibrium" the 
discussion of which is reserved for a later section dealing with 
equilibria generally, under the heading of Statics. 

This chapter may fittingly be concluded with table 6, which exhibits 
the principal modes of interdependence of biological species, and 
summarizes the analytical characters of these, as discussed above. 

11 J. Liebig, Die Chemie in ihrer Anwendung auf Agricultur, 1876, p. 334. 
See also ibid., pp. 332, 333, 381, 382. 



i-l 

o 





O *:? 


^5 5 




**< 

o 


O 




"^ S _ 


o 


.2 


N * S 


05 


" 


i "-< 'S i "o 


S* C! 


JS 


"o 


5 


S S "s - .E ^ 


02 S 


ft '5 


T3 


^ 


g 1 ^ ~ -Sfl 
^ i < i-< 








S 


O 








*. 

ft 


? 


OB 


r 5 4 


S3 




"2 

S"- 


I 


~C 


i ^3 a "P 
', T - > .2 o 




bp 

S 


- d ' 

^ "a '- 








53 "g >* '43 y > 


^ fc 'a 








^ 3 1 


m 


1 fcb ? 


*? 



O 

O 



Q! S s - 

i - .S 

ic "x ^ 'S 



H s 

? -p 



S -^ 

H C S2 

,? - 

Q -C T3 



-J g 

ft _ -i-i 



.9 .2 



T': 



.2 S 

v= ^3 



> 

'42 Ml 

o a 



T3 g fcO 



- " HI 

as 'S -*S 

1 S> 
& &o 



CQ - 

L.2 ^ 

' W cu 6 



fl ^ 



^3 tb ' 



ft CO fl 

5,'x 



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r-s 



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L.g ^ 



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L-i 



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lestruct 




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99 



CHAPTER IX 
ANALYSIS OF THE GROWTH FUNCTION 

Elegant intellects which despise the theory of quantity are but half devel- 
oped. A. N. Whitehead. 

The Form of the Growth Function F. The fundamental equations 
(1) of Chapter VI express in a very general, and for that reason 
somewhat colorless way, the interdependence of the several compo- 
nents of evolving systems of the kind here under discussion. * 

In the special cases with one, two and three dependent varial^teg 
that have been presented as examples, the particular form affif the ^&^ 
concrete meaning of the functions F appearing in these equations -* 
has been illustrated for these specific instances, without any attempt 
at systematization from a general standpoint. It is desirable now to 
make a somewhat detailed analysis of the functions F in their more 
general aspect. 

A natural step to take is, first of all, to split up the function F 
into a positive and a negative term; that is to say, to express the 
rate of increase of the mass Xi of the component & as the balance, 
the surplus, of the mass Ui added to that component per unit of 
time, over the mass Vi eliminated therefrom per unit of time. Thus 

dXi 

-~r t .i\-r t (i) 

Growth of Aggregates. Among the components of systems of 
the kind in which we are here mainly interested, a particularly 
important type are those built up of a large number of essentially 
similar units or individuals. Such are the aggregates of molecules 
that constitute the components (chemical elements and compounds) 
of the systems with which physical chemistry is concerned; such, 
also, are the aggregates of individual organisms that constitute 
the biological species, the component population groups, of which 
are built up the systems in which organic evolution takes its course. 

In the case of an aggregate of this kind, if N is the number of 
individuals, and m their average mass per head, we have 

100 



ANALYSIS OF GROWTH FUNCTION 101 

Xi = miNi (2) 

dXi dNi dnii . . 

= mi + N l - (3) 

If the average mass per individual, nii, is constant, the second term 
of the right hand member in (8) drops out, and we have simply, 



This holds strictly for aggregates of similar molecules, for example, 
whose masses are all equal and constant. It will often hold with 
close approximation (as will be set forth in greater detail shortly) 
for populations of living organisms of one species. 

dNi 
Now -J7 1 the rate of increase in numbers of the aggregate Si, 

naturally appears, after the manner indicated above, as the balance 
of the number of newly formed individuals Bi per unit of time, and 
the number Di eliminated per unit of time. When these symbols 
refer to a population of living organism, Bi is the (total) birth rate 
and D i the (total) death rate per unit of time. We have, then, 

f-^-A (5) 

at 

which it is often convenient to write 



at 

the lower case letters &, d denoting birth rate and death rate per 
head per unit of time. 

Combining (4) and (5) we have 

^-(Ifc-DOmi (7) 

at 

Demographic Functions. The quantities B, D, or 6, d lend 
themselves to further analysis in terms of more fundamental char- 
acteristics of the aggregate. In a qualitative way everyone is 
familiar with the manner of the elimination of individuals from a 
population by death: some are carried off in infancy, some in child- 



102 ELEMENTS OF PHYSICAL BIOLOGY 

hood, adolescence, and maturity, until the remnant is finally called 
in old age. Quantitatively this fact finds expression in an actu- 
arian's life table, or the corresponding life curve, of which some 
examples are shown in figures 15 to 17. Starting with some large 
number,, say a million, of newly born individuals, counted at birth, 
if we follow this sample batch of population through life, we find 
them thinning out, at first rather rapidly in infancy and child- 
hood (steep part of curve on left) : then more slowly (more gentle 
slope) in mid-life; and faster again as the natural term is approached. 
At any particular age a there are thus left, out of the original batch, 
a fraction p(a) of survivors. The fraction p(a), which we may speak 
of as the survival factor, 1 is a measure of the probability, at birth, 
that a random individual of the batch shall reach age a, under the 
conditions under which the data assembled in the life table were 
collected. The value of p(a) for every age of life depends, of course^" 
on the general conditions of life in the population. It therefore 
varies in different localities and at different epochs, as illustrated 
in figures 15, 16, 17. When it is desired to bring out the fact that p(a) 
depends on the time, it may be written p(a, f). But as a rule the 
change with time is not very rapid and we may often consider p(a) 
as a function of the age a alone. We shall do this in the present 
analysis^ which relates to a population in a selected locality under 
essentially constant conditions of life. 

If we denote by N a the survivors to age a, out of an original 
batch A r counted at birth, we have 

JV = N p(a) (8) 

We will -write 

dN a 



/1A\ 

\LO) 

' 



or 

dN a d 



> r , j 

N a da da 



The coefficient ju a thus defined is termed the force of mortality at 
age a. From its definition it is clear that it measures the death 
rate per head in a population composed entirely of individuals of 
age a. 

1 The function p (a) is that commonly denoted by l x in actuarial notation, 
p.nd tabulated in the principal column of a "Life Table," 



SSfSS] 



\ 



\ 



\ 



\ 



\ 



\ 



\ 




s.ooo 



70,000 



64,000 



FIG. 15. SOME HISTORICAL HUMAN SURVIVAL CURVES, EXHIBITING AN EVOLU- 
TIONARY TREND TOWARD LONGBB AVERAGE DURATION OF LIFE 
The improvement is probably rather one of general hygiene than of man's 
physiological constitution. The earlier figures are of very doubtful accuracy. 

103 



104 



ELEMENTS OF PHYSICAL BIOLOGY 



AGE IN YEARS 



65,000 



-45,000 

40,000 

35,000 
30,000 
25,000 
20/500 
15,000 
IO.OOO. 
5.000 



x: 



X 



4\ 



\ 




il 



60 70 



ASE IN YEARS 




30,000 
25,000 
2O.OOO 
I5.OOO 



FIG. 16. STJEVIVAI, CUEVES FOB THE STATE OF MASSACHUSETTS, FOB THE 
THBEE DECADES 1890-1900-1910. AFTEB GLOYEB 

The data on -which these curves are based are naturally more reliable than 
those of the older life tables shown in figure 14, and exhibit very clearly the 
upward trend of the average length of human life in recent decades. 



ANALYSIS OF GROWTH FUNCTION 



105 




AEE M YEAJIS 



FIG. 17. SURVIVAL CURVES FOE DIFFERENT COUNTRIES, SHOWING INFLUENCE 
OP LOCAL CONDITIONS UPON LENGTH OF HUMAN LIFE. AFTER GLOVER 

A particularly simple case is that in which \i a is independent of 
a, the force of mortality is independent of the age, or is the same at 
all ages, We then have by integration of (10) 



and 



p(a) 



(11) 
(12) 



106 ELEMENTS OF PHYSICAL BIOLOGY 

Such a simple life curve as this is not to be expected in a species 
of living organisms. It implies that the individual does not age, that 
his chance of living another year is just as good at ninety years of 
age as at fifty or at ten or at five; he can die, as it were, only by acci- 
dent; he is perpetually young. Survival curves of this form do 
occur and play a significant role in the aggregates of atoms and mole- 
cules which the chemist and the physicist make it their province 
to study. The atoms of an element in radioactive transforma- 
tion, for example, are picked off, one by one, according to a law of 
this form, and so are the molecules of a chemical compound decom- 
posing by a monomolecular reaction. If, in such a case, the plot 
the function p(a) is drawn on logarithmic paper, evidently a straight 
line is obtained, since 

log e p(a) = jua (13) 

(14) 



da 

The force of mortality is here seen as the (constant) slope of the 
curve representing log e p(a). 

In the more general case it is also often convenient to plot p(a) 
on a logarithmic scale. This has been done in figure 18 for the 
United States survival curve shown in figure 17. It is seen that the 
curve thus obtained is at first convex toward the axis of a, but soon 
becomes concave toward that axis and then remains so to the end. 
The significance of this is, of course, that the force of mortality 
is very high in infancy, decreases in early childhood, until it reaches 
a minimum about the twelfth year of life; and finally increases con- 
tinually to the end of the life span. 

The detailed analysis of the human survival curve is a matter 
of interest not only to the student of evolution, but also to the guard- 
ian of public health and to the insurer of human life, the actuarian. 
The essentially practical requirements of these has led to a highly 
developed technique, amounting virtuaUy to a separate branch of 
science, in the preparation and analysis of life tables. Of this phase 
of the subject no more needs to be said here, since there is a volumi- 
nous special literature available. Only the more strictly biological 
aspect of the matter is for us here of immediate interest, and of this 
more will be said later, in discussing the physical basis underlying 
the survival curve. 



ANALYSIS OF GROWTH FUNCTION 



107 



Survival Curve Data. Without having recourse to any refine- 
ments of mathematical analysis it is clear that a close relation exists 
between the survival curve of a given species and its rate of increase, 
its fate in the straggle for existence and for dominance. It might 



10,000 



/o 




K 



O -? 8 IS. 16 SO & S3 X 36 -fO 44 -fff .52 S6 60 64 68 7S 76 80 ff* 88 9 -36 /OO 

Ag<s in Years. 

FIG. 18. SURVIVAL CURVE PLOTTED ON LOGARITHMIC SCALE. 
UNITED STATES 1910 

The slope of the curve thus plotted measures the Force of Mortality, This 
slope is at first very steep, decreases to about the twelfth year of life, when it 
reaches a minimum (point of inflection), and then increases again continuously 
to the end of life. 

be expected, therefore, that the study of such survival curves for 
different species of organisms should have formed an essential part 
of quantitative studies in evolution. As a matter of fact, however, 
data for survival curves of organisms in their natural environment 



108 ELEMENTS OF PHYSICAL BIOLOGY 

are, for obvious reasons not easily obtained. It is difficult enough 
to make an accurate census of ages in a supposedly intelligent and 
responsible human community, where the cooperation of the Individ- 
ual can at least in a measure be engaged. A census of ages in the 
population of field, forest and stream must indeed be a severe test 
of the ingenuity of any investigator that should approach such an 
enterprise. Not that it is utterly hopeless. Isolated data can and 
have been gathered. Every layman knows that the age of trees, for 
example, can be estimated at least approximately by the number of 
rings in a cross section of the trunk. The age of certain fishes can be 
gaged from tell-tale marking on their scales. The age of certain birds 
can be told from their plumage. An estimate of the average age of 
herring gulls has been made, on this basis, by J. T. Nichols. 2 But 
data of this kind are at best scant. The problem is more manage- 
able in the case of domestic species, or of species in captivity. The 
most complete study of this character is probably the work of R. 
Pearl and S. L. Parker with colonies of fruit flies (Drosophila) 
grown in an experimental "universe," a glass bottle containing a 
suitable quantity of banana juice. 3 The survival curves thus ob- 
tained are singularly like those for the human species, when allow- 
ance is made for the difference in the total life span. The fruit 
fly's allotted days, in the most favorable case, number about ninety, 
or, say, one day for each year of human life. In figure 19 are shown, 
plotted on the same diagram, three survival curves; one of these is 
that of the human population of the United States in 1910; the 
second is the survival curve for one of the numerous varieties of 
fruit flies. 

Por only one other organism, Proales decipiens (a rotifer), a life 
table and curve has been prepared, on the basis of observations 
by B. Noyes. 4 The life curve has been computed by Pearl and Doe- 
ring 5 and compared with that of man, on the basis of the life span 

2 J. T. Nichols, in The Condor, vol. 17, 1915, p. 181; for other data on the 
longevity of animals see C. S. Minot, The Problem of Age, Growth and Death, 
1908, pp. 226, 266; A. Weismann, tJber die Dauer des Lebens, Jena, 1882. See 
also A. T. Masterman, Report on the scales of freshwater fish in relation to 
age determination. H. M. Stationery, Office 1924. 

3 R. Pearl and S. L. Parker, American Naturalist, vol. 55, 1921, p. 503; vol. 
56, 1922, p. 403. 

* B. Noyes, Jour. Exp. Zool., vol. 35, 1922, p. 225. 

* R. Pearl and C. R. Doering, Science, vol. 57, 1923, p. 211. 



ANALYSIS OF GHOWTH FUNCTION" 



109 



measured from the point at which, the force of mortality is a mimi- 
mura to the extreme end of life. It is the curves thus obtained that 
are shown in figure 19. As will be seen, they exhibit a close analogy. 




30 4O SO 60 70 

CENTILES OF LIFE SPAN 



8O 



90 



fOQ 



FIG. 19. LOGARITHMIC SURVIVAL CURVES FOR MAN, DROSOPHILA, AND 
PBOALES DECIPIENS 

Plotted according to centiles of life-span; the human life curve is plotted 
with the twelfth year of life (point of inflection, see figure 18) as zero of the 
time scale. After R. Pearl. 

Influence of Age Distribution Upon Rate of Growth of Population. 

For our present purposes it is not sufficient to fix our attention on a 
group of individuals at the moment of their birth, and to observe 
the gradual dirninution of this group by deaths; we must take in 



110 ELEMENTS OF PHYSICAL BIOLOGY 

view an actual population, comprising individuals of all ages, and 
we must enquire into the effect of deaths upon such a group as this. 
If the survival curve for such a population were of the simple 
form 

p(a) = e-v (12) 

with n, the force of mortality, independent of a, it is evident that 
the age distribution in the population would have no influence upon 
the total death rate. For if individuals of all ages are equally 
susceptible to death, it is evidently immaterial how the population 
is constituted as regards age. The death rate per head, in such a 
population would, in fact, be simply equal to the force of mortality. 
The Stable or "Normal" Age Distribution. But in the popula- 
tions with which the biologist and the vital statistitian deals, the 
force of mortality varies very decidedly with the age, and it might 
therefore be supposed that any discussion of the rate of increase of 
a population of organisms must fully take into account the age dis- 
tribution. This supposition, however, involves an assumption, 
namely, the assumption that the age distribution itself is variable. 
Now, in point of fact, the age distribution is indeed variable, but only 
within somewhat restricted limits. Certain age distributions will 
practically never occur, and if by arbitrary interference, or by a 
castastrophe of nature, some altogether unusual form were impressed 
upon the age distribution of an isolated population, the "irregu- 
larities'"'' would tend shortly to become smoothed over. There is, 
in fact a certain stable type of age distribution about which the act- 
ual age distribution varies, and toward which it returns if through 
any agency disturbed therefrom. 5 The form of this distribution, 
in an isolated population (i.e., with immigration and emigration 
negligible) is easily deduced, as follows: 

If we denote by N (f) the total number of the population at time 
t, and by N ($) c(\a} da that fraction of the total whose age is com- 
prised, at time t, within the limits a and a + da, it is evident that 
the individuals of this element of the population are the survivors 
of the B(t-a)da persons born at times (<-o). Hence if p(a) 
is the survival factor, we have 

s For a formal proof of this see F. R. Sharpe and A. J. Lotka, Phil. Mag., 
April, 1911, p. 435; A. J. Lotka, Proc. Natl. Acad., vol. 8, 1922, p. 339. 



ANALYSIS OF GKOWTH FUNCTION 111 

B (t - o) p(o) da = tfft) c(o) da (15) 



If we denote by D (t) the total death rate at time t, we have, evi- 

dently 

'*' (17) 



We are supposing that we are dealing with a population in which 
the survival factor is constant, i.e., independent of t. If c(a) also is 
independent of tf, the integral in (17) is evidently a constant and 
we have 



. ) = const. = d (18) 

where d is the death rate per head. 
On the other hand, since c(w) is independent of the time, we have 

c(0) = const. = b (19) 

Brief reflection shows that the value of c(o) for zero age is the birth 
rate per head. Thus we have 

6 d = r - const. (20) 

where r is the "natural rate of increase" of the population. 
We have further 

B(t - a} = bN(t - a) (21) 

= bN(tie~ ra (22) 

since the natural rate of increase r is constant. Thus by (16) 

c(a) = be- fa p(a) (28) 

The normal age distribution (23) is of fixed form in th'e sense 
that, once established, it perpetuates itself. More tlikn this it is 
also > stable > in the sense that, if disturbed by a temporary change 
m the conditions of life (e.g., war), it will spontaneously return upon 
restoration of normal conditions. 



112 ELEMENTS OF PHYSICAL BIOLOGY 

A rigorous proof of this stability of the age distribution (23) 
cannot be briefly given, and for details of such proof the reader must 
be referred to the author's publications in the journal literature. 8 
The general character of the proof may, however, be indicated. 
If the original population has any arbitrary age distribution, such 
as that represented by the more heavily drawn curve in figure 20 
by judicious trimming we could reduce the population to the nor- 
mal distribution represented by the lower curve tangent to the heavy 
curve; or, we could, by filling in gaps, supplement the population 
to fit the upper tangent normal distribution curve. The trimmed 
down population, having the normal age distribution, would always 
retain it. The same is true of the supplemented population. The 
actual population will therefore always lie between the trimmed and 
the supplemented. Moreover, it can be shown that at intervals 
of about one hundred years (the span of life) new tangent curves can 
be drawn to the actual distribution curve, the new tangents lying 
between the old. Thus the two tangent curves ultimately approach 
until they coincide, and then, necessarily, the actual distribution 
curve lying between them coincides with them also. That is to 
say, the actual conforms with the normal age distribution. 7 

It must be understood that the normal or stable form of age dis- 
tribution represents merely a broad type, toward which actual 
age distributions will tend. However, the approach seems to be 
at times very close, as is shown by the figures in table 7 giving the 
observed and the calculated age distribution for England and Wales 
in decennium 1871-1880. A graphic representation appears in 
figure 21, which shows the observational data, plotted (in dotted 
lines) as a stepped curve. The corresponding figures calculated by 
the formula (13) are plotted in two ways, namely, first as a stepped 
curve (drawn in full), for comparison with the observational data; 
and also as a continuous curve. The latter brings out a feature that 
may be noted in passing, namely the fact that the curve of age dis- 
tribution is very flat, roughly linear, over a wide range, from the 

7 An exceedingly interesting effort of early date to demonstrate the ulti- 
mate approach to geometric increase of the birthrate, independently of initial 
conditions (e.g. starting with a single pair of parents) is to be found in 
L. Euler, Recherches g6n<rales sur la mortalite". See also E. T. Gumbel, 
Jahresber. Deutsch Math, verein., vol. 25, p. 251. 



ANALYSIS OF GROWTH FUNCTION 



113 




FIG. 20. DIAGRAMS TO ILLUSTRATE PROOF OP STABILITY OF NORMAL AGE 

DISTRIBUTION 

Reproduced from A. J. Lotka, Proc. Natl. Acad. Sci. ; vol. 8, 1922, p. 339 



TABLE 7 

Population of England and Wales 1871-1880, as an example of "normal" age 

distribution 



a- 1 , o 


MALES 


FEMALES 


PERSONS 




Calculated 


Observed 


Calculated 


Observed 


Calculated 


Observed 


0-5 


142 


139 


135 


132 


138 


136 


5-10 


118 


123 


114 


117 


116 


120 


10-15 


107 


110 


104 


104 


106 


107 


15-20 


9S 


99 


95 


95 


96 


97 


20-25 


88 


87 


86 


91 


87 


89 


25-35 


150 


144 


148 


149 


149 


147 


35-45 


117 


112 


117 


115 


117 


113 


45-55 


84 


84 


87 


87 


86 


86 


55-65 


57 


59 


63 


61 


60 


59 


65-75 


29 


31 


36 


35 


32 


33 


75- co 


11 


12 


13 


15 


12 


13 




1,001 


1,000 


998 


1,001 


999 


1,001 



114 



ELEMENTS OP PHYSICAL BIOLOGY 



Si, 



.C3S 

30 

.028 

.026 

.OSf 

.022 

420 

,0/8 

.0/6 

.O/-f 

MS 

.010 

.008 

.006 

.OO$ 

.002 

.OOO 



\ 

^ 



.-=. 03373 &- 



10 -30 



-50 60 70 SO SO /<> 

a = age, 

FIG. 21. "STABLE" AGE DISTRIBUTION, AS EXEMPLIFIED BY THE POPULATION 
OF ENGLAND AND WALES IN THE DECADE 1871-1880 



I IK 

ANALYSIS OF GHOWTH FUNCTION 1JLtJ 

fifth to the eightieth year of life. 5 This, of course, is a special fea- 
ture of a human population when the natural rate of increase r 
lies in the neighborhood of a certain value. 

Minor fluctuations of the age distribution will not greatly affect 
the birth rate and the death rate. Since actual populations approxi- 
mate the normal age distribution, i.e., that defined by equation (23), 
it seems permissible and it is certainly expedient to assume, in further 
discussion, that the normal age distribution is actually established; 
we may then virtually disregard the influence of the age distribu- 
tion upon the rate of increase of the component. This element is, 

as it were, automatically ruled out of further discussion, by the nat- 
ural establishment of the normal age distribution; 9 a circumstance 
which is in so far fortunate, as we are here interested in the relation 
of the rate of growth to the more fundamental biological character- 
istics; the age-distribution appearing merely as an adventitious 
element complicating the relation, without being essential to the 
fundamental characterization of the species. 

Demographic Relations in "Normal" Population, It is worth 
while to note briefly in passing that in the case of a population in 
normal age distribution, many demographic relations assume a 
simple form. So, for example, the relation between birth rate per 
head 6 and death rate per head d is here given by the formula 10 



1/b = g-rp( ) d (25) 

Jo 

which, to second order approximation, is reducible to the simple 
form 

1 - U U 

__ __ + j=*L (26) 

where L is the mean length of life, defined as 

Compare J. Brownlee, The Use of Death Rates as a Measure of Hygienic 
Conditions, Report to Medical Research Council, London, 1922, pp 36-37 
8 Of. G. Eijkman, Onthr " J.--.-TTI .. .. ~ . >j.r- 

!, p. 269; 



10 A. J. Lotka, Quart. Publ. Am. Statist. Assoc., 1918, p. 121; 1921, p. 998. 



116 ELEMENTS OF PHYSICAL BIOLOGY 

Ceo 
p(a) da (27) 

while U is defined 11 by 

/"6co 

L ' = ap(a) da (28) 

<Jo 

L' 
U = Z"' (29) 

As an illustration it may be mentioned that in the saniv, population 
(England and Wales, 1871-1880) which as already been referred 
to, the relation (26) is found by actual computation to be, numerically 

0.767 0.233 

___ + ___ = 41 _3 5 ( ma i es ) ^ 

0.7369 0.2G31 

. _ -- j -- . _ 44,62 (females) (31) 

Oi 

The observed values of 6 and d, together with those computed by 
the formulae (22), (23), are shown in table 8. It will be seen that 
the agreement is good. 

The relation (26) between b and d lends itself readily to graphic 
representation by means of a diagram involving only straight lines. 
This is shown in figure 22. The method is as follows. 

_ r 
Along OX mark off a length OP = 



L 

U 

Along OY mark off a length OQ == 

L 

Complete the rectangle QOPM. 
Suppose we are now given 

6 - 0.0337 
It is required to find d 

Along OX mark off 0V = 0.0337 

Join VM and produce it to meet OY in W 

Read off at W on the scale of OY 

d = 0.0200 



11 U is proper fraction. It then follows from (26) that L is intermediate 

, 1,1 

between - and -; this circumstance has been noted by Bortkewitch, Mitt- 

lere-Lebensdauer. 



ANALYSIS OF GROWTH FUNCTION 



117 



A single equation, such as (25), connecting the two quantities 
b and d, is of course insufficient to determine their value. To do 
this requires a second independent relation. Such a relation Is 
furnished by the following considerations: 

The law of the fixed age distribution holds separately for each 
Thus, if we denote JV/ the total number of the female popula- 



sex. 



TABLE 8 





(OBSEBVED) 


d 
(OBSERVED) 


d 
(COMPUTED) 


Males 


0.036921 


0.022612 


0.02221 


Fe n ioles 


0.033727 


020001 


0.02000 












b-,0337 



.008 .016 

b Bir1~h rafs pe.r head per annum. 

FIG. 22. DIAGRAM OF RELATION BETWEEN BIRTH RATE PER HEAD 6 AND 

DEATH RATE PEE HEAD d IN POPULATION WITH STABLE 

AGE DISTRIBUTION 

tion } by 6/ the number of female births per unit of time and per head 
of female population, and finally by pj- (a) the survival factor in the 
female population, then the number of females of an age between 
a and a + da is given by Njbje~ n p f (a) da. If these reproduce, on 
an average, 0/ (a,) females per unit of time, then the total number of 
female births per unit of time is evidently given by 



118 ELEMENTS OF PHYSICAL BIOLOGY 



C a 

I 

t/oi 



( 32 ) 



where a i} a are the lower and upper age limits of the female repro- 
duction period. But Nfy- = B f ; hence 



(a)8 f (a} da (34) 

This is the required second relation 12 between 6 and d. The birth 
rate and death rate in a population of fixed age distribution are 
thus completely determined as soon as the functions p f (a) and 
/?/ (a) are given. 

Aside from its direct interest as the second relation required to 
complete the determination of 5 and d in a population with fixed age 
distribution, equation (34) is also of value in enabling us to deduce 
certain secondary results, of which two will here be noted. 

Rate of Increase per Generation. To derive our first conclusion 
from (25), we expand e~ ra under the integral sign. We find 



1 = /3(o) p(o) da - r aj8(a) p(a) da + ... 35 

t/oj Jai 

A. little reflection shows that the first integral measures the ratio 
between the total number of births in two successive generations. 
Denoting this by R, and the second integral by S, we have 

22 = 1 + rS - . . . (36) 

a formula wjhich connects the rate of increase per head per annum 
r and the rate of increase R in the total number of births in one 
generation, per generation. It will be seen that this relation is 
not one that could very well be foretold by any simple elementary 
or common sense principle. It is this relation that is implicitly 
involved in W. R. Thompson's treatment of a problem in parasitol- 
ogy cited in Chapter VIII (page 87) ; at least, we must know this 
relation if we are to interpret his results in terms of the usual tune 
unit, such as the year, whereas Thompson reckons in generations. 

13 A. J. Lotka, Jour. Washington Acad. Sci., 1913, p. 293. 



ANALYSIS OF GROWTH FUNCTION 



119 



Effect of Selective Slaughtering. A second deduction from equa- 
tion ',34} follows from the fact that the integral extends only between 
the age limits of the reproductive period. In consequence of this 
the rate of increase, per head, of the population is independent of 
the form of the life curve (the survival factor) outside this period; 
thus the slaughtering of the "superannuated" members of a herd 
has no effect upon its rate of increase, though both death rate and 
birth rate are augmented (by equal amounts). 12 The economic 
significance of this, as a means for raising the productive capacity 
of the herd, considered as a food factory, is serf-evident. 

It is true, as previously noted, that generally the influence of 
age distribution upon the rate of growth of a species is eliminated 
from discussion by the spontaneous establishment of the fixed or 
normal distribution. But the subject referred to in the preceding 
paragraph clearly shows that there are exceptions to this general 
rule. We have here an instructive example in which the influence 
of the age distribution upon the course of events is so fundamental 
that a discussion of the case which should fail to cover this feature 
would be lacking in an essential particular. Indiscriminate killing 
of one species by another, as practised by the untutored savage or 
the dumb animals, has the effect of reducing the ordinates of the life 
curve of the food species more or less along its whole extent. This 
is illustrated in figure 23. We may suppose that the life curve of 
some species, wild cattle, for example, is that shown in a full line, 
curve I, and that curve II represents the life curve for the same species 
after the habitat of the species has been invaded by a tribe of primi- 
tive hunters, too thoughtless or too unintelligent to regulate their 
depredations in accordance with anything of the nature of game laws. 
Curve III is the type of curve that would be produced by selective 
killing guided by intelligent control, as distinguished from random 
lolling. The verticals erected at a\ and a 2 represent the limits of 
the period of reproduction for the cattle. The slaughtering, in the 
case of curve III, takes place exclusively after the end of the period 
of reproduction. This is an extreme case, which, in practice, for 
obvious reasons, would be only distantly approached. For both 
in game preservation and in animal husbandry on the farm many 
factors have to be considered; not only the quality of the meat of 
animals at different ages, but the cost of raising and maintenance. 
It is out of the question to restrict the slaughtering to the post- 



120 



ELEMENTS OF PHYSICAL BIOLOGY 



reproductive period. The unnecessary male may, in fact, be slaugh- 
tered as soon as the cost of his upkeep exceeds the corresponding gain 
hi marketable value of his carcass. Just what is the most advantage- 
ous tune for his slaughter is a question in agricultural economics which 
has been discussed, among others by A. Gouin and P. Andouard. 13 
These authors compute that to bring up three calves, from weaning 
to the age of three and one-half years, requires about 33,000 kgm. 
of hay (or their equivalent); this quantity would suffice to bring 




FIG. 23. DIAGRAMMATIC ILLUSTRATION OF INFLUENCE OF RANDOM AND OP 
SF.LECTIVE SLAUGHTERING UPON SURVIVAL CURVE OF BIOLOGICAL SPECIES 

seven head of cattle to the end of their second year, which would 
give a gain, in meat, of 40 per cent, as compared with three head 
brought to the age of three and one-half years. 

Intelligence as a Discriminating Agency. It is particularly worth 
while to note how in this connection human intelligence exerts 
its influence upon the course of physical events by substituting 
systematic selection in the place of the more haphazard, more ran- 
dom actions characteristic of the mentally less developed species. 

13 Bull. Soc. Natl. d' Agriculture, Paris, 1910, p. 695. 



ANALYSIS OF GROWTH FUNCTION 121 

These latter must. In many ways, remain, dependent upon certain 
average manifestation, whereas man, in a corresponding situation, 
is able to discriminate and address himself directly to individual 
elements of which these averages are the expression in the gross. 
In the manifold interactions on a macroscopic scale that consti- 
tute the perennial struggle for existence on nature's battlefield, 
the lower organisms are in many respects situated in a position 
analogous to man's relation toward the ultra-microscopic elements 
of his environment, the molecules and atoms. These he can handle 
only in bulk, unable to avail himself of the distinctive features of 
this or that particular atom or molecule. 

Just as our senses and our bodily members are inadequate for 
the task of handling individual atoms, so the mental or other dis- 
criminating powers of the lower organism are often inadequate to 
lead it toward any other than a rather random selection, and by 
no means an optimum selection, among the somewhat varied oppor- 
tunities of self-service presented to it. 

However, though man does far excel the other creatures in this 
respect, the difference is, after all, one in degree and not in kind. 
Many, if not all organisms, possess in some degree the power of selec- 
tion, are in some measure independent of pure haphazard. This 
introduces an altogether peculiar complication into the dynamics 
of systems comprising living organisms, a complication of which the 
statistical dynamics of molecular physics are free. Not only 
is the living organism capable of performing, on a macroscopic 
scale, exploits analogous to those which in the world of molecules 
are permitted only to such figments of the imagination as Maxwell's 
demon; but this power of "cheating chance," as it were, is 
possessed in different degree by the several living organisms, 
and a dynamics of systems comprising living matter must necessarily 
take account not only of this faculty, but of the gradations in this 
faculty which have a large part in assigning to the several biological 
species their place in the scale of evolution. This will require the 
development of special methods. It is essential that we bear in mind 
constantly the ultimate aim of our reflections. The transformations 
of matter, the change in its distribution among the components of 
the physical system in the course of evolution, are the first to strike 
the eye, and are properly the first to receive our systematic considera- 
tion, just because they are of more obvious and elementary character. 



122 ELEMENTS OF PHYSICAL BIOLOGY 

But our fundamental aim must ultimately be to gain an enlarged 
understanding of the dynamic relation involved, of the play of forces, 
the transformations of energy, 

Kinetics of Intra-Group Evolution. It is not intended to attempt 
here a systematic discussion in any sense exhaustive of the course of 
events in ultra-group evolution, that is to say, in the redistribution 
of matter among the several sub-types of which a biological species 
is composed. We shall however briefly note an enterprise, led more 
particularly by J. B. S. Haldane/ 4 to investigate the trend of 
evolution in a population in which selection is operating upon a 
character subject to Mendelian inheritance. 

Casel. Haldane considers first of all the simple case of a species of constant 
total population, consisting of two types (phenotypes) A and B that do not 
interbreed, but react upon each other merely through competition in the same 
environment. 

Haldane treats the case as follows : 

Let the nth generation, counted immediately after fertilization, 15 consist of 
types A and B in the ratio u a : 1, and let the coefficient of selection be k, i.e., 
let (1fc) of B survive (to breeding age) 16 for every one of A. Then the sur- 
vivors (to breeding age) of the nth generation, and hence the first numbers 17 
of the (n-j-l)th, will be in the ratio 



14 J. B. S. Haldane, Trans. Cambridge Phil. Soc., January, 1924, vol. xxiii, 
pp. 19-41. Part II, read July 14, 1924, has not yet reached the author. 

15 The words in italics are here added to Haldane 's text, in accordance with 
the first paragraph of his paper, page 20. 

18 The words in italics are here added to Haldane's text, in accordance with 
his paper, page 23, line 6. 

17 The meaning of this term is not altogether clear. It seems to refer to the 
total births in the (n + l)th generation, or, in other words, to the (n+l)th 
generation, counted at birth. This does not seem altogether consistent with 
the rest of the argument, notably the wording referred to in footnote 15. On 
the other hand the terms referred to in footnote 16 are vague unless reproduc- 
tion takes place once and once only in the life of the individual, since in general 
there is not only one single age of reproduction, so that the fraction surviving 
to breed cannot be represented by any single number. It seems that it would 
be better to base the argument on the total number born in each generation, 
i.e., on the generation, counted at birth; and to regard the ratio R between 
the births in two successive generations as a function of /3 (a) and p (a), as set 
forth in Chapter VIII equation (24) and Chapter IX equations (35), (36). We 
would then start with equation (38) of page 123 as a fundamental assump- 
tion; beyond this the argument would remain essentially unchanged. 



ANALYSIS OF GROWTH FUNCTION 123 

w n :l-A = Un + i:l (37) 

Ua + i "rr& (38) 

If u be the original ratio of A:B in the Oth generation, then 

u a = (1 - Ar)- n o (39) 

If we write yn. for the proportion of 2?'s to the total population of A and 

B in the nth generation, then 

(40) 



1 -f u n 1 4- (1 k)~ n u 

* = y + (1 _ ^1, (1 _ y o) ^^ 

If we start with an equal number of births of A and B 

2/o = i (43) 

1 



i i f~t 7.^1 n 
1 -f- (I K) 

If h is very small, i.e., if selection is very slow, then approximately 

1 



(44) 



(45) 



fc n = log ^ (46) 

Vn 

In equation (45) we recognize once more the Verhulst-Pearl relation. It 
is seen that in the circumstances to which the discussion relates, the better 
adapted of the two types grows, along the typical S-shaped curve, at the ex- 
pense of the less well adapted, ultimately displacing it entirely. This is quite 
in accord with what we should expect, since the total population A + B is 
constant, that is to say, it just holding its own. Any constituent of the popu- 
lation that falls below the average in adaptation, must therefore be unable to 
hold its own, and diminishes continually. 

The curve representing graphically the change of the population increase 
of type A at the expense of B, which is ultimately displaced entirely is shown 
in figure 24 for the case k = 0.001, i.e., that 999 B's survive to reproduce, 
for every 1000 A's. In these circumstances 9184 generations are needed for 
the proportion of A'B to increase from 1 per cent to 99 per cent. 



124 



ELEMENTS OF PHYSICAL BIOLOGY 



Case 2. Selection of a Simple Mendelian Character, with intermingling 
of dominant and recessive type. Kaldane next takes the following case: 

Consider the case of a population containing two, one, or no "doses" of a 
completely dominant Mendelian factor A. Mating is at random and selection 
acts in equal degree in both sexes upon the character produced by the factor. 
Pearson 18 and Hardy 19 have shown that in a population mating at random, 
the square of the number of lieterozygotes is four times the product of the 
numbers of the two iiomozygous classes. Let u n A. : la be the proportion of the 
types of gametes produced in the (n 1) <A generation. Then in the nth gen- 
eration the initial proportion of the two classes of zygotes will be 



:2u n Aa:la 



(47) 



iGOr 



A 



-5COO 



+5000 



FIG. 24. GROWTH OP FAVOHED TYPE IN MIXED POPULATION OF 
Two PHBNOTYPES 

Constant total population. Abscissae = number of generations; ordinates 
= percentage of favored type in total population. After J. B. S. Haldane. 



The proportion of recessives to the whole population is 



(48) 



Now only (1 k) of the recessives survive to breed, so that the survivors 
are in the proportion 



a Aa: (1 k) aa 



(49) 



18 K. Pearson, Phil. Trans. Boy. Soc., 1904, A 203, p. 53. 
18 G. H. Hardy. Science, 1908, vol. 28, p. 49. 



ANALYSIS OF GROWTH FUNCTION 125 

The numbers of the next generation can most easily be calculated from the 
new gai:;etic ratio iir~ i. This is immediately obvious in the case of aquatic 
orga-uisfiia 7,iio shed their gametes into the water. If each zygote produces IV 
giiiietes v/aieh conjugate, the numbers of gametes of type A and a respectively, 

are. clearly. 

CVtin 2 T A r w) A and (Nu a + N { 1 - k } )o (50) 

so thut 

(51) 



1 + n /C 

Xow if vre know the original proportion of recessives y , we start with a 

population 

u -AA:2uoAa:!Aa (52) 

where 

^o = y ~* - 1 (53) 

and we can at once calculate 



1 + MO & 

and thence u^ and so on. 

For complete selection we have k = 1 (recessives all die). Then 



n = n + M (56) 

t/ n = y (l+ W y J)-2 (57) 

If we start with a population containing J recessives, the second generation 

will contain the third ^, the nth - Thus 999 generations will be 

(n + IP 

required to reduce the proportion to 1: 1,000,000, and we need not wonder that 
recessive sports still occur in most of our domestic breed of animals. 
When selection is not very intense, we can proceed as follows : 



(58) 

(59) 



126 ELEMENTS OP PHYSICAL BIOLOGY 

When k is small 



(60) 



100 



I 

K, 

5 




= u a u + log 



(61) 



(62) 



(63) 



1 



7 



-5000 

Generations. 



+5QOQ 



10000 



FIG. 25. EFFECT OP SELECTION ON POPTJLATION COMPRISING Two PHENOTYPES 
WITH MENBELIAN INHEEITANCE 

Upper curve, dominants favored; lower curve, recessives favored. Abscissae 
= generations; ordinates = percentage of population with the favored char- 
acter. After J. B. S. Haldane. 

If we start from a population containing 25 per cent recessives U Q = 1, 
kn = n + iogen - 1 (64) 

In figure 25 is shown the growth curve for the dominants when k 4- 0.001 
(upper curve) and for the recessives when k = 0.001 (lower curve), i.e., 
the favored type has an advantage of 1 in 1000, as in figure 24. In each case 
16,582 generations are required to increase the proportion of the favored type 



ANALYSIS OF GROWTH FUNCTION 127 

front 1 per cent to 99 per cent, but dominants increase more rapidly than reces- 
sives when they are few, and more slowly when they are numerous. The change 
occurs mci=t rapidly when y a , the proportion of recessives to the total popu- 



Haldane deals also with several other cases, for the details of 
which the reader must be referred to the original. A continuation 
of Haldane's article is anticipated at the time of this writing. 



CHAPTER X 
FURTHER ANALYSIS OF THE GROWTH FUNCTION F 

We fat all creatures else to fat us, and we fat ourselves for maggots. 
Shakespeare, 

Adjustment of Birth Rate to Optimum. In the preceding dis- 
cussion of the equations (25) and (34) of chapter IX it has been 
supposed that the form not only of p(a), but also of /3(a), the rate of 
procreation at different ages, is fixed. It is only on this supposition 
that the two equations (25) and (34) of Chapter IX together deter- 
mine both 6 and d. In point of fact the function (3 (a) is undoubtedly, 
for most species of organsms, very elastic (much more so than p(a), 
the survival factor), and capable of adapting itself to varying cir- 
cumstances. This is especially so in the case of man, who exhibits 
in particularly high degree the rather astonishing phenomenon of 
a portion of matter whose growth is at least partially under the con- 
trol of a will in some manner associated with it. But, in the organic 
world at large alsoj there is presumably at least some tendency for 
the adjustment of the procreation factor so to take place as to make 
the rate of increase r a maximum under the existing conditions. 
Too high a procreation factor would lead to excessive sacrifices in 
progeny that could not be raised to maturity, and would increase 
the death rate more than the birth rate. On the other hand too 
small a procreation factor would obviously fail to give the maximum 
attainable rate of increase. Somewhere between the two extremes 
a certain optimum procreation factor will make r a maximum. 
From this point of view the two relations that effectively determine 
the actual values of the two variables 6 and d are 

i f*<o 

-= I e -ra( a ) d a (l) 

and 

r = maximum compatible with 



e~ ra {$(a} p(a) da 
128 



(2) 



ANALYSIS OF GROWTH FUNCTION 129 

The view that the rate of procreation thus expands or contracts 
in sympathy with the expanding or contracting food supply (or 
economic conditions generally) has been developed in detail (for 
the human species) by R. Lascaux in his work La Production et la 
Population (1921), That some such adjustment occurs with many 
biological species is a very plausible, one might say an inevitable 
supposition; but the approach to the ideal optimum is probably 
often only very imperfect, if only because the nature of the case calls 
for a large "factor of safety."'' 

In any event it is true that the birth rate does not play so unquali- 
fiedly a dominant role in determining the rate of growth of a species 
as might appear on cursory reflection. The equation (5) of Chap- 
ter IX, expressing the rate of growth of the species in terms of the 
birth rate and death rate, while it renders correctly the quantitative 
relations to which it refers, is only a partial or one-sided representa- 
tion of the facts, and is even open to misinterpretation. Incau- 
tiously construed it might be taken to imply that growth of an aggre- 
gate of living organisms takes place by births of new individuals into 
the aggregate. This, of course, is not the case. The new material 
enters the aggregate in another way, namely in the form of food con- 
sumed by the existing organisms. Births and the preliminaries of 
procreation do not in themselves add anything to the aggregate, but 
are merely of directing or catalyzing influences, initiating growth, and 
guiding material into so many avenues of entrance (mouths) of the 
aggregate, provided that the requisite food supplies are presented, 
provided that the system is, in a sense, "supersaturated" with 
regard to the species seeking to grow therein. The final result 
may not depend very greatly on the number of births, somewhat 
as the final state of a crystallizing solution is independent of the 
number of crystal germs initially sown therein. 

It will be desirable to develop our analysis in such manner as 
to bring out the relations thus involved. 

Aggregates of Constant Units. In aggregates of a simpler kind, as 
presented to our view in ordinary physico-chemical systems, each 
individual unit retains its identical substance unchanged throughout 
its period of existence as such unit. So, for example, a molecule of 
water consists of two particular atoms of hydrogen united to one 
specific atom of oxygen; and these same atoms continue to exist 
together as the building stones of the molecule as long as this con- 
tinues in existence as a water molecule. 



130 ELEMENTS OF PHYSICAL BIOLOGY 

In these circumstances the mass of each unit is obviously constant 
throughout its period of existence as such: and furthermore, addition 
to the component, or elimination therefrom, can take place only by 
the actual entry or departure of a complete unit. If, therefore, the 
mass of each unit is rtii, and if Bi new units are added to the aggre- 
gate per unit of time, while Dj are eliminated, we have, in this case, 
very simply, 

^=(Bi->i)mi (3) 

at 

Aggregates of Variable Units. For aggregates of living organisms 
we can also write an equation identical in form with (3), as has 
already been noted in Chapter IX; Bi is in this case the total birth 
rate, DI the total death rate, and m^ the average mass per head of the 
living population. But this is an inadequate representation of the 
significant facts. The equation, thus written, glosses over certain 
important characteristics of living organisms. Unlike molecules in a 
system in the course of chemical transformation, each unit in an 
aggregate of living organisms does not retain its substance unchanged 
in identity or in total mass. In fact, each unit is itself an aggregate 
within the larger aggregate that constitutes the species or biological 
group, and for each individual unit (organism) separately we can 
write an equation analogous to equation (1) of Chapter IX 



where U'i is the total mass taken up (ingested) per unit of time by the 
unit organism, and Vi is the total mass eliminated therefrom per unit 
of time. So, for example, in the course of one year a boy ten years 
old and weighing 32.5 kgm. may consume about 600 kgm. of food 
(inclusive of water and oxygen), may eliminate about 599 kgm of 
wastes, and will grow in actual mass by about 1 kgm., so that we have 

~ = 600 - 599 = 1 = O.OSmi (5) 

at 

The Stream of Substance Through, the Form of the Organism. 

It will be observed that a portion of the intake, but a portion only, is 
expended in adding to the total mass of the unit. The remainder 



ANALYSIS OF GROWTH FUNCTION 131 

B,-17',-^ (6) 

at 

is expended without, apparently, 1 - any resulting increase in the total 
mass of the unit. This constant expenditure of substance, and the 
equally constant intake required to balance it, is a fundamental char- 
acteristic of the units here under discussion. In the adult, whose 
mass is (on an average) approximately constant, we have simply 



and the entire intake goes to meet the requirements of maintaining 
the mass of the unit at constant level. 2 

Turning now from the consideration of the individual unit to that 
of the aggregate of N such units, evidently, if the average intake per 
unit of time per individual is U'i, and if the average elimination is 
Vi, then we shall have for the rate of increase of the total mass Xi of 
the aggregate. 

cLTi _ 

= NU'i- NV'i - Nm'idi (9) 

at 

where di is the death rate per head per unit of time and m'i is the aver- 
age mass of a unit (organism) at death. 

Two Types of Organisms: Economical and Lavish Birth Rate. 
The relative importance of the second and the third term in the right 
hand member of the equation (9) differs greatly in different biologi- 
cal species. At the one extreme we have a type of which perhaps the 
most characteristic representative is man. With a mean length 
of life of about fifty years, his body must be replaced about twice 
in a century to maintain the population equilibrium. If we assume 
(as a rough but sufficient approximation) that the average weight of 
man at death is 50 kgm., this means that the third term, 



1 Indirectly a part of the excess Ri of the mass intake over the mass increase 
may contribute to that increase, namely by furnishing some of the energy re- 
quired for anabolism. But we are here discussing mass relations only. The 
energy relations are reserved for separate consideration later. 

- Except during gestation, if the mass of the fetus is reckoned in with that 
of the mother. 



132 ELEMENTS OF PHYSICAL BIOLOGY 

vy 50 

in a stationary population, is about ^p kgrn. for the entire popu- 

ou 

lation, or just about 1 kgm., or say 2 pounds per head per annum. To 
put it crudely, of the food consumed by each human individual in a 
year, 2 pounds go, on an average, to replace the bodies of his fellows 
departed that year. This, it will be seen, is an insignificant, almost 
wholly negligible fraction of the 1000 pounds 3 or more than he con- 
sumes, in all, in a year. Of the total food consumed by the human 
race, then, about 0.2 per cent 3 goes to replace the bodies eliminated 
by death. The remainder is for current maintenance of the living. 
And the total food consumption 3 may be of the order of 7 to 10 times 
the mass of the population per annum. 4 

But, as already stated, man represents an extreme type, the ex- 
treme economy of life, with low death rate and correspondingly low 
birth rate. Of the opposite extreme, lavish, seemingly wasteful 
extravagance, examples are exceedingly common, though it may not 
be easy to give full quantitative detail. Among the most wasteful 
breeders are, no doubt many aquatic species, including fish, since 
their young are ill protected and become ready victims of other 
species. So a ling weighing 54 pounds was found to be carrying 
twenty-eight million eggs. 5 An oyster may have sixty million eggs. 
But some familiar land animals are prolific enough, even if they do 
fall far behind the standards just exemplified. The brown rat may 
have five or six litters averaging about eight or ten each, in a year. 6 

Domestic Animals Kept for Produce. Accurate figures can be 
obtained in case of domestic animals. While these do not represent 
so extreme an example, a special interest attaches to them owing to 
their direct relation to human food economics. The most prolific 
among domestic animals is the pig. In reasonably good farm con- 
ditions a sow should average three litters in two years, each of seven 
farrows, of which five are successfully raised and marketed. 

Even with the high mortality artificially induced by man in his do- 
mestic stock the item of running expenditure in feed for mere main- 
tenance is far in excess of the replacement cost, that is to say, the feed 

3 Exclusive of oxygen. 

4 For quantitative data on growth in man see C. S. Minot, The Problem of 
Age, Growth and Death. 

6 J. A. Thomson, The Wonders of Life, 1914, p. 130. 
s H. H. Donaldson, The Rat, 1915, p. 190. 



ANALYSIS OF GROWTH FUNCTION 



133 



stored up and finally utilized in the carcass of the slaughtered animal. 
From a detailed study of the vital economics of beef production made 
at the University of Missouri 7 figure 20 is reproduced here to show 
these relations. The convex curve shows the average growth per 
head in a group of steers fed with a ration regulated to secure a maxi- 



MOOO 



/DO SOO 30O -90O 00 600 700 goo SCO /OOO //OO /200 t30O HOO OOO 




FIG. 26. FEED CONSUMED, AND INCREASE IN LIVE WEIGHT OF 

STEERS AT SEVERAL AGES 

Dry matter consumed is represented on one-tenth the scale of the live 
weight. After Moulton, Trowbridge and Haigh. 

mum of growth, without storage of surplus fat; the approximately 
straight line mounting upward shows the steadily increasing inte- 
grated amount of feed consumed since birth. Only the dry weight 
of the feed is plotted, and the scale employed is ten times more 

7 University of Missouri, College of Agriculture, Bulletins 43, 54, 55 (E. C. 
Trowbridge and L. D. Haigh). 



134 



ELEMENTS OP PHYSICAL BIOLOGY 



condensed than that used for the live weight else the second 
would rise too steeply as to lie for the most part far beyond the HnvT 
of the page. Thus is shown the great disproportion between the feed 



TABLE 9 
Average Yearly Gains of Steers* 



PERIOD 




GROUP I 


GROUP II 


GROUP III 


days 

30 
to 
360 

360 
to 
720 

to < 
1,080 

1,080 
to 

( 
to | 


Weight gained 


pounds 

605.3 
3,075.0 
1.83 
5.08 

560.7 
6,314.1 

11.26 

390.8 
6,652.9 
1.09 
17.02 

268.9 
6,304.6 
0.75 
23.45 

JL j CJ&Q / 

22,346.6 
1.30 
12.24 


pounds 

409.7 

1.24 
4.71 

320.8 
3,619.3 
0.89 
11.28 

126.9 
3,629.2 
0.35 
28.60 

270.6 

4,259.9 
0.75 
15.74 

11 oo n 
j J.ZJO . \J 

3,438.0 
0.80 
11.91 


pounds 

241.6 
1,265.0 
0.73 
5.24 

235.6 
2,420.1 
0.65 
10.27 

121.2 
2,811.7 
0.34 
23.20 

311.2 
3,562.3 
0.86 
11.45 

911.6 
0,059.1 
0.65 
11.03 


Dry matter eaten 


Daily gain 


Dry matter per pound gain 
Weight gained 


Dry matter eaten. . . 


Daily gain 


Dry matter per pound gain. 
Weight gained 


Dry matter eaten.. . 


Daily gain 


Dry matter per pound gain 
Weight gained. . . 


Dry matter eaten 


Daily gain 


Dry matter per pound gain 
Weight gained. . . 


Dry matter eaten 


Daily gain 


Dry matter per pound gain 


Animals of group I were fed all they would eat. 



Srowth 



not 



body of the growing steer - and 

ceraM ; ' S &r M the interest of the P^uoer is con- 

cerned, in mere mamtenance, for the private satisfaction and benefit 



ANALYSIS OF GROWTH FUNCTION 135 

of the animal, so to speak. The numerical data on which figure 26 
is based are exhibited in table 9, together with the corresponding 
figures observed when the animals are somewhat underfed and over- 
fed respectively. 

The instances that have been cited man on the one hand, and the 
highly prolific species, both feral and captive, on the other are elo- 
quent illustrations of the elasticity of adaptation. Clearly, a species 
may hold its own, in the straggle for existence, either by the aid of 
well-developed protective devices resulting in a low death, rate, and 
requiring only a correspondingly low birth rate; or, a less well pro- 
tected species may balance a high death rate by an equally high birth 
rate. Which of these two methods would be chosen in the natural 
course of events is a question that it might be difficult to answer on 
any general a priori principle, so long as attention remained fixed on 
a single species. Perhaps one would have expected evolution to turn 
in a favor of the more economical method of meeting a low death rate 
with a low birth rate. In point of fact both types of organism the 
economical type (as judged by its own standard) with low death rate, 
and the wasteful with high death rate exist side by side in abun- 
dance. This is a good example to illustrate the purely relative charac- 
ter of fitness, and to remind us once more that we cannot expect any 
success in attempts to define the direction of evolution in terms of a 
single species. It is not the individual species, the individual com- 
ponents of the system, that evolve, but the system as a whole, com- 
prising all the species and their environment. The species of the 
economical type, with low death rate, are largely dependent for their 
subsistence on the presence of species of the opposite type; we must 
think here of a competition, not between individual species, but be- 
tween groups of species, groups consisting, in the simplest case, of 
two species each, a food species or prey, and a feeding or predatory 
species. Of two such groups, that one will, other things equal, have 
the advantage in the struggle, in which high productivity of the food 
species is accompanied by economy of life on the part of the feeding 
species. From the point of view of the hog, so to speak, the high mor- 
tality in the pen is a disastrous inefficiency and maladaptation, a 
misfortune to be borne, as best it may, with porcine philosophy 1 . 
From the point of view of the consumer on the other hand, this high 
mortality is, quite on the contrary, a measure of the efficiency, the 
eminent fitness of swine as producers of pork; and his only regret 



136 ELEMENTS OF PHYSICAL BIOLOGY 

is that so much of the feed placed in the trough goes merely to carry on 
"what may be called the personal activities of the animals them- 
selves." 8 It is to be noted, however, that only a part of the material 
accountable as waste from the standpoint of the food species is gain 
for the feeding species. Deaths from disease are a pure loss to both 
species. 

Similar reflections, of course, apply, mutatis mutandis, to those cases 
in which the feeding species derives its nourishment from some cur- 
rent product of the life activity of the food species or host, instead of 
from its carcass. The most notable example of this in the food econ- 
omy of man is his exploitation of the milch cow, who is a far more 
efficient producer than the beef steer. The latter at best consumes 
over 6 pounds of nutriment for every pound of product. 9 According 
to the investigations of the National Research Council about 18 per 
cent of the energy of grain fed to cattle is recovered for human con- 
sumption in milk, but only about 3.5 per cent in beef. Similarly, 
crops on a given area will yield about four to five times as much pro- 
tein and energy when fed to dahy COW T S as when used for beef produc- 
tion. In providing mineral substances and vitamines the milk of 
cows contrasts even more favorably with the beef animal. The 
vitamines and calcium salts contained in hay and grain are stored in 
the muscular tissue only to a slight extent, but are in relative abun- 
dance in milk. 10 From the standpoint of the dairyman a thoroughbred 
prize cow, such as Glista Ernestine (a Holstein), which gave in one 
year 833 pounds of butter fat, and in one hundred days 10,000 pounds 
of milk, is a very model of efficiency, producing more than her own 
weight in milk each month. But from the point of view of the bo- 
vine species such record performances are gross inefficiency, approach- 
ing in some cases perilously near to total biological unfitness, for some 
of the record Jersey cows are probably unable, under the conditions 
of the stable at any rate, to raise their own calves the over-rich 
milk would probably kill the young animal. 

Network of Chains of Interrelated Species. The relation between 
man and the domesticated species of animals and plants on which he 

8 I have here borrowed a felicitous phrase from an anonymous writer on 
the editorial page of the New York Times, February 10, 1921. 

9 University of Minnesota, Agr. Exp. Station Bulletin 193, pp. 68, 69 
(T. L. Haecker). 

10 Jour. Franklin Inst., vol. 190, 1920, p. 155. 



ANALYSIS OF GROWTH FUNCTION 



137 



EO largely depends for food, in the present state of civilization, is only 
a particularly tangible, a particularly accessible example of an intri- 
cate network of relationships that connect more or less closely all 
living species. In this network each species or component is inter- 
laced, like a link in a meshed coat of mail, with other species, which 
in turn connect with still others, and so forth. In our effort to 
get some sort of mental grasp of the complicated interlocking of these 
elements we seize upon some one link, some one species or component, 
and we note, first of all, that whatever is eliminated from one com- 
ponent of a self-contained system must pass into one or more other 
components of the system. So, for example, the component Si 
may be a herd of cattle. The matter eliminated from this component 
goes in part as food to build up or sustain a human population; in 
part it goes as fertilizer on the fields to furnish nutriment for crops; 
still other parts are worked up into various industrial products, such 
as leather, glue, etc. We thus have, in schematic representation, 



Cattle 



\ 



Human 
population 



\ 
Leather 



s 



S S 



Fertilizer 



L 

\ 



\ 



s k 



On the other hand, the substance of the herd itself is recruited from 
certain other components of the system, grass, clover, corn, etc., so 
that we may further develop the scheme 



Clover 



Grass 



\ 



Corn 
/ 



\ 



Cattle 



\ 



Human 
population 



\ 



\ 



Leather 






\ 



N 



Fertilizer 



Transformation Factors and Their Economic Significance. In 

general any one component thus appears as a link in a complicated 
chain or rather network of chains; the component S t , for example 



138 ELEMENTS OP PHYSICAL BIOLOGY 

receives a certain fraction at, i of the mass VtXt eliminated per unit 
of time from the component St', it passes on to the component S& 
a certain fraction ik of the mass ViXi eliminated from Xi itself. 

/ l~y 

The rate of growth n 2 of Xi is the balance of the sum Ui of all con- 

tributions it receives over and above the sum V\ of all the contri- 
butions which it makes to other components, thus 

dXi 

= mXi - viXi = Ui - Vi (10) 

at 

= ZatiVtXi - S/3 ik i>iXi (11) 

the first summation being extended over all those components St 
which contribute to Xi and the second over all those components 
8k to which Si contributes. 

But we may also analyse the contributions to and from the com- 
ponent Si in another way. We may say that, of the total contribu- 
tions per unit of time UiXi to the mass Xi, a certain fraction yuUiXi 
is derived from Sf. Then 

(12) 



= v f Xf (13) 

7 it 



and, substituting (13) in (10), 



Lastly, if the system is not self-contained, we must add a term Ji 
for "imports" per unit of time, and a term EI for "exports" per 
unit of time, that is to say, 






-^ = vtX f - ViXi + Ii-Ei (15) 

dt 7n 

When Si is the human species, the coefficients a, jS, 7 have an obvious 
economic significance. The restriction of this remark to the human 
species must not be taken to imply that there is in this feature some- 
thing wholly peculiar to man, but rather, that underlying our economic 
manifestations are biological phenomena which we share in common 
with other species; and that the laying bare and clearly formulating 



ANALYSIS OF GROWTH FUNCTION 139 

of the relations thus involved In other words, the analysis of the bio- 
physical foundations of economics is one of the problems coming 
\ within the program of physical biology. Hints as to the direction 

in which we may or must look for light on this phase of our problem 
have now been noted upon several occasions. So it was observed 
that the components of a life-bearing system can be divided into two 
classes, relative to the component Si, namely, on the one hand those 

components S- } for which -^ ~^T was positive, or, as we may say, 
those useful to the species Si, those having for it a positive value, 

and. on the other hand, components 8% for which ^ 3i l <0, com- 

V.A ic at 

ponents harmful to Si, or having for it a negative value. Else- 
where we have noted the classification of components into replace- 
, able and indispensable components, a classification that at once 

recalls elementary economic reflections. 

These hints we note in passing. They may serve to put our minds 
in a state of preparedness for the more formal and decisive attack of 
the problem, to which we shall be led in the last division of our en- 
quiry, dealing with the dynamics of life-bearing systems. 



Jf 



STATICS 



CHAPTER XI 

GENERAL PRINCIPLES OF EQUILIBRIUM 

Repeatedly, in preceding chapters, occasion has arisen to refer to 
stationary states or equilibria. Inevitably, in the discussion of the 
kinetics of evolution, one is led to consider incidentally certain 
conditions and special cases in which the velocities of the changes in 
the evolving system are zero; when, that is to say, the system under 
discussion is in a steady or stationary state, in equilibrium. Viewed 
from this avenue of approach equilibrium presents itself as a special 
case of motion or change, namely motion or change with zero velocity. 
Indeed, something very like equilibrium occurs also with velocities 
that are merely small, not vanishingly small. In such case the 
phenomenon of moving equilibrium may present itself, as we shall 
have occasion to observe in greater detail in due course. 

Stationary states equilibria and near-equilibria play an im- 
portant role in nature, and it is desirable at this point to give them 
something more than incidental consideration; to sketch, at least in 
outline, their systematic study; to stake out, in the rough, that field 
which, in our survey of the Program of Physical Biology (Chapter V) 
was designated as the Statics of Evolution, and was systematized 
according to the schedule 

Statics 



"I 



Equilibria Moving equilibria Displacement of 

(steady states) equilibrium 

It will be convenient, in the development of the subject, to follow, 
in the main, the schedule thus set forth. 

Kinetic, Dynamic, and Energetic Conceptions of Equilbrium. 
While we shall, in this section, conceive a stationaiy state 
from the standpoint of kinetics, defining it as a state in which certain 
velocities vanish, it must be noted that there are also other concep- 
tions of equilibrium. Etymologically the word equilibrium is tied, 
in stricter usage, to a dynamic conception: Aequa libra, the poised 
balance, is symbolic of a state in which forces are balanced, in which 

the resultant force vanishes, 

143 



144 ELEMENTS OF PHYSICAL BIOLOGY 

A third conception of equilibrium, differing from the second, the 
dynamic, only in point of view, not in scope, is derived from a con- 
sideration of energy relations. A system in dynamic equilibrium is 
found to be characterized by the attainment of a minimum (or some- 
times a maximum) of certain functions having the dimensions of 
energy; a state in which the virtual work done in any very small 
displacement compatible with the constraints vanishes. 1 So, for 
example, a ball placed hi a hemispherical cup, is in equilibrium when 
its potential energy is a minimum compatible with the geometry of 
the system. More generally, equilibrium is, according to this view, 
defined as a state in which certain potentials have a minimum (or 
a maximum). 

Pedantic usage would demand that the term equilibrium be re- 
served for states satisfying the dynamic and energetic conditions of 
rest or invariability in time. It would deny the appellation equi- 
librium to certain states commonly so designated. Metabolic equi- 
librium, population equilibrium, and the like, are not true equilibria, 
in this narrower sense, but are steady states maintained with a con- 
stant expenditure, a constant dissipation, of energy. It is not neces- 
sary, however, at present, to lay any stress on this distinction. The 
occasional use of the word equilibrium in speaking of what is merely 
a steady state maintained with a continuous expenditure of free 
energy is not likely to cause any serious confusion; and we may as 
well take the usual liberties in the matter, whenever this course is 
dictated by convenience and does not offend against essential prin- 
ciples. Where express distinction becomes necessary, we may speak 
in specific terms of true equilibrium and quasi-equilibrium, respect- 
ively, to denote the two separate types included hi the generic term 
"stationary state" or "steady state." 

A complete treatment of the entire field of the statics of evolving 
systems should, to be entirely systematic, cover both types of 
stationary states. There are, however, two reasons for departing 
somewhat from such strictly systematic arrangement. The first 
is that the statics of true equilibria have been developed to a high 
degree in the discipline of thermodynamics, so that an exposition of 
the pertinent principles and conclusions would be little more than 

1 Stability of equilibrium demands, further, that the work done on the 
system in any small, but finite, displacement, be positive, that the potential 
energy be a minimum (maximum being, in this case, excluded). 



GENERAL PRINCIPLES OF EQUILIBRIUM 145 

a transcription into these pages of what can be found abundantly set 
forth elsewhere in the standard literature. However much one might 
be tempted, in the interest of a well rounded presentation, to sketch 
at this point at least an outline of the relevant chapters of thermo- 
dynamics, economy of space dictates the briefer expedient of referring 
the reader to the existing literature, so abundant that it seems super- 
fluous to mention titles. 

A second reason for passing lightly over true equilibria at this 
point, is that the steady states with which we are most frequently 
and most closely concerned in the field of organic evolution (our 
main topic here), are of the second class; not true, equilibria in the 
dynamic sense, equilibria in which all forces are balanced; but 
what we have termed above quasi-equilibria, states maintained 
constant or approximately so with a continual expenditure, a con- 
tinual dissipation or degradation of available energy. To such as 
these we shall give our chief attention, though in part our discussion 
will be framed broadly to cover indifferently either type of steady 
state. For the sake of example, too, reference will be made, on 
occasion, to systems evolving toward a true equilibrium; systems for 
which the law of evolution is capable of direct expression In com- 
paratively simple thermodynamical terms; systems which, by that 
very fact, are peculiarly adapted to serve as paradigms exhibiting 
the characteristic form of a law of evolution. 

General Equilibrium Condition. As has already been noted in- 
cidentally, the general condition for equilibrium, or, to be more 
precise, for a stationary state, is obtained by equating to zero the 
velocity of growth of each component of the system, thus 

= Fi(Xi, Xz, . . . X n ) (1) 

at 

F! = F z = . . . = F n = (2) 

This condition, in general, furnishes n independent equations, 
which determine one or more sets of values of the variables X, thus 



Xz ~ * ' (3) 



146 ELEMENTS OP PHYSICAL BIOLOGY 

If the values C thus determined are real and positive 2 they evi- 
dently define an equilibrium or a steady state, the character (stability 
mode of approach) of which depends upon the nature of the roots 
X of a certain characteristic equation, as has been indicated on an 
earlier occasion. 

Different Types of Equilibrium. Graphic Representation. A 
particularly graphic representation of the different types of equilib- 
rium is obtained if, instead of seeking solutions of the fundamental 
equations (1) expressing Xi, X 2 . . . X n in terms of t, we on the 
contrary eliminate t from this system of equations. This is very 
readily effected by division, which leads to the new system 

dXi dXz dX n 

T! = ~F~* = ' ' ' " 71 (4) 

This system of equations defines a family of curves passing through 
the equilibrium points, which here appear as singular points. The 
situation is particularly transparent in the case of two variables 
Xi, X 2 , since this readily permits of plotting the integral curves in 
rectangular coordinates in the plane of the paper. We have already 
had occasion incidentally to employ this method of treatment in an 
example in Chapter VIII, in which the conflict between a host species 
and a parasite species was examined analytically. Without going 
into extensive technical details it is advisable now at least to enumer- 
ate and briefly describe the several types of equilibria and the 
topography, characteristic of each type, presented by the integral 
curves in and about a singular point. These types are somewhat 
numerous, even if we restrict ourselves to the case of two variables, 
and brevity is therefore imperative. 

Type 1. Roots Xi and X 2 real and negative. Equilibrium is stable; in- 
tegral curves run directly into singular point as in figure 27, A. 

Type 2. Roots Xi and X 2 real and positive. The topography is similar to that 
of type 1, but integral curves are traversed outward from singular point. 
Unstable equilibrium, figure 27, B. 

Type 3. Roots Xi and X 2 real and of opposite sign. Integral curves in general 
do not pass through singular points, but curve away from it. Unstable equi- 
librium, figure 27, C. 

2 Masses cannot assume negative or imaginary values. Hence negative 
roots may fail to define equilibria; a similar statement holds regarding 
complex roots. 



GENERAL PKDSTCIPLES OF EQUILIBRIUM 147 

Type 4. Roots Xi and X 2 complex, real parts negative. The integral curves 
are spirals winding into the origin, forever approaching it without ever reach- 
ing it. Stable equilibrium, figure 27, D, 

Type 5. Boots Xi and X 2 complex, real parts positive. The topography is 
similar to that of type 4, but integral curves are traversed outward from 
singular point. Unstable equilibrium, figure 27, E. 

Type 6. Roots Xi and X pure imaginaries. This gives rise to several dis- 
tinct subtypes. 

Subtype F. Integral curves are closed loops enclosing the origin. Process 
is purely periodic. Figure 27, F. 

Subtype G. Integral curves are spirals winding inward. Stable equilib- 
rium. This is the case treated in Chapter VIII, where a representative dia- 
gram will be found. Figure 27, G. Another subtype is similar to G but spiral 
winds outward. Unstable equilibrium. 

Subtype H. Integral curves are spirals winding about a closed loop. 

Types I AND J occur when \i = X 2 . Figure 27, 1, J. 

As an example illustrating the occurrence of two types of equilib- 
rium, two types of singular points, the topographic chart of the 
integral curves defined by the Ross equations for the spread of malaria 
under certain conditions is shown in figure 28. It will be seen that 
there are two singular points, one at the origin 0, unstable, of type 
C; the other at T, stable, of type A. This chart obviously suggests 
"stream lines" and a three dimensional model. Such a model 
(purely qualitative) is shown in figure 29. The feature of interest is 
that a singular point like 0, of type C, is represented by a col 
("notch") in the landscape; whereas the stable equilibrium of type 
A is represented by a pit, as at the point T. 

While this model refers to a very particular case, it serves to bring 
out a noteworthy fact, namely, that there are necessarily certain 
regularities in the occurrence of the various types of equilibria. So, 
for example, it is clear that two pits of the character of the point T 
cannot occur without some other type of singular point between 
them, just as it is physically impossible for two mountains to rise 
from a landscape without some kind of a valley between. For a 
detailed study of this phase of the subject the reader must be re- 
ferred to the mathematical literature. 3 

3 For further discussion of the various types of singular points that may 
occur the reader is referred to the mathematical literature, of which the 
following may be mentioned: E. Picard, Trait<5 d' Analyse, 1891, vol. 1, pp. 83, 
123; 1893, vol. 2, pp. 183, 193, 196 (footnote); 1896, vol. 3, pp. 228, 238; v. Dyk, 
Sitzungsber Bayer. Akad. Wissensch. Miinchen, March 6, 1909,^AbhandL 15; 
Abhandlungen derKgl. Bayer. Akad. Wissensch., March, 1913, vol. 26,Abhandl. 
10; Sitzungsber, 1891, p. 23; 1892, p. 101; H. Liebmann, Lehrbuch der Differ- 
ential gleichungen, 1901, pp. 101, 102, 134. 



ELEMENTS OF PHYSICAL BIOLOGY 










FIG. 27. SOME FUNDAMENTAL TYPES OP EQUILIBRIUM, IN A SYSTEM WITH Two 
DEPENDENT VAEIABLES 



GENERAL PRINCIPLES OF EQUILIBRIUM 



149 




FIG. 28. MAP OF INTEGRAL CURVES FOR THE Ross MALARIA EQUATIONS, AS AN 

EXAMPLE EXHIBITING Two SINGULAR POINTS, OP TYPE 1 AND 3 (SEE 

FIGURE 27, A AND C) 

The heavy lines are integral curves; the lighter lines are auxiliaries 
(isoclines) employed in constructing the graphic solution of the differential 
equations. (Reproduced from A. J. Lotka, Am. Jour. Hygiene, January 
Supplement, 1923.) 



150 



ELEMENTS OP PHYSICAL BIOLOGY 



. ,JH'/!' <>';'' 



X" \' A >' " "ft *M' f t' "'" s. '"-' ; 




GENERAL PRINCIPLES OF EQUILIBRIUM 151 

Metastable Equilibrium. The graphic representations of the 
malaria equilibrium furnish the occasion for another remark of general 
character regarding certain equilibria. The circumstance that gives 
rise to the first malaria equilibrium, the one in which the malaria 
rate is zero, (point in figs. 28 and 29) is the autocatakinetic charac- 
ter of the growth, of a malaria endemic . This is a common character- 
istic of the growth of living systems; growth is initiated by a nucleus 
of the same species of matter that is added by the growth. Con- 
versely, in the entire absence of any nucleus of a particular species of 
living matter, growth of that species cannot take place, even though 
all other conditions for such growth may be satisfied, even though 
the system may he, as it were, supersaturated with regard to that 
species of matter. In these circumstances an equilibrium may be 
presented which is unstable in the sense that, upon the introduction 
of a suitable nucleus, growth immediately sets in. 4 Equilibria of 
this type, which are stable in the absence of a suitable "nucleus" 
but in which change is immediately initiated upon introduction of 
such a nucleus, have been termed "metastable" equilibria. 

Exceptional Cases: A brief reference must suffice regarding 
certain exceptional cases that may arise. So it may happen tbat one 
of the roots X of the characteristic equation vanishes. An example 
of this was encountered in dealing with the Ross malaria equations. 
It was found that as the number of mosquitoes per head of the 
human population approaches a certain critical value, two singular 
points approach each other, and finally fuse, giving one "double" 
point. 5 

Another special case that may arise, and whose mention must here 
suffice, is that of multiple roots of the characteristic equation, the 
case in which two or more of the roots are equal. 6 

4 In inorganic systems an analogous state of affairs is observed in super- 
saturated solutions or vapors which, are brought to crystallization or to con- 
densation by the introduction of a suitable nucleus. Dynamically the char- 
acteristic of a metastable equilibrium is that the thermodynamic potential of the 
system, though a minimum, is not an absolute minimum. 

6 See A. J. Lotka, Am. Jour. Hygiene, 1923, vol. 3, January supplement, 
p. 12. 

6 Compare H. Liebmann, loe. cit., pp. 102, 134; A. J. Lotka, Zeitschr. f. 
physikal. Chemie, 1912, vol. 80, p. 16. 



CHAPTER XII 

CHEMICAL EQUILIBRIUM AS AN EXAMPLE OF EVOLUTION UNDER 

A KNOWN LAW 

I wanted to remind the biologists that in the early stages of life what they 
are accustomed to speak of as natural selection passes over into what might 
be described as a mere physical selection of stabler compounds. K. Pearson. 

One of the simplest examples of equilibria in systems of the type 
that interests us here systems composed of several groups each 
consisting of numerous similar individuals as units is the equi- 
librium resulting from a pair of balanced or opposing chemical 
reactions. 

This case illustrates so well, in their simplest form, a number of 
typical traits of the phenomena here under discussion, that it will 
pay to give it brief consideration. 

We shall select for this purpose the simplest possible type of 
balanced chemical reaction at constant volume and temperature, 
namely a reaction which is monomolecular in both directions. A 
substance Si undergoes a transformation into S%, and Sz in turn is 
converted back into Si, one molecule alone taking part, in each case, 
in the transformation. If Xi and x z are the respective concentrations 
of Si and $2, we have, at a given temperature, by the law of mass 
action, the rate of decomposition of Si and Sz respectively. 

(Ztei) = - faxi (1) 

(D^) = - fax* (2) 

Or, since at constant volume concentrations x are proportional to 
numbers n of molecules 

(Dm) = - fciin (3) 

(Dnz) font (4) 



where fci, k 2 are coefficients (functions of the temperature) character- 
istic of the reaction. 



152 



CHEMICAL BQUILIBBIUM 153 

The rate of increase of the substance S is the excess of its rate of 
formation 6 over its rate of decomposition, in strict analogy to the 
birth rate and death rate in a human population 

(fti-fcOm (5) 

at 



(6) 

at 

In a population of living organisms the material for the formation 
of new individuals must ultimately be derived from the bodies of 
those that have died. But the connection is a complicated one in- 
volving many steps. In the population of molecules here under 
consideration the relation between birth rate and death rate is of the 
simplest possible form. Each molecule of Si that "dies" becomes a 
molecule of 82, and vice versa. Thus equations (5), (6) assume the 
form 



and in equilibrium 



, , 

kiUi (7) 

at 



- = kiHi ^22 (8) 

at 



K\ 



If we fix our attention upon HI molecules of Si at the moment of their 
formation, we can apply to these particular molecules the equation 
(3), from which we have, by integration 



1 * (10) 

similarly for S 2 

= naCO)*-*** (ll) 



\ 
But 77:7 is the probability pi(a), at the moment of its formation, 



that a molecule of Si picked at random at such moment, will reach 
age o. The life curve for the molecules of Si is thus defined by 

Pi(a) = <r kia (12) 



154 ELEMENTS OF PHYSICAL BIOLOGY 

and for Sz 

pj (a) = e-^ (13) 

while the mean lengths of life are 

., 



/T 

= I 
Jo 



and in equilibrium 

^ (16) 

ft 2 La 

the molecules are present in amounts proportional to their respective 
mean lengths of life, although, they are "born" in equal numbers, 
since fan* = AVZ.I. The significance of this is brought out in the 
diagram figure 30, in which the population of molecules is plotted 
"in age groups," for the substance Si and S 2 separately. Since the 
birth rate is the same for both populations, they begin at a common 
ordinate; but the curve for 82, the substance with greater k, greater 
force of mortality , lies entirely below that for Si; the areas of the two 
curves are, in fact, proportional to the mean lengths of life of the 
molecules of the corresponding substances. Thus, in the struggle 
for existence the stabler (fitter) molecules of Si have the advantage, 
being, on an average, longer-lived. 

There is thus an obvious analogy between the course of events in 
such a population of different species of molecules, on the one hand, 
and a mixed population of different species of organism on the other, 
an analogy which extends into details for the exposition of which 
space is lacking here. 1 The analogy is not a meaningless accidental 
circumstance, but depends on identity of type in the two cases. It 
can be said quite generally (so as to apply to either case) , that in a 
material system in which physical conditions vary from instant to 
instant and from point to point, certain individual constituents 
(molecules, organisms) may have a transitory existence as such, 
each lasting just so long as its conditions and those of its neighborhood 
continue within certain limits. Although the "life period" of each 
individual constituent may be thus limited, an aggregate of a number 

1 For such details see A. J. Lotka, Am. Jour. Sci., vol. 24, 1907, pp. 199, 375. 



CHEMICAL EQUILIBRIUM 155 

of such individuals may nevertheless have prolonged existence, pro- 
vided that the fluctuations in the conditions of the system, from point 
to point and from instant to instant, do not exceed certain limits, 
and that by some process or other new individuals are formed as the 
old are eliminated. Of the character of the fluctuations, and their 
relation to the "length of life" in the case of living organisms, more 
will be said in a later chapter. As to the circumstances, the fluctua- 
tions, that lead to the translation of a molecule in chemical reaction 
from one state into another, we may with advantage adopt a view- 




3OOO 



FIG. 30. AGE DISTRIBUTION IN POPULATION OF MOLECULES OF Two SUB- 
STANCES IN MONOMOLECULAR CHEMICAL EQUILIBRIUM 

The birth rate per head, of both species, is the same as indicated by their 
common zero ordinate; but the species having the lesser force of mortality 
(reaction constant) predominates, as shown by the greater area under the 
corresponding curve. (Reproduced from A. J. Lotka, Am. Jour. Science, 
1907, p. 208.) 

point set forth in some detail by the writer on an earlier occasion, 2 
and expressed more recently by Professor Baly 3 in these terms : 

Every complete reaction consists of three separate stages, with each of 
which is associated its characteristic energy change. In general, molecules 
in the free state exist in a phase which is non-reactive, and in order to carry out 
any reaction it is first of all necessary to bring them into a reactive phase. 
This, which is the first stage of the reaction, requires that a definite amount 

2 A. J. Lotka, Am. Jour. Sci., 1907, p. 213 et seq. 

3 E. C. Baly, Photosynthesis. Nature, 1922, p. 344. 



j.uu ELEMENTS OP PHYSICAL BIOLOGY 

of energy should be supplied to each molecule, the amount necessary being 
the difference in energy contents of the initial phase and the particular phase 
necessary for the reaction in question. 

The second stage of the reaction is the atomic rearrangement whereby 
new molecules are produced, and it is this stage, and this stage alone, which 
is represented by the equation of the reaction. 

The third and final stage is the change in phase of the newly synthesised 
molecules, whereby they pass into their normal and non-reactive phases. 
These last two stages are both accompanied by an escape of energy. If the 
sum of the amounts of energy evolved in the second and third stages is greater 
than that absorbed in the first stage, the reaction is exothermic; whilst an 
endothermic reaction is one in which the energy necessary for the first stage 
is greater than the total amount evolved in the second and third stages. 

It should be remarked that the second stage is, apparently, passed 
through in an exceedingly brief space of time, so that at any instant 
only an imperceptibly small amount of substance exists in the transi- 
tional state. We are, in fact, almost wholly devoid of any informa- 
tion regarding matter in this state, and the words of Schonbein 4 
hold true in almost their full force today: "Presumably, between the 
state in which two portions of matter exist after completion of chem- 
ical combination, and the state in which they previously existed 
separately, there is a series of transition states of which the chemistry 
of today knows nothing." Probably the only positive and direct 
experimental evidence we have of matter in this intermediate state 
between two compounds is furnished by the superlatively refined 
methods of Sir J. J. Thomson and Dr. F. W. Aston, which not only 
reveal but actually weigh such decapitated molecules as CHs, whose 
length of life is measured in ten-mil lionths of a second. 5 

As to the agencies, the "fluctuations" that provide, every now and 
again, the requisite energy to carry a transforming molecule "over 
the crest of the hill," there is first the thermal agitation of the mole- 
cules, second the influence of incident light in photochemical reac- 
tions, and third the influence of catalysts, whose action probably 
depends on a flattening of the path over the hill crest, the point of 

4 Jour. Prakt. Chem., vol. 55, I, p. 152. 

B Compare A. J. Lotta, loc. cit., p. 214. F. W. Aston, Science Progress, 
1912; I. Langmuir, Jour. Am. Chem. Soc., 1920, vol. 42, p. 2190. Perhaps in 
this connection should be mentioned also recent studies on the duration of 
atoms in their several quantum states. See E. C. Tolman, Proc. Natl. 
Acad. Sci., 1924, vol. 10, p. 85; L. A. Turner, Phys. Rev., 1924, vol. 23, .> 

p. 464; F. M. Kannenstine, Astrophys. JL, 1924, vol. 59, p. 13. ^ 



CHEMICAL EQUILIBBIUM 157 

departure and the final state remaining unchanged. For discussions 
of these technical details the reader must be referred to the literature, 
a few of the more recent publications being noted in a footnote below. 6 
While the details of the manner of the "birth" and "death" of the 
molecules in chemical transformation are, as yet beyond the range 
of the observation of the physicist, the fundamental laws of ener- 
getics, which hold true generally, and independently of particular 
features of mechanism, are competent to give substantial information 
as to the end product, at any rate, of the evolution of such a system 
as considered in the simple example above. The final equilibrium 
must accord, as regards its dependence on temperature, pressure and 
other factors, with the second law of thermodynamics, which may 
thus be said to function as a law of evolution for a system of this kind. 
This is a point worth dwelling on a little at length, inasmuch as our 
knowledge of the form and character of the law of evolution for this 
special type of system may be expected to serve as a guide in the 
search for the laws of evolution in the more complicated systems, 
belonging to an essentially different type, which confront us in the 
study of organic evolution. The second law of thermodynamics can 
be expressed in various ways, but the form in which it serves our 
present purpose best is that which states that the system evolves 
toward a state in which certain functions (thermodynamic potentials) 
of the variables defining its condition are at a mrnimum, somewhat 
as a ball placed in a hemispherical bowl ultimately comes to rest in 
the position in which its (gravitational) potential is a minimum, 
namely, at the lowest point of the bowl. Mary laws of nature are 
conveniently 7 expressed in this form, as minimum (or maximum) 

8 Regarding the r61e played by thermal agitation and by radiation see G. 
W. Todd and S. P. Owen, Phil. Mag., vol. 37, 1919, p. 224; I. Langmuir, Jour. 
Am. Chem. Soc., 1920, vol. 42, p. 2190; W. H. Rodebush, Jour. Am. Chem. 
Soc., vol. 45, 1923, p. 606; J. M. Lowry, Trans. Faraday Soc., vol. 17, 1922, p. 
596; J. A. Christiansen, Zeitschr. phys. chem., vol. 103, 1922, p. 91. Regarding 
the influence of radiation see especially the publications of Professor Baly. 
See also J. Mellor, Chemical Statics and Dynamics, 1904, pp. 394, 414, 415; 
and Perrin and Hammick, Atoms, 1923, p. 168. The literature on catalysis 
is so extensive that no attempt is made here to give even a key to it. 

7 Fundamentally this is a matter of convenience, and does not predicate 
anything narrowly characteristic of natural laws. The fact that the course 
of events is uniquely determined implies that the laws which determine that 
course can be expressed in the manner referred to. For a discussion of this 
question see J. Petzoldt, Maxima and Minima und Okonomie, Altenburg, 
1891, pp. 17 et seq. 



158 ELEMENTS OF PHYSICAL BIOLOGY 

laws, and it is to be expected that the law of evolution in life-bearing 
systems also, (where, as we shall see later, mechanism cannot be 
lightly waved aside into the convenient catch-all of the laws of 
thermodynamics), will be found to receive its most convenient 
expression in this form. In another respect the case of chemical 
evolution may confidently be expected to be found a good model 
in the treatment of the broader problem of evolution. It is to be 
noted that the law of chemical evolution is expressed in terms of the 
system as a whole. It is the thermodynamic potential of the entire 
system that approaches a minimum. Biologists have rather been 
in the habit of reflecting upon the evolution of individual species. 
This point of view does not bear the promise of success, if our aim 
is to find expression for the fundamental law of evolution. We shall 
probably fare better if we constantly recall that the physical object 
before us is an undivided system, that the divisions we make therein 
are more or less arbitrary importations, psychological rather than 
physical, and as such, are likely to introduce complications into the 
expression of natural laws operating upon the system as a whole. 

As regards the formulation of the laws of evolution in form of a 
maximum or minimum principle, it should be remarked that one such 
principle follows directly from the fundamental equations of kinetics 
as set forth in Chapter VI. 

If we multiply the first of these equations by Xi, the second by X 2 , 
and so on, we obtain 



at 



-2 . 

~TT ^ ^1X1X2 + 022X2- +...-}- a2n.Xn.X2 + 

at 



(17) 



dt K n "" " nn- n. 

Hence by addition 

A 

-S & = 2Q(x h xt, . . . x n ) + . . . (18) 

where Q represents a quadratic form. The relation thus obtained is 
not of general utility in this form. However, by a linear substitution 



CHEMICAL EQUILIBRIUM 159 

& = N lXl + N,X, + . . . + 2ST n a; n (19) 

the equation (18) can be transformed into 



~ 
at 



(20) 



where Xi, X 2 , . . . X n are the n roots of the characteristic equation for 
X, the same X's that function as exponents in the series solution of the 
original system of equations. 8 Now it will be recalled that the condi- 
tion for stability at the origin is that all the real parts of the roots 
shall be negative. But in that case the quadratic form Q' is definite 
and negative. Hence the condition for stability at the origin can 
be expressed by saying that the quadratic form Q' must be definite 
and negative; or, by saying that Q' must have a minimum at the 
origin. And the law of evolution, near the origin, evidently is, 
according to (20), that S 2 continually decreases. (At points remote 
from the origin the terms of higher order, which have here been 
omitted, may cause increases in S.) 

The chief interest of the minimum principle here indicated lies in 
its analogy 9 to certain theorems in dynamics and thermodynamics, 
for which reference must be made to the literature, in particular to 
P. Duhem, Traite d'Energetique, 1911, vol. 1, pp. 460 et seq.; F. 
Michaud, Ann. de Phys., 1921, vol. 16, pp. 148 et seq. 

8 For the sake of simplicity the argument has here been presented in the form 
in which it appears when all the roots X are distinct and real. For a detailed 
discussion of the conditions of stability when some of the roots X are multiple 
or complex see E. Goursat, Cours d' Analyse, 1915, vol. 3, pp. 31-43. 

9 The analogy to the dynamical cases treated in the reference cited becomes 
particularly plain if we bear in mind that 



= when i =j= j 



= 2Xi when i j 
so that the quadratic form Q' can be written 

' dQ' 5Q' 



160 



ELEMENTS OP PHYSICAL BIOLOGY 



where the bracketed exponent (2) denotes the symbolic square, in which 
'- } is> replaced by 



\JTC w\x W vjj 

-, and the product =-r- - >T~J i g replaced by -^ ^--. 

\ 

The condition that the form so defined shall be negative, is that the deter- 
minant 



shall be negative, and also all determinants derived from it by striking out 
the last p lines and the last p columns. 

In the present case the same condition, can be expressed in simpler form 
to the effect that Xi, \^, . . . \ a must all be negative. But it is worth 
while, in order to bring out the analogy, to note also the more complicated 
general form of the condition. 



CHAPTER XIII 
INTER-SPECIES EQUILIBRIUM 

Since the struggle for existence is chiefly a struggle for subsistence, a careful 
comparative account of the food of various competing species and genera at 
different places and seasons and at all ages of the individual .... can- 
not fail to throw much light upon the details, causes and effects of the 
struggle. Forbes. 

Equilibrium Condition in More Particular Form. The fundamen- 
tal relations of statics are derived immediately from the correspond- 
ing equations of kinetics by substituting in the latter the value zero 
for the several velocities. This has already been noted with regard to 
the equations of kinetics in their most general form. In somewhat 
more particular form, useful in common numerical applications, 
we have a condition for equilibrium derived from the system of 
equations (14) of Chapter X 



. 

X t - ViXi (1) 

dt 7if 



(2) 



7 if 

X f JIM 



i (3) 

It should be noted that these formulae hold equally well if the 
masses are measured in ordinary units (e.g., pounds) or if they are 
measured in "head of population," with the proviso, of course, that 
the coefficients ui, Vi, are in each case expressed in corresponding 
units. 

The equation (1) expresses the fact that, for each component, the 
total inflow is just balanced by the total outflow, so that nowhere in 
the system is any accumulation of mass going on. This clearly 
implies that, unless there is complete equilibrium, the matter in the 
system must be in circulation, it must be going through one or more 
cycles. Such cycles are, indeed, very characteristic features in the 
scheme of nature. 

161 



162 ELEMENTS OF PHYSICAL BIOLOGY 

Numerical Illustration. We may, by the way of illustration, apply 
the formula (3) to the equilibrium between the several biological 
species comprised in a life-bearing system. For obvious reasons 
numerical data are most readily available for man and the species 
directly under his control. So, for example, we may let Xt. represent 
the mass (or number) of a human population, and Xt the mass (or 
number) of a population of sheep serving as food for that human 
population. In the United States in 1918 the consumption of mutton 
(or lamb) per head of the population per annum was 5.417 pounds. 
This is not strictly an equilibrium ration, since our population is 
increasing. However, the difference between this and the equilib- 
rium ration is probably small. In our example we will therefore 

put 

jitui = 5.417 pounds = 0.1096 sheep 1 (4) 

Again in the United States in 1918 the number of sheep slaughtered 
per annum was 23.22 per cent of the standing herd. Hence 

a fi t>i = 0.2322 (5) 

so that 



Xf = "^ Xi (6) 

f 0.2322 

= 0.4718 Xi W 

In 1918 

Xi = 103,587,955 head (8) 

Hence 

Xt = 48,873,000 head (^ 

i According to the Year Book of the Department of Agriculture, 1920, p. 
759 the number of sheep slaughtered under Federal inspection m 1918 was 
8 769,498. According to R. Pearl, The Nation's Food, 1920, p. 61, this repre- 
sented 77 per cent of all the sheep slaughtered in that year, so that the total 
number slaughtered was 1 1,370,000. The total dressed weight of these, accord- 
ing to the Year Book, p. 826, was 502,214,000 pounds, which makes the average 
of one Bhoop carcass 49.45 pounds. 

The standing herd of sheep in 1918, according to the Year Book, p. 701, 
was 48,C03,000 on farms, or, adding a correction for animals not on farms ! say 
48,963,000. The percentage of animals slaughtered in a year out of the stand- 
ing herd, was therefore 23.2216 per cent. 

For a review of various estimates of the output of herds of cattle, sheep 
swine, etc., the reader ia referred to a paper by R. H. Rew in the Journal of 
the Royal Statistical Society, 1902, vol. 65, p. 666. 



INTER-SPECIES EQUILIBRIUM 163 

The actual standing herd of sheep in 1918 was 48,963,000 head of 
which 90,000 head furnished mutton for export, the United States 
not being a self-contained system. 

It is to be noted that in this example the products 7jf U[ and 
oifi vi are more easily ascertained than the individual coefficients <y 
it, a, v. Inasmuch as these coefficients, in the formula (3), appear only 
in these products, it is not necessary, for the purposes of this example, 
to ascertain the values of the coefficients separately. 

The example of the equilibrium between a human population and 
the national herd of sheep, cited primarily for the purpose of illustrat- 
ing the equilibrium equation (3), incidentally brings out some other 
points that may be noted in passing. We meet here a pointed sug- 
gestion of economic factors entering into play in the processes which 
we are studying. For the coefficients a 7, u, v, have obvious economic 
relationship. So, for example, Vf, the proportion of sheep slaughtered 
per annum (in a stationary state of the system), is of the nature of 
interest on the standing herd, which latter, in turn, is of the nature of 
capital. The gross interest rate of 23.2 per cent is, of course, greatly 
diminished, in effect, by the extensive accessories, representing a 
further investment of capital, and by the general running expenses 
required, in addition to the mere herd, to produce, transport, and 
market the ware. On the other hand, certain secondary products 
(e.g., wool) add their quota to the returns on the invested capital. 

Again, the coefficient Aif, which measures what fraction of the total 
consumption by the component Si (human population) is derived 
from St (sheep), is clearly a factor of economic significance. Mutton 
.is typically a commodity of the replaceable type beef, pork, fish, 
etc., furnishing ready substitutes. In such case as this the factor 7 if 
will be elastic, capable of assuming, in ready response to slight 
changes in general conditions, a whole range of values from zero up. 
In the case of less readily replaceable commodities the coefficient 7 
wih 1 be of more rigid habit. 

The full significance and the precise nature of the relation between 
the biological and the economic characteristics of a system must form 
the subject of special considerations to which we shall find ourselves 
led inevitably later, in our efforts to gain insight into the dynamics of 
life-bearing systems. At this juncture it may not be amiss to indicate 
in preparation of a viewpoint to be more fully developed later, that 
if economic factors force themselves upon our notice primarily in the 



164 ELEMENTS OF PHYSICAL BIOLOGY 

consideration of systems comprising a human population, this is riot 
because the operation of economic stresses is peculiar to human 
aggregations, but only because these stresses find their ready numerical 
expression and measure in such communities; owing to the develop- 
ment of a system of social cooperation and division of labor, coupled 
with a very special mechanism of adjustment by "economic 
exchange/' which is peculiar to man. For though not a few other 
species, bees, ants, etc., display a social organization in some respects 
perhaps superior to ours, their organizations make use of other 
expedients than the transfer of ownership through a universal 
medium of exchange, in bringing about the allocation, to each indi- 
vidual, of his share in productive effort and in product. 

For obvious reasons our information regarding the interdependence 
of the several biological species and other components of our life- 
bearing system is most complete and most exact in so far as it relates 
to species under human cultivation, species that contribute, as pro- 
ducers, to our political economy. However, this does not mean that 
we arc wholly cut off from all information regarding the life balance of 
other species. Two sources, two methods of observation furnish us 
with data on this subject, namely, first, biological surveys, and second 
analyses of the stomachs of sample specimens. A third method would 
coiiHisli in establishing experimental systems comprising several 
HpocioH of organisms and making periodic censuses by direct count, 
after tho manner of the work of Pearl and Parker with a single 
tuxu'ioB (Drosophila). There is here an attractive field open for 
wViirch Perhaps the readiest, though not the most interesting 
approach to this problem would be the study of mixed bacterial 
crowbhH ay along the lines followed, for a single species, by H. G. 
Thornton, Annals of Applied Biology, vol. 9, 1922, p. 241. 

Biological Surveys. Biological surveys, supplemented by esti- 
mate* depending more or less on personal judgment, are aimed to 
rivo UB Jmo degree of quantitative description of our world by mves- 

oranisms. A 



the number and the variety of living organisms. 
biolORioal survey would enumerate the several general and 
ound in the locality examined, and would furthermore give 
mowuro of tho extent of each species, either in numbers or m some 
1 "u tohte tonne. It would give us a species of "General Demol- 
v'' cor globe. Needless to say, in this matter we are very far 
lined perfection. The best that can be done is to 



INTER-SPECIES EQUILIBRIUM 165 

give rather crude estimates, based, in the most favorable instances, on 
counts or observations made with some degree of care, but without 
pretense of great precision. 

As to the number of species, some interesting figures are given by 
J, A. Thomson. 2 On the small island of Britain alone 462 different 
birds have been observed; the total number of living species of birds 
he estimates at not less than ten thousand. Of vertebrates he quotes 
an estimate by H. Gadow. 3 The total number of recent species this 
author puts at 24,241, as follows: 

Mammals 2,702 

Birds 9,818 

Reptiles 3,441 

Amphibians 925 

Fishes 7,328 

Primitive vertebrates 27 

24,241 

The vertebrate elite, however, forms but a small minority in the 
scheme of nature. It has been intimated that, if the present order 
of things should come to a term, the supremacy would, as likely as 
not, pass from the crowned vertebrate Homo sapiens to the now 
despised, presently perhaps to be feared, creeping thing, the insect. 
Indeed, it has been pointed out that were it not for the relentless 
internecine warfare which its members carry on among themselves, 
we should very soon find ourselves driven out of house, home and 
granary by the insect pest. Even as it is, though the largest insects 
barely exceed, individually, the size of some of the smallest verte- 
brates, yet, as D. Sharp remarks, "the larger part of the animal 
matter existing on the lands of the globe is in all probability locked 
up in the form of insects." He estimates th,e number of insect species 
that have been definitely named, at 250,000, and suggests that this 
is only about a tenth of the total. The number of plant species has 
been estimated at 200,000. Darwin records the finding of 20 species 
in a patch of turf four feet by three. 

As to the numerical strength of the several species, here again some 
telling figures are given by J. A. Thomson. 4 

2 J. A. Thomson, The Wonder of Life, 1914, p. 11. 

3 See also H. Gadow, The Wandering of Animals, 1913, p. 74. 
* J. A. Thomson, loe. cit., pp. 9-10. 



166 



ELEMENTS OF PHYSICAL BIOLOGY 



_ At the spring maximum of the Rotifer Synchoeta there may be about three 
millions to a square yard of lake. At the summer maximum of the slimy Alga 
Clathrocystis ceruginosa there may be 500 millions to the square yard; at the 
autumn maximum of a well-known diatom Melosira varians, which has a sum- 
mer maximum as well, there are about 7000 millions to the square yard, so that 
the waters of the lake form a veritable living soup In an ordi- 
nary sample from a warm part of the Atlantic and from a depth of 500 metres 
(which is the most densely populated as far as plants go), there are likely 
to be about 5,000 plant-cells to a liter; but there may be as many as a 
quarter of a million 

Elsewhere Thomson tells us that in the midst of a swarm of fish at 
spawning time in the Norwegian fjords a boat may be so lensely 
packed in among the mass of fish that an oar stuck upright into the 
swarm remains standing for an appreciable time after the hand relin- 
quishes its hold. 5 

Examination of Stomach. Contents. The second method by which 
information has been gathered regarding the interdependence of biolog- 
ical species consists, as already stated, in examining the contents of 
trie stomachs of sample specimens. This method has been applied 
particularly to birds and fishes. The results of such an analysis of 
the feeding habits of the common crow and of the starling are strik- 
ingly brought to view in the accompanying charts figures 31 and 32, 
reproduced by courtesy of the Department of Agriculture from Bulle- 
tins 868 and 1102. Such a chart does not, of course, yield any direct 
information regarding the relative abundance of the several species 
upon which the crow feeds, but it does give us at least an indication of 
a resultant compounded of that relative abundance and a number of 
other factors, such as the preference or selective tastes of the crow, 
the greater or less degree of protective characters with which nature 
has endowed the various species exposed to attack, etc. 

The converse problem, also, has been investigated, namely the 
extent to which different species of birds participate in the destruction 
of one selected noxious insect. So, for example, Bulletin 107 (1914) 
of the Department of Agriculture lists 45 different species of birds 
that were found to have fed upon the alfalfa weevil. A similar study 
by H. C. Bryant 8 was carried out during a grasshopper outbreak in 

B For an account of bird censuses in the United States see M. T. Cooke, 
Bulletin No. 1165, Bureau of Biological Survey, U. S. Department of 
Agriculture. 

6 University of California Publications in Zoology, 1912, no. 1, vol. 11. 



INTER-SPECIES EQUILIBRIUM 



167 



California, when "in the infected areas the grasshoppers were com- 
puted to number from 20 to 30 per square yard." Bryant's results 
are shown, in part, in tabular and diagrammatic form in figures 
33 and 34 3 reproduced from his original publication. 








. 31. SEASONAL ANALYSIS OF THE STOMACH CONTENTS OF CROW 






^ 

*' ; ; 




'^jfiftitAr.^' i 
"~\^^/&8SS8 

V^&3PI 




FIG. 3:2. SEASONAL ANALYSIS OF THE STOMACH CONTENTS OF STARLING 

The same author has also given us a classic in his extended study 
"A Determination of the Economic Status of the Western Meadow 
Lark in California." This paper contains among other things a 



1(58 



.ELEMENTS OF PHYSICAL BIOLOGY 



detailed bibliography up to 1913, and a historical survey of the 
methods employed and the investigators who have labored in the 





: '' ' I" 1 :: :-"'.: :':: .. :: ? ; .V . 


,; :, ' ;-:. ,;..'. . 




..,'' ,';! V. ::..'::- ::::,.:.:.; 'r-'.; 





! 


| . ., g , 




'if 

r 

w 


Bullock Oriole- 
Cliff Swallow- 


4,050 
2.2S5 




Western Kingbird- 


1,260 




Burrowing Owl-.- 


I.2SO 




California Shrike- 


1,200 




Anthony Green Heron- 


1,050 




Sundry- 


593 



TOTAL DESTRUCTION OF GRASSHOPPERS PEP SQUARE MILE DAILY, IS0.453 
FlG. 33. COMPARATIVE DAILY DESTRUCTION OF GRASSHOPPERS BY SEVERAL 

SPECIES oir BIRDS 



After H. C Bryant 



ANIMAL FOOD 



VEGETABLE FOOD 



Jan. 

Feb. 

Mar. 

Apr. 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

TOTAL 



VM/M/////////A, 



Fia. 34. SEASONAL FOOD HABITS OP THE MEADOW LARK 
After H. C. Bryant 

field. The results obtained by Bryant exemplify the proverbial 
voracity of birds. Young birds require about one-half their own 
weight in food each day. In the course of a year the average meadow 



IXTEK-SPECIES EQUILIBHIUM 



169 



lark, weighing say, 4 ounces, consumes about the following quantities 

of food. 



pounds 




% ft 





FIG. 35. STOMACH CONTENTS OP A BREWER'S BLACKBIRD 

Since an adult bird weighs about 4 ounces, this means that it con- 
sumes on an average about 24 times its weight of food in a year. 
Dr. Bryant remarks: "If we consider that there is an average of one 
meadow lark to eveiy two acres of land available for cultivation 
(11 million acres) in the Sacramento and San Joaquin Valleys, and 
that each pair of birds raises an average of four young, it takes over 
343| tons of insects each day to feed the young birds in the valley 
alone." His findings regarding the seasonal changes in the food of 
the meadow lark are summarized in a number of charts of which one 
is reproduced in figure 38. An illustration of the voracity of birds, 
and their destructiveness to insects is also seen in figure 35 (from Bulle- 



170 ELEMENTS OP PHYSICAL BIOLOGY 

tin 107 of the Department of Agriculture) showing the stomach con- 
tents of a Brewer's Blackbird, for this bird was found to have gorged 
upon 374 larvae, 65 pupae and 3 adults of the alfalfa weevil. Obser- 
vations on the feeding habits of young English sparrows are recorded 
by E. R. Kalmbach in Bulletin 107 of the United States Department 
of Agriculture. This author remarks (p. 54) : 

From a series of five observations it appears that the parent English spar- 
rows visited their nest on an average about once every 5 minuted, or a little 
more than 11 trips an hour. The four adults captured had as food for tlieir 
young 2 kernels of wheat; 17 alfalfa weevil larvae; 1 ground beetle, 9 weevil 
larvae and a caterpillar; and 23 weevil larvae, respectively. Three other 
adults taken in the fields had food for nestlings in their bills. This amounted 
to IS weevil larvae and an aphid in the first, 5 larvae in the second, and 3 
coccinellid larvae. 13 weevil larvae, and 2 pupae in the third. 

Though this is rather heterogeneous assortment, it would appear that 15 
larvae of the weevil or their equivalent in bulk of other insects would be a fair 
estimate of an average amount of food brought in at each trip by adult birds. 
In fact, it is certain that the material brought in frequently greatly exceeded 
this amount. 

Allowing 15 larvae at each trip and 11 trips per hour, these birds would 
bring in 165 larvae per hour. Then, assuming that the young were being fed 
for 12 hours each day, a conservative estimate, we would have a total of 1980 
larvae consumed by one brood in one day. Straw-thatched sheds containing 
upward of 100 nest holes, both old and new, are frequent, and it is not uncom- 
mon to find farmyards where this number of nests are occupied. There are 
also ample nesting sites about the other buildings and in the ever-present 
Lombardy poplar, cottonwood, or box elder. Such a colony of birds would 
devour a daily total of 198,000 larvae, or an equivalent bulk in other food. As 
the young birds remain in the nest for at least 10 days and are probably fed 
several days longer by the adults, they will have eaten food equivalent to the 
bulk of 1,980,000 larvae during their nestling life. 

Intra-Species Equilibrium. As has been remarked on a previous 
occasion, it is not intended, in this volume, to take up the discussion 
of the evolutionary changes within the confines of a species. Passing 
notice may, however, be given to the fact that the equilibrium within 
a Mendelian population has been discussed by G. H. Hardy 7 and by 
R. C. Punnett 8 and latterly by J. B. S. Haldane. 9 (See p. 122.) 

7 G. H. Hardy, Science, 1908, vol. 28, p. 49. 

8 R. C. Punnett, Mimicry in Butterflies. 

8 J. B. S. Haldane, Cambridge Philosophical Society, 1923. 



CHAPTER XIV 

INTER-SPECIES EQUILIBRIUM AQUATIC LIFE 

Aquiculture is as susceptible to scientific treatment as agriculture; and the 
fisherman, who has been in the past too much the hunter, if not the devas- 
tating raider, must become in future the settled farmer of the sea, if his 
harvest is to be less precarious. W. A. Herdman. 

From what has already been set forth the direct economic im- 
portance of studies in general demology should be sufficiently clear, 
if this term be used to denote the quantitative study of the popula- 
tion of the several species of organisms living together in mutual 
interdependence through their food requirements, feeding habits, 
and in other ways. 

In no other field, perhaps, has the study, from this angle, and 
under this economic impetus, been so systematically undertaken, 
as in the biology of aquatic species. On the one hand the three- 
dimensional extension of the systems here involved (as distinguished 
from the essentially two-dimensional spread of land species over the 
earth's surface'), facilitates, in certain respects, the operation of 
sampling (by the use of the dragnet) and counting; on the other, 
the close relation of such investigations to the practical problems 
of our inland and our ocean fisheries has furnished alike the economic 
occasion and the financial support for work on an extended scale. 
The methods employed have by this time developed into a more or 
less standardized technique. The dragnet, already referred to, 
and the stomach and gills of fish, acting, as it were, as natural drag- 
nets, themselves caught within the collector's man-made dragnet, 
are among the principal accessories in this 'field of investigation. 
L. H. Tiffany recommends particularly the gizzard shad as a con- 
venient collector and sampler of Algae. 1 Contrasting these natural 
samplers with man-made contrivances he remarks: 

These living tow nets (i.e., gizzard shad) do not get caught on snags and 
roots, the string does not break, and the algal collection is very representa- 
tive of the body of water from which the fish were taken. It is only neces- 

1 Science, 1922, vol. 56, p. 285. 

171 



172 ELEMENTS OF PHYSICAL BIOLOGY 

sary to catch the young fish and examine their stomachic and intestinal 
content to secure a proportionate sample of the plankton. 

Tiffany examined specimens from streams and ponds in Illinois, 
and also from Ohio. He points out that the gizzard shad fulfills 
an important rule as an intermediary link in the food chain: algae, 
shad, game-fishes, man. 

Thus, the gizzard shad is making useful for man the energy stored in plant 
forms which occupy no land areas, which do not interfere with the ordinary 
disposition or utilization of bodies of water ('except the occasional contam- 
ination of water for drinking purposes by some algae), which involve no 
labor of cultivation on the part of man, and which are of no value for direct 
humaa consumption. 

The world's population in the last hundred years has increased about 
150 per cent. Along with this increase has had., to corne a corresponding 
increase in the world's food supply. One of the ways in which this necessity- 
has been met is the securing of new acres of soil in which to grow crops. It 
is easily seen, however, that there is a limit to new acreage. In the future, 
therefore, we may have to turn more of our attention to the cultivation of 
the waters for food supplies. We may have to develop an industry of aqui- 
culture as we have developed an industry of agriculture. The time is 
rapidly approaching when fish will be more highly prized as food and more 
extensively used than now. As that time comes, the cultivation of algae 
will be a first step toward greater fish production. A second step may be 
the introduction of fish like the gizzard shad into fish ponds and lakes to 
make more readily available the phytoplankton for fish food. 

In a summary survey of the Food Resources of the Sea, 2 G. W. 
Martin makes similar observations. He remarks: "So far as the 
actual cultivation of the sea's resources, as distinguished from their 
mere exploitation, is concerned, we have made only the feeblest 
beginnings." Somewhat in the same vein is W. A. Herdman's 
comment: "Aquiculture is as susceptible to scientific treatment 
as agriculture; and the fisherman who has been in the past too 
much the hunter, if not the devastating raider, must become in the 
future the settled farmer of the sea, if the harvest is to be less pre- 
carious." Viewing the matter from a slightly different angle W. F. 
Wells of the New York Conservation Commission draws attention 
to the fact that in our modern great cities, with the widespread 
adoption of the water system of sewage disposal, valuable fertilizer 
material is lost from its natural place in the fields. By enriching 

2 Scientific Monthly, 1922, p. 456. 



INTER-SPECIES EQUILIBRIUM 173 

the vegetation in the water and furnishing abundant life thereto, 
it may again be restored to the people as fish and shell fish in the 
place ^of beef and mutton. And the exchange is not such a bad 
bargain. For it has been found that in carp ponds, for example, 
the production of market ware was 95 pounds per acre, as contrasted 
with 73 pounds of beef per acre of farmland. 3 Perhaps one of the 
most telling illustrations of the economic importance of pisciculture 
is presented to us in the Alaska purchase: Within fifty years after 
the acquisition of our Northern province, it had yielded, in its salmon 
fisheries alone, seven and a half times its purchase price. 

The quantitative study of ocean life (on which must be based an 
intelligent system of marine aquiculture) may be said to elate from 
1880, when Henson introduced the use of the dragnet. To this 
has since been added the use of bottom samplers or grabs; also an 
ingenious, if less trustworthy method of making a census of the 
marine population, which consists in catching a number of live fish, 
marking them, throwing them back in the water, and then noting 
the^ percentage of marked fish in the fishermen's catch during the 
period that follows. In this way it has been estimated, for example, 
that the North Sea contains about fifteen hundred million plaice, 
a figure about equal to the earth's human population. 

The field of utility of the dragnet and most of the other methods 
described is evidently limited to the larger denizens, such as are 
effectively held in the meshes of a net. Even a fine silk net will 
fail to hold ^a very numerous constituent of the population of the 
sea, a constituent that is highly important not only on account of 
its great extent, but also because of the role it plays in the food 
traffic of marine life. Lohmann showed (1911) how these fine 
organisms (the nannoplankton') can be collected by the use of a 
centrifuge. 4 Allen has developed a special dilution culture method 
of count for the nannoplankton organisms, which is modelled after 
the pattern of bacterial count technique. He showed sea water 
to contain 464,000 organisms per liter (exclusive of bacteria). Al- 

* It is true that beef is much superior in food value, pound for pound, but 
it is also much more costly to produce. It should also be noted that the yield 
from carp ponds is very high as compared with that of marine fisheries E 
J. Allen (Food from the Sea, 1917, quoted by W. F. Thompson, Scientific 
Monthly, 1922, p. 546) estimates the yield in the North Sea at 15 pounds per 
acre. 

4 G. W. Martin, loc. cit., p. 461. 



174 



ELEMENTS OF PHYSICAL BIOLOGY 



lowing for systematic errors Allen thinks a population of one million 
organisms per liter (one per cubic millimeter) to be a conservative 
estimate. This is not excessive crowding, in view of the size of 
these organisms, as illustrated by the diagram, figure 36, reproduced 
from G. W. Martin's article. Before the extent and significance 
of this nannoplankton was realized, the amount of food required 
by the animals of the sea seemed so much in excess of the amounts 



\ 



FIG. 36. DENSITY OF MICROORGANISMS (EXCLUSIVE OF BACTERIA) IN SEA 

WATER 

About one organism, measuring 6 microns in diameter, is found per cubic 
millimeter of water. The relative dimensions are here shown. After G. W. 
Martin. 

revealed by the earlier methods of collection, as to give rise to the 
suggestion (Putter 1907-1909) 

that the nutrition of marine animals was on an entirely different plane from 
that of land animals, and that a large number of them, especially the smaller 
ones, absorbed dissolved organic matter directly from the water, without 
the mediation of plants. Putter's arguments have not been generally ac- 
cepted, and more recent studies have invalidated many of them. Never- 
theless, it is possible that something of this sort is more general than we 
realize. Mitchell (1917) reported an experiment strongly indicating that an 
oyster can utilize dextrose dissolved in sea water. 

The most elaborate attempts to calculate the production of the sea have 
been those of the Danish biologist Petersen and his associates. As a result 
of their studies, these workers have come to the conclusion that the plank- 
ton plays a very small part in the nutrition of the animals of the sea, and 



INTEK-SPECIES EQUILIBRIUM 



175 




176 ELEMENTS OF PHYSICAL BIOLOGY 

that the fundamental food of all marine forms in northern waters at any 
rate is the "dust fine detritus" of the sea bottom, derived primarily from 
the eel grass, Zostera. 

These investigators have studied in particular the conditions in 
the Kattegat, a rather shallow arm of the sea between Denmark 
and Sweden, about 150 miles in extreme breadth and 90 miles in 
extreme width. Their principal conclusions are exhibited in the 
diagram figure 37, and are as follows: 

It is assumed that about half of the total amount of Zostera annually 
produced in this area is washed elsewhere by the currents. The balance, 
estimated at 24,000,000 tons, serves as the basis for the animal life of the 
area. The useless animals, that is, those that are of no value to man and 
do not serve as food for fish, feeding directly on the Zostera, amount to about 
5,000,000 tons. Useful animals, mainly those capable of serving as food 
for fish, are estimated at 1,000,000 tons. These are not all utilized by food 
fish, however. Starfish account for perhaps 200,000 tons; 500,000 tons are 
eaten by the larger gastropods and crustaceans, of which only a part are 
consumed by fish; while plaice and other flatfish consume about 50,000 tons 
producing 5000 tons of human food annually. Cod are much less economical, 
since they get their food at third hand, so to say, and each ton of the 6000 
tons produced annually represents about one hundred times as much of the 
original synthesized organic food. On the other hand, the cod help to keep 
down the predatory gastropods and crustaceans (see figs. 38 and 39). The 
herring is the most important food fish feeding on the plankton, (mainly on 
copepods) and it in turn is eaten by the cod. Perhaps the most striking 
feature brought out by these figures is the comparatively trifling amount 
of human food finally produced from such a large amount of organic material. 

Summary of Methods. A tabular summary of some of the princi- 
pal methods by which data have been secured regarding relative 
and absolute frequency of organisms and species is given in table 10. 

Food Chains. It has already been remarked, in dealing with the 
general kinetics of the type of systems here under consideration, 
that each component of the system appears as a link in a chain or 
a network of chains, receiving contributions from components 
(sources') above, and discharging material into other components 
(sinks') below. Food chains, such as spoken of by Tiffany in the 
passage quoted on page 172, are a particular example of such chains 
of components. The study of food chains is one of the important 
tasks of the economic biologist. For we cannot afford to restrict 
our attention to the immediate source from which we draw our 



INTER-SPECIES EQUILIBRIUM 



177 




By courtesy of the Illustrated London News 

FIG. 38. THE VABIED DIET OF THE CODFISH 



178 



ELEMENTS OF PHYSICAL BIOLOGY 



-a .f 



CO 

a 

o 

ft 



he O 

o> ri 



o 






I--- 







S.2 






!- 



ft 



02 .5 



INTER-SPECIES EQUILIBRIUM 



179 



supplies of food for the human population. The sources of these 
sources also demand attention. The problem forces itself upon 
our notice primarily (in the present state of society) in connection 
with agriculture. The fields cannot continue indefinitely 'to yield 
undiminished annual crops if the materials drawn from them are 
not in some way replenished. One important constituent needs 
no human intervention: carbon dioxide, owing to its gaseous form, 
automatically seeps in by diffusion as fast as it is absorbed by the 




FIG. 30. KEY TO FIGUKK 3 

green plants. The same is true in some degree of free nitrogen , 
though the capacity of plants to assimilate this element is ^ strictly 
limited. 5 Water, also, is, in most agricultural areas, provided by 
the automatic meteorological processes of evaporation and conden- 
sation in rainfall. But as to certain other essential materials, 
notably combined nitrogen, phosphorus, potash and sulphur, the 
inherently immoUW constituents of the fertile soil, for these auto- 

* Science. November 24, 1922, p. 605. 

"Fiir sicli micht beweglich," Liebig, Die Chemie in ihrer Anwendung 
auf Agricultur, 1876, p. 382. 



180 ELEMENTS OF PHYSICAL BIOLOGY 

matio replacement does not occur in sufficient measure ^ to satisfy 
the agricultural needs of the densely populated countries of this 
age. It becomes necessary for man to feed his food. Early man 
and primitive man, may reap where he has not sown. BuMong 
ago our tribe turned from the life of a nomad and hunter to tilling 
the soil and to animal husbandry. Thus was established a system 
of symbiosis with the links next above us in the food chain : the 
harvest ripening on the plain; and the cattle, grazing upon the 
pasture in summer, fed from the crib in winter. But early agricul- 
ture was essentially of the nature of a mining industry. It drew 
from the soil as from a bottomless well, without thought of a possible 
exhaustion of the source, or of any feasible replenishment to dimin- 
ishing resources. Except that, by a semi-automatic, semi-empirical 
process, natural fertilizer was allowed to restore to the soil at least 
a part of its strength to bring forth a crop. One more step forward 
and man graduated from mining farmer into manufacturing farmer. 
The field became a factory fed with raw materials in the form of 
saltpeter, potash salts and phosphate fertilizer, imported, if need 
be, from afar; and producing its output of agricultural flora arid 
fauna. Lastly, in our own generation, we have learned to divert 
into the life stream the sluggish element, so essential to life, so ill- 
named by the French -azote; to make ourselves independent of the 
saltpeter beds, to assure our future against a nitre famine by open- 
ing the inexhaustible mine of the atmosphere. It is a singular thing 
that this element, so accessible, so abundant, in which we arc 
literally bathed within and without, every instant of our life, should 
so long have remained foreign to our industrial economy. Strange 
circumstances, yet not without close parallel. For even now we 
are powerless to avail ourselves effectively of the golden flood of 
energy that daily pours upon us without limit from above while 
we turn earthward to dig laboriously for the plainly exhaustible 
supply of coal to supplement our limited bodily energies. 

Food Chains in Aquatic Species. The principle that long food 
chains are essentially wasteful finds particular application also in 
the practical problem of the economic and rational utilization of 
marine organisms for human sustenance. As Professor Martin 
observes, the most economical course would be to utilize marine 
vegetation directly as food for man and his domestic animals. The 



INTER-SPECIES EQUILIBRIUM 181 

use of algae as food for the table can hardly be expected to become 
an item of any consequence. Its use as cattle fodder presents 
better prospects. But our chief reliance will no doubt continue 
to be on the assimilation of marine plants by fish. To quote again 
Professor Martin: 7 

Since man prefers to harvest the plant life of the sea indirectly, those 
animals which feed directly on the plants are able to increase with less waste 
and at a more rapid rate, considered in total populations, than those which 
feed on other animals. Most of our food fish, for example, feed on smaller 
fish; these in turn feed upon small crustaceans and the latter eat the micro- 
scopic plants and detritus, so that in many instances the fish we eat are re- 
moved three or four steps, perhaps more, from the original food source. This 
is more significant than may seem apparent at first glance, since it involves 
an enormous waste. Before any organism can grow, the energy needed 
merely to live must be supplied, and by the time a crustacean is eaten by 
a minnow, or a minnow by a food fish, it will, on the average, have consumed 
a quantity of food several times its own weight. These facts are well brought 
out in the statistics of Petersen, and the diagram figure 37 based thereon. 
The edible shellfish, however oysters, clams, mussels and the like feed 
for the most part directly on the marine plants and this is one reason why 
the extension of the shell fisheries represents so much promise. 

Another advantage of this branch of aquiculture is also to be noted, 
namely, that 

most shellfish, like land crops, stay where they are planted. Even the scal- 
lop, which can swim about after a fashion, is restricted in its movement, 
and could readily be controlled. Oyster culture is already a great and im- 
portant industry, but it has not nearly approached its possibilities. Clam 
culture is still in an embryonic state, and scallop culture has yet merely 
been suggested. When some of the problems confronting the establishment 
of these industries have been solved, we may hope to have acquired addi- 
tional information concerning the ecology of the sea, which will help us in 
our approach to the more difficult problems of the future. 

Primary, Secondary and Tertiary Foods. It is often convenient 
to classify the foods for human consumption according' to their 
relative position in that portion of the food chain which is under 
human control. Commonly the meats of domestic animals are 

7 For some further bibliographic indications regarding the food consumed 
by fishes see A. S. Pearce, Ecology, vol. 1924, p, 258. See also W. A, Herd- 
man, Founders of Oceanography, 1923; J. Johnstone, Introduction to Ocean- 
ography, 1923. 



182 ELEMENTS OF PHYSICAL BIOLOGY 

classed as secondary foods, since the production of these meats 
takes plate in two steps, first the growing of the fodder (for the 
most part materials not comestible by man), and second the trans- 
formation of a part of this fodder, in the animal economy, into food 
adapted for human consumption. On the other hand the fisher- 
man's haul is for us primary food, growing feral, without human 
intervention. 

This classification must not be pressed. Where fields are supplied 
with fertilizer it might well be maintained that the cr^ps of wheat, 
potatoes, etc., commonly classed as primary, are secondary foods, 
while butchers' meats are tertiary. Even the catch of fish, and 
huntsman's quarry may not be strictly primary, in so far as game 
laws and regulations regarding the pollution of lakes and rivers 
represent some degree of symbiotic intervention on the part of man. 
Fine points apart, the distinction between the primary foods (crops 
and fish) and the secondary foods (butchers' meats) is economically 
most significant, for the consumption of fodder by farm animals 
is an item not merely comparable with human food consumption, 
but exceeding this latter manyfold. The fact, of course is, that 
farm animals are far from being economical and efficient converters 
of raw materials into food for human consumption. They repre- 
sent a luxury, a humoring of the tastes of men at the expense of 
their purses. With the present density of population we can afford 
the luxury. Presumably the future will see retrenchments, with 
pastures and cornfields converted to wheat. Still tastes arc not 
accidental thiogs. Allowing for vagaries and exceptions, the 
things we like are, on the whole, good for us and for the species. 
Whether man can maintain his present status with a materially 
abridged meat ration is perhaps an open question. Should the 
answer be in the negative, the conclusion would seem to be forced 
upon us that an overcrowding of the earth would react unfavorably 
upon the vigor of the race; quality would be sacrificed to quantity. 
How this might affect the ultimate fate of our species is a subject 
for speculation. The pessimist might take a cue from palaeontology, 
recalling that the extinction of a species seems to follow, not in- 
frequently, close upon its period of greatest development. The 
optimist, on the other hand, might perhaps extend the suggestion 
that when overcrowding does come, the ones to survive most surely, 
if not most abundantly, will be those whose superior qualities 



INTER-SPECIES EQUILIBRIUM 183 

will enable them, in spite of intensified competition, to draw to 
themselves a sufficiency of the more desirable, though perhaps not 
absolutely essential articles of consumption. Natural selection 
would thus operate by the preferential survival of an aristocracy, 
while a submerged tenth would furnish a drain for the discharge of 
the unfit. Certainly, in the interests of the species, it were better 
that the inferior constituents be purged from the system than that 
they should drag down the general level to mediocrity and perhaps 
below the line of viability. But these are speculative reflections. 

Cycles. Food chains, were we able to trace them through their 
entire course, would undoubtedly be found to form closed cycles 
or a network of cycles. This is indeed a practical necessity for the 
continued performance of the processes or organic nature, processes 
that have gone on essentially unchanged in their general character, 
however modified in detail, for many millions of years. 

A few of the simpler food chains we may be able to follow with 
something approaching completeness through their cycle. For 
the most part, however, the system of interlocking cycles in nature 
is complex beyond all reasonable hope of detailed analysis in its 
entirety. 

If we are satisfied to omit innumerable details, we can trace, for 
each of the most important chemical elements 7 concerned, the broad 
outline of its cycle in nature. The elements and simple compounds 
principally concerned are 

Carbon (dioxide) COz 

Oxygen O 2 

Nitrogen free N, NH 3 , nitrites and nitrates 

Water H 2 O 

Phosphorus (phosphates, etc. ) 

Brief consideration will presently be given to each of these cycles 
in turn. First, however, it will be well to review some of the es- 
sential facts regarding the occurrence of the chemical elements, 
generally, in nature. For the drama of life is like a puppet show in 
which stage, scenery, actors and all are made of the same stuff. The 
players, indeed, "have their exits and their entrances," but the 
exit is by way of translation into the substance of the stage; and 
each entrance is a transformation scene. So stage and players are 
T}ound together in the close partnership of an intimate comedy; and 



184 ELEMENTS OF PHYSICAL BIOLOGY 

if we would catch the spirit of the piece, our attention must not all 
be absorbed in the characters alone, but must be extended also to 
the scene, of which they are born, on which they play their part, 
and with which, in a little while, they merge again. 8 

8 Since the words above were written I have run across the following singu- 
larly apposite passage in- John Morley's Introduction to Wordsworth Col- 
lected Poetic Works: "Wordsworth's claim, his special gift, his lasting con- 
tribution, lies in the extraordinary stremxousness, sincerity and insight with 
which he first idealizes and glorifies the vast universe around us, and then 
makes of it, not a theatre on which men play their parts, but an animate 
presence, intermingling with our works, pouring its companionable spirit 
about us, and 'breathing grandeur upon the very humblest face of human 
life,'" 



CHAPTER XV 
THE STAGE OF THE LIFE DRAMA 

When the elements have been mingled in the fashion of a man, and come 
to the light of day, or in the fashion of the race of wild beasts or plants or 
birds, then men say that these come into being', and when they are separated, 
they call that in common parlance, death .... let not the error pre- 
vail over the mind that there is any other source of all the perishable crea- 
tures that appear in countless numbers. Empedocles. 

Our stage is a tripartite world: The heavens above, the waters 
of the sea, and the solid ground beneath our feet; the atmosphere, 

TABLE 11 
Principal components of earth's surface 





VOLUME 
MILLIONS 


DENSITY 


MASS MILLIONS 


PUB CENT 


Atmosphere 


cu. miles 




short tons 

5 82 X 10 16 


0.03 


Ocean 


302 


1.03 


1.42 X 10 18 


6.58 


Solid crust 


1,633 


2.7 


2 01 X 10 19 


93.39 













the hydrosphere and the lithosphere. The total mass of the earth is 
about 6.5 X 10 21 tons. But it is only the outer crust that interests 
us here, for the deeper layers have little or no part in terrestrial life. 
If we arbitrarily take a layer ten miles thick for the crust, the distri- 
bution of the material among the three main divisions is, according to 
F. W. Clarke, about as shown in table 11. 

The Atmosphere. There are two ways of confining a gas. The one 
most familiar in the laboratory and in products of human workman- 
ship generally, is to enclose the gas in a suitable envelope, such as a 
glass vessel, or the cylinder of an engine; to put something around 
the body of gas to be confined. The other way, nature's way on a 
large scale, is just the opposite, and consists in putting something 
into the gas, or putting the gas around something. It is so the earth 
holds her atmosphere by gravitational attraction. Her hold is not 
impartial. She draws closest to her the densest constituents, and 

185 



186 



ELEMENTS OF PHYSICAL BIOLOGY 



gives longer leash to the lighter. The atmosphere, in consequence, 
is not a homogeneous body, but varies in composition with altitude. 
At the same time, owing to its elasticity, the air in its lower strata 
is compressed by the weight of the overlying atmosphere, so that 99 
per cent of the whole is contained within a shell 30 km. (18| miles) 
thick. The remaining 1 per cent extends out into space without any 



Of CLOUDS * QROlMAW OUST J 




FIG. 40. CROSS SECTION OF THB ATMOSPHERE, SHOWING SOME FEATURES 

CHARACTERISTIC OF DIFFERENT ALTITUDES 

After W. J. Humphreys 

assignable limit, but at any rate to a height of some 300 km. (185 
miles), as evidenced by the aurora. A graphic representation of the 
broad divisions of the atmosphere is shown in figure 40, adapted from 
Wegener and Humphreys. 1 A more detailed and exact statement of 

1 Physikalische Zeitschrift, 1911, vol. 12, p. 172. See also W. J. Humph- 
reys' work, The Physics of the Air (Lippincott, 1920), pp. 68, 69. Also, the 
same author, Bulletin Mt. Wilson Weather Observatory, vol. 2, 1909, p. 67; 



STAGE OF THE LIFE DRAMA 



187 



O F CONSTANT TffMPf MTV fie. 




FIG. 41. COMPOSITION OF THE ATMOSPHERE AT DIFFERENT LEVELS 
After W. J. Humphreys 

Journ. Franklin Institute, vol. 175, 1913, p. 208, 212. A singular view has 
lately been put forward by L. Ve"gard. He identified certain green lines in 
the auroral spectrum with lines observed when solid nitrogen is rendered 
phosphorescent by x-rays. He concludes that the upper atmosphere contains 
solid nitrogen. (See Nature 1924 vol.113 p. 716.) Ve"gard's view has been op- 
posed by J. C. McLennan, Roy. Soc., June 19, 1924. 



188 



ELEMENTS OF PHYSICAL BIOLOGY 



its composition at different altitudes, up to 140 kin., is given in 
table 12 and illustrated graphically in figure 41, derived from 
Humphrey's work. 

A complete discussion of the r61e played by the atmosphere in the 
round of terrestrial life would amount to nothing less than a treatise on 
meteorology, such as forms no part of the present project. What 

TABLE 12 
Percentage distribution of gases in the almosphere 



HEIGHT 


OASES 


PER CKNT 
OP 
TOTAL 
A.TMO- 

sniiDnE 


Argon 


Nitro- 
gen 


Water 
vapor 


Oxygen 


Carbon 
dioxide 


Hydro- 
gen 


Helium 


Total 
pressure 


km. 
















mm. 




140 




0.01 








99.15 


0.84 


0.0040 




130 




0.04 








99.00 


0.96 


0.004C 




120 




0.19 








98.74 


1.07 


0.0052 




110 




0.67 


0.02 


0.02 




98.10 


1.19 


0.0059 




100 




2.95 


0.05 


0.11 




95,58 


1.31 


0.0067 




90 




9.78 


0.10 


0.49 




88.28 


1.35 


0.0081 




80 




32.18 


0.17 


1.85 




64.70 


1.10 


0.0123 




70 


0.03 


61.83 


0.20 


4.72 




32.61 


0.61 


0.0274 




60 


0.03 


81.22 


0.15 


7.09 




10.68 


0.23 


0.0935 




50 


0.12 


86.78 


0.10 


10.17 




2.76 


0.07 


0.403 




40 


0.22 


86.42 


0.06 


12.61 




0.67 


0.02 


1.84 




30 


0.35 


84.26 


0.03 


15.18 


0.01 


0.16 


0.01 


8.63 


99.0 


20 


0.59 


81.24 


0.02 


18.10 


0.01 


0.04 




40.90 


94.5 


15 


0.77 


79.52 


0.01 


19.66 


0.02 


0.02 




89.66 


85.5 


11 


0.94 


78.02 


0.01 


20.99 


0.03 


0.01 




168.0 


78.0 


5 


0.94 


77.89 


0.18 


20.95 


0.03 


0.01 




405.0 


46.7 





0.93 


77.08 


1.20 


20.75 


0.03 


0.01 




760.0 






important factors weather and climate are in the business of provid- 
ing the sustenance of life is a matter of common knowledge, and a 
very particular concern of the farmer. Yet we must here be satis- 
fied with little more than a passing reference to meteorology, noting 
only a few elementary facts which bear directly upon the subject in 
hand, the circulation of the chemical elements in nature. 

Losses from the Atmosphere. A first question that suggests itself 
in this discussion of the economy of nature is this: Since the atmos- 
phere is "open at the top," so to speak, is there not a loss, a constant 
leakage of gas out into space? The answer to this question must be 



STAGE OF THE LIFE DRAMA 189 

sought in terms of the molecular constitution of the gases of our 
atmosphere. A cubic centimeter of air contains (at 0C.) about 3.15 
X 10 19 molecules. These are in continuous agitation, somewhat 
after the manner of a swarm of gnats, except that they flit about with 
speeds comparable with that of a rifle bullet (about 500 meters per 
second) rather than with the leisurely flight of an insect. At a tem- 
perature of 0C. a molecule of nitrogen has, on an average, a velocity 
of 492 meters per second. A molecule of hydrogen, under the same 
conditions, would have an average velocity of 1839 meters per second. 
It must be understood that these figures represent, in each case, a 
mean about which the velocities of individual molecules cluster, so 
that a certain proportion of them will fall below and others will exceed 
the figures stated. At the earth's surface the average distance 
travelled between two successive collisions is about ^iroTolTo cm - 
But in the upper ranges of the atmosphere conditions are very 
different. If we follow the estimates and computations of J. H. Jeans, 
we find that at an altitude of 3200 km. the atmospheric pressure is re- 
duced to about 1/10 14 of its value at sea level; but even at this low 
pressure there are still about 300,000 hydrogen molecules per cubic 
centimetre. (At this altitude all other gases except hydrogen are 
practically absent) . The mean free path between collisions is now 
10,000 km. or about If times the earth's radius. In such circum- 
stances collisions between molecules are rare, and for the most part the 
molecules move freely through space in parabolic or elliptical orbits, 
and become virtually diminutive satellites of the earth. Since the 
day of Jules Verne's story From the Earth to the Moon it has been a 
matter of popular knowledge that a body projected from the earth 
with a velocity exceeding 7 miles per second will go off in a hyper- 
bolic orbit, never to return. This applies to the molecules of a gas. 
Any of them that may be travelling outward with such a speed in 
the region where collisions are so rare as to be negligible, will leave 
the earth for good and will thus be lost to our atmosphere. The 
rate of leakage from the atmosphere thus depends on the number of 
molecules per unit of time that acquire the limiting (outward) veloc- 
ity of 7 miles per second. This number, in turn, depends on the 
temperature in the region under consideration, a point regarding 
which our information is very uncertain. But an exact knowledge 
of this temperature is not needed to compute a major limit, a max- 
imum figure which the rate of escape certainly cannot exceed. It 



190 



ELEMENTS OF PHYSICAL BIOLOGY 



is thus found that under present conditions 2 the earth holds her 
atmosphere so effectively that there cannot be any appreciable 
leak even in many millions of years. 

Cosmic losses from the atmosphere then, are, for nil practical pur- 
poses; wholly negligible. Certain other subtractions from and acces- 
sions to the atmosphere we shall have occasion to note as we consider 
the circulation of the several elements. As a matter of fact the com- 
position of the atmosphere in the region in which living organism 
have their habitation is very nearly uniform 3 and constant, except 

TABLE 13 

Constituents of the, atmosphere 





AT HAHTH 

For cout by 

volume 


8 H imp AC XI 

1'or cent by 
weight 


IN BNTinn 

ATMOHPKHmU 

Total amount 


Nitrogen 


78.03 
20.99 
0.03 
' 0.94 
0.01 

0.0012 
0.0004 


75.45 
23.21 
0,05 
1.30 
0.0003 


metric tons 

3.9 X 1Q 15 
1.2 X 10 15 
2.2 X 10'* 
6.2 X IQ U 
1.3 X 10' 1 
1.3 X 10 13 
4.7 X 10i 
0.4 X 10 
0.3 X 10 9 
1.2 X 10" 


Oxygen 


Carbon dioxide 


Argon 


Hydrogen , 


Water 


Neon 


Krypton 


Helium 


Xenon , 





Earth's surface = 1,97 X 10 8 square iniloH ~ 5.5 X 10 18 square foot. 
One square mile = 2.79 X 10 7 square fcofc. 
One metric ton = 2205 pounds. 



s It may be noted in passing that in the earth's pant history conditions 
may have been different. If at any time the temperature of the upper at- 
mosphere was about 750C., then there must have been a very distinct loss 
of hydrogen by leakage into space. The moon, and certain of the planets 
having a lesser gravitational pull or a higher temperature (Mercury), have 
probably lost in this way any atmosphere that they may have had. For a 
detailed discussion of this and other points in connection with the escape 
of gases from the atmosphere the reader may be referred to J. H. Jeans's 
Dynamical Theory of Gases, 1921, Chapter XV. See also K A. Milne, Trans. 
Cambr. Phil. Soc., vol. 22, 1923, p. 483; J. E. Jones, ibid., p. 535. 

8 Except in the neighborhood of volcanoes, and in lesser degree, in or near 
large cities or manufacturing centers, where large amounts of waste gases 
may be discharged into the atmosphere. 



STAGE OF THE LIFE DRAMA 



191 



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^^^11 1 fl 

TD "~* r ^ w o. w ^ 

S ,c) d pd /7 1 ^ O 

*H O CQ Q, Pi rQ rQ 

O rT to ft 






w * 43 ^ 


U .3 .3 fl 3-3 rt 






Water. . 


> rt =) p) 

s|2| 

ra r> a) % 

-r-i X ^ oj 

P O PE| O 


, . rl OQ 03 8 .C OQ B 

M- pj <o to 3 m a) 1-5 
"2 3 p) rt .3 eg pi .s 

S % ?-2 ^ S'rS 

"o o i| i| r ^ o ,| a 
o>o)S^OPHSQ 


C5 pTrl [Xj 

* -i -h-H 



192 



ELEMENTS OF PHYSICAL BIOLOGY 



as regards its moisture content, and wo may accept for the composi- 
tion of the atmosphere at the earth's surface, moisture excluded, the 
figures shown in the first two columns of table 13. The third column 
shows the total amounts of the several constituents of the entire 
atmosphere, according to W. J. Humphreys (Monthly Weather 
Review, vol. 49, June, 1921, p. 341). 

Cosmic Accessions to the Atmosphere. Meteorites falling upon 
the earth from space bring with them certain o entities of entangled 
or occluded gases. While this contribution tt the atmosphere is at 
the present time, presumably, of negligible dimrnsions (see also page 
195, Cosmic Accessions to the Lilhospfwrc), yet in the course of the 

TABLE 15 
Comparison of air and aqiutlic atmosphere 







HIilA 




HII A. 




8 13 A. 




A tic i'i<m 

IiITffllt* 


WAT I')U 
15 "O. 
PHU 


Allt IIY 
VOM1MI8 


W. VI' I'll I 

15 "0. 

JIV 


AIK nr 

VVJQIOIrt 1 


WAT Eli 
15 "C. 
BY 






U'CHK* 




vofjirMii 




William.' 




cc. 


(1C. 


/XT ce.nl 


/><:r ct'.n,t 


'IXiT Cllllt 


per cant 


o 


209.9 


6.8 


21.0 


lfi.0 


23.2 


12 8 


N 


780.3 


11. ,'J 


78.0 


29,0 


75.4 


21 7 


C0 2 


0.3 


21. 7f 


0.03 


50.0 


05 


05 6 

















* Measured at 0G. and 760 nun. Ug. 

f42.7ingm.; according to F. W. Clarke, Data of CicocluMnistry, Geological 
Survey Bulletin. 491, 1920, p. 142; G. Linck, KroiHlaufvorgiitige in dor Erd- 
gescMchte, Jena, 1912, p. 6. 

long procession of ages past this source may not have been wholly 
insignificant. Data on this question, are at best very uncertain, 
and a mere passing reference must suffice. 4 

The Hydrosphere. In comparison with the ocean alt other aggre- 
gations of water upon the earth are insignificant in aimmnt. The 
bald statement of the total volume of the ocean 302 million cubic 
miles 'conveys but little to the mind. More impressive it is to 
recall that the average depth of the sea is 2$ miles, and that, even if 
these waters were spread over the whole earth, leaving no continents, 
the average depths would still be If miles. 

The average composition of the ocean is shown in table 14. Here 
again, the figure for the volume of total dissolved solids, 4.8 million 
cubic miles, is made more readily comprehensible by a graphic illus- 
tration. The salts of the ocean, made into one solid block, would 

* F. W. Clarke, Data of Geochemistry, U, S. Geological Survey Bulletin 
695, 1920, pp. 58, 269, 282. 



STAGE OF THE LIFE DRAMA 193 

cover the entire United States and Alaska to a depth, of Ixfr miles; 
or according to J. Joly, they would encrust the whole earth to a depth 
of 112 feet. 5 

The Aquatic Atmosphere. Aquatic species perform their respira- 
tion in contact with an atmosphere of gases held in solution in the 
water that surrounds them. This atmosphere is very different both 
in concentration and also in composition from, that in which we live, 
as is apparent from table 15. 

A comparison of the several columns in table 15 is an object les- 
son on the adaptability of living organisms to varied conditions. 
The atmosphere in which fish and other marine animals live in com- 
fort would not only drown us with its principal constituent, water, 
but, even if this were removed, the residual gases would suffocate us 
for lack of oxygen; and if the deficiency in this gas were made up by 
the addition of the amount required to bring the percentage up to 
that to which we are accustomed, we would still be choked by the 
excessively high percentage of carbon dioxide. 6 

The Lithosphere. Immense as the ocean appears to us, with its 
average depth of 2| miles, yet it constitutes less than vsV<r of the 
total mass of the earth, whose bulk is thus concentrated chiefly in 
lithosphere. Of the deeper layers of this lithosphere we have but 
scant and indirect knowledge. Earthquakes give evidence of some 
change in constitution about half way down to the center of the globe. 
Conditions and occurrences at such depth as this would seem, in the 
present state of our knowledge, to have little bearing upon the life 
at the surface. Other indirect evidence regarding the earth's inter- 
ior is derived as follows : The volume of the globe being known from 
triangulation, and its weight from direct determination with a bal- 
ance 7 or in other ways, the mean density of the earth is found to be 

6 F. W. Clarke, ioc. cit., p. 24; Sci. Trans. Roy. Soc. Dublin, 1899, vol. 7, 
p. 30. 

6 It must be admitted, however, that much of this COg in sea water is par- 
tially neutralized by alkali. 

7 A concise survey of the principal determinations of the mass of the earth 
will be found in J. H. Poynting's little book (in the Cambridge Manuals series) 
The Earth (1913) It may add interest to the bald figures to note hero in 
passing that the density of the earth's crust (2.7) is not very widely different 
from that of the moon (3.46). This fact has a certain significance in connec- 
tion with Sir Charles Darwin's theory of the origin of the moon, according to 
which our satellite originally formed part of the earth and was thrown off 
by a species of tidal disruption. The bulk of the moon, then, would be formed 
of material derived from the outer layers of the earth. 



194 



ELEMENTS OF PHYSICAL BIOLOGY 



TABLE 16 
Average composition of terrestrial matter* 



LITHO8PHERB 
(93 PERCENT) 



HYDBOSPHBBB 
(7 PEE CENT) 



AVEBAGK 

INCLUDING 

ATMOSPHERE 



Oxygen 49. 19 

Silicon 25 . 71 

Aluminum 7 . 50 

Iron 4.68 

Calcium 3.37 

Sodium 2.61 

Potassium 2 . 38 

Magnesium 1 .94 

Hydrogen ."': 0.872 

Titanium 0.648 

Chlorine .228 

Bromine 

Phosphorus . 142 

Carbon . 139 

Manganese .108 

Sulphur .093 

Barium .075 

Chromium .062 

Zirconium .048 

Vanadium .038 

Strontium .032 

Fluorine .030 

Nickel 0.030 

Nitrogen 0.030 

Cerium, yttrium .019 

Copper .010 

Lithium 0.005 

Zinc 0.004 

Cobalt 0.003 

Lead 0.002 

Boron .001 

Glucinum .001 



100.000 



85.79 



0.05 

-1-14 

0.4 

0.14 

10.67 

2.07 
0.008 

0.002 
0.09 



100.000 



46.68 

27.60 

8.05 



03 
63 

72 



2.56 

2.07 

0.145 

0.696 

0.095 

0.152 
0.149 
0.116 
0.100 
0.079 
0.066 
0.052 
0.041 
0.034 
0.030 
0.031 

0.020 
0.010 
0.005 
0.004 
0.003 
0.002 
0.001 
0.001 



100.172 



* Adapted from F. W. Clarke, Data of Geochemistry, 1921, p. 35 ; Clarke and 
Washington, Proc. Natl. Acad. ScL, 1922, vol. 8, p. 114. 

5.5. But the mean density of the rocks outcropping at the surface 8 
is only 2.7. Whatever may be the character of the earth's interior, 

8 Compare also E. D. Williamson and L. H. Adams, Jour. Washington 
Acad. Sci., 1923, vol. 13, p. 413; H. S. Washington, ibid., p. 453. 



STAGE OF THE LIFE DRAMA 195 

it is thus evident that it is composed of/lenser material than we find 
at the surface. In point of fact, comparison with meteorites, and 
other evidence, make it appear likely that the earth's interior is vir- 
tually a metallic regulus (chiefly iron), encrusted with a slag not un- 
like that which separates out and floats on the molten mass of metal in 
a blast furnace. Such, essentially, is the raw material of our land- 
scape, such our habitation, such the ground on which we tread and 
from which we draw the substance of our body. For the fertile soil 
in the plain is but the weathered variant of the granite strength of 
the hills, and we ourselves but a strangely metamorphosed portion 
of the world-stuff, the slag coating of a metal core. 

Cosmic Accessions to the Lithosphere. The earth receives a con- 
stant shower of meteorites from interstellar space, at an annual rate 
of some 20,000 tons. 9 This seems a large amount. As a matter of 
fact, spread over the surface of the globe (197 million square miles), 
the accumulated meteoric material of a thousand million years would 
make a layer only 1 inch thick, if its density were that of water, or a 
correspondingly thinner layer of denser material. 

Composition of the Earth's Crust. Table 16 adapted from F. W. 
Clarke's Data of Geochemistry and a more recent publication by 
Clarke and Washington, shows the average composition of the known 
terrestrial matter. The first column, in particular, gives the figures 
for the solid crust. This table exhibits a number of facts and rela- 
tions of interest. Perhaps the first significant circumstance that 
strikes the eye, in glancing at the table, is the very unequal deal 
with which nature has distributed matter among the ninety odd 10 
known elements. One-half the lithosphere, and one-quarter of the 
atmosphere are made up of the element oxygen. 

The eight most abundant elements of the earth's crust (oxygen, silicon, 
aluminum, iron, calcium, sodium, potassium and magnesium) the only ones 
whose amounts are over 1 per cent constitute together over 98 per cent of 
the earth's crust. These, with hydrogen, titanium, carbon and chlorine 
twelve in all make up 99.5 per cent; thus leaving only one-half of one per 

9 S. Arrhenius, Worlds in the Making, 1908, p. 108. See also Young, 
Astronomy, 1904, p. 475. 

10 Uncountable isotopes aside. 



196 



ELEMENTS OF PHYSICAL BIOLOGY 



Ba 
Cr 0.08 

tt LJL_ 



S 0-18 
O.ll a 



d2\g.$8 



IS 
Aly 
o.or 



Ca 

3.ZZ 



Si 

Sff.80 



o 

SO.OS. 



Compos. '/ Van of arf/>'o 



At 
7.30 



A/a 



Z.S8 



a p r 

a?o r F Mn 
/y n 0.11 ato o.og 



s 

O.I1- 



Fe 

O.Ol 




63.0 



0.10 O.H 



Z.S 



Compost ft'an a'f Human Boc/y. 



FIG. 42. COMPARISON OF COMPOSITION OF EARTH'S CRUST AND HUMAN BODY 
Figures indicate percentages 



STAGE OF THE LIFE DRAMA 



197 



cent for all the other elements, among them some quite indispensible for 
our existing civilization. 11 

Relation to Composition of the Organism. Of the elements spe- 
cifically significant for the living organism, only one, oxygen, is pres- 
ent in great abundance. Carbon, hydrogen and nitrogen, the prin- 
cipal "organic elements/' are among the less abundant constituents 
of the globe. On the whole it may be said the living organisms are 
composed of comparatively rare elements. We are, indeed, earth- 
born, but yet not altogether common clay. 12 This is well brought out 

TABLE 17 
Average composition of human body 





POUNDS 


PERCENT 


Oxygen 


97 20 


63 03 


Carbon 


31 10 


20.20 


Hydrogen 


15.20 


9.90 


Nitrogen 


3 80 


2 50 


Calcium 


3 80 


2 50 


Phosphorous 


1 75 


1.14 


Chlorine 


0.25 


0.16 


Fluorine 


22 


14 


Sulphur 


22 


0.14 


Potassium 


0.18 


0.11 


Sodium. . . 


16 


0.10 


Magnesium 


0.11 


0.07 


Iron 


01 


01 








Total 


154.00 


100.00 









in the chart figure 42, which shows, side by side, the average composi- 
tion of the known terrestrial matter, and, in comparison, the approxi- 
mate composition of the human body. This latter is not exactly a 
representative sample of the totality of living matter (see tables 17 

11 H. S. Washington, Jour. Franklin Institute (1920), vol. 190, p. 7. Tho 
figures have been slightly modified in accordance with the latest data of 
F. W. Clarke and H. S. Washington, Jour. Natl. Acad. ScL, 1922, vol. 8 p. 
114. 

12 Indeed, taken literally the expression "common clay," as applied to 
man, is an extreme case of poetic license; for aluminum and silicon the 
chief constituents of clay, and taking second and third place in rank of abun- 
dance among the components of the earth's crust, are both present only in 
tracea in the human body. 



198 



ELEMENTS OP PHYSICAL BIOLOGY 









|-|| 


ii d 


^a l" W! n> *H ^ d 

rj O O CD T3 O O .r3 










"o --s o 


d3 >> m Ct fl pC( X! 








Ss CS Kn 




C5 O _g o d bD O 




















ao rv H 












OQ *"^ *^H 

^ ""9 

fli H ^H 

c _3 o 
f ftX 


11 B 

slS 


| K|| a |j| B 




1 




I 'g g 
= 5 g 

^^1 

-P ,M 
J 

o tB-a 


O g M 

d Jj <u 

J3 > 

CD ^ 

9 4 

'3 a " 

is-s 


11 iPiSi! 

03 m ' : <tiwr i M ta ^TCQO) 

^1 1 S & l S S.g i 8 S 








w-T.S jn 


o ,S 


"mpn ^ra'S'SpQ^'^^o 








!r* 9 -<j 


rS rJ-T 


03 .u TT "-ua fl^Q 03 r~\ T^ S^cS 








"i h ' 


o "jip 5 


aM 








& 


*-^ ri /^ 


W " ' *~> OJ M l_i '' -*-* * n .-H ^ 








rt ^^ *^ 


ri S t"^t 


rj Cl ""* CQ o3 CJ 'T^ d f-I f-i d DQ 








J-< rn m 


ft ^ 


03 gfcl!>^c3gC^c3o3 






CQ 

a 

CQ 


8 8 

q o .B 


_fl 


i ^-s ^^ i i 


















c3 


TJ ft o 


^ 


^S^a ^ TS < 






tfl 


a) ft 


o 


o o C a) Pt ft ^ 


# 

eo 

s 

t v> 




{* 
O 

bC 

fl 


1^ . 


ft 

m 


a, -e f^ - '7 ' S's'S'^ 

jU^ .1 :! 


8 




'> 


K a 


ft 


-2^^ "^ **H "Srl^Irt 


e 




\^4 


O !-< 


T3 


* ^ O ^ ("5 cJ ^ 03 M rl cJ 


Cs 


H 




U 


j-j 


r ' ^Ca^ *~i ^fc.w 


u 

o 


3 


_g 


cfg 


cS 


Q.^d ^ ^ ^^gi g _g 


e 


j 

P< 


SJ 

rt 


-a S -g p 


s 


cf 1 ~w -g .t2 o 3 So 3 "o 'fl 


^ 




ID 


2 S-^ M d| 


*o 


"* p. K. bjQ t|_5 H ^j pjC] Q^ 


S> 




HJ 








5* 




(P 


"** CL C 


"ti 


~*-^ . rH CJ -|J O C^ C3 f ~ H (1 ^** 






^ 








v^ 




ft 


d ^ s c 


Q* 


' H -+-3'-c3KJrj ^ S) ""* ^ 


Q 












^pos^t^on 




>^ 

1 

1 

d 


s-5^-1 

n e ^ 3 

>> G fl 

W 


"3 

g 


llliillilill 

253 ^Ti g^S^ -5 ^g ft 

j ( <cj (^ pL| p] 


R 


^ 


*H 

CO 










o 


-t-2 













rt 

(D 


td o o iz 




M d 0) 




H 

0] 





"^ 


w 


^ f=5 <sj m 






,2 












P3 




m 






|j 




S a 


s 


d R 




w 

a 

H 






J 


1 1 'S | 




J 








t cj| QJ rj ,J 




W 




"tj 'P Sr h 


o 


A ^ bO P) 








^j .a KJ t "H 


_j 


~ n ^ oS O 








Wuo^ 


PH 


,5 n M r ^ >H 
CO AH ^i O M 




s 




ta 








ft S3 




(a ** ^ 








^ * s 












B P 




o ^J M 


t> 


1O !> "*?H CO 




B g 




^ CD 00 T^ 


TH 


CM TjH l> CXD 1O 








JtS O H 


t>" 


CCl t^ Ci <7^| 00 




O P. 












u 




^00 


U5 


<M .H CO CO TH 




o ft 




00 U5 








3 o 




O O O rH 

o o o o 


>* 

o 


CO O W *-* 
O >-l CO O CXJ 




2 & 




l-l t-4 H 


CO 


c<i o> # p ic 

CO CO CM "^ ^O 



^ 



STAGE OF THE LIFE DRAMA 



199 



-P 

d 




-P 
rt 


.2 






ri 


S) 














03 








'CQ 


-p 










-d 






d 


















d 

,J2 




d 
d 

X5 


03 
1 






13 

d 


"d 










d 




o3 


ft 






CO 


-< 










ft ^ 




GQ 


". 






d 


o 










GQ 


^ 


13 


rd 






o3 


-2 










*c8 

a 


ft 




ft 

a 






3 


83 










"d 




"d 




03 
O 




[o 


CQ 


CQ 








13 


d 


13 


1 


'3 
O 




13 
e3 


03 
bO 

d 
o 


"3 

a 








d 


-a 


.3 


13 


J 




.2 


ft 

CQ 


'd 

03 








.1-1 


o 


-p 


o 


CO 






CQ 


^ 








-p 

d 


o 


d 

03 


3 


bfi 




"p 

d 


g 


rS 








03 
CO 
03 


.3 


CO 
03 

F-l 


.9 


j 




03 
CQ 

03 


S 


bfl 

a 








M 

PH 




pn 








F-< 

PH 












elieved essential to all plants, but 


not demonstrated; found in ma- 


rine plants, especially Phseophyceas 
resent in many plants ; believed by 


some to be essential ; abundant in 


03 
-p 

.3 
3 

'o 

03 
ft 
CQ 
03 

88" 
bfl 

"3 

d 
1 

a 


Phseophycese 


ound in all plants ; present in large 


quantities in the Diatomacece, 
both fresh-water and marine; in 


form of "silica" constitutes 0.5 ; 


to 7 per cent of the ash of ordinary 


marine alga3 


pq 




PH 








fo 












03 
























* 




O 








w 
















rv.. 




















rt, 

a 




.3 








&-. 

d 
















'C 








o 












;*:j 




o 








.S 












o 
OJ 




6 








.F-4 

GQ 












co 
























C33 




^o 




















CM 




CM 




















CO 




CD 
























CO 
































CO 












B 

CO 




1C 








oo 












CM 




co 























,3 


s s 


&4H K^H CQ 

O O 03 


r9 




r-< 


fcfl bD 


., d 






a 


"I ;-| 


"P* CQ O 


o 




"cl 


CQ CQ 


03 ~ ^ 


02 








j 03 aj 






C3 


t*} t^i 


JS -d -P 


CO 






FH Lj 1 


Tn CO C3 


03 




JH 
CD 

,d 


CD 03 

l> > 


2 d X) 
f 3 .3 o 


"K 




bfl 


.2 .3 


-e 
o - S 


6 







r-S ra 

'S 13 


1 rS t> 
^ CD d 

03 03 -r-i 


^ 




^ 


3 urj 


g -^ 13 


t-T 

r-l 




.2 


'd d 'd 

d ,O oJ 


d "S "IS "3 
.2 3 g ^ 


O5 

TH 






'-p 




-p~ 




.5 " 
'-P b 
d ff 
CQ c!i 

CQ 


-P M 03 
CQ O C) 

2 P* S 

a g 

d ^d 


1 ra 

rv d 03 -d 

o d -3 

M CQ 2 

flj P.Q 3 


_bO 

"S 

ft 
o 




H 


HH M 


hH 


o 


co 

a 


|.3.S 


JS 


.3 


03 

d 


CQ 




f^ 




o 


"r~j 







IT* 


_ o 


C3 


S^ Mj |-Q 


^? 


8 


CQ 

O 


FH 


c3 <^ 


c3 


&> 


^ 


o 










bO 

.3 


I ! i 

02 2 -5 


O 
03 

CO 


1 


F4 


JH 


0? ^ [-^ 


03 


S 


!* 


a 


-p ~ 13 CQ 


co~ 


^ CO 


^ 


-p 
d 


d d r d S 

r2 ^ 3 


-p ^ 


oT ^ 

o'3 5 


M 

d 

03 


03 
co 


"ft -^ ^. 

o3 " bD 


d a 


3 a g 


M 


03 




r^ 03 


FH J*3 




F-< 

ft 


li'll 
3 5 '| 9 


"ft _d 

03 "FH 
3 03 


go J 

O S 03 


: 




aF-l ft H 


H H 


F-I d M-I 




d 

03 


v o 

Z ^ CQ 

1 1 


O R 

CO 

d d 


f g 

HH 


"o 


03 








d 


+3 








o 


CQ 








-P 


"a 

1 


M 


d M 

s pq 


h 


"o 


w 




03 




1 






CQ 










rt 03 


03 


*bJD 






S C-I 


.3 


* EJ 




03 
.3 


bfl '3 

3 g 


'C 
o 


? 




O 
M 


S PQ 





S 




CO 






1 




CO 






j , 




t- 






aj 




i ( 






o 




O 






^d 




CM 

Oi 


CO CM 
O O3 


o 


o 
ft 

03 

Qj 







"S * 


o 


rM 



d 

ft C 
03 CQ 



200 



ELEMENTS OF rriYBTCAL BTOLOftY 







9 d 


IJJ 

Pi 






4 <U 


M 






d b* 1 


O 








m 






"S d 

CO 


a 






w m 

CD > 


m 

O) 

o 






af^9 ,2 


d 






'~3 ^ C3 


.J3 


oQ 




W cj (LH 




3 




0-3 g 


m 


a 




^ 3 d 

3 'd 2 rt 


^^ ^ 


i 




s a a s i 


a -9 






'9 '3 g bs M 


'3 S 






f d d-5 h d 


d 






p CD ' H fl, aj 

^ a s g s 
d s g g a g 

,9,3 H H 


CD P- 

a ^3 

o 
KI d 




00 

a 








M 








|H 








O 








bD 






1 


_d 






3 


*rH 

_pj 


w en OT en CQ M 


W r/ j r/3 r/] 




"3 


+- 1 "P 4-j ~tn! 'tj ^f^ 

d d pi d d o 

d d 9 <3 JB rr) 


d 'S d d 

d 3 ^ d 




Q) 

OT 


ft ft p, ft ft p. 


ft p, ft ft 




g 

ft 


^ ^: cu E- t 1 ^ 
CD CD Q ^cU CD pj 


[S CD 1* \f. 
CD d CD CD 

t)^ M *4H *4H 




' 


"^ **t o l " ^ o 
d d co d TO r/3 


^ ^ , 
wg [/j C3 C3 




d 


pi d d d d d 

M M M M M M 


d d d d 

1 1 M M M 




fn 








op 






p 


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ELEM: 




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-^^pqfqOO h5h-] 


r H H 4^J 

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31 is 

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f.. rH 


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6 d< 
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rH O O O 


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rH <M 


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ft 



cu q H 

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-fl 



STAGE OF THE LIFE DKAMA 



201 



and 18) but will serve well enough for the present pupose. The chart 
brings out very pointedly the selective character of the organism's 
activity in gathering to itself the substance of its body. Thus car- 
bon, which both in function and in relative quantity figures so promi- 
nently in living matter, appears as an insignificant lifctle block in the 
chart of the earth's crust. A similar contrast, if not quite so extreme, 
is seen in the case of nitrogen. With aluminum and silicon the com- 
parison works the other way about very plentiful in the earth's 
crust, these elements are practically absent from the human body. 13 
Taking the mother earth as a whole, and the organism as a whole, 
it certainly cannot be said that there is much evidence of "inheritance 

TABLE 19 
Composition of the salts in sea water and in blood serum in per cent* 







SEA WATER 


BLOOD SBBDM 


Sodium 


Na 


30.59 


39 


Magnesium 


Mg 


3.79 


0.4 


Calcium 


Ca 


1.20 


1 


Potassium 


K 


1.11 


2.7 


Chlorine 


Cl 


55.27 


45 


Sulphate ion 


S0 4 


7.66 




Carbonate ion 


C0 3 


0.21 


12 


Bromine 


Br 


0.19 




Phosphoric acid . 


PaOfl 




0.4 











* Maccallum, Trans. Koy. Soc. Canada, 1908, II, p. 145. 

of parental characters" in their respective compositions. Still, resem- 
blance is not wholly lacking. This becomes evident if we compare, 
not the entire organism with the whole of the earth's crust, but the 
blood of a mammalian, for example, with the water of the ocean. This 
comparison is made in table 19 and figure 43. The likeness thus seen, 
imperfect as it is, can hardly be ascribed to accident. The fact is, 

13 Silica furnishes, however, the skeletal support in a variety of living 
forms (radiolaria, sponges, plants). Cf. G. Bunge, Physiological and Path- 
ological Chemistry, 1902, p. 23-24. For a detailed discussion of the distri- 
bution of the chemical elements in organic nature see Vernadsky, Revue Ge"n. 
Sci. The reader interested in this phase of the subject should not fail to 
acquaint himself with this article, which came to the writer's attention too 
late to be given more than this passing note here. 



202 



ELEMENTS OF PHYSICAL BIOLOGY 



Cl 
55.3 



Na 
30.6 



SoJJds 
in 



7.66 



3.79 



KU 



Br 
O.f3 



O.O 



0.4 



1.0 



2.7 



0.4 



Soh'ds 

in 
Blood Serum 



No 
39 



an a dry fi 



Cl 
45 



. 43. COMPARISON OF SEA WATER AND BLOOD SERUM 



STAGE OF THE LIFE DKAMA 203 

as pointed out by Palitzsch, 14 that aquatic species are in such intimate 
contact, both at their body surface, and more particularly in their 
gills, with the surrounding water, that the latter might almost be 
considered continuous with their bloody fluids, so that sea water may 
justly be "placed in the same category as the other physiological 
fluids." "Frederiq 15 has shown that the amount of sodium chloride 
in the blood of Crustacea varies, and all but corresponds, with the 
density of the water in which the creature has been kept." More 
highly organized aquatic species have made themselves in greater 
degree independent of the salinity of their environment; 18 and finally, 
it would appear, when the marine ancestors of terrestrial vertebrates 
emerged from the sea and adventured life on dry land, they packed, 
as it were, a portion of their saline environment in their baggage, and 
took it along with them on their excursion as an essential part of their 
milieu interieur. And to this day, according to this view, we our- 
selves cany about with us in our arteries and veins, if not a portion 
of the actual ocean, at least a roughly approximate replica of its 
brine. For, as L. J. Henderson 17 remarks: "Not only do the body 
fluids of the lower forms of marine life correspond with sea water in 
their composition, but there are at least strong indications that the 
fluids of the highest animals are really descended from sea water." 
Some such indications may be seen in the reflections (conceived from 
a slightly different point of view) of G. Bunge, 18 "I am convinced that 
the remarkably high percentage of salt in vertebrate animals, as well 
as the desire to take salt with our food, can be satisfactorily explained 
only by the theory of evolution." In support of this consideration 
Bunge points out that in the weathering of rocks by the action of 
rain-water charged with carbonic acid, the sodium is dissolved and 
carried off as carbonate, while the potassium largely remains behind 
in combination with silica. The sodium carbonate being washed to 

14 Comptes-rendus, Laboratoire de Carlsberg, 1911, vol. 10, part I, p. 93. 
See Chapter I, footnote 19. 

16 Arch, de Zool. Exp. et Gen., 1885, Ser. 2, vol. 3, p. XXXV; see also D'Arcy 
Thompson, Growth and Form, 1917, p. 127. 

16 Compare D'Arcy Thompson, loo. cit., p. 127-130; Claude Bernard, In- 
trod. a 1' etude de la me"decme exp., 1855, p. 110 as quoted on p. 17 (and foot- 
note 20) of Chapter I. 

17 The Fitness of the Environment, 1913, p. 187. 

18 Loc. cit., 1902, p. 101-103, 



204 ELEMENTS OF PHYSICAL BIOLOGY 

the sea undergoes double decomposition with the alkali earth chlo- 
rides, these latter being deposited as carbonates (limestone and dolo- 
mite) while the sodium remains in solution as salt. Thus sea water 
is rich in sodium chloride and poor in potassium, while on dry land 
the balance is essentially reversed. 19 Plants and invertebrate ani- 
mals, Bunge points out, contain little sodium, unless they live in a 
highly saline habitat, in or near the sea, or on salt steppes. Yet the 
land vertebrates are all remarkably rich (comparatively) in salt, in 
spite of the scanty supply around them. 

Is not the large amount of sodium chloride found in the present inhab- 
itants of dry land another proof of the genealogical connection which we 
are forced to accept from morphological facts? There is no doubt that each 
of us in his individual development has come through a stage in which he 
still possessed the chorda dor satis and the branchial arches of his sea-dwel- 
ling ancestors. Why may not the high average of salt in our tissues be also 
inherited from them? 

Support for the supposition thus suggested is seen by Bunge in the 
fact that the younger a vertebrate is in its individual development, 
the more salt does it contain. Furthermore, cartilage contains the 
highest percentage of sodium of all the tissues of our body, and is 
also the tissue of greatest antiquity. The human skeleton is origi- 
nally composed of cartilage, which is replaced, for the most part, by 
bone as the individual matures. 

These are facts which lead most readily to the interpretation th? * the 
vertebrates living on dry land originally came from the sea, and aw still 
continuing to adapt themselves to their present surroundings, where they 
can get but little salt. We prolong this process of acclimation by taking 
advantage of the salt strata which have been left on the land by our primeval 
element, the salt flood. 

Chemical Correlation in Soil and in Organism. Our ancestral 
resemblance to the soil from which we spring is also exhibited by 
evidence converging from a different source. II. S. Washington, 

19 This observation must be accepted with some caution. Compare 
Whitney, Science, 1922, vol. 56, p. 218. "Until we determine the actual loss, 
through chemical denudation, of silica, alumina, iron, potash and other 
electrolytes in the colloidal state, carried by rivers, we are in no position 
to even speculate as to whether erosion is a selective process which might 
change the chemical composition of the soil." 



STAGE OF THE LIFE DEAMA 



205 



in his studies on The Chemistry of the Earth's Crust, already cited, 
draws attention to the fact that in the rocks soda and iron tend to be 
associated together as a pair on the one hand, and potash and mag- 
nesia on the other. This is well brought out in the diagram figure 
44, reproduced from Washington's memoir, in which it is seen that 
the points representing the analysis of a number of rock samples tend 
to group themselves about the diagonal of the square, indicating that 




FeO 



FlG. 44. COKBELATION IN THE OCCURRENCE OF Na, Fe AND ~K, Mg IN ROCKS 

A large number of analyses here plotted show a marked tendency to array 
themselves along the diagonal, showing that high percentage of Na is com- 
monly associated with high percentage of Fe; K and Mg follow a similar 
relation. After H. S. Washington. 

high content of soda goes together with high content of iron, but with 
low potash and low magnesia; and vice versa. The point of special 
interest to us here in the present connection is that to which Dr. 
Washington draws attention in the words: 

Curiously enough, the same correlation between these two pairs of ele- 
ments, soda and iron, and potassium and magnesium, seems to hold good in 
the organic world. This is apparently shown by the following facts: In 



206 ELEMENTS OF PHYSICAL BIOLOGY 

autotrophic plant metabolism potash is an essential element, as is also mag- 
nesium, in that chlorophyll (which in the leaves acts as the carbon-trans- 
ferring substance) is a magnesium salt of a complex organic acid, while sodi- 
um and iron are generally toxic toward (at least the higher, gymnospermous 
and angiospermous) plants. On the other hand, sodium, rather than potas- 
sium, is the alkali metal essential to the higher animals, salt being a very 
necessary article of diet (in part because of its chlorine, and in part because 
of its sodium, content), and sodium chloride is present in the blood plasma; 
and at the same time, hemoglobin and its derivatives (which act as oxygen 
carriers, and are analogous to chlorophyll in plants) are iron salts of organic 
acids closely related to that of chlorophyll; while, similarly potassium and 
magnesium are more toxic toward the higher animals than are the other 
pair. 

This singular parallel must not, of course, be looked upon as an 
instance of resemblance due to anything of the nature of inheritance 
of ancestral traits in the biological sense. Rather must it be con- 
nected in our minds with the fact that systems composed of the same 
fundamental substances, will display certain analogies through inter- 
play, in them, of the same chemical affinities. 

Accessibility of Valuable Earth-Constituents. Such a comparison 
as has been made above of the relative abundance of the several ele- 
ments in the living organism and in the environment from which it 
draws its supplies, would be misleading if attention were not drawn 
to another factor aside from abundance, which enters strongly into 
play in the quest for the necessities of life. More important than 
mere abundance is accessibility. For, a substance may be present in 
comparatively large quantities, and yet be difficult to lay hold of, 
either on account of its wide dispersal in dilute form, or for other 
reasons. On the contrary, a comparatively rare substance may be 
procurable with relative ease, if it occurs segregated in concentrated 
or otherwise readily accessible form. Perhaps the most telling illus- 
trations of this are to be found in industry. The element copper for 

2 

example is found only to the extent of about -r per cent in the 



earth's crust. Yet it is one of the most important metals in the arts, 
and is not ordinarily thought of as particularly rare. This is because, 
in those regions where it does occur, it is found in concentrated form, 
either as native metal, or as rich ore. Other instances are readily 
cited. Tin, lead and zinc are all rarer than copper, and each rarer 
than its precursor, in the order named. Still rarer are silver, tungs- 
ten, gold, bromine and platinum, all of which find important use in 



STAGE OF THE LIFE DRAMA 



207 



^ 

O r-l (-H r-t 



WrH 



M 






Si 



r-i CM CO 



42803 22 19 



iO CO t- 00 CJ 



1SI 



n S 




02 
W 



O *z 
W ffl 
02 o ,_, 

O CU 

-> J _O 

pa 5 

R H 



-<1 
^ 

O 



p 

O 

M 

W 

fM 



208 ELEMENTS OF PHYSICAL BIOLOGY 

the arts. But the mode of occurrence of these substances is such that 
they can be gathered or rained with comparative ease. It has been 
pointed out by H. S. Washington that the elements, as arranged in 
Mendeleeff's table, naturally fall into two groups divided by a zig- 
zag line, as shown in figure 45. Above this line are the rock elements 
or petrogenic elements, that enter into the principal rock-forming 
minerals (and also, the gases of the atmosphere). Below the line 
are the ore elements or metallogenic elements, which commonly occur 
in concentrated form as ores and as native metal. 

Now man's industrial activities are merely a highly specialized 
and greatly developed form of the general biological struggle for 
existence ; and this same feature of accessibility and of concentration 
in segregated supplies (ores and the like), which is a prime con- 
dition for the very existence of some of our industries, is also involved, 
in closely analogous manner, in the more primitive life processes. 
Our fields demand fertilizers bringing ammonia, nitrates, potash, 
phosphates, etc., in suitably concentrated form, if they are to bear a 
harvest commensurate with the needs of a modern community. 
And this again is merely an accentuated example of the still more 
primitive needs of the unsophisticated flora and fauna of virgin nature. 
Of scattering, dissipating processes there are plenty. Rain and snow 
wash most of what is soluble, and much that is not, into the rivers 
and^ut to sea. Our own activities in modern intensive agriculture 
briiig each year to the land a highly concentrated diet of fertilizers, 
which in the very act of cultivation are scattered and diluted many 
thousand times. And our modern sewage system is deliberately 
wasteful of vital substances, which it discharges into streams and 
out TO sea. All this dissipation must in some way be balanced if the 
regime is to continue. Thus the circulation of matter in nature must 
no/fc only provide for the mere presence of certain substances on which 
^che maintenance of life depends, but it must furnish them in suitable 
' concentration and, generally, in available form. It must, therefore, 
in many cases include, as a definite step, a segregating or concen- 
trating process 20 as well as simple motion through a cycle. 

We shall have occasion to note concrete illustrations of this in the 
separate consideration of the circulation of the several elements, to 
which we now proceed. 

20 The significance of this from the point of view of energetics will engage 
our special consideration in a later section. 



CHAPTER XVI 
THE CIRCULATION OF THE ELEMENTS -THE WATEH CYCLE 

The great Sea-water finds its way 
Through long, long windings of the hills; 
And drinks up all the pretty rills 
And rivers large and strong: 

Then hurries back the road it came 
Returns on errand still the same; 
This did it when the earth was new; 
And this for evermore will do 
As long as earth shall last. 

Words worth. 

The ancients, totally blind as they were perforce to the fine details 
of material transformations revealed by the search light of modern 
chemistry, nevertheless recognized in its broad features the cycle of 
life, the circulation of the elements in nature. "Dust thou art, 
and unto dust shalt thou return," we read in an old book of wisdom. 
Heracleitus (536 to 470 B.C.), promulgator of the famous doctrine 
Tr&vra /Set has a more detailed, if not more accurate conception of the 
cycle of Nature, which he formulates in these terms: 

Earth 
S \ 
Fire Water 

Vapor 
(Air) 

The human mind was not yet schooled, then, to polish the facets of 
this rough gem, and bring out the sharp-edged truth as we see it 
today 

Solid 

\ 
Liquid 

Vapor 

209 



210 ELEMENTS OF PHYSICAL BIOLOGY 

But all honor to the minds that discerned through the mists of dawn 
the bold features of the landscape to be revealed in the sunlight of 
later day. Today we recognize not four elements, but over ninety, 
not counting those modern variants, the isotopes. And we follow in 
much detail not one cycle, but, as particularly pertinent to life, five 
major cycles the circulation of water, carbon, oxygen, nitrogen 
and phosphorus. This was noted already at the conclusion of 
Chapter XIV, but the discussion of the cycles was deferred to give 
space to a preliminary survey of the scene in which these cycles churn 
the planet's surface in their age-long duty. 

We are now prepared to take up the thread where we broke off; 
we turn our attention first to the water cycle. 

Water Requirements of Human Body. We do not ordinarily 
class water as a food, though we partake of it by the same channel .. | 
that gives entrance to the materials commonly so classed, and 
although the lack of water, if we are by any circumstance deprived 
of this substance, is felt even more acutely than an interruption in 
the adequate supply of food. The fundamental basis for this dis- 
tinction, its origin in the unsophisticated mind, is undoubtedly the fact 
that we have a separate sense of thirst, distinct from the signals of 
hunger and appetite originating from nutritive demands of the body. 
And this naive, unsophisticated distinction is entirely in accord with 
the reasoned analysis of the respective functions of water and of 
food in the narrower sense. It is undoubtedly just because of this 
difference in function that thirst and hunger have been developed as 
separately recognized sensations. Water acts merely as a vehicle; 
unlike the food, which undergoes extensive and complicated reac- 
tions within the economy, water leaves the body essentially as it 
enters it, unchanged chemically, though charged (in part) with sub- 
stances in solution. 

It would be a gross error, however, to suppose that water, because 
it functions thus in accessory capacity, and escapes the more intimate 
transmutations of metabolism, can be lightly regarded in making a 
survey of the participation of the several elements in the cycle of 
nature. It must be remembered that water constitutes as much as 
60 per cent of the total mass of the human body, for example, and a 
still greater proportion of the substance of most of our food-stuffs, 

as shown in table 20. _ 

.,*f? 



WATER CYCLE 



211 



Thus an adult human being consumes per diem about 3 liters of 
water of which about 1 liter is contained in his solid food. In point 
of fact he consumes about 5 pounds of water for every pound of dry 
solid matter ingested. It is thus seen what an important item water 
is in the daily economy of the human organism. 

The excretion of water by the kidneys, lungs, intestine and skin 
is somewhat in excess of the intake. The excess of the outgo over 
the intake is formed in the body by the oxidation of hydrogen 
organically combined. 1 

Water Requirements of Plants. Rainfall as a Limiting Factor. 
In the economy of most plants the traffic of water is of even 
greater importance 2 than in man and land animals generally, and 

TABLE 20 
Moisture content of some common foods 





PER CENT 




PER CENT 


"RAAf (frpqM 


43-65 
40-71 
66 
11 
87 
27 
12 
35 


Sugar granulated 



78 
81 
63 
94 
86 
1 


Fish 


Cabbage 




Cucumbers 


Rntfpr 


Potatoes 




Tomatoes 




Strawberries 




Walnut, California 


White bread 







indirectly the moisture needs of plants are, of course, of funda- 
mental importance also to the animal population feeding on the 
vegetable growth of the soil, so that the water supply of a territory 

1 L. J. Henderson (The Fitness of the Environment, p. 133) estimates that 
a man weighing 60-70 kgm. excretes daily: 

grams 

Water 2500-3500 

Carbon dioxide 750- 900 

All other substances 60- 125 

and that water is, accordingly, three-fourths and carbon dioxide one-fifth 
of the total excreted. The proportion of water excreted from kidneys, skin, 
lungs and intestines, is given by Kirk (Physiology, p. 208) as 1:0.5:0.22:0.09, 
or 11.5:5.75:2.5:1. 

2 L. J. Henderson, loc. cit., estimates that of the materials ingested by 
ordinary green plants, more than nine-tenths is water, and carbon dioxide 
at least five sixteenths of the remaining tenth. 



212 ELEMENTS OF PHYSICAL BIOLOGY 

may function as the basic limiting factor of the total life which that 
territory is able to support. A study of these relations with partic- 
ular reference to the human population of the United States, has 
been made by W. J. McGee, who remarks : 3 

Hellriegel in Germany and King in this country have shown that crop 
plants require for their growth_a quantity of water, measured by transpira- 
tion, averaging from 300 to 600 (with a mean of about 450) times the weight 
of the plants after drying; and common field experience indicates that, in 
addition to the moisture passing through the plants, the soil requires an even 
larger quantity to maintain a texture suitable for crop growth much of 
which passes away through evaporation and seepage. On this basis "the 
agricultural duty of water" in this country has been formulated as the pro- 
duction of one-thousandth part of its weight in average plant crop. Reck- 
oning human food and drink on this basis, and assuming that meats require 
(chiefly in the growth of plants used as feed for the animals) ten times the 
quantity of water represented in vegetal food, it appears that the adult who 
eats 200 pounds each of bread and beef in a year consumes something like 
1 ton of water in drink and the equivalents of 400 tons in bread and 4000 tons 
in meat, or 4401 tons in all figures corresponding fairly with the results of 
intensive agriculture in arid districts. Accordingly, the "duty of water" 
considered in relation to human population may be stated roughly as the 
maintenance of a human life a year for each 5 acre-feet used effectively in 
agriculture. 

Now mainland United States (i.e., the chief body of our territory, ex- 
clusive of Alaska and the insular possessions) comprises something over 
3,000,000 square miles, or somewhat less than 2,000,000,000 acres of land; yet 
the annual rainfall the sole original source of fresh water averages barely 
2* feet (30 inches), or hardly 5,000,000,000 acre-feet. So while the land area, 
if peopled to the density of Belgium (over 640 per square mile,) would carry 
a population of 2,000,000,000, the water supply suffices for only 1,000,000,000. 

The conclusions of McGee may have to be modified in point of 
detail, and some of his figures may perhaps have to be revised; but 
the general principle underlying his reflections attract our attention. 
The moisture needs of the living population (all species included) 
are a large and fundamental item in biological economy; whether 
this item proves the ultimate limiting factor of population growth, 
as McGee suggests, is a question whose answer must be sought in 

3 Science, 1911, vol. 34, p. 429; Yearbook of the Department of Agricul- 
ture, 1910, pp. 169-176; Bureau of Soils Bull. 71 (1911), pp. 7-14; World's 
Work, 1912, vol.. 23, p. 443. Compare also L. J. Briggs, The Water Require- 
ments of Plants, U. S. Department of Agric., Bureau of Plant Ind Bul- 
letins 284, 285. 



WATER CYCLE 213 

terms of Liebig ? s Law of the Minimum; a dearth of other essentials 
may make itself felt before the limit of available moisture is reached. 

The Sources of Supply. Such, then, in broad outline, are the 
moisture needs of organic nature; as such they have existed, in greater 
or less degree, for millions of years, and have been satisfied, and will 
continue long to be satisfied, from a source essentially inexhaustible 
because constantly replenished by the return flow : The great reser- 
voir is the ocean, with its 302 million cubic miles of water, and an 
evaporating surface of over 144 million square miles. Annually 
there rise from this into the atmosphere about 63,300 cubic miles of 
water, to which some 22,800 more are added by evaporation from the 
land, making a total of 86,100 cubic miles. This figure also repre- 
sents the total precipitation in rain, snow, etc., but of the total 
about 56,700 fall back directly into the ocean, and only the balance, 
29,400 is available for the needs of the land. It has been noted that 
the evaporation from the land is about 22,800 cubic miles. The 
difference between this and the precipitation on land, the balance of 
6500 cubic miles, is the drainage from the land to the ocean by rivers. 

No attempt will be made to estimate what proportion of the precip- 
itation on land is derived from evaporation over the sea, and what 
proportion comes from the land itself. Some idea of the relation, 
however, can be formed from a consideration of the difference or the 
ratio of the rainfall within the area drained by rivers and the amount 
actually discharged by them into the sea. John Murray 4 has col- 
lected information on this subject, with the result shown in table 21, 
which covers 33 of the world's principal rivers. It will be seen that 
the total rainfall in the area of these rivers is 10,186 cubic miles, 
the discharge to the sea is 2182 cubic miles, leaving a difference of 
8004 cubic miles unaccounted for. A certain portion of this perhaps 
represents seepage, but the bulk must correspond to water re- 
evaporated from the land and from inland waters. It will be ob- 
served that for the 33 rivers combined the proportion of the dis- 
charge to sea to the total rainfall is about one-fifth. For individual 
rivers the ratio varies widely, between the extreme of 0.58 (Rhone) 
and 0.027 (Nile). Naturally the climate very materially affects this 
figure. 

4 Scottish Geographical Magazine, 1887, vol. 3, p. 76. 



214 



ELEMENTS OF PHYSICAL BIOLOGY 



There is also a circulation of waters of the sea in very large di- 
mensions. According to L. J. Henderson 5 the Gulf Stream in the 
Straits of Yucatan carries 200 million tons per second, 6 travelling 

TABLE 21 

Showing the drainage area, annual rainfall, annual discharge, and ratio of 
discharge to rainfall, of S3 rivers in different parts of the world 



POSITION 
OP MOTJTH O 
BIVBB 


RIVER 


DRAINAGE 
AHBA 


ANNUAL 
RAINFALL 


MEAN 
ANNUAL 
DISCHARGE 


MEAN 
RATIO 






square miles 


cubic miles 


cubic miles 




50-60N. 


Rhine 


32,600 


19,500 


10,100 


2,049 




Oder 


51,100 


14,700 


2,500 


5,803 




Niemen 


36,450 


10,355 


3,783 


2,737 




Vistula 


65,800 


19,908 


5,657 


3,508 


40-50N. 


St. Lawrence 


565,200 


338,967 


87,312 


3,904 




Danube 


320,300 


198,736 


67,511 


2,746 




Po 


27,100 


23,887 


13,322 


1,794 




Volga 


592, 300 


152,384 


43,736 


3,484 




Seine 


23,250 


10,266 


5,469 


1,877 




Rhone 


34,850 


22,439 


14,066 


1,724 




Dnieper 


197,450 


56,093 


22, 195 


2,527 




Loire 


42,600 


18,210 


7,810 


2,332 




Dniester 


30,950 


8,792 


3,274 


2,685 


30-40N. 


Yang-tse-kiang 


689,100 


408,872 


125,043 


3,421 




Hoang-ho 


387,150 


' 117,711 


28,591 


4,159 




Nile 


1,293,050 


892, 120 


24,334 


30,998 




Pei-ho 


65,000 


22,354 


1,650 


13,551 


20-30N. 


Mississippi 


1,285,300 


673,064 


125,603 


5,446 




Rio Grande 


232,300 


113,655 


12,676 


8,966 




Indus 


360,050 


104,416 


26,032 


4,886 




Ganges 


588,450 


549,791 


43,263 


16,169 


10-20N. 


Magdalena 


92,900 


116,746 


59,451 


1,964 




Irawali 


181,950 


180,849 


82,298 


2,256 




Kistna 


81,300 


61,025 


14,776 


4,137 




Godavery 


154,850 


95,924 


16,841 


5,708 


0-10N. 


Orinoco 


429,700 


603,397 


122,242 


4,936 


Equator 


Amazon 


2,229,900 


2,833,830 


527,951 


8,009 


0-10S. 


San Francisco 


212,900 


218,459 


22, 197 


9,842 




Congo 


1,540,800 


1,213,044 


419,291 


3,213 


20-30S. 


Orange 


267, 150 


50,913 


21,875 


2,327 


30-40S. 


Olifant 


14, 300 


2,472 


0,679 


^,639 




De La Plata 


994,900 


904,687 


188,740 


091 




Uruguay 


151,000 


130,890 


32, 136 


X073 


Total 


13,272,000 


0,186,460 


2,182,485 







5 The Fitness of the Environment, 1913, p. 182. 
8 Across any cross-section of the stream, presumably; the statement is 
not clear on this point. 



WATER CYCLE 



215 



with, a mean velocity of about 80 miles per day. This circulation in 
the ocean has of course no direct part in the water cycle of the organic 
world, but indirectly is most important on account of its climatic 
effects. 



m- 



\ r 



Oceo/% 

///&./m. 
mill $f mi. 






figures \rifhout denomination a fie cubic 



FIG. 46. CIRCULATION OP THE ELEMENTS IN NATURE. THE WATEE CTCLEI 

Water Cycle Diagram. The principal figures relating to the 
circulation of water on the globe are exhibited in diagrammatic form 
in figure 46, which tells the story more effectively than words. It 
may here be added in explanation that the 3000 cubic miles of 



216 ELEMENTS OF PHYSICAL BIOLOGY 

moisture contained in the air are practically restricted to the lower 
6 miles or so of the atmosphere. For the rest, this moisture is un- 
evenly distributed, as everybody knows from personal weather 
observation. Water vapor and condensed water differs in this 
respect from the other permanently, gaseous constituents of the 
atmosphere. (See table 12 and figures 40, 41.) 

Fraction of Total Water Circulation Taking Part in Life Cycle. 
Only a fraction of the total circulation of water actually passes 
through the organic cycle. We may make an attempt as follows to 
obtain a rough idea of the order of magnitude of the fraction 
thus concerned. 

If the entire land surface were cultivated to produce crops at the 
rate adopted as standard by W. J. McGee, the growth produced 
(figured in dry weight) would be T ^u~ ff of the rainfall. Furthermore, 
this growth would evaporate, by transpiration, about 500 times its 
own weight of water, (this is assuming one crop per year). It would 
therefore evaporate just about one-half the annual rainfall. But the 

22 800 

total evaporation on the land is OQ'QQQ = tnrce fourths of the an- 
nual rainfall on land, the remaining fourth being drained to sea by 
rivers. Hence, of the water evaporated on land, one-half times 
four-thirds = two-thirds is evaporated by plants and thus takes 
direct part in the organic cycle. In comparison with the evapora- 
tion by plants, that from animals is undoubtedly negligible, espe- 
cially in view of the coarseness of our data. If we put the evapora- 
tion on land as one-fourth of the total evaporation, we finally arrive 
at the value one-sixth as that fraction of the total water in circu- 
lation, which takes actual part in the organic circulation. 

Desert areas cannot materially alter this estimate, since they con- 
tribute but little to either side of the account, both evaporation and 
life being meagre or absent. In some measure this remark also ap- 
plies to frigid wastes of the polar regions, where the low temperature 
makes for comparatively low evaporation (a factor counter-balanced, 
it is true, in some degree, by the extensive cover of ice and snow) . 
For temperate zones McGee's figure for cultivated fields is undoubt- 
edly too high to apply as an average for the entire land. In the trop- 
ics, on the other hand, it is perhaps not excessive. On the whole the 
fraction one-sixth computed as above is probably too high, but per- 
haps it serves to give us an idea of the order of magnitude involved. 



WATER CYCLE 217 

Another estimate leading to a materially lower result, is obtained 
as follows: If we accept Engler's estimate that one-fiftieth of the 
atmospheric carbon dioxide, that is to say, 4.4 X 10 10 metric tons, 
takes part in the organic cycle; and we adopt the figure given by 
L. J. Henderson 2 that the water taken up by plants, is about 11 times 
the C0 2 which they absorb, we obtain, as a very rough estimate of 
the water engaged in the organic cycle, an amount of 5 X 10 U 
metric tons, or, in round numbers, 120 cubic miles. This, then, is 
about vfar of the total annual circulation of water, or about $%-$ of the 
total rainfall on land. 



CHAPTER XVII 
THE CARBON DIOXIDE CYCLE 

Behold how great a matter a little fire kindleth. St. James. 

If the lamp of life is a poetic symbol, it is an image essentially 
true to fact. Not only is life, in particular animal life, largely a 
combustion process: like the flame, life reaches out for fuel, and 
with the power gained, strains again for more. Like the flame it 
consumes, and it spreads. And as the fire sends out sparks, of which 
many die, but a few, falling upon favorable ground, flare up as a 
second generation, in reproduction of the parent flarne; so the living 
creature scatters its seed, some to die, but some also to live again 
the life of the parent. "But," someone perhaps will remark, "a 
fire may start without preexisting flame; whereas all life is itself 
begotten of life." Is this distinction really so fundamental? In 
nature undisturbed by man the starting of a fire spontaneously is 
a rare event; and that, after all, is the most that we can say posi- 
tively regarding the origination of life from the non-living it is 
either so rare or so unobtrusive 1 an event as to have escaped our 
observation. No doubt it took man many thousands of years to 
acquire the art of lighting a fire, may not in the lapse of time a 
second Prometheus arise to teach us also how to kindle the torch 
of life? Let us not delay his coming by closing our minds to the 
possibility. 2 

1 Compare F. J. Allen's view, as presented by L. L. Woodruff in The Evolu- 
tion of the Earth and its Inhabitants, 1919, p. 102: "Life at this stage was 
of the humblest kind, since there were no definite organisms, only diffuse 
substances trading in energy, and between this stage and the evolution of 
cellular organisms an immense period elapsed." If this picture of the begin- 
ning of life is true to fact, the process was unobtrusive ; probably, if we 
were shown a specimen of such elementary "living" matter, we should not 
recognize it as such. All this is in accord with what has been said in an 
earlier ^ chapter regarding the definition of life. If we continue to use the 
word life, this is merely a matter of convenience and does not imply any 
departure from the point of view set forth in the opening chapters. See 
also p. 19. 

218 



CARBON DIOXIDE CYCLE 



219 



Be that as it may, the fundamental fact remains that slow com- 
bustion, oxidation as the chemist calls it, is a dominant feature in 
the physiology of animal life, and that the leading roles in this 
action are played by the elements carbon and oxygen. 

In our method of securing our supply of these elements there is 
a certain dyssymmetry. Carbon we eat in our meals; oxygen we 
breathe in in respiration. But in function the two elements stand 
in essentially symmetrical relation; the two together and impartially 
furnish us with the requisite energy for our life activities. ^ Thus 
we must regard oxygen as food as much as carbon. This fact 
deserves a passing note, since it is sometimes stated that assimila- 
tion of inorganic food is a characteristic of plants, as distinguished 
from animals. The statement rests on an arbitrary and wholly 
gratuitous exclusion of oxygen from our list of foods. It just so 
happens that there is one item on the animal's menu, namely, oxygen 
that is gaseous and is spread broadcast; does not therefore have to 
be hunted and captured. Toward this the animal assumes the 
same attitude which, presumably, plants adopt toward all their 
foods: he takes it in unconsiously. This touch of plant nature 
which we recognize in ourselves should serve to give us a sympathetic 
insight into the "psychology" of plants. At the same time it re- 
minds us once again of the esentially arbitrary character of the 
division of organisms into two classes, animals and plants. One 
and the same organism possesses both animal and plant characteris- 
tics, and this is true even of that most highly specialized of ^all 
animals, the human being. In view of the symmetry in function 
that exists between carbon and oxygen, and the inseparable relation 

2 It is easy to strike a match, but this is merely a way of borrowing tho 
efforts of others, those who have made the match possible, and those who 
have manufactured it. How many city dwellers could, by their unaided ef- 
forts, start a fire where none was before? Anyone who, in an emergency, 
may have been forced to attempt the feat will appreciate how among tho 
ancients "the spark of fire was zealously guarded and soon invested with 
sacred attributes .... The chief function of the vestal virgins in Homo 
was to keep the perpetual fire; and in the Catholic church today with its 
never extinguished light we have the last survival of what was once a social 

custom " Another curious survival of this custom is quoted 

by E. A. Seligman (Principle of Economics, 1908, p. 69): "Whenever the 
location of gas works is changed the fire is transferred by a brand from tho 
old to the new building. Under no consideration would a new fire bo started." 



220 ELEMENTS OP PHYSICAL BIOLOGY 

in which, they stand in the life processes of the organism, we shall 
consider jointly, in this chapter, the circulation of carbon on the 
one hand, and of oxygen on the other. 

The Carbon Cycle. A very particular interest attaches to the 
carbon cycle. Carbon is the organic element par excellence, whose 
absence from any chemical substance stamps this forthwith, by 
common if somewhat arbitrary consent, as inorganic: whose pres- 
ence affords the soil ? ,, \ season for the growth of what might be 
termed the tropical jungle in the domain of chemistry. For in the 
compounds of carbon nature seems to have run riot, in a revel of 
creative versatility, as if vying to set a record unapproached else- 
where in all the realm of chemistry, for number, variety and com- 
plexity of her children. Other elements 'oxygen, nitrogen, phos- 
phorus, sulphur, iron, indeed play a significant role in life processes; 
but the indispensable bond that ever links all other ingredients in 
organic unity is carbon. Furthermore, carbon is preeminently the 
energy carrier, the standard coin of the organic real, in which both 
the first cost of installation, of anabolic tissue building, and also 
the running cost of operation, of metabolism, is defrayed. 

Indescribably complex far beyond the understanding of the 
organic chemist of today as are the metamorphoses that carbon 
undergoes in the economy of the organism, its source and its gate of 
entry into the organic cycle are comparatively simple. Some two 
and a half million million tons (2.2 X 10 15 kgm.) of carbon dioxide, 
in the air, and perhaps twenty to twenty-five times this amount 
contained in the waters of ocean, lakes and rivers, these constitute 
the store from which all life ultimately draws its supply. 

Of this vast store, according to an estimate made by C. Engler, 3 
about one-thousandth part actually takes part in the cycle of life. 
The total carbon locked up in living organisms, which would be 
a measure, in a way, of the spread of life on our globe, is difficult 
to gage even roughly. One hardly knows how much or how little 
significance to attach to an estimate by A. G. Hogbom 4 that the 
total quantity of carbon in all living matter is of about the same 
order as that contained in the atmosphere, namely, 6 X 10 11 metric 

3 Linck, Kreislaufvorgaxige in der Erdgescliichte, 1912, p. 6; Engler, tJber 
Zerfalls-prozesse in der Natur. 

4 Clarke, Data of Geochemistry, 1920, p. 49. 



CAKBON DIOXIDE CYCLE 221 

tons; an amount which, spread over the entire surface of the globe, 
would cover it with a film of carbon 1 mm. thick, or with a film of 
living matter about | inch thick. 

The organic carbon cycle, reduced to its simplest terms, is a 
closed chain of three links. 

Atmosphere 



/ Green 

Animals* Plants 

Green plants, under the influence of sun light, absorb C0 2 from the 
atmosphere and convert it, with elimination of oxygen, into the many 
and complex compounds of the plant substance. 5 Animals consume 
plants (directly or indirectly) as food, and in the course of the 
operations of their typically active lives (as compared with the 
typically passive, vegetative existence of the majority of plants) 
they reoxidize the carbon reduced in the photosynthetic plant 
processes, and return C0 2 to the atmosphere, thus completing the 
cycle. 

In actual fact this simple fundamental cycle is complicated by a 
number of influences. The decay of dead animals and plants adds 
a comparatively small item to the discharge of C0 2 into the atmos- 
phere. Plants are somewhat mor-e resistant to complete decay 
than animals, and one result of this is the accumulation of notable 

6 To discuss here the chemistry of photosynthesis in plants would lead 
us too far afield. Very important advances have been made recently in 
this field of biochemistry. It must suffice here to refer to the original liter- 
ature of which the following articles may be mentioned: E. C. Baly, Photo- 
synthesis, Nature, March 16, 1922, p. 344. Report of discussion on photo- 
synthesis at the British Association Meeting, Nature, December 23, 1922, 
p. 856. I. M. Heilbron, The Photosynthesis of Plant Products, Nature, 
April 14, 1923, p. 502. 0. Baudisch, On the Formation of Organic Compounds 
from Inorganic by the Influence of Light, Science, April 20, 1923, p. 451. 
0. Baudisch, The Influence of Light on Inorganic Matter and Life Processes, 
Jour. Industrial and Eng. Chemistry, May, 1923, p. 451. J. C. Bose, Effect 
of Infinitesimal Traces of Chemical Substances on Photosynthesis, Nature, 
July 21, 1922, p. 95. Baly, Heilbron and Parker, Photochemical Produc- 
tion of Formaldehyde, Nature, September 1, 1923, p. 323. J. H. Mathews, 
Trends in Photochemical Research, Jour. Ind. and Eng. Chem., September, 
1923, p. 885. 



222 ELEMENTS OF PHYSICAL BIOLOGY 

quantities of reduced carbon in the form of peat and coal. This 
process of fossilization is slow, and would not in itself, in any short 
period, materially affect the carbon cycle. It has, however, fur- /\ 

nished the occasion for a phenomenon which, judged in a cosmic , ' 
perspective, represents a purely ephemeral flare, such as must ulti- 
mately appear utterly insignificant in the geological calendar, if 
duration alone is considered; but which to us, the human race in 
the twentieth century is of altogether transcendent importance: 
The great industrial era is founded upon, and at the present day in- 
exorably dependent upon, the exploitation of the fossil fuel ac- 
cumulated in past geological ages. 

We have every reason to be optimistic; to believe that we shall 
be found, ultimately, to have taken at the flood this great tide in 
the affairs of men; and that we shall presently be carried on 
the crest of the wave into a safer harbor. There we shall view r\ 

with even mind the exhaustion of the fuel that took us into port, 
knowing that practically imperishable resources have in the mean- 
while been unlocked, abundantly sufficient for all our journeys to 
the end of time. But whatever may be the ultimate course of 
events, the present is an eminently atypical epoch. Economically 
we are living on our capital; biologically we are changing radically 
the complexion of our share in the carbon cycle by throwing into 
the atmosphere, from coal fires and metallurgical furnaces, ten 
times as much carbon dioxide as in the natural biological process 
of breathing. How large a single item this represents will be rea- 
lized when attention is drawn to the fact that these human agencies 
alone would, in the course of about five hundred years, double '-r 

the amount of carbon dioxide in the entire atmosphere, if no com- 
pensating influences entered into play. In point of fact the per- f 
centage of carbon dioxide in the atmosphere exhibits remarkable I 
constancy and there are several very large items, in addition to 
those already touched upon, both on the ingoing and outgoing side ' 
of the account. The case of man has been singled out for mention 
here merely because our knowledge of the human population and 
economy enables us to make a reasonably close estimate of 
his contributions. The quota supplied by the remaining animal 
species can hardly even be guessed at. But probably the greatest 
source of atmosphere C0 2 are volcanoes and mineral springs. Coto- 
paxi alone has been credited with an annual discharge of two million 4 
tons of the gas. *- * [ 



CAEBON DIOXIDE CYCLE 223 

On the debit side there is first of all the item of consumption by 
plants. E. H. Cook, 6 from very uncertain data, computes that 
leaf action alone more than compensates for the production of 
carbon dioxide, consuming about one-hundredth of the total at- 
mospheric oxygen in a year. Yost 7 computes that if the entire land 
area were planted with sun flowers, about 6.5 X 10 11 tons of CO 2 
would be absorbed per annum. Forests would be considerably 
less efficient, and would take care of about 2.8 X 10 10 tons per an- 
num, or, say in round numbers one-hundredth of the atmospheric 
carbon dioxide. An older estimate, by Liebig, puts the annual 
output of the soil of Central Europe at 2.5 tons of dry organic matter 
per hectar, or, say 1 ton per acre. Allowing 40 per cent carbon 
in such organic matter we find for [the total annual production 
of carbon in plants 13,000 million (1.3 X 10 10 ) tons. This is 
about ten times the world's annual coal consumption, and about 
one-fiftieth of the total carbon in atmospheric carbon dioxide. 
Arrhenius points out that if all this carbon fixed by plants were 
deposited in peat bogs, the atmosphere would be depleted in half 
a century. But, of course, only a small proportion of the bodies 
of plants are thus "horded" and removed from the organic life cycle. 

A figure of perhaps greater interest, because based upon observa- 
tions of processes actually going on in a selected portion of the 
universe, is given by W. R. G. Atkins. From the observed change in 
the hydrogen ion concentration in the water of the English Channel, 
this author has calculated that 250 metric tons of organic carbon 
(figured as hexose) were produced per square kilometer between 
July and December. From similar observations made at Port 
Erin, Moore found a production of 300 metric tons per square 
kilometer during the six months that included the vernal maximum, 
of diatom production. 8 

An important item among the withdrawals from the atmosphere 
is the absorption of carbon dioxide in the weathering of rocks, with 
replacement of silicates by carbonates. A. G. Hogborn reckons this 
item as about balancing the reproduction of carbon dioxide in the 

F. W. Clarke, loc. oit., p. 48; Phil. Mag., 5th ser., vol. 1882, p. 387. 

7 Pflanzenphysiologie, 1913, p. 151. 

8 Journal of Marine Biol. Assoc. October, 1922, vol. 12, no. 4, Nature, 
January 27, 1923, p. 132. 



224 ELEMENTS OP PHYSICAL BIOLOGY 

combustion of coal. Its accumulated record is seen in the sedi- 
mentary rocks, which, according to F. W. Clarke, 9 contain 30,000 
times as much as C0 2 as are today present in the atmosphere. 10 
Sterry Hunt "illustrates the effect of weathering by the statement 
that the production from orthoclase of a layer of kaolin (china clay) 
500 meters thick and completely enveloping the globe would con- 
sume 21 times the amount of C0 2 now present in the atmosphere." 
Chamberlin and others estimate that it would take about 10,000 
years to consume the present amount of atmospheric C0 2 by the 
weathering of rocks. Loss of C0 2 by peat formation may be esti- 
mated at the same figure. The formation of COa by the burning 
of coal would, according to these estimates, cover the loss by weather- 
ing and peat formation combined, seven times over. 

Finally, there is the great reservoir of the ocea, in equilibrium 
with the atmosphere, and absorbing, under present conditions, some 
18 to 25 times as much C0 2 as it leaves in the air above it. Thus 
the sea acts as a vast equalizer; of every ton of C02 thrown into 
the atmosphere by volcanoes, or by coal fires, for example, the 
ocean ultimately receives directly or indirectly, about 1900 pounds, 
only the balance of 100 pounds remaining in the atmosphere. It 
is thus seen that even extensive contributions from the lithosphore 
have but a slight effect upon the atmospheric store, and fluctuations 
are in this way ironed out and moderated. Arrhenius 11 points 
out, moreover, that at the present time the carbon dioxide content 
of the air over the ocean is on an average 10 per cent lower than 
over land. From this, and the fact that generation of C0 2 by coal 
(and probably also from volcanoes) has in late years been in- 
creasing, he concludes that the air is, at the present epoch, becom- 
ing richer in this gas. 



8 Loc. cit., p. 48. See also C. Shuchert, The Evolution of the Earth and 
its Inhabitants (Yale Press, 1919), p. 52. 

10 Hogbom's figure, quoted by Arrhenius (Worlds in the Making, 1908, 
p. 54), is 25,000 for limestones and dolomites. Am. Jour. ScL, 3d ser, 1880, 
vol. 19, p. 349. Clarke, loc. cit, p. 48. 

11 Loc. cit., p. 54. Arrhenius' figure differs somewhat from the one given 
above. He supposes that the sea takes up five-sixths of the CO Z thrown 
into the air, i.e., 1 ton would yield up 1667 pounds to the ocean, leaving 333 
pounds in the air. 



ft 



CARBON DIOXIDE CYCLE 225 

As to which side of the account shows a net balance, in the carbon 
cycle, we have no certain knowledge. Arrhenius builds his con- 
ception of the future industrial development of our race on the 
expectation that the atmosphere is gaming in carbon dioxide, under 
the present regime of "evaporating" our coal mines, as it were 
into the air. On the other hand, if our atmospheric C0 2 is of 
volcanic origin, and the balance is maintained today with the aid 
of discharge from the lithosphere, then the ultimate extinction of 
the earth's plutonic fires would bring in its train the depletion of the 
atmosphere and secondarily the extinction of life. "The cessation 
of volcanism would signify the end of life on the globe." A similar 
position is taken by C. Schuchert, 12 who further remarks: 

We should add that if there were again as much life as there is at present, 
all the carbon of the atmosphere would be in the living plants and animals, 
and, if such a condition were possible death would come to them all .... 
Life and its abundance at any time are conditioned by the amount of this 
gas (COt) present in the atmosphere. 

This remark of Schuchert's is suggestive as illustrating in concrete 
manner the relative amounts of carbon concerned in the life balance. 
It is, perhaps, somewhat misleading in making no mention of the 
equalizing influence of the ocean which has been noted above. In 
point of fact, if all the C0 2 in the air were withdrawn, a nearly equal 
amount would rise from the ocean to take its place. 

A summary, in graphic form, of the principal relations in the 
carbon cycle noted in the preceding paragraphs, will be found in 
figure 47, which should aid in giving a comprehensive picture of 
the situation. < ; 

The Oxygen Cycle. The organic oxygen cycle is, of course,, 
directly related to the carbon cycle, although other features also 
enter into operation in regulating the oxygen balance of the atmos- 
phere. The complementary relation between animals (essentially 
oxidizors of carbon) and plants (essentially reducers of carbon diox- 
ide) is indeed a biological fact of fundamental importance at the 
present stage of evolution. But if we look back through the vista 
of ages, to the time before the advent of life, such as we^know it, 
our curiosity is aroused as to the origin of the atmospheric carbon 

i The Evolution of the Earth and its Inhabitants, 1919, p. 52. 



226 



ELEMENTS OP PHYSICAL BIOLOGY 




H 
O 



o 



NA 



B 

W 


w 
tJ 

W 



ft 
o 

o 

e 

! 
t-3 
P 
O 



M 

O 



(JABEON DIOXIDE CYCLE 227 

dioxide and oxygen. Various views have been upheld on this 
subject. F. W. Clarke 13 remarks: 

It is likely that carbon dioxide has been added to the atmosphere by vol- 
canic agency, in some such manner as this: Primitive carbon, like the graph- 
ite found in meteorites, a,t temperature no greater than that of molten lava, 
reduced the magnetite of igneous rocks to metallic iron, such as is found in 
many basalts, and was itself thereby oxidized. Then, discharged into the 
atmosphere as dioxide,, it became subject to the familiar reactions which 
restored it to the lithowphere a,s coal or limestone. 

Arrhonius, 14 referring to Koehno's reflections on this subject, 
points out that the atmosphere contains about 1.2 X 10 1 ! 5 tons of 
oxygen, an amount which roughly* 6 corresponds with the mass of 
fossil coal in the sedimentary rocks. "The supposition appears 
natural, therefore, that all the oxygen of the air may have been 
formed at the expense of atmospheric carbon dioxide. Probably 
all the oxygen of the air owes its existence to plant life." 

F. W. Clarke resumes the views of a number of investigators as 
follows: 10 

C. J. Koehne assumed that the primitive atmosphere contained no free 
oxygon, and he has boon followed by T. L. Plupson, 17 J. Lemberg, 18 J. Steven- 
son, 10 and Lord Kelvin." Lomberg and Kelvin, however, do not go to ex- 
tremes, but admit that possibly Homo free oxygen was present even in the 
earliest times. Lemberg argued that the primeval atmosphere contained 
chiefly hydrogen, nitrogen, volatile chlorides, and carbon compounds; the 
oxygen which is now free, being Mum united with carbon and iron. The 



13 F. W. Clarke, loc. oil., p. 55. 

"Worlds iu the Making, 1908, p. 58. 

111 The correspondence is rather distant if we accept Engler's estimate of 
the world's coal reserves, namely, !J X 10 1S tons, containing 75 per cent car- 
bon.. Hoc Lin ok, loo. oil;., p. 37, Kngler'H estimate is probably low. The 
World Altnanao, 1921, p. 201., given 7.5 X H) n! tons. This would correspond 
to 1.5 X 10 13 tons oxygon, as against 1.2 X ID 11 ' tons in the atmosphere. It 
is true that these ostinmteM of coal reserves cover only such coal as it would 
pay to mine. 

F. W. Clarke, loc. oil;., 1021, p. 50. 

17 Chom. News, ISO.'J, vol. 07, p. i:?5. Also several notes in vols. 68, 69, 
and 70. For Koohno'n work wee PhipHou'n papers, 1893-1894. 

"Zeitsohr. Deutsoh, gool. (lenell, 1888, vol. 40, pp. 030-634. 

I'PhiloH. Mag., 1900, 5th ser., vol. 50, pp. 312-,'JOO; Oth ser., 1902, vol. 4 ; 
p. 435; 1905, vol. 9, p. MS; 1900, vol. 11, p. 220. 

* Ibid., 1899, 5th Her., vol. 47, pp. 85 89. 



228 ELEMENTS OF PHYSICAL BIOLOGY 

liberation of oxygen began with the appearance of low forms of plant life, 
possibly reached a maximum in Carboniferous time, and has since diminished. 
Stevenson's argument is much more elaborate, and starts with an estimate 
of the uncombined carbon now existent in the sedimentary formations. In 
the deposition of that carbon, oxygen was liberated, and from data of this 
kind it is argued that the atmospheric supply of oxygen is steadily increasing, 
while that of carbon dioxide diminishes. The statement that no oxygen has 
been found in the gases extracted from rocks is also adduced in favor of the 
theory. First, an oxidized crust and no free oxygen in the air; then proc- 
esses of reduction coming into play ; and at last the appearance of lower 
forms of plants, which prepared the atmosphere to sustain animal life. The 
arguments are ingenious, but to my mind they exemplify the result of at- 
taching excessive importance to one set of phenomena alone. It is not clear 
that due account has been taken of the checks and balances which are ac- 
tually observed. At present the known losses of oxygen seem to exceed the 
gains. For example, C. H. Smyth 21 has estimated that the oxygen with- 
drawn from the air by the change of ferrous to ferric compounds, and so 
locked up in the sedimentary rocks, is equal to 68.8 per cent of the quan- 
tity now present in the atmosphere. 

G. Bunge 22 also supports the view that atmospheric oxygen is 
continually diminishing, becoming bound by the ferrous oxide 
resulting from the decomposition of silicates. Accumulation of 
carbon dioxide in the atmosphere, at any rate under present condi- 
tions, is also assumed by S. Arrhenius, as has already been remarked. 23 

21 Jour. Geology, 1905, vol. 13, p. 319. 

22 Text book of Physiological and Pathological Chemistry, 1902, pp. 16-17. 

23 See Jour. Franklin Inst., 1920. vol. 190, pp. 114-121. 



CHAPTER XVIII 
THE NITROGEN CYCLE 

If the denuuul becomes inHiHteut enou K h, wo cannot doubt that methods 
will be dovimul which mil K iv us the desired results. To question that would 
bo to admit thai; man haw nearod the culmination of his evolutionary career 
and is preparing to bequeath the iwwtery of the earth to hia successor who- 
ever that may be.' (7. W. Martin, ' 

Natural Demand and Supply. The proportion of nitrogen to 
carbon in the human body IB 1 :3, in the atmosphere it is 5,500: 1. A 
human adult contains in IUH body about 42 pounds of nitrogen, and 
over 50 pounds of curium. Over every square foot of the earth's 
surface rifles a column containing Homo- .1500 pounds of nitrogen, and 
only about. 1/4 pound of carbon. The demand and the supply of 
these two element appear, therefore, at first sight, to be altogether 
out of all proportion favorable to nitrogen. Yet, in point of fact, the 
practical problem of Heeuring an adequate supply for the substance 
and expansion of life w incomparably more complex in the case of 
nitrogen than in the cawo of carbon. The reason for this somewhat 
remarkable, inversion in to bo noon in the fact that nitrogen is readily 
aecoHsibio an food for living organisms only when it occurs in certain 
chemical combinations, and nitrogen thus combined is far from 
plentiful. It has I een estimated by T. II. Norton that this available 
or "nomadic." nitrogen -i.e., that which taken part in the migration 
through the organic, cycle -amounts to only about two one-millionths 
of the total nif.rogen of the atmosphere, or, way, to about 8 X 10 9 
tons. In fact, njUrogon w today probably the chief of those limiting 
factors' which, in accordance with Liobig's law of the minimum, 
establish the bounds for the extreme expansion of living matter upon 
the earth. At the name time the circumstance of the chemical 
idiosyncrasies of the element nitrogen introduces a certain com- 
plexity into the nitrogen cycle, which strikes the eye at a glance in 
the charts, figures -18 and 40, exhibiting the essentials of the nitrogen 

1 Compare ("}. Bunge, I'liymolotfioal and Pathological Chemistry, 1902, 
p, 17; Grinmsll J<uu, Qu. Jour. lOconomioH, 1920, vol. 34, p. 394. 

220 



230 



ELEMENTS OF PHYSICAL BIOLOGY 




NITEOGEN CYCLE 



231 



'Nitrogenous 
Vegetable. 




\tmosf>harit\ 
, Nftrogan 



/ V ^A>^ 

J/IM'^***^ 






J x 






! 


ll 


1 




I 




S 


: 


^ 


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Nitrogenous 

Animal 
Compounds! 



Urea 



Ammonia 



Kl<!, '!!), OltOANIC NlTHOUIW CntOULATION 

". -18 H!H>WH in hrondor outline the main feature of the 
oycki, while figure -ID cx!nl)i(,,s in greater detail especially those stages 
in the eyde UuU. am muni, iudijuately aKsociated with life agencies. 2 

'' For dcituilH (in UUH ])linH<> of the milijocfc the reader must be i-oferred 
to Mio Hpocutl liUu'iil.iinv A. good Hiinunary, fairly detailed and complete, 
yot coticiHO, will IHI found in [{ llubor, Zur Sfcickstoff-Frage, Born 1908 
pp. 1-10. 



232 ELEMENTS OF PHYSICAL BIOLOGY 

Gate of Entry into Nitrogen Cycle, The natural gateway for 
the entry of atmospheric, elementary nitrogen, into the organic 
cycle is a narrow one. So far as at present known, only a limited 
class of organisms possess the faculty of "fixing" this element, that 
is, taking it in its gaseous state from the atmosphere and converting 
it into the condensed (liquid or solid) form, in which only it has com- 
mon acceptation as coin of the organic realm. The organisms known 
to take part in this natural process of nitrogen fixation are three, 
namely certain bacteria having their habitat in the soil; certain 
leguminous plants (peas, beans, clover, alfalfa), working in conjunc- 
tion, in symbiosis, with nitrogen-fixing bacteria lodged in tubercles 
upon their roots; and, thirdly, the wheat plant has recently been 
shown to possess the independent faculty of assimilating nitrogen 
from the air. This recent demonstration, 3 of course, suggests the 
ready question whether after all, a number of other plants may not be 
similarly endowed. This remains as a matter for further investiga- 
tion, but it is improbable that we shall have occasion to change 
materially our present impression, namely, that the natural avenues 
by which elementary nitrogen gains admission from the atmosphere 
into the cycle of life are rather narrowly restricted. As to other 
avenues opened up by the man, these will be considered presently. 

Leak of Nitrogen out of Circulation. While there is thus a 
narrowly restricted class of vegetable organism through which 
nitrogen trickles in a thin stream from the elementary supply in the 
atmosphere into the life cycle, the majority of plants derive the 
supply for their biological needs from ready formed nomadic nitro- 
gen in the soil, that is to say nitrogen combined in the form of 
ammonium salts, nitrites and nitrates. These substances are sub- 
ject to oxidation and reduction in the soil under the influence of 
various bacteria, as indicated in the chart figure 49. The result of 
these changes is that a certain fraction of the nomadic nitrogen is 
continually leaking out of the circulation and joins the general 
reservoir of free nitrogen in the atmosphere. This is only one of a 
number of items on the losing side of the balance sheet. Other items 
will be found in following up the details of the two charts already 

3 C. B. Lipman and J. K". Taylor, Science, November 24, 1922, p. 605. These 
authors report that in their experiments wheat plants assimilated 13 to 21 
per cent of their nitrogen content from the air. 



NITROGEN CYCLE 



233 



referred to. There is loss in the autumnal leaf fall of deciduous 
plants; in the decay of dead plants, or in their fossilization as peat, 
lignite and coal. Forest fires, and the burning of wood and coal; 
the distillation of coal for illuminating gas; the oxidation of coal in 
metallurgical furnaces, the coking of coal in ovens of the so-called 
beehive type; all these are operations in which a greater or less pro- 
portion of the combined nitrogen in the coal is liberated into the air 
in the free, unavailable form. In view of the great loss which this 
represents in the economy of our food resources, the highest impor- 
tance attaches to the modern drift away from the beehive coke oven 
to the by-product oven, in which the major part of the nitrogen in 
the coal is recovered as ammonia. 

TABLE 22 
Fraction, of total output of coke in the United States, produced in by-product ovens 



YEAH 


PERCENT 


YEAH 


PER CENT 


YEAR 


PER CENT 


1890 





1910 


17.1 


1917 


38.6 


1900 


5.3 


1915 


33.8 


1918 


46.0 


1905 


10.7 


1916 


35.0 


1919 


56.2 



These by-product ovens were introduced in 1893. It is estimated 
that during the period from 1893 to 1910 alone, through the con- 
t Limed use of the old beehive type coke oven, over 9,300,000 tons of 
ammonium sulphate were wasted, representing, at the prices then 
prevailing, a value of 553 million dollars. In addition to this must 
be reckoned a further loss in the resulting field crops. Had all the 
nitrogen wasted in the beehive ovens been spread as fertilizer on the 
field, this would have increased the crops some 20 per cent. 4 An 
idea of the extent arid significance of the healthy modern drift to- 
wards replacement of the beehive by the recovery coke oven may be 
gathered from table 22, reproduced from an article by Grinnell Jones 
in the Quarterly Journal of Economics, 1920, vol. 34, p. 402. H. E. 
Fischer, writing in the Journal of the Franklin Institute, 1920, vol. 
190, p. 191, remarks that if all the coal in the United States were used 
as coke, and the ammonia recovered in the process, this alone would 

4 This and other data regarding nitrogen losses here set forth are drawn, 
largely, from an article by J. D. Pemiock in the Journal of Industrial and 
Engineering Chemistry, 1911. 



234 ELEMENTS OF PHYSICAL BIOLOGY 

furnish one million tons of ammonia, which corresponds to about 
one-half the world's total production of nitrogen compounds. 

Returning to the chart (fig. 48) and continuing to trace the prog- 
ress of nitrogen in the organic cycle, we note next that combined 
nitrogen is absorbed from plants by animals in their food. It is 
rejected from the animal economy in part as excretory matter 
(manure, etc.), in part in the bodies of dead animals, in so far as these 
are not themselves consumed as food. A large item here, in the 
economics of the human community, is the refuse from slaughter 
houses. Certain portions of this are recovered for various uses 
(glue, leather, etc.). Some is made into fertilizer. Much of it 
goes to waste, and thus gives opportunity for another leak of nitrogen 
out of the life cycle to the elementary form in the atmosphere. It is 
difficult to form any estimate of the extent of this loss, but there can 
be no doubt that it represents a waste of hundreds of tons of nitrogen 
daily. Much also is lost from the other item of animal waste ma- 
terials, not a little of the loss being occasioned by modern methods of 
sewage disposal in large cities. Such methods represent, from the 
standpoint of agricultural economy, a luxury, which however, will 
be thought worth the price if the means are at hand to make good 
the loss from other sources. Those portions of animal refuse which 
are placed on the soil of crop-bearing fields and pastures return, at 
least in part, into the organic cycle. 

Accessory Sources of Combined Nitrogen. It is of course abso- 
lutely essential for the continuance of the life cycle that the losses 
of combined nitrogen which have been noted should in some way be 
compensated by equal or greater accessions to the total amount of 
nomadic nitrogen. One source of such compensating revenue has 
already been noted, namely the direct assimilation of elementary 
nitrogen from the atmosphere by a narrowly restricted class of plants. 
There are two other natural sources. Volcanoes and furnaroles 
belch notable quantities of ammonium chloride into the air; nitric 
acid is also formed by the action of lightning, while ammonia is 
produced by the passage of the silent electric discharge (aurora) 
through the atmosphere. Arrhenius 5 estimates that the amount of 
nitrogen annually bound in this way amounts to about 1.4 X 10 9 

B S. Arrhenius, Worlds in the Making, 1908, p. 144. See also Haber, 
Zeitschr. f. Angev. Chemie, 1910, p. 685. 



NITEOGEN CYCLE 



235 



metric tons, or one part in 3 millions of the total atmospheric nitrogen. 
The products are washetl into the soil by the descending rain, to- 
gether with more or less of the same substances that have escaped 
into the atmosphere from the ground and are thus restored to the 
soil. Estimates which have been made of the quantities involved 



3.6 I 



.8 



O 

oo 




IB30 



6O 



TO 



WOO /O 



SO 90 
YEAR. 
FIG. 50. THE RISE OF THE SALTPETER INDUSTKY 



SO 



30 



are somewhat conflicting, but on the whole the gains of the soil in 
this way are held to exceed its losses. 6 

The stages and agencies so far reviewed may be collectively desig- 
nated as those constituting the "natural nitrogen cycle," as dis- 
tinguished from a group now to be considered, which are charac- 

6 F. W. Clarke, loc. cit., 1920, p. 52; Linck, Kreislaufvorgange, 1912, pp. 
6-7. It has also been put forward (Sch.dn.bcin) that a certain amount of 
nitric acid is formed in the evaporation of moisture from the earth (Bunge 
Physiological Chemistry, 1902, p. 11). But this is doubted by Ostwald. 
(Grundlinien der Anorganischen Chemie, 1912, p. 384.) 



236 ELEMENTS OF PHYSICAL BIOLOGY 

terized by human interference with the course of nature. It Is 
hardly necessary to point out that such a distinction between natural 
and artificial agencies is merely a convenient use of brief terms; the 
fact must never be lost sight of that man himself is very essentially 
part of nature, and that his development, whether physiological, 
psychological, sociological, economic, or what not, is part of the 
great process of nature. 

Human Interference in Nitrogen Cycle. Man's earliest con- 
scious, purposive intervention in the nitrogen cycle dates from 
antiquity, and primarily consisted merely in taking more or less 
pains, in an empirical way, that the nitrogenous waste material of 
animal economy be, as far as possible, restored to the soil. Perhaps 
the first recorded use of fertilizers not derived from current wastes 
of domestic animals is the exploitation of guano by the Incas, which 
dates from antiquity, and was brought to the notice of Europe by 
de la Vega in 1604. It seems to have aroused no interest until 
attention was again drawn to it two hundred years later by von 
Humboldt and by Justus Liebig, and large scale importations of 
guano into Europe began soon after this. A greater event in the 
history of agriculture was the opening up, in 1831, of the Chilean 
nitre beds. Without this source of saltpeter the modern develop- 
ment of intensive agriculture, and the consequent growth of popula- 
tion in all civilized countries, would have been at the least greatly 
hampered. The rapid rise of the saltpeter industry is clearly ex- 
hibited in table 23 and the corresponding graph figure 50. 

While our chief interest here is in the agricultural use of Chile 
saltpeter, its consumption in the industries is altogether too extensive 
to be passed by without mention. J. D. Pennock 7 gives the figures 
shown in table 24 for the relative amounts of saltpeter consumed in 
different uses. 

It should be observed that Pennock's figures relate to peace time 
conditions. Even so, nearly one-half the consumption is taken up 
in the manufacture of explosives. Nitrogen thus employed is, of 
course, lost to the life cycle. A certain loss also concurs in the re- 
fining of the caliche (native saltpeter), and in the production of 
nitric acid and sulphuric acid 8 therefrom. 

7 J. D. Pennock, Jour. Industr. and Eng. Chem., 1911, p. 172. 

8 When manufactured by the Chamber process. 



NITROGEN CYCLE 



237 



TABLE 23 
Growth of the saltpeter industry 





SHORT TONS 


(I) 


(II) 

Sodium nitrato 


1830 


soo 




1831 




112 


1850 


22,800 


22,350 


1SSO 


222,559 


257,060 


1890 


1,050,119 


998,970 


1900 


1,471,500 


1,490,950 


190(5 


1,795,000 


1,835,190 


1911 


2,482,000 


2,624,250 


1913 


2,730,000 


3,055,800 


1914 


2,422,000 


2,715,050 


19 If! 


1,728,000 


1,935,140 


1916 


2,868,000 


3,210,008 


1917 


2,955,000 


3,319,920 


1918 


2,821,000 


3, 170, 106 



(III) 

Nitrogon on basin of 
15.05 por con I 



17.5 
3,498 
40,230 
156,339 
233,334 
287,207 
410,095 
478,230 
424,900 
302,850 
502,370 
519,570 
496, 120 



The figures in column I are the Chilean nitrate production, as given by Par- 
sons and Petit, Brokers. The figures in oolxims 11 and III, from 1831 to 19 11 
inclusive, represent the World's consumption of saltpeter according to C!(5ni 
Civil, vol. 62, p. 192. The figures from 1913 to 1918 in oolums II and II I ropi'e- 
serit the total production of Chilean and Indian nitrate, according to Griunell 
Jones, Jour. Frankl. Inst., 1920, vol. 134, p. 398. The precipitous drop in the 
Chilean production in 1915 was due to a blockade established by the GermariH 
during the early stages of the, World War. See Fig. 50, in which circles indi- 
cate production, the drawn out curve consumption. 

TABLE 2t 

Distribution of Chili saltpeter consumption in the United States in 1010 among 

different uses 



In manufacture of fertilizer. 
In manufacture of dyestuffs. 

In general chemistry 

In glass 

In explosives 

In nitric acid 

In sulphuric acid 

Unaccounted for 



13 

12 

10 

4 

41 
9 




100 



238 ELEMENTS OF PHYSICAL BIOLOGY 

Origin of Nitre Beds. The origin of the nitre beds is uncertain. 
The presence of boron in the deposits, and the association of this 
element with ammonia in volcanic emanations, have been regarded 
by some as evidence that the saltpeter is of ultimately volcanic origin. 
Others have ascribed it to organic sources, such as altered guano 
deposits. But whatever be their origin, this is certain, that the salt- 
peter beds represent an accumulation of ages, and that the present 
rapid rate of consumption is out of all proportion with the rate of 
formation of the deposits. In other words, here, as in the case of 
coal, we are living on our capital, and must prepare ourselves for its 
impending exhaustion. 9 It is true that our other sources of combined 
nitrogen notably ammonia from coke ovens supplement our 
drafts upon the nitre beds, and thus help to defer the day of scarcity. 
But coal itself is a limited stock, and other sources of combined 
nitrogen seem quite inadequate for the needs which we have de- 
veloped under the stimulation of temporarily bountiful supplies. 
It is a peculiarity of living substance that in times of plenty it tends 
to grow beyond the bounds compatible with ultimate stability; it 
overshoots the mark so to speak; the curve along which it approaches 
its equilibrium is very apt to be humpbacked, or it may be oscil- 
latory. 10 The prospect of a period of actual diminution (not mere 
marking time) to follow upon a period of exuberant prosperity, is 
one that an organism gifted with foresight must look upon with 
disquietude. Such foresight may, then, lead an organism so gifted, 
to make efforts to provide for untoward future exigencies, either by 
laying by supplies, in times of plenty, for times of stress; or by 
devising means, if possible, to increase, by new measures, the supplies 
which, under the old regime, would presently fall short of require- 
ments. Man has not always made a display of brilliant foresight, 
but in this instance, in making ready for the exhaustion of the nitrate 
supply, he has taken time by the forelock, and all indications are 
that long before the emergency arises he will have made himself 

_ 9 The probable date of this exhaustion has been variously estimated. 
Little value can be attached to positive statements. More significant, per- 
haps, is the negative report made in 1913 to the Chilean Government by the 
Inspector General of Nitrate Deposits: "There is no fear of the Chilean 
nitrate deposits being exhausted for two hundred years" (Grinncll Jones 
loc. cit., p. 401). ' 

"Compare what has been said on this subject in Chapter XI. 



NITROGEN CYCLE 239 

ready to meet it. For the last decade has seen the development, to 
full industrial capacity, of several processes for the fixation of atmos- 
pheric nitrogen, its conversion into compounds directly or in- 
directly adapted to enter the cycle of nomadic nitrogen. For 
details regarding these modern industrial developments the reader 
must be referred to the technical literature. 11 It must suffice to 
indicate here very briefly the nature of the several processes. 

1. The Birkeland and Eyde Process, is essentially man's 
imitation of the production of nitric acid by lightning. Air is 
passed through an electric arc fanned out into a broad disc by a 
magnetic field. The process is commercially viable only where 
very cheap power is available, and has been developed mainly in 
Scandinavia, with the use of water power. 

2. The Cyanamide (Frank and Caro) Process effects the ab- 
sorption of atmospheric nitrogen by calcium carbide in the electric 
furnace. The product can be employed directly as a fertilizer, or can 
be made to yield ammonia and other nitrogen compounds. 

3. The Haber Process effects the synthesis of ammonia from 
nitrogen and hydrogen under pressure (100 to 200 atmospheres) 
in the presence of a catalyst. An allied process is that of Claude, 
which works at very high pressure (1000 atmospheres). ia 

4. The Biicher Process, which has not yet passed beyond the 
experimental stage, yields cyanides; these can also, if the market 
warrants it, be made a source of ammonia. 

A highly significant development is the union of the Habcr 
ammonia process with the Solvay process, whereby the carbon 
dioxide obtained as a waste product in the manufacture of the 
hydrogen for ammonia synthesis, is utilized in the production of 
sodium carbonate; while, on the other hand, the formation of large 
quantities of the nearly worthless calcium chloride waste of the 
Solvay process, as ordinarily conducted, is avoided. Inasmuch us 
"soda ranks second only to sulphuric acid among all chemicals in 
magnitude of output (1,390,628 short tons in the United States in 
1918) and fundamental importance, .... this (combination 
of the Haber and the Solvay processes) may well prove to be the most 

11 Sec for example the articles by G. H. Fischer and Grinnell Jones already 
cited. 

12 H. E. Fisher, Jour. Franklin lust., 1920, vol. 190, p. 201. 



240 



ELEMENTS OF PHYSICAL BIOLOGY 



1,6 




FIG. 51. THE RISE OF THE FIXED NITROGEN INDUSTRY 



NITROGEN CYCLE 241 

significant development in industrial chemistry of the present 
decade." 13 

5. The Ostwald Process, A subsidiary process bridging the 
gap from the product (ammonia) of the processes of the Haber and 
Frank and Garo types, to the market requirements of nitric, acid 
(nitrate and nitrites), is the Ostwald process for the catalytic oxida- 
tion of ammonia. 

The Meteoric Rise of Nitrogen Fixation Industries. In the period 
during arid immediately following the World War the situation 
in the nitrogen industries was abnormal, production being tempo- 
rarily activated to fever heat, inasmuch as nitrogen compounds 
are among the most indispensable of war materials. Tims it came 
about that the development of nitrogen fixation had for its imme- 
diate motive not so much the constructive spirit of the arts of 
peace, providing for the future needs of men, as the malice and 
forethought of the conspirators of war. The conflict left on our 
hands, upon the conclusion of the armistice, both completed and 
unfinished manufacturing plants in excess of immediate needs in 
times of peace. Legislative difficulties also hampered well-designed 
efforts to convert these plants to industrial use. These arc tem- 
porary conditions; although one may not be able to foresee exactly 
how, in detail, these industries will finally adjust themselves, there, 
can be little doubt that from now on synthetic nitrogen compounds 
will continue to be drawn in increasing amounts from the atmosphere 
into the life cycle. The phenomenal growth of this infant industry 
within the past ten or twelve years is forcibly brought out in the 
graph (fig. 51) and the corresponding table 25. It will bo observed 
that in 1909 only about 1 per cent of the world's needs in combined 
nitrogen were satisfied from the new-born industry. In .1.917 its 
contribution had swollen to 30 per cent, and by 1920 the capacity of 
existing plants was adequate to furnish 43 per cent of the world'n 
requirements. 

This extraordinary development is something much more than a 
fundamental new departure in industry. It represents nothing lens 
than the ushering in of a new ethnological era in the history of the 
human race, a new cosmic epoch. In the short span of a dozen 
years 'geologically speaking in an instant- man has initiated 
transformations literally comparable in magnitude with cosmic 

13 Grinnell Jones, loc. cit., p. 414. 



242 



ELEMENTS OF PHYSICAL BIOLOGY 







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NITEOGBN CYCLE 243 

processes. Accepting Arrhenius' liberal estimate of the total quan- 
tity of combined nitrogen washed down to the soil in the annual 
rain fall over all continents of the globe, namely 400 million tons, 
it is seen that the new industry even now is capable of furnishing a 
supplementary supply equal to one six-hundredth of this prodigious 
quantity. 14 

Economic and Energetic Significance of Concentration. We are, 
of course, greatly more interested in this six-hundredth which is 
under our control 'and of which a due proportion falls, in con- 
sequence, upon our fields in concentrated form 'than in the very 
much larger quantity that nature scatters with sublime indifference 
on stony places and good soil alike. This is just one of those cases 
to which reference has already been made in a general way. It is 
not so much the quantity of the material provided by nature that 
counts, as its accessibility; and accessibility here means, among other 
things, suitable concentration. This question did not so obviously 
project itself into the discussion of the carbon cycle, because the 
__ natural source of carbon is atmospheric carbon dioxide, which, being 
a gas, in the very nature of things spreads evenly, and presents itself 
unsought, by a spontaneous process, at the mouth of the hungry 
plant. But the combined forms of nitrogen are for the most part 
solids or solutions, occurring in definitely localized amounts of greatly 
varying concentration. The labors forced upon us in our efforts to 
satisfy the nitrogen needs of our fields are, to be precise, not primarily 
work of production, but virtually work of concentration; or to be more 
exact, work of bringing about concentration at the particular locality 
where it is wanted by transportation if need be. It is only because 
we find k easier, in some instances, to produce than to concentrate 
existing supplies, that we elect the former expedient; just as we may 
prefer to feed a boiler with a fresh supply of water, rather than to 

u For land and sea together Arrhenius estimates 1500 million tons of nitro- 
gen in the rain fall. 

Note added in correcting 1 proof. 

Since the writing of this chapter there have become available Trade Infor- 
mation Bulletins No. 220 and 240 of the U. S. Department of Commerce, 
which give further and more recent data. In Bulletin 240 J. M. Braham 
estimates the capacity of the world's nitrogen fixation plants at 490,000 
tons for 1923. The reader interested in this topic may also consult J. R. 
Partington, The Nitrogen Industry, publiBhcd by Constable, 1924. 



244 ELEMENTS OF PHYSICAL BIOLOGY 

return to it the condensed exhaust from the engine. That the mere 
concentration of existing supplies should at all require the doing of 
physical work is a circumstance of particular interest, not only in its 
economic relations, 13 but also, and quite particularly, from the stand- 
point of energetics. This is a matter that will duly engage our 
attention in a later section, devoted to the energetics of the several 
processes that have here been considered in their purely material 
or stoiehiometi'ic aspect. 

Meanwhile it is interesting to observe that such localized sources 
of concentrated supplies as those presented in the Chilean nitre 
beds virtually function as centers of attraction toward which gravi- 
tates a stream of human beings 'Or their representatives in the form 
of ships and other conveyances arriving in search of cargo and going 
out laden with material. To an ultramundane observer who should 
survey the scene in suitable perspective, the activities around the 
nitre beds must appear very like the busy swarming of a colony of 
ants around the treasure trove of some silvan inhabitant departed 
this life; who, having completed his earthly career, is now yielding up, 
in the dissolution of death, such energies as still remain locked up 
in the carcass. Attractions such as this are, in a sense, merely 
apparent; they are the outward symptoms of a complicated chain of 
cause and effect 10 characteristic of the behavior of living organisms. 
Yet they are often so consistent in their action that it would not be 
unreasonable to essay a systematic treatment of the movements in 
a world comprising such centers of attraction and such moving pawns, 
on the basis of brute tropisms unanalyaed into their ultimate com- 
ponent agencies. Here it must suffice to have pointed out that our 
highly complex industrial system, our far-flung intricate network 
of lines of traffic by land and sea, is but a sublimated copy, on a 
heroic scale, of the hustle and bustle that is going on all around us in 
nature, in response to attractions, tropisms, determinants of the 

15 A striking illustration of this is cited by Haber (Zeitschr. f Angew 
Chemie, 1910, I, p. 685). If the gold in sea water were extracted and" ap- 
portioned evenly to all the human inhabitants of the globe, we should all 
be millionaires three times over; yet it does not pay to as much as begin this 
extraction. 

_ 15 Commonly accompanied by that anticipatory inversion of the sequence 
in time, of effect and cause, which is the earmark of purposive action. 



NITHOGEN CYCLE 245 

moves of an army of checkers over the mosaic of the earth's 
topography. 17 

Total Circulation Tends to Increase. The study of the 
nitrogen cycle furnishes us with a first occasion to take note of a 
phenomenon the full significance of which will become apparent in 
dealing with the dynamics of evolving systems. It is to be observed 
that the general trend of man's effort, especially in this new epoch 
of nitrogen fixation, has been towards drawing into the organic 
circulation a greater amount of matter, enlarging the wheel of the 
mill of life, so to speak. There can be little doubt that this trend 
will continue and increase in the future, and that it is the expression 
of one aspect of a general law; 18 the other aspect of this law, and its 
full significance, must be reserved for later discussion, as already 
intimated. 

17 For a discussion of the natural concentrating processes the reader may 
be referred to the following articles: A. C. Lane, Nature's Coneentraiors, 
Engineering and Mining Journal, 1897, vol. 03, p. 54-2. ,1. C. Russell, Con- 
centration as a Geological Principle, Bulletin Ccol. 8oc. An., 1907, vol. IS, 
pp. 1-28. E. Blackweldcr, The Geologic Role of Phosphorus, Aia. Jour. 
Sci., 1910, vol. 62, p. 285. W. Lindgren, Concentration and Circulation of 
the Elements from the Standpoint of Economic Geology, Economic Geology, 
1923, vol. IS, pp. 419-44.2. 

18 The phenomenon is, of course, closely related to that In which R. Lus- 
caux refers as "unc propriete particuliere do la vie: cclle do rextentiion" 
(La Production ct la Population 1921, p. 37). ftcc also A. J. Lotka, I'roc. 
Nat 'I Acad. Sci., 1922, p. 47. 



CHAPTER XIX 
THE PHOSPHORUS CYCLE 

There is no coming into being of aught that perishes, nor any end for it 
.... but only mingling, and separation of what has been mingled. 
Empedocles. 

Immobile Elements. The circulation of water, carbon dioxide 
and oxygen in nature is greatly assisted by the freely occurring 
processes of evaporation, condensation (rainfall) and diffusion. In 
the case of nitrogen these processes still give some aid, as in the dis- 
tribution broadcast of atmospheric nitrogen, and in the formation j. 
and precipitation of nitrogen "fixed" by lightning, etc. In phos- 
phorus we have, on the contrary, a typical example of the inherently 
immobile elements needful to the living organism to adopt Liebig's 
phrase (fur sich nicht beweglicli) . The successive steps in the con- 
centration, diffusion, and reconcentration of this element, as available 
for the substance of the organism, accordingly display a characteristic 
complexity. Some of the principal items and steps in the phos- 
phorus cycle are set forth in diagrammatic form in figure 52. 

Natural Phosphorus Supply of Soils. The virgin soil contains, 
in general, a certain natural supply of phosphates. So, for example, 
Van Hise 1 reports that the virgin soil of Ohio, Illinois and Wisconsin 
contained, to a depth of 8 inches, 2077 pounds of PaOg per acre. / 
After fifty-five years of cultivation this figure had sunk to 1813 pounds 
per acre, a loss of 36 per cent. These figures show the extreme im- 
portance of a conservation of our resources of phosphorus. The loss 
probably occurs partly through erosion by rain water charged with 
carbonic acid, which dissolves phosphates in the soil and in rocks, 
and ultimately "washes a certain proportion out to sea. To this 
unavoidable loss, however, is added a large item of preventable loss 
through our failure to ensure that the phosphorus of animal wastes 
be returned to the soil. So, for example, farmyard manure contains 
over three-fourths of the phosphorus in the feed and bedding supplied 
to the animals. It is therefore very essential that this be returned 

1 Ann. Acad. Polit. Soc. Sci., 1909, vol. 33. . , 

246 



PHOSPHORUS CYCLE 



247 




o 



o 
W 
FM 



248 ELEMENTS OF PHYSICAL BIOLOGY 

to the soil as completely as possible. Of the one-fourth of the phos- 
phorus fed to the animals, and not accounted for in the manure, a 
considerable fraction appears in the bodies of these animals, especially i 
in the bones. These, then, also should find their way back to the * 
soil, as they do to some extent through the practice of using bone 
meal, either as such, or after conversion into superphosphate, 2 
as fertilizer. This practice is materially assisted by the modern 
methods of meat production on a large scale, with very complete 
utilization of by-products. 

Leakage of Phosphorus from Circulation. The human cadaver 
is in the great majority of cases returned to the soil in the 
regular course of events, although under conditions which, obviously 
do not render it very readily available for crop production. An 
adult contains about 1| pounds of phosphorus, or 3.4 pounds IW 
If we allow one-half of this for a "unit of population," i.e., 1.7 pounds 4 
P 2 6 , with a death rate of 1.3 per cent per annum, we find that the ^ 
amount of P 2 5 annually committed to the cemeteries of the United 
States is about 1105 tons. This is about the equivalent of 3300 
tons of phosphate rock, or about one-thousandth of the annual 
production of that material in the United States. 

But a very much larger amount of waste is occasioned from the 
human population by the practice of running the sewage from cities 
into rivers and thus to sea. Van Hise estimates that annually 
400,000 tons P 2 5 or the equivalent of 1,200,000 tons of phosphate 
rock are thus ran to waste. He remarks: "The wide dispersal of 
the vast quantities of phosphorus which it took the process of nature 
an indefinite period to segregate, must cease. The loss is irrop- Jj 
arable." Much has been done in recent years to comply with this 
demand. 

Phosphate Rock and the Migration of Phosphorus. In the 
meantime, in our phosphorus economy also, as in the case of the 
combined nitrogen of the Chilean nitre beds, we are living on our 
capital. For, as our fields tend to become depleted of phosphorus 
under intensive agriculture, we restore some of the rarefied clement 
to the tired soil by drawing upon the accumulations of ages, in the 
form of phosphate rock. As a matter of fact, in this we are welding 

2 By treatment with sulphuric acid, which renders the phosphorus more 
readily available to plants. These are technical details that cannot be on- 
tered into here. The reader must be referred to the pertinent agricultural A- 
and technological literature. 



PHOSPHOEUS CYCLE 249 

the closing link in a very remarkable endless chain of nature. For 
the phosphates washed by the rivers 3 into the sea serve as food to the 
marine vegetation and indirectly to the fishes and other aquatic 
species. 4 These act in this case as concentrating agents, the bones 
and teeth of fish, and some shells of Crustacea and molluscs, being 
comparatively rich in phosphorus. 5 In its further migration the 

3 For details the reader may be referred to an article by E. Blackwclder 
in the Am. Jour. Sci., 1916, vol. 62, p. 285, from which the following particu- 
larly pertinent passage may here be noted: "Of the vast quantity of dis- 
solved mineral matter annually delivered to the sea by the run-off, it is esti- 
mated that about 0.45 per cent consists of phosphorus pentoxide. Using 
the best available figures for the amount of water thus brought to the ocean 
annually, it is calculated that if the phosphatic material in the form of solid 
tri-calcium phosphate were loaded into standard railroad cars it would fill 
a train stretching continuously from Boston to Seattle and would be 7 to 12 
times as great as the world's total production of phosphate rock in 1911. 
Nevertheless, so great is the volume of the oceans, and so vast the area of 
their floors, that if all this material were deposited in solid form uniformly 
over the bottom of the sea, it would build annually a layer less than 0.2 mm. 
thick. Of the phosphorus poured into the sea, so large a proportion is util- 
ized by living beings that the net working balance dissolved in oceanic water 
constantly averages less than 0.005 per cent, expressed as PzOs, or, in other 
words about 0.18 per cent of the dissolved salts. In this solution, phos- 
phorus seems to have reached the most dilute state in which it exists during 
the course of its complex migrations. Its subsequent transformations gen- 
erally tend to ever greater concentration, almost until the cycle is closed 
upon itself. 

4 Compare also W. Lindgren, Concentration and Circulation of the Ele- 
ments from the Standpoint of Economic Geology: "In the sea water the blue- 
green algae concentrate phosphorus, certain molluslcs or crustaceans feed 
on the algae, and other meat-eating mollusks devour the vegetarians. Small 
fishes eat the molluslcs, large fishes eat the small, finally seals and birds swal- 
low the fishes, and so in about six transformations the phosphorus originally 
contained in the sea-water may come to rest in deposits of guano on desert 
islands or in accumulations of bones of vertebrate denizens of the sea" (Eco- 
nomic Geology, 1923, vol. 18, p. 431). 

6 In this connection may be noted again a passage from Blackwelder's 
article, p. 289 (see footnote 3): "As phosphorus ascends in the evolutionary 
scale of animals, its concentration tends to increase, although irregularly. 
The protozoan, air dried, contains less than 0.6 per cent PaOc. According 
to Juday quantities of minute crustaceans from Lake Mendota contain in 
the air-dried condition 1.8 to 2.4 per cent of PaGc, or several times that of 
the protozoans. A Russian biochemist, Sempelovski, found in entire fresh 
specimens of a cartilaginous fish (the common skate) 0.91 per cent PaOs, 
whereas the average for eight Teleostean fishes with well-developed bones 
was about 1.5 per cent. Certain brachiopods, such as those of the family 
Lingulidae form shells of fibro-crystalline tricalcium phosphate probably 
either the mineral dahllite or staff elite." 



250 ELEMENTS OF PHYSICAL BIOLOGY 

phosphorus here splits into two streams. On the one hand the hard 
parts of dead fish and other sea animals fall to the bottom and form 
a phosphatic deposit. So, for example, it is reported that in certain 
localities a single draft of the dredge has brought up 1500 shark's 
teeth from the sea bottom. These deposits become further enriched 
through the replacement of their calcium carbonate by calcium 
phosphate under the action of the sea water. 6 Subsequently some 
of the deposits so formed have been raised, in a crust upheaval, 
above the sea level, so as to form sedimentary strata from which 
we now derive some of our supplies of phosphate rock. 

The other division of the stream in the flow of phosphorus is per- 
haps one of the most remarkable examples of a cycle in the economy 
of nature. The fish of the sea are eaten by birds, who flock in great 
hordes and have their nesting places upon rocky islands and shores. 7 
There an accumulation of immense amounts of guano has taken 
place in the course of centuries and ages. Of this guano some has 
been returned directly to the land by the agency of man. Other 
portions, of more ancient origin,, have undergone transformation, 
and have passed into fossil form by reaction with the rock base on 
which they were in the first instance deposited. This is the origin 
of a second class of (metamorphic) phosphate rock, which also wo 
mine and spread on our field, so that this loop in the chtiin also is 
closed. 

Soil Losses of Phosphorus. From this sketch of the migration 
of phosphorus in nature it is seen that qualitatively the path of tho 
element is a closed circulation. Unfortunately the cycle is quanti- 
tatively quite incomplete. Van Hise, quoting Whitson's invest! ga- 
tions, shows that, on a very conservative estimate, tho soil of the 
United States loses annually some 2 million tons of P 2 G , the equiva- 
lent of 6 million tons of phosphate rock. This is about double the 
total output of our phosphate quarries, and about four times our 
domestic consumption of that output. It is thus scon that tho 
situation with regard to our supply of phosphatic fertilizers is an 
exceedingly serious one it would perhaps not be out of place to say 

For a detailed discussion of some of these concentrating processes and 
related matters the reader is referred to F. W. Clarke, loc. cit., 1921, pp. 132 
495, 502. See also Chapter XVIII, footnote 17. 

^ 7 For an excellent illustrated account of the part played by the Guanay 
bird in this cycle see R. C. Murphy, Natl. Gcogr. Mag. Sept. 4, 1924, p. 279. 



PHOSPHORUS CYCLE 251 

ao alarming one. For here we have no reserve which we may hope 
to find means of tapping in the future, such as is presented to us, in 
the case of nitrogen, by the inexhaustible supply in the atmosphere. 
Phosphorus is at best a comparatively rare element, constituting 
only about 0.14 per cent of the earth's crust (see table 16, 
Chapter XV). 

The general and alarming decrease in the crop yield per acre in various 
states so well described by Mr. James J. Hill, 8 is largely due to the depletion 

of the soil in phosphorus The work (at the Ohio Agricultural 

Experiment Station 9 ) upon different fertilizers shows that for the soils tested 
in their experiments phosphorus was the controlling element in producing 
an increase in the cereal crops. 10 

And elsewhere 11 Van Ilise remarks : 

The average rock contains twenty times as much potassium as phosphorus. 
Therefore, looking toward the distant future, if we consider ratios, we may 
unhesitatingly assert that the problem of maintaining the fertility of the 
soil in phosphorus will be twenty times as difficult as for potassium; but 
this ratio by no means measures the real difference, for when a deposit con- 
tains a moderate percentage of a substance it may be possible to utilize it 
commercially, whereas, if the percentage falls below this amount it is with- 
out value. 

Phospbtatic Slag as Fertilizer. To the consideration of the 
migration of the element potassium thus referred to by Van Hise, 
we shall presently turn our attention. Before leaving the subject 
of the migration of phosphorus, one secondaiy source of phosphate 
fertilizer remains to be noted here, namely, the by-product (slag) 
obtained in certain processes of steel manufacture, in which the 
phosphorus contained in the ore (and very objectionable as a con- 
stituent in steel) becomes segregated, and is thus eliminated, in the 
slag. This latter, by suitable processes, is converted into a very 
serviceable fertilizer. 12 

8 The Natural Wealth of the Land, and its Conservation. Paper given 
at the White House Conservation Conference, May 13, 1908. 

9 Ohio State Agr. Coll. Bull. 141, 182. 

10 Van Hise, loc. cit., p. 704. 

11 Idem, loc. cit., p. 701. 

12 For details regarding the use of phosphatic slags as fertilizer the reader 
may be referred to G. S. Eobertson, Basic Slag and Rock Phosphates, Cam- 
bridge University Press, 1922. 



CHAPTER XX 
CYCLES: CONCLUSION AND SUMMARY 

The saltness of the sea is due to the numerous springs of water, which in 
penetrating the earth, find salt mines, and dissolving parts of these carry 
them away with them to the ocean and to the other seas, from whence they 
are never lifted by the clouds that produce the rivers. Leonardo da Vinci. 

The Circulation of Chlorine and the Alkalis. It will be con- 
venient to consider jointly the migration of the elements chlorine, 
sodium, and potassium in nature, inasmuch as they are closely 
connected. 

There is a piece of laboratory apparatus known as the Soxhlet 
Extractor, of which the chemist makes use when he wants to pre- 
pare a solution, an extract, of one of the constituents of a mixture 
of substances. This apparatus, as represented in figure 53, operates 
on a simple principle. The solvent (water, ether, petroleum spirit, 
etc.) is placed in the flask A heated by a bimsen flame B, so as to 
drive vapors of the solvent up through the tube C to the top of a 
tubular vessel D containing the material M to be extracted. The 
whole apparatus is open at the top, but escape of vapor is prevented 
by a condenser tube E cooled by a water jacket F. The Vapor 
condensing in E drips down upon the material M, and dissolves 
out the substance to be extracted. The condensate accumulates in 
the vessel D and rises in the syphon tube I until it reaches the top 
of the syphon, whereupon it drains back into the flask A and is 
reevaporated, this cycle being repeated indefinitely as long as desired. 
Since the vapor of a liquid containing a non-volatile substance in 
solution is pure solvent, the action continues until practically all 
the soluble substance has been extracted. 

It is almost literally true that we pass our lives in the midst of a 
gigantic Soxhlet apparatus. The flask is the sea basin; the solvent 
is the water of the ocean, the rain, and our rivers and lakes. The 
material extracted is the earth's crust (rocks, soil, etc.). The place 
of the Bunsen burner is taken by the sun which raises water vapor 
from the ocean's surface, into clouds which drift over the land. 

252 



CYCLES: CONCLUSION AND SUMMARY 



253 





FIG. 53. THE SOXHLET EXTRACTION APPARATUS 

The action of this apparatus is closely analogous to the natural extrac- 
tion of soluble constituents from the earth's crust by the water in circu- 
lation through clouds, rain, rivers and the sea, under the influence of the 
sun's heat. 



254 



ELEMENTS OF PHYSICAL BIOLOGY 









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CHLOBIDE CYCLE 








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CYCLES: CONCLUSION AND SXJMMAEY 255 

The cold upper atmosphere acts as a condenser (see fig. 54), beyond 
which no clouds can pass out above. Presently the moisture of the 
clouds is precipitated as rain over the face of the earth. It drains 
into rivers and lakes back into the sea, charged now with the soluble 
constituents of rock and soil. This operation has been going on 
over and over for ages, with the result that the greater part of the 
more soluble constituents of the rocks is by this time collected 
in the ocean, imparting to its water its characteristic salt taste. 
It is worthy of more than passing note that these relations, in all 
essentials, were recognized by that universal genius, Leonardo da 
Vinci, whose remarks on this subject appear at the head of this 
chapter. 

The principal soluble constituents of the earth's crust are the 
carbonates and chlorides of the alkali metals, sodium and potassium. 
These, then, mainly take part in the extraction process described. 
There is, however, an important difference in the behavior of sodium 
and potassium in this process. In the igneous rocks sodium and 
potassium are present in very nearly equal proportions (see table 
16). Yet the ocean is very much richer in sodium than in potassium 
(see table 14). What becomes of the potassium? 1 It is a circum- 
stance highly significant for terrestrial life that potassium salts seem 
to be largely absorbed from their solutions on their passage through 
soil and clay. Thus the soil would retain a supply of the element 
so essential for plant growth, while the less vitally important sodium 
'in other respects so similar to its next kin potassium has in 
large part passed on into the ocean. 2 

Nevertheless, potassium is not present in most soils in profusion; 
under intensive agriculture the soil becomes impoverished in this 
constituent also, and recourse must be had to sources of potassium 
salts in concentrated form, the deposits left by the drying up of 
ancient seas, to make up the deficiency. In this field, also, the 
World War has materially affected the complexion of agricultural 
economics. Its influence has been twofold. In the first place, since 

1 In this connection, and for details regarding the circulation of Na, K,Cl, 
and the related question of the age of the ocean, the reader may be referred 
to F. W. Clarke, Data of Geochemistry, pp. 136, 137, 145, et seq. 

2 These suppositions must be viewed with a certain caution, as has already 
been pointed out; see p. 204, footnote 19. 



256 ELEMENTS OF PHYSICAL BIOLOGY 

the only areas highly productive of potassium salts were contained 
within the domains controlled at that time by Germany, it became 
necessary for the Allies to find other sources of the needed element. 
One outcome of this was a temporary development of potash re- 
covery from the waste of cement works and other materials. Un- 
fortunately much of the commerce thus started had to be abandoned 
again when the customary sources of potash became once more 
available after the close of the war. 

The second effect of the war upon the potash situation arises 
from the political changes which it brought about. The Alsatian 
potash deposits, formerly controlled by the same monopoly as the 
German Stassfurt deposits, are now in French domains, and the 
monopoly is broken. 3 

Some of the quantitative aspects of the migration of chlorine 
and sodium are shown in figure 54. 

The Circulation of Sulphur. Sulphur occurs in abundance in 
inorganic nature in the form of the sulphates of the alkalies and 
alkaline earths. Plants assimilate these compounds directly 
and then form proteids containing about 0.3 to 2 per cent of sul- 
phur. In this form it is assimilated by animals, who excrete the 
element chiefly in the form of sulphates. These, returned to the 
soil, complete the cycle. 

Tlie Circulation of Iron. The importance of iron in the economy 

of the living organism is out of proportion to the comparatively 

small amount of this element actually present in the body. Thus 

the body of a human adult holds only about 4.5 grams of iron, 

contained, for the most part, in the red blood corpuscles. The 

importance of this comparatively small amount of the metal arises 

out of the fact that it fulfills the essential function of an oxygen 

carrier, a catalyst as it were, mediating the transfer of oxygen from 

the air in the lungs to the tissues of the body through the blood 

stream. Similarly, in plants, the iron is contained chiefly in the 

chlorophyll, whose catalytic action is a fundamental condition for 

the assimilation of carbon dioxide from the air. This catalytic 

action of iron is attributable to the ease with which it passes from 

ferrous to the ferric condition and vice versa, and plays a significant 

3 G. Jones, Q. Jour. Econ., 1920, vol. 34, p. 392, 



CYCLES: CONCLUSION AND SUMMARY 



257 



idle not only within the body of the organism, but also In the soil, 
where it hastens the oxidation of carbonaceous matter, thus render- 
ing carbon once more available for the organic cycle. 4 

Summary of Cycles. In conclusion of this chapter a few remarks 
and tables regarding the circulation of the elements in general 
may be offered. 

In retrospect we may observe that alcharacteristic stamp is 
placed on certain of the elementary cycles by the form in which 

TABLE 26 
Supply of plant foods in soil 

Number of years the supply of several elements would last, utilizing soil 
to a depth of 7 inches, and producing annually a crop of 100 bushels of com. 
Average compositon of soil assumed equal to that of 2110 samples of common 
rocks in the United States. (C. G. Hopkins, Annual Acad. Sci. 1909, vol. 33, 
p. 638). 



N 
















g 














Soil 


1 

| 


K 


P 


Fe 


Ca 


Mg 




50 


700,000 


2,600* 


130 


200,000 


55,000 


7,000 


10 



* Assuming stalks returned to the land. 

each element occurs or takes part in the circulation. Thus, the 
gases oxygen and carbon dioxide occur in nearly uniform distribu- 
tion, so that their migration is free from certain complications that 
arise in the case of the other elements. Water occupies a position 
intermediate between the gaseous 'elementsjand^those which like 
phosphorus, potash, etc., as solids, are subject to local segregation, 
and thus introduce problems of transportation in one form or another. 
As vapor, water drifts with air currents. But owing tn the phenom- 
enon of precipitation, water, unlike the permanent gases, is very 
unevenly distributed, the supply available for life processes being 
strictly a matter of climatic conditions. Thus, in desert regions 
water functions as the limiting factor of life. Nitrogen, although 

4 G. Bunge, Physiological and Pathological Chemistry, 1902, p. 21. 



258 



ELEMENTS OF PHYSICAL BIOLOGY 



gaseous in the elementary state, is chiefly operative in combined 
forms, so that its distribution in available form, is also a locally 
varied phenomenon. 

All these facts have their influence not only on the primitive 
flora and fauna as a function of geographic site, but play also an 
important role in those secondary life phenomena which we com- 
monly describe as commerce and trade:. 

Two tables 26, and 27, are, finally appended, the one giving cer- 
tain data of interest regarding the Supply of Plant Foods in the 

TABLE 27 
Rate of participation of the elements in cycles of nature 





METBIC TONS 


CIRCU- 
LATION BY 
WEIGHT 
ONE PART 

IN 


AUTHORITY* 


STANDARD 
OP 

HEFBBENCE 


Annual 
circulation 


Total in 
Standard of 
Reference 


A. 

145 
145 
144 


G. 


L. 


M. 
434 


H 2 O 


1.4X10 14 
4.4X10 10 
3.5X10 10 
1.4X10 9 


1.3X10 18 
2.2X10 13 
1.2X10 15 
3.9X10* 5 


10,000 
50 
35,000 
3,000,000 


22, 59 


4 

7 
7 
7 


Ocean 
Atmosphere 


CO. 





N 





* Authorities : A. = Arrhenius, Worlds in the Making, 1908 ; C. = Clarke, 
Data of Geochemistry, 1921; L = Linck, Kreislaufvorgange, 1912; M. = McGee, 
Science, 1911, vol. 134. The numbers in the column "Authority" refer to 
pages of the works cited. 

Soil, according to C. G. Hopkins; the other giving estimates of the 
Rate of Participation of the Elements in the Cycle of Nature. 

It seems hardly necessary to point out that the quantitative 
estimates cited in these chapters on the circulation of the elements 
in nature represent only very rough approximations, the best per- 
haps that can be attained in the present state of our knowledge. 
As F. W. Clarke 3 remarks, "Such estimates may have slight numeri- 
cal value, but they serve to show how vast and how important the 
processes under consideration are." Rough as the data are, they 
give us, presumably, at least an idea of the order of magnitudes 
involved. The least that can be claimed for them is, in the words 
of Clarke 5 once more: "In calculations of this sort there is a certain 
fascination, but their chief merit seems to lie in their suggestiveness." 

6 F. W. Clarke, Data of Geochemistry, 1920, p. 48. 



CHAPTER XXI 
MOVING EQUILIBRIA 

Aus dieser Untersuchung wird kein Dualismua hervorgehen, sondern eine 
Wissenschaft, welche Organisches und Anorganisches umfasst, und die den 
beiden Gebieten gemeinsamen Thatsachen darstellt. E. Mack. 

In preceding pages we have considered as examples of biological 
"equilibria," states that quite obviously can be regarded only as 
rough approximations to equilibria or steady states; and we have not, 
so far, examined critically the justification for this attitude. It is 
desirable to give at least brief consideration to this matter. 

It is common custom, in dealing with the relatively simple systems 
studied in physical chemistry, to assume that a sufficiently slow change 
in one parameter (e.g., volume) defining the state of the system, brings 
in its train a succession of states each of which is essentially equi- 
librium. So, for example, if we slowly raise the piston in a gas-tight 
cylinder containing X grams of water and Y grams of water vapor at a 
temperature 6, it is commonly assumed that at every instant the 
quantities X, Y are such as correspond to equilibrium at the tempera- 
ture 8. 

The Principle of Continuity. The basis of the assumption referred 
to in the preceding paragraph is rarely if ever discussed. Obviously 
it is to be sought in the principle of continuity. If the parameter P 
is constant, at the value P , the variables X, Y, . . . defining the 
state of the system have certain values X , YQ, . . . We tacitly 
assume that if the parameter PO is nearly constant at the value P 
(that is to say, passes through P in very slow change) then the vari- 
ables X, Y will have nearly the value of Xo, Y , . . Or, in the 
notation of an earlier section, if 

^-i^tt:,,*,, . . .P) (i) 

at 

and if, with P = P = constant 

^ = p z = . . = p i = . . . = o (2) 



260 ELEMENTS OF PHYSICAL BIOLOGY 

gives 

Xi = (?i = constant (3) 

then we assume that with 

P = P() (4) 

where P(t) is a slowly changing function of t, we shall have 

Xi = d(t) (5) 

where Ci(t") is a root of the system of equations 

Fi(i) = F z (ti = . . . = Fi(t) . . . = (6) 

(for all values of 

It should be noted that, strictly speaking, this involves a contra- 
diction. For if the velocities F are zero, the variable X cannot be 
changing. And, in point of fact, the result (5) represents a first 
approximation which is not in all cases free from significant error. 

Higher Approximation. It is possible, in certain cases, to proceed 
to second, third and higher approximations by successive steps, or, 
as will be shown, by a single formula. So, for example, for a system 
in two variables X, Y, we may write, first of all 

d -j = F^X, Y, i) (7) 

^ = F(X, Y, t) (8) 

'The first approximation here is 

F! = F z = (9) 

X = X 1 (t) (10) 

Y = Fi(<) (11) 

The second approximation we obtain by differentiating (10), 
(11), so as to obtain the derivatives Xi, YI, which, although not 
zero, are nevertheless small, according to our supposition of a slow 
change. Substituting these in (7), (8) we find 

Fi - Xi'(t) (12) 

F, = F,'(0 , (13) 



MOVING BQUILIBEIA 261 

Hence 

X = Xt(t) (14) 

F = F 2 (*) (15) 

And so on, for successive higher approximations. But this process 
can be contracted into a compact expression. We have 

^J = ?f 1 , ^Oj d JE *>1}*Y 
dt ~ di" bX dt bY dt ' 

^! = 5f> _)_ ^J^I L ^. 2 ^I 
d d* d,Y di + dF d< ( 

If we substitute in (16) (17) 

f-X/> (18) 

dF 

Tt = YS0 (19) 

the right hand member must vanish, in view of (9), (10), (11) and 
we have 

+*'+*- 



from^which it is seen that X 2 (t), F 2 (0 can be expressed directly as the 
solution of the system of equations 



Similarly the (n + i) th approximation is found by writing 

_' = _ = o (24) 

Special Case. Returning to the general case of n variables, sup- 
pose that for all values of X l X z . . . differing appreciably from 



262 ELEMENTS OF PHYSICAL BIOLOGY 

the equilibrium values, the velocities ] - ... are negligible 

(Z6 QJ(I 

dXr 

as compared with some one of them, say -j-. Then we can write, 

at 

practically 



X t , . . . X n ) = (25) 



F n (Xi, Xz, . , . X r , . . . X a ) 
where ^ r is excluded from the system (25) . This defines 



X 2 = C z (X r ) (26) 

etc. 

In addition to this we then have the equation 

TTLT 

* = F t (Ci, C*, . . . X t , . . . C n ) (27) 

at 

= F r (X r ) (28) 

Hence 



which is directly integrable 

? ,v x (30) 



In such case as this, then, that particular change which is much 
slower than all the others, sets the pace and controls the whole process. 
It acts as a brake, as a limiting factor. 

RADIOACTIVE EQUILIBRIUM 

Moving equilibria play an important role in evolutionary processes 
of the most varied type, as emphasized almost ad nauseam by Herbert 
Spencer, 1 though some of the most typical and at the same time 
most fundamental examples were unknown to him. For, the most 
exact, quantitatively precise illustrations of moving equilibria are 
to be seen in the evolution of chemical elements by successive steps 

1 First Principles, Chapter XXII. 



MOVING EQUILIBRIA 



263 




ggsiggaga^^ 




FIG. 55. URANIUM AND ITS PRODUCTS OF RADIOACTIVE DISINTEGRATION 

(U = uranium; To = ionium; Ra = radium; Rn = radon == radium emana- 
tion; Po = polonium; Pb = lead.) Each element in the chain is produced 
from its predecessor either by the emission of an alpha particle, i.e., a doubly 
charged helium atom, in which case the atomic number is decreased by two 
units; or by the emission of a beta particle, i.e., an electron, in which case 
the atomic number increases by one unit. 



264 ELEMENTS OF PHYSICAL BIOLOGY 

of atomic disintegration, accompanied, in most cases known to us, 
by radioactive manifestations. It is not within the plan or compass 
of this work, to give a detailed account of what has by this time grown 
into an extensive special field of physical science. It must suffice 
to refer to the chart (fig. 55) of one of the typical series of radioactive 
transformation chains, and to state briefly the simple law of transfor- 
mation of such elements by spontaneous atomic disintegration : The 
amount of a substance transformed per unit of time is directly pro- 
portional to the amount of that substance present, so that if Si is the 
i th substance in a transformation chain 

and if we denote by Xt the mass of Si, then we have a system of 
equation 

"V T7" "\ T7" /fjrO 

-Ai-^-x-AA (32) 

where the coefficients X are constants, invariable under all condi- 
tions to which observation to the present date has extended. 

It will be seen that the system of equations (32) is a simple special 
case of the general form discussed in Chapter VI. Its solution 2 
is of the form there indicated, but the simplicity of the differential 
equations is reflected in the integrals, which here appear as finite 
series, the expression for the mass of z th substance, being 

Xt = a,-,ie~ Xlt + ai,2e~ X4t 4- . . . + ai,t<T"V (33) 

The series contains only linear terms, and breaks off at the term in a#. 

If X A is (numerically) the least of the X's, then, evidently, after a 

sufficient lapse of time the term in X& outweighs all other terms, which 

thus become negligible, so that 

Xi ctik 

Y k = (34) 

The coefficients a are easily determined 3 as functions of the X's. It 
is thus found that 

^ " (Am - X*) (X*+ 2 - X,) . . . Ow_! - X*) (X, - A*) if * > * (35) 

am 

- if i < k (36) 

2 For a somewhat remarkable method of integration (by a multiple 
integral), see A. Debierne, Les ide"es modernes de la Matiere, 1913, p. 328. 

8 See, for example, E. Rutherford, Radioactive Substances, 1913, pp. 422, 
423. 



MOVING EQUILIBEIA 



265 



Thus, after a sufficient lapse of time, the substances Si, S 2 , . . . 
Sk are always present together in constant proportion, so that we 
have a moving equilibrium of a veiy simple type, illustrated graphi- 
cally in figure 56, in accordance with some of the constants given in 
tables 28 and 29. The most slowly decaying substance here acts as 

TABLE 28 

Radioactive equilibrium of radium in contact with its disintegration products 
on the basis oj data in Jour. Am. Chem. Soc., 1923, vol. 45, pp. 872-873 





AMOUNT IN 
EQUILIBRIUM 


l/X = MEAN LIFE 


Radium 


1.00 ton 


2,440 years* 


Radon 


6 . 23 grams 


5.55 days 


Radium A 


3 37 mgm. 


4 32 minutes 


Radium B 


30.18 mgm. 


38 7 minutes 


Radium C 


21.91 rngm. 


28 . 1 minutes 


Radium D 


9.75 kgm. 


23.8 years 


Radium E 


8.08 grains 


7 2 days 


Radium F| 


220.01 grams 


196 days 









*Half-decay period = = 190 years. 

fPolonium. 



the controlling, slowly variable parameter, and sets the pace with 
which all the subsequent members in the transformation chain keep 
step, so that the polygons representing the system in its successive 
stages are geometrically similar. (Compare fig. 58 on p. 277.) 

The second of the two expressions for the ratio a ifi: /a kk calls for 
brief comment. If i < /c, that is to say if the substance Si precedes, 
in the transformation chain, the substance Sk which has its lowest 
disintegration rate, then Si does not appear at all in the equilibrium. 
Hence when an aggregation of substances in radioactive equilibrium 
is found in nature, the substance at the head of the chain (the "par- 
ent substance") is always the one of slowest disintegration rate. But, 
obviously we cannot from this draw any conclusion as to whether or 
not it is itself a product of disintegration of a pre-parent of more rapid 



O i-% A 



decay 



.ate. Aay such pre-parei* 



OP PHYSICAL BIOLOGY 

as it were, have been 




CONTACT WITH ITS DISIN- 
M davs (half -decay period) 









torn a geometric series 

Tte different equations 
transformation "dily 



to deterge the 

. H. Mitchell, PhU. Mag., 
23, p. 353. 



. , ^rairw of radioactive 
f^ ation> a nd there is 
rf OTCCess i v e approxima- 
. However, the first 



, P- ' A ' 



MOVING EQUILIBBIA 



267 



approximation is so simple, that it is commonly applied. Equating 
the right hand member of (32) to zero we find immediately 

-j = *L I (37) 

and by an obvious extension 

- ~* (38) 

Afc Xi 

It is easily shown that L i} the reciprocal of X;, is the "mean length of 
life" of an atom of the substance $,> We may write (38) 

~ - ~ (39) 

which expresses the fact that, in first approximation, the amounts of 
several substances present together in radioactive equilibrium arc 
in the ratio of the respective mean lengths of life. 5 This result can 
also be read out of (35) if \\ h \, the least of the |X|'s, is negligible in 
comparison with all the other |X|'s, so that the denominator reduces 
to the product 

It is thus seen that the closeness of the first" approximation depends 
on the relative magnitude of X& and the remaining X's. In many 
chains of radioactive transformation the parent substance is very 
slow in its disintegration, and the first approximation (giving what 
Rutherford has termed the secular equilibrium) is exact within the 
limits of experimental error. But if one of the more rapidly decaying 
members is isolated and is then allowed to come into equilibrium with 

5 This is a special case of a general law that if all the exponents \ arc real 
and negative, the final stages of the process of evolution are characterized by 
constancy in the ratios of the Variables .T. Compare p. 261, Special <7a.svj; 
also, Lotka, A. J., Proc. Am. Acad. Sci., vol. 55, 1920. Ifc should be noted, 
however, that in the general case, xt denotes not mass of Si, but CXCGHB of 
that mass over the equilibrium mass of Si. In the radioactive equilibrium 
there is no distinction between X and x, since the ultimate value of both 
is zero. 

For the second and higher approximation, applied to the radioactive 
equilibrium, the reader may be referred to A. J. Lotka, Proceedings Natl. 
Acad. Sci., 1921, vol. 7, p. 170. 



268 



ELEMENTS OF PHYSICAL BIOLOGY 



its own products of disintegration, the error of the first approxi- 
mation may become appreciable. 7 This is shown, for example in 
table 29, which exhibits the amounts of radon gas (radium emanation) 
and its several products of disintegration in radioactive equilibrium. 
It will be observed that in the case of radium C there is a discrepancy 
of about 1 per cent between the amount computed by first approxi- 
mation and the true amount. 

Radioactive Chains as Cosmic Clocks. It must be noted that all 
that has been said above regarding the amounts of the substances 
present in radioactive equilibrium does not apply to the last link in 
the chain, the end product. This does not, of course, take part in 
the equilibrium, but accumulates, if non-volatile, as in the case of lead, 
or, it may in part escape and be lost to observation, as in the case of 
helium. 

TABLE 29 

Radioactive equilibrium of radon (radium emanation) in contact with its dis- 
integration -products, on basis of data in Jour. Am. Chem. Soc., 
1923, vol. 45, pp. 872-873 





X (PER SECOND) 


L = 1A 


EQUILIBRIUM AMOUNT 


Exact 


First approximate 


Radon. 


2.085 X 10- 6 
3.85 X 10 ~ 3 
4.30 X 10-" 
5.92 X 10-* 


5.55 days* 
4.32 minutes 
38.7 minutes 
28 . 1 minutes 


l.OOOkgm. 
0.5416 grams 
4.874 grams 
3 . 552 grams 


l.OOOkgm. 
0.5418 gram 
4.849 grams 
3 . 522 grams 


Radium A 


Radium B 


Radium C 





*Half~decay period = 0.69315 L = 3.85 days. 

If the amounts of parent substance and end product are large as 
compared with the amount of intermediates, the amount of any one 
end product formed is evidently simply proportional to the amount 
of parent substance lost by disintegration in a given time. The 
chain of substances in transformation behaves, in fact, much like a 
sandglass clock having a number of bulbs and from the accu- 
mulation in the end bulb we can obtain an indication of the age of 
the system, on the assumption that originally all was in the top bulb, 
that initially only the parent substance was present. The applica- 
tion of this principle to radioactive mineral deposits has given us a 
quantitative time scale in historical geology where before we had to 

7 Compare E. Rutherford, Radioactive Substances, 1913, p. 430. 



MOVING EQUILIBRIA 



269 



rest satisfied with a crude chronology recognizing only order of pre- 
cedence, or at best dealing in exceedingly uncertain jjestimates of lapse 
of time. Thus the investigation of radioactivity, remote as it seems 
from the field of life phenomena, has nevertheless contributed to 
biology essential information regarding the time that has been avail- 
able for the evolution of the earth and its inhabitants. The estimate 
reached upon this basis is that the age of the radium-bearing rocks 
(uranium ore) examined is at least eight million years, and at most 
seventeen hundred million years old. For a resume" of various esti- 
mates of the age of the earth the reader may be referred to G. 

TABLE 30 

Geologic time table 
After Sclmchert 







FROM BAItHBLI, 1917 
ON tniANIUM BASIS 


Cenozoic 


per cent 

5 


per cent 

4 


Mesozoic 


12 


11 


Paleozoic 


28 


30 


Late Proterozoic 


15 


) 


Early Proterozoic 


15 


J- 55 


Archeozoic 


25 











Schuehert, The Evolution of the Earth and its Inhabitants, 1919' 
pp. 56 et seq.; 80; and to the Proceedings of the American Philo- 
sophical Society, 1922, vol. 61, pp. 247-288. See also E. Ruther- 
ford, Radioactive Substances, 1913. Schuchert's estimate is that 
"geologic time endured about eight hundred million years," dis- 
tributed among the several geological eras as indicated in table 30. 
The Origin of the Elements and the Ultimate Genesis of the 
Organism. The case of radioactive equilibrium has here been in- 
troduced primarily by the way of illustration, as probably the most 
typical example in nature of a moving equilibrium in a system in the 
course of evolution. But the matter is also of more material interest 
to us in our survey of the evolution of the earth as the abode of life. 
For, as has already been emphasized, we are not only on the earth but 
of it; we have thus a two-fold interest in the evolution of its substance 
first, as providing the stage upon which our life drama is set; and 
second, as furnishing the material of our bodies. Of these same ele- 



270 ELEMENTS OF PHYSICAL BIOLOGY 

ments that make up the earth's crust we also are composed: their 
genesis is therefore also the first, remote chapter in the genesis of 
our own bodies. Through the discovery of radioactive chains of ele- 
ments we hold a clue regarding the fundamental influences that 
have determined the quantitative chemical composition of our world, 
and have thus appointed the measure of the supplies available for 
our needs. Those elements whose genesis is known to us came into 
being in perfectly definite proportions. Presumably the same is 
true also of those whose precise mode origin is still unknown. There 
is good evidence to support this view. We have at present no detailed 
quantitative knowledge of the laws which determine the value of the 
decay coefficients X of the radioactive elements, and which thus ulti- 
mately fix their relative abundance in equilibrium. But a significant 
qualitative relation has been pointed out by W. D. Harkins. 8 When 
the elements in a radioactive chain are arranged in order of their 
atomic numbers, 9 and are separated into two groups, those of odd 
and those of even number, it is found that each even-numbered ele- 
ment is more abundant than the adjacent odd-numbered elements. 
And, what is of particular significance, the law of relative abundance 
of odd and even-numbered elements extends also to those elements, 
regarding whose precise mode of origin we have not, as yet, that sure 
knowledge which is gained by direct observation within the four 
walls of the physical laboratory. (See fig. 57.) 

8 Jour. Am. Chem. Soc., 1916, vol. 38, pp. 863, 869; 1923, vol. 45, pp. 1420- 
1433. Compare also F. W. Aston, Nature, March 15, 1924, p. 394. For 
other regularities observed in the length of life of radioactive elements see 
K. Fajans, Radioaktivitat (Sainmlung Vieweg Heft 45) 1921. 

9 The chemical elements, arranged in ascending order of atomic weights, 
beginning at hydrogen = 1, may be given ordinal numbers 1, 2, 3, etc., in- 
dicating their position in the series. These ordinal numbers have been found 
to have important relation to the atomic architecture. They have been 
termed the atomic numbers. The definition here given is not quite exact; 
in certain places allowance must be made, gaps left for unknown elements, 
and the several isotopes of one element receive the same atomic number, 
though differing in their atomic weights. A more precise definition is the 
following: The atomic number of an element represents the excess of posi- 
tive over negative charges in the constitution of the atomic nucleus. Each 
atomic number also represents the place occupied by the element in Men- 
deleef's table (Jour. Am. Chem. Soc., 1923, vol. 45, p. 868). For further in- 
formation the reader must be referred to the special literature; of compre- 
hensive works the following may be mentioned: Bragg, X-rays and Crys- 
tals; F. W. Aston, Isotopes. 




FIG. 57. RELATIVE ABUNDANCE OF THE ELEMENTS 

Each element of even atomic number is more plentiful than the adjacent 
elements of odd stomic numbers. Diagram according to W. D. Harking, 
based on analysis of meteorites. (Jour. Am. Chem. Soc., 1916, p. 863.) 

271 



272 ELEMENTS OF PHYSICAL BIOLOGY 

But the laboratory is not a prison, and the eye of the physicist is 
free to sweep the sky, where nature's great smelteries gleam at night. 
With the aid of the spectroscope he has studied the multitudes of the 
stars, and has recognized in them a number of distinct stages of evo- 
lution. Life's day is far too short to give the observer any oppor- 
tunity to study directly the evolutionary changes in any one star. 
But by piecing together the observations made upon the mixed popu- 
lation of stars of different ages, it has been possible to construct with 
considerable certainty the main stages in stellar evolution, just as the 
stages of human life could be gathered from a single observation of 
a mixed population comprising persons of all ages. The evidence 
points clearly that the elements, such as we know them, are the 
product of "the general brewing of material which occurs under the 
intense heat in the interior of the stars." Out of such foundry came 
our own abode, if we accept the well-considered views of Eddingtor.. '" 
"I do not say that the earth was a gaseous body when it first became 
recognizable as an independent planet, but I am convinced that its 
material was at one time merged in a completely gaseous sun/' 
And since we are of earth, ours also is the same origin. The hand that 
writes these words and the eye that reads them alike are composed 
of the selfsame atoms that came into being, ages and ages ago, in 
the young sun. Far, far more wonderful than any dream of old 

10 A. S. Eddington, The Borderland of Astronomy and Geology, Nature, 
1923, p. 18, also, The Interior of a Star, Supplt. to Nature, May 12, 1923. The 
T- der who wishes to acquaint himself in greater detail on this subject may 
refer to Eddingtons's -work Stellar Evolution. In the interest of unbiassed 
presentation it must be noted here that T. C. Chamberlin (The Origin of 
the Earth, 1916) has put forward a theory of the origin of the earth and the 
planets which is at variance with that sustained by Eddington. On the 
other hand it is also proper to mention a fundamental objection to theories 
of cosmogony of the type of that of Chamberlin and Moulton, which is based 
on the supposition that the luminous stars are formed by the collision of 
dead suns. "The distances separating the stars are enormous compared 
with their own dimensions. Sir Frank Dyson once used the illustration of 
twenty tennis balls distributed at random throughout the whole interior of 

the earth, to give a model of the density of distribution of the stars 

Taking a very liberal view of the kind of approach that can be held to con- 
stitute a collision, it is estimated that a star would suffer a collision about 
once in a hundred million million years" (Eddington). For a survey of 
the modern views on this subject see J. Barrell, The Evolution of the Earth 
(Yale University Press, 1919). 



MOVING EQUILIBBIA 273 

mythology is the story of our creation. Thus was the birth of man 
prepared in the grey dawn of time ; thus the metal of his frame com- 
pounded in the flaming furnace of a star. .... 

TERMINAL STAGES OF THE EARTH'S EVOLUTION 

Geophysics and Geochemistry. For the last stages in the evolu- 
tion of the elements and their chemical combinations we do not look 
to the stars. We can study them at close quarters in the field and in 
the laboratory. In this way, with the application of physics and 
chemistry to general problems of geology, have grown up the sciences 
of geophysics and geochemisty. Indeed, it naturally might be 
supposed that on the terrestrial phases of inorganic evolution we 
should be altogether better informed than on those prior stages, far 
remote in time and space, which run their course in distant suns. 
But this is true, at best, only in restricted measure. It is a singular 
circumstance that, in some ways, we are better informed regarding the 
physics and chemistry of the stars, of which the nearest, outside the 
solar system, is twenty-five million million miles distant, than regard- 
ing that of our own planet. To say that the earth's surface layers 
accessible to our direct observation are comparable, scale for scale, 
to the shell of an egg, is to err on the side of liberality. The deepest 
burrow into the earth made by human agency, the mine shaft at 
Morro Velho, Brazil, 11 is 1-|- miles (6400 feet) deep or only about 
frsT of the earth's diameter. Direct observation can therefore give 
us at best only the most uncertain information regarding thecon- 
ditions at even moderate depths. Where the crust has been creased 
and thrown into folds, subsequent denundation may have exposed 
layers of some 50 or 60 miles aggregated thickness. 12 But, though 
this gives us an invaluable record of some of the most significant 
chapters in the earth's history, it adds little or nothing to our knowl- 
edge of conditions of temperature and pressure even at comparatively 
trivial depths, and regarding chemical composition also it gives us, 
after all mere surface indications. Indeed, our information on all 
these points is very largely of a negative character. We know from 
the earth's average density that the composition of the core must be 
very different from that of the shell. We know that the temperature 

u Sir Charles Parsons, Nature, February 19, 1920, p. 677. 
12 G. Schuchert, The Evolution of the Earth, Yale University Press, 1919, 
p. 67. 



274 ELEMENTS OF PHYSICAL BIOLOGY 

gradient observed in boreholes near the surface averages an increase 
of about 1F. for every 60 feet (1C. for every 35 meters) descent, but 
of the further course of temperature at greater depths we know with 
reasonable certainty only that it cannot continue at this gradient, 
which would give a phantastic temperature of 300,000F. (1 80,000C.) 
at the center. Lord Kelvin's calculations, based on the rate of cool- 
ing of the earth, and the more recent figures of the same character 
given by Van Orstrand, are rendered uncertain in their application 
owing to the presence of radium, in unknown amounts, evolving heat 
in its distiiitegration. Strutt has made the tentative estimate that 
the temperature rises uniformly to a depth of about 30 miles, and 
after that remains sensibly constant at 2700F. 

A little more definite is our information regarding the pressure in 
the earth's interior. A first approximation of its value is found by 
considering the earth as a fluid. It is thus found 13 that the pressure 
at the center would be three million atmospheres. In any case there 
can be no doubt whatever that the pressures reached vastly exceed 
anything at our command in the laboratory, where a pressure of 
twenty-four thousand atmospheres, employed by P. W. Bridgman 
in his researches, stands out as a record achievement, though it coiv 
responds to a depth of rock of only 56 miles. 14 

It must be clear from what has been said above, that all conjectures 
as to the physical, chemical and subatomic transformations going on 
in the earth's interior are subject to a very large margin of uncertainty. 
In this connection it is well to recall the words of F. W. Clarke: 15 

The chemistry of great pressures and concurrently high temperatures is 
entirely unknown, and its problems are not likely to be unravelled by any 
experiments within the range of our resources. The temperatures we can 

command, but the pressures are beyond our reach We may 

devise mathematical formulae to fit determinable conditions; but the moment 
we seek to apply them to the phenomena displayed at great depths, we are 
forced to employ the dangerous method of extrapolation, and our conclu- 
sions are not verified. 

13 This supposition, in calculating pressures, probably does not err far 
from the truth. The researches of P. D. Adams (Journal of Geology, Feb- 
ruary, 1912), P. W. Bridgeman and others have shown that at depths of some 
30 miles rocks probably give way like butter to the pressure of the layers 
above them. 

" W. D. Lambert, Jour. Washington Acad. Soi., 1920, p. 126. Sir Charles 
Parsons, loc. cit. 

15 Data of Geochemistry, p. 271. 



MOVING EQUILIBRIA 



275 



In these circumstances we can feel but little confidence in inferences 
based upon our laboratory observations, relating to radioactive ami 
other possible atomic transformations going on at greater depths 
within the earth. If the degree arid character of radioactivity which 
we observe in the accessible surface layers were to continue through- 
out the mass of the earth, the amount of heat developed would be 
much in excess of the observed losses by radiation. 10 Unless there- 
fore, we are to draw the highly improbable inference that the tem- 
perature of the earth's mass is steadily rising, we are forced to one of 
two assumptions. Either the radioactive elements arc segregated 
chiefly in the earth's crust; or, the present rate of heat loss by radia- 
tion from the earth does not represent its average rate. This latter 
is the alternative elected by J. Joly 17 in an original conception. Ac- 
cording to this there are alternate periods of accumulation of heat in 
the solid rocks, followed by periods in which these rocks, having finally 
become melted, well to the surface in a death-dealing flood of fire. 
Thus, by convection, a process far speedier than conduction, through 
the solid rock mass, heat is dissipated until, after sufficient cooling, 
a second period of quiescence, with a solid earth's crust, is ushered hi. 
And so, in long waves of perhaps some thirty million years duration, 
the planet alternates between periods of hospitable clemency and 
periods intolerant of life. 

There is, for us living inhabitants of this globe, a certain wildly 
romantic element, a feature of calamitous tragedy, in the hypothetical 
picture of the world's history thus summoned up before our 
imagination. 

In its biological aspect how great and wonderful it all is I The living being 
working out his destiny on this poor raft, unknowing of the fiery ocean upon 
which this world is floating: unknowing of the inevitable sinking and up- 
lifting which in truth largely controls the destinies of his race. .Death- 
dealing forces all around, and yet the light of life shining age after age upon 
the earth. 

16 Compare V. Moritz, Dor Stoffwechsel der Erde, Zeitschr. f. Eloldro- 
chemie, 1922, p. 421. 

17 J. Joly, Movements of the Earth's Crust; lecture under the auwpicoH of 
the Royal Dublin Society, published in Nature, 1923, p. 003. A third pos- 
sibility is that under the extreme conditions of temperature and pressure 
prevailing in the earth's interior reversal of the familiar radioactive dis- 
integrations, or similar endothermie processes may go on. (Jour Natl 
Acad. Sci., 1924, p. 89. 



276 ELEMENTS OF PHYSICAL BIOLOGY 

Such conceptions as this, stimulating as they are to the imagina- 
tion in reconstructing for us an image of the remote past and distant 
future, must be entertained with reserve, remembering the words of 
caution quoted above from Clarke's classic work. We must be 
prepared to consider the possibility that under the extreme conditions 
of temperature and pressure prevailing at great depths other subatomic 
transformations than those known to us in the laboratory may occur. 
Perhaps some evidence of this is seen in the evolution of helium as a 
component of natural gas, in amounts (up to 1.5 per cent 18 ) in excess 
of anything readily accounted for on the basis of the observed radio- 
activity of the rocks. And, while the subatomic transformations 
known to us are exothermic, accompanied by liberation of heat, others 
undoubtedly are endothermic, associated with absorption of heat. 
We seem to have carte blanche, in the present state of knowledge, in 
our speculations regarding the net heat balance of the elemental 
transformations that may be going on under our feet. 

On surer ground rest our conceptions regarding the organization of 
matter, especially in the more superficial layers of the earth, under the 
action of ordinary physical and chemical influences. That the prime 
factor effecting the first and fundamental segregation of the lighter 
elements is flotation under gravity can hardly be doubted; this 
statement would in fact, be little more than a platitude if we were 
assured that the elements themselves remain unchanged under the 
extreme conditions of temperature and pressure prevailing in the earth's 
interior. Beyond this prime factor the study of mineral and rock 
formation becomes a complex chapter in applied physical chemistry, 
the consideration of which is not within the plan of this work. The 
reader who wishes to follow out further this phase of the subject will 
find a comprehensive survey of the field in an article Dcr Stoffwech- 
sal der Erde, by V. Moritz, in the Zeitschrift fur Elektrochemic, 
1922, pp. 411-421; and in the memoir The Chemistry of the Earth's 
Crust by H. C. Washington, which has already been quoted. 

Organic Moving Equilibria. Of moving equilibria in the organic 
world, data are most readily available for the system comprising man 
and his domestic animals. Here the human race acts as the control- 
ling factor, drawing its dependents after it in its growth. The equi- 

18 R. B. Moore, Nature, 1923, p. 91; Cady and McFarland have reported 
one instance of 1.84 per cent. J, Joly, Radioactivity and Geology, 1909, 
p. 218. 



MOVING EQUILIBEIA 



277 



librium polygon for the principal items of animal husbandly in the 
United States is shown in figure 58. The geometric similarity of 
successive polygons is in this case only approximate, the proportion of 
the several components varies somewhat; except in the case of the 
sheep population, however, the variation is moderate over the half- 
century from 1871 to 1921. (Compare fig. 56 on p. 265.) 

Aside from the features for the express illustration of which the 
diagram figure 58 was drawn, it also serves to point once more to the 




-70 



FIG. 58. EouiLiBEitnvi POLYGON .FOE THE HUMAN SPECIES AND SOME OF THE 

SPECIES ON WHICH IT DEPENDS FOU ITS FOOD SUPPLY. SCALES 

READ IN MILLIONS 

fact already emphasized, that the concept of evolution, to serve us in 
its full utility, must be applied, not to an individual species, but to 
groups of species which evolve in mutual interdependence; and 
further, to the system as a whole, of which such groups form 
inseparable part. 

It would be conveying a false impression in a very essential respect, 
to exhibit the example illustrated in figure 58, without a comment 
in emphatic reservation. Although, in a roughly approximate- 
way, it is true, as shown by the polygon diagram, that in its relation 



278 



ELEMENTS OF PHYSICAL BIOLOGY 







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MOVING EQUILIBRIA 270 

to certain staples of agricultural production, our population lias 
advanced in a succession of moving equilibria; yet, tbo progress of 
modern industrial civilization on the whole is essentially the very 
antithesis of a moving equilibrium conditioned by and following upon 
the changes of a slowly varying parameter. Quito on the contrary, 
the development of this age is rather of the nature of a rocket-like 
ascent with a speed altogether unparalleled in all previous history of 
organic evolution, and at the cost of rapid depletion of capital 
resources. Certain aspects of this phenomenon are reserved for 
consideration in a later chapter. Here it will bo sudiciently to the 
point to draw attention to table 31, reproduced from H. Pearl's 
essay on The Population Problem, which shows the altogether dis- 
proportionate increase in the growth of our material accessories iu 
recent years, as compared with that of the population itself. 

The human species, considered in broad perspective, a,s auui , t inc.liK l- 
ing its economic and industrial accessories, has swiftly and radically 
changed its character during the epoch in which, our life has been laid. 
In this sense we are far removed from equilibrium ...... a fact which is of 

the highest practical significance, since it implies that a period of 
adjustment to equilibrium conditions lies before us, and ho would be 
an extreme optimist who should expect that such adjustment can be 
reached without labor and travail. We can only hope that our race 
may be spared a decline as precipitous as is the upward slope; along 
which we have been carried, heedless, for the most part, both of our 
privileges and of the threatened privation ahead. While such sudden 
decline might, from a detached standpoint, appear as in accord with 
the eternal equities, since previous gains would in cold terms balance 
the losses, yet it would be felt as a superlative catastrophy. Our 
descendants, if such as this should be their fate, will see poor com- 
pensation for their ills in the fact that we did live in abundance and 



. Pearl, Geographical lioviow, 1922, vol. 12, p. 038, 



MOVING EQUILIimrA 



< 1 J 



to certain staples of agricultural production, our population 
advanced in a succession of moving equilibria; yet the p roarer 
modern industrial civilization on the whole is essentially tin- 
antithesis of a moving equilibrium conditioned by and follmvim'; upo 
the changes of a slowly varying parameter. Quite on the cmtinin , 
the development of this age is rather of the nature of a rurkef -Hie 
ascent with a speed altogether unparalleled in all previous hi:>f urv nt" 
organic evolution, and at the cost of rapid depletion of capital 
resources. Certain aspects of tins phonomo.ii.on are reserved l<u- 
consideration in a later chapter. Here it will bo NudioirnMy 1" the 
point to draw attention to table 31, reproduced from \\. ('earl's 
essay on The Population Problem, which shows the altotfof her dr- 
proportionate increase in the growth of our material arrejisorie;, hi 
recent years, as compared with that of the population if self, 

The human species, considered in broad porHpeetivo, aH.'iimit inelud' 
ing its economic and industrial accessories, ban .swiftly and rndirally 
changed its character during the epoch in which our life has been laid. 
In this sense we are far removed from equilibrium -a facf which n < it" 
the highest practical significance, since it implies thai- a period 1*1' 
adjustment to equilibrium conditions lieH before UH, n,nd he would be 
an extreme optimist who should expect that such adjiiHtmenJ can be 
reached without labor and travail. We can only hope I Imi our rnee 
may be spared a decline as precipitous a,s I'H the upward nlupe ult.nf, 
which we have been carried, heedless, for the mowt part, both <.f .ur 
privileges and of the threatened privation ahead. While mich iujd lea 
decline might, from a detached standpoint, appear JIM hi aivnnl with 
the eternal equities, since previous gains would in c.old l.musk'tlain-f 
the losses, yet it would be felt as a superlativo (!ji,l ( /i.sl ( nphv. Mm- 
descendants, if such as this should be their fate, will HOC poor rum 
pensation for their ills in the fact that we did live hi abundance ;i nd 
luxury. 

)!1 R. Pearl, Geographical Review, 1922, vol. 12, p. (;JH 



MOVING EQUILIBRIA 279 

to certain staples of agricultural production, our population has 
advanced in a succession of moving equilibria; yet the progress of 
modern industrial civilization on the whole is essentially the very 
antithesis of a moving equilibrium conditioned by and following upon 
the changes of a slowly varying parameter. Quite on the contrary, 
the development of this age is rather of the nature of a rocket-like 
ascent with a speed altogether unparalleled in all previous history of 
organic evolution, and at the cost of rapid depletion of capital 
resources. Certain aspects of this phenomenon are reserved for 
consideration in a later chapter. Here it will be sufficiently to the 
point to draw attention to table 31, reproduced from R. Pearl's 
essay on The Population Problem, which shows the altogether dis- 
proportionate increase in the growth of our material accessories in 
recent years, as compared with that of the population itself. 

The human species, considered in broad perspective, as a unit includ- 
ing its economic and industrial accessories, has swiftly and radically 
changed its character during the epoch in which our life has been laid. 
In this sense we are far removed from equilibrium a fact which is of 
the highest practical significance, since it implies that a period of 
adjustment to equilibrium conditions lies before us, and he would be 
an extreme optimist who should expect that such adjustment can be 
reached without labor and travail. We can only hope that our race 
may be spared a decline as precipitous as is the upward slope along 
which we have been carried, heedless, for the most part, both of our 
privileges and of the threatened privation ahead. While such sudden 
decline might, from a detached standpoint, appear as in accord with 
the eternal equities, since previous gains would in cold terms balance 
the losses, yet it would be felt as a superlative catastrophy. Our 
descendants, if such as this should be their fate, will see poor com- 
pensation for their ills in the fact that we did live in abundance and 
luxury. 

1(1 R. Pearl, Geographical Review, 1922, vol. 12, p. 638. 



CHAPTER XXII 
DISPLACEMENT OF EQUILIBRIUM 

Die Physik wird aus dem Studium des Organischcn an sicli noch schr vio.l 
neue Einsichten scliopfen miissen, bcvor sie auch das Organischo bowiiltigcn 
kann. E. Mack. 

In preceding pages we have passed in review some of the principal 
features of interest presented by systems maintained constantly at or 
near equilibrium, while one of more of the parameters determining 
such equilibrium were slowly changing, thus engendering a moving 
equilibrium. 

One might proceed to a consideration, on a more general basis, 
of the changes brought about in an evolving system through changes 
of any kind, including rapid ones, in the parameters. In the most 
general case this would amount to the discussion of a system of 
differential equations of the form. 






X n , t) 



in which the time t entered explicitly into the function F. 

It is not proposed to take up the study of this perfectly general 
case; it must suffice to point to the mathematical literature regard- 
ing equations of this form. 1 

^ But there is another special phase of the general problem which, 
like the case of slow changes, yields with comparative ease to 
analytical. treatment; namely, that special phase which enquires 
only into the ultimate effect, upon equilibrium, of a given total 
change in a parameter, leaving aside all questions relating to the 
path by which the displacement of equilibrium takes place. Such 
a separate consideration of this special and restricted phase of the 
general problem is rendered possible by the fact that, in certain 
cases at any rate, the displacement of the equilibrium is independent 
of the path of the change, and depends only on the given initial and 



m, lE !S f r !f ample > E " Picard > Tra ^ d'Analyse, vol. 3, 1908, pp. 187, 188, 
194, 197; E. Goursat, Cours d' Analyse, vol. 2, 1918, pp. 482, 498. 

280 



DISPLACEMENT OF EQUILIBRIUM 281 

final values of the parameters whose modification provokes or is 
associated with the change. So, in physico-chemical transforma- 
tions ("changes of state") the principle of Le Chatelier enables us 
to predicate, within certain limits, the sign of the displacement of 
equilibrium conditioned by a change in certain of the parameters 
upon whichjthe equilibrium depends. 

THE PRINCIPLE OF LE CHATELIER 

The principle of Le Chatelier is best illustrated by a simple 
example. Consider the simple chemical reaction 

2H 2 + O a =2H a O + 58.3 oal. 

At high temperatures this reaction is reversible; that is to say, it 
takes place to some extent in the direction of the upper arrow, but 
also to some extent in the direction of the lower arrow, and an 
equilibrium is finally established between these two opposing reac- 
tions. Now this is what the Le Chatelier principle tells us: 

If we add either H alone or alone to the system, the equilibrium 
is shifted in the direction of the upper arrow, that is to say, in 
such direction as to absorb some of the added constituent. 

Similarly, if we heat the system, the equilibrium is shifted in the 
direction of the lower arrow, that is to say, in the direction of the 
reaction which absorbs heat. The principle, as enunciated by 
Le Chatelier z himself, is: 

Every system in chemical equilibrium, under the influence of a change of any 
single one of the factors of equilibrium, 3 undergoes a transformation in such 
direction that, if this transformation took place alone, it would produce a 
change in the opposite direction of the factor in question. 

The factors of equilibrium are temperature, pressure, and electromotive force, 
corresponding to three forms of energy heat, electricity and mechanical 
energy. 

The second paragraph of the principle as quoted above, requires 
special emphasis. It is often omitted, even by authors of the highest 

2 Recherches sur les Bquilibres Chimique, 1888, pp. 48, 210; Comptes Ren- 
dus, 1884, vol. 99, p. 786; Mellor, Chemical Statics and Dynamics, 1904, pp. 
435H136. 

8 It appears that some French writers employ the term "facteur d'e'quilibre" 
as synonymous with "intensity factor of an energy." (Cf. F. Michaud, Ann. 
de Phys., vol. 16, 1921, p. 132.) 



282 ELEMENTS OP PHYSICAL BIOLOGY 

repute/ with the result that a vagueness is introduced for which 
Le Chatelier himself cannot justly be made responsible. This 
vagueness is then often rendered still worse by departures from, the 
original wording, aimed at an extension of the scope of the hiw to 
all conceivable systems and "factors," an extension which is gained 
with a total sacrifice of all validity of the principle. So, for ex- 
ample, if we seek to apply the principle as quoted above, but omitting 
the restriction of the second paragraph, to the water equilibrium 
already mentioned, and if we select as "factor" of equilibrium not 
pressure but volume, the principle would lead us to reason as 
follows: On diminishing the volume of the system, that trans- 
formation will take place which, did it take place alone (i.e., at 
constant pressure), would be accompanied by increase in volume; 
a conclusion which is false. As has been shown by Ehrcnfest/ 1 
the error arises through failure to discriminate, in the application 
of the principle, between the intensity factor (e.g., pressure) and 
the capacity factor (e.g., volume) of an energy. 

It must appear singular that so obvious a defect of the principle, 
as commonly quoted, should so generally have escaped attention, 
and should for example, have passed unnoted through seven cditionw 
of so excellent a work as Nernst's Theoretische Chemie. Khronfost 
points out that the explanation lies in the very vagueness of the 
principles, which permits it to be construed in each case to suit 
circumstances. The principle is commonly applied fix post facto, 
and its competence to predict thus escapes any serious test. This, 
however, is only a partial explanation. After all, the fundamental 
reason for the tardy recognition, and the still more tardy admission 
in the general literature, of the weakness of tho principle, an com- 
monly quoted, must be sought in an inherent weakness of the human 
mind: by a curious inversion of what might be expected in logical 
sequence, the last things to receive critical scrutiny are always the 
fundamental premises of our arguments. This 'is true both as 
regards the judgment of the average individual, of the people ut 
large, and often even of the man of very superior intellect. One 
recalls, in this connection, MacAuley's remarks regarding Dr. 
Johnson: "How it chanced Jhat a man who reasoned upon his 

4 See, for example, W. Nernst, Theoretische Chemie, 1913, p 60S 

' f ' Sf ! iem " 19U ' V L 77) P ' 735 ' Cf ' also 
e, 1911, vol. 1, p. 467. 



DISPLACEMENT OF EQUILIBRIUM 283 

premises so ably should assume his premises so foolishly is one of 
the great mysteries of human nature." 

If such an outwardly slight departure from Le Chatelier's original 
enunciation as the omission of his second ' 'explanatory" paragraph, 
thus completely destroys the validity of his principle, what is to 
be said of such sweepingly vague settings as in the following- 
examples : 

The broadest definition of the principle of Le Ghaielier is that a system tends to 
change so as to minimize an external disturbance (W. D. Bancroft, Journal of 
the American Chemical Society, 1911, p. 92). 

Every external action produces in, a body or system changes in such direction, 
that in consequence of this change the resistance of the body or system against the 
external action is increased. 

If we regard the faculty of adaptation of animals and plants from the point 
of view that the organisms undergo, under the influence of external actions, 
changes which render them more resistant to those actions, then the property 
of non-living matter which is expressed by the principle of Le Chatelier-Braun 
may be regarded as a sort of adaptation of such non-living matter (Chwolson, 
Trait6 de Physique, 1909, vol. 3, p. 547). 

If the equilibrium of a natural complex (system of masses, organism, system 
of ideas') is disturbed, it adapts itself to the stimulus (Reiz] which causes the dis- 
turbance, in such manner that the said stimulus continually diminishes until 
finally the original or a new equilibrium is again established (J. Lowy, Jvosmos, 
1911, p. 331). 

The last two examples are of particular interest to us here as 
suggesting application of the principle to biological systems. As a 
matter of fact, such application of the vaguely formulated principle 
(in a form in which it would be injustice to link it with the name of 
Le Chatelier) antedates by many years its enunciation by the 
French physicist. The following passages in Herbert Spencer's 
First Principles a're pertinent : 

Among the involved rhythmical changes constituting organic life, any dis- 
turbing force that works an excess of change in some direction is gradually 
diminished and finally neutralized by antagonistic forces, which thereupon 
work a compensating change in the opposite direction, and so, after more or 
less of oscillation, restore the medium condition. And this process it is which 
constitutes what physicians call the vis mcdicatrix naturae, 

This is a conclusion which we may safely draw without knowing the special 
re-arrangements that effect the equilibration: If we see that a different mode 
of life is followed after a period of functional derangement by some altered 
condition of the system if we see that this altered condition, becoming by 



284 ELEMENTS OF PHYSICAL BIOLOGY 

and by established, continues without, further change, wo havo no altornafcivo 
but to say that the now forces brought to boar on the wyHtom have boon com- 
pensated by the opposing forces they Imvo evoked (I<!irnt Principles, (Chapter 
XXII, EquiUbriatwn t 173). 

Almost simultaneous with Lo Ohatelicr's publication (1884) is 
the following pronouncement. 

L'4tre vivant cst agonc6 do to Ho mauioro quo ohaquo influence povturbatrice 
provoque d'elle memo la miso on activity do I'apparoll oomponsateur qui doit 
neutraliser et rcparer lo dominate (I/sou Frdddricq, A roll I von do Zoolome 
Exp. et G<Sn., ser. 2, vol. 3, 1885, p, xxxv). 

- Now it is not denied that such oxproHHionn U,B thin have, a co.rtain 
utility, as describing with, fair accniracy a goodly proportion of a, 
class of phenomena to which they rolat<\ ]tii/. <.o 'A'cwi^iiak) such 
statements, as "Lo Giiatelier's l'rin<tiplo," w^tfffotty nuKloadtng. 
That principle, in its exact and narrower formulation IB rigorously 
true, as much so as the laws of thonrvodyjianiioH froni which it c,tm 
be deduced; it has no exceptions, any more than tluvre Ls any 
exception to the law that heat flown by simple* oonduction from the 
hotter of two bodies to the colder. 

The alleged "principle," an applied to biological H.y.stc.mH, lacks 
the sureness which the true Lo Chatdicr principle POHHWHOH, in its 
stricter formulations, in physical choiniHtry. An org/infom may, 
by exposure to a certain influence A, Ixujomo moro rosiHtaut to thd 
influence, as in the caso of acquired immunity after an attack of 
infectious disease, or after habitation to Hiicl/a poiMou as aracmic:. 
But, by exposure to another influence B it may boeomo USHH rowiHtant 
to B, as in the case of cumulative poiaoriH, or of a-naphylaxiH. The 
Le Chatelier principle does not enable us horo to pmUct in which 
direction the effect will take place in a new and untried wiwo of some 
influence C. 

Conditions of Validity of Le Omtelier's Principle. The question 
arises why the principle thus breaks down in ita aj^licsation to 
biological cases of the kind cited. The answer is found by ex- 
amining the basis on which the proof of tho principle rests. 
Such an examination brings out the fact that one of tho nocoasary 
conditions for the applicability of the principle is stability of the 

ZT V^ 11 a PP lication made. Now the equilibria 
commonly contemplated in physical chemistry are stable, so that 



DISPLACEMENT OF EQUILIBEIUM 285 

this condition is satisfied. But it is not always satisfied in the 
equilibrium of the living organism. The organism is, indeed, 
stable with regard to many of the commonly occurring attacks of 
its environment. But it is of little consequence to the species 
whether, for example, the individual organism is stable with regard 
to the ingestion of a large dose of strychnine, for in nature such 
ingestion will occur so rarely, if at all, as to influence in no appre- 
ciable degree the life of the species. It is not necessary for the 
stability of the species, that the individual be stable at all times. 6 
In point of fact, we know perfectly well that sooner or later each 
individual finds itself in a condition of instability, by "accident" 
or sickness, and dies. An analysis 7 of the basis of the principle of 
Le Chatelier reveals the fact, among others, that all demonstrations 
of this principle postulate, as a fundamental characteristic of the 
systems to which it applies, that they be in stable equilibrium. The 
principle can, therefore be applied at best only with cautious 
reservation to living organisms, reservation such as, for example, 
Le Dantec 8 makes: "In studying as closely as possible the con- 
sequences of disease in living organisms, when they survive such 
diseases, I have drawn attention .... to the fact that all 
these consequences, such as acquired immunity and the production 
of antitoxic sera, can be summarized in the principle of Le 
Chatelier." But with such reservation the principle loses its chief 
utility, which consists in its power to predict the course of events. 
Indeed, it might be accused, in such restricted form, of being little 
more than a tautological platitude, which tells us that if the system 
or unit in question is stable, then it is stable. This is not quite 
such a damning accusation as may at first sight appear, for the 
same can be brought against the principle of the survival of the 
fittest, which nevertheless has proved supremely fertile in biological 
research. In point of fact there is a close relationship between 

6 Compare what has been said in the discussion of chemical equilibrium 
regarding the stability of aggregates composed of individuals, themselves of 
limited stability, of limited life period (Chapter XII), 

7 Such an analysis, carried out in considerable detail, has been given by the 
writer in Proc. Am. Acad. Arts and Sci., 1922, vol. 57, pp. 21-37. The impor- 
tance of the restriction to stable equilibria, in connection with biological sys- 
tems, has also been pointed out by C. Benedicks, Zeitschr. f. phys. Cheinic, 
1922, vol. 100, pp. 42-51. A. J. Lotka, Am. Jour. Hygiene, 1923, p. 375. 

8 La Stability de la Vie, 1910, p. 24. 



286 ELEMENTS OF PHYSICAL BIOLOGY 

the two principles. But it is important to note that the principle 
of the survival of the fittest is avowedly statistical in character, and 
is to be applied to organisms in the gross. This is true, also, of the 
principle of Le Chatelier in physico-chemical systems; its field of 
application is to aggregates of molecules, not to the individual. 
But the applications that have been essayed in biology have been 
made to the individual; such application can at the best yield a 
judgment of probabilities. In physical chemistry we deal for the 
most part with stable equilibria. But in biology, as has already 
been pointed out, though the races that come under our observa- 
tion possess stability as races (else they would not have survived 
to be our contemporaries), it does not follow at all, that each and 
every individual is at all times in a state of steady equilibrium. 

Aside from the limitation in the applicability of th&-prin"ciple to 
stable systems, other limitations appear in such an analysis of its 
foundations as has been referred to above. So, for example, loose 
analogy to the physico-chemical equilibrium, as affected by the 
addition of a quantity of one of the reacting substances, might lead 
one to draw the erroneous inference that in a community infected 
with malaria, the introduction of additional malaria parasites would 
shift the equilibrium in the direction of a higher malaria rate. 
But there is every reason to expect, on the contrary, that the 
equilibrium remains unchanged by such addition. For a close 
analysis of the reason for this divergence in the two cases the 
reader must be referred to the original paper already cited. It must 
suffice here to state briefly that this reason is to be found in the 
existence in the physico-chemical case of equations of constraint, 
relations between certain variables, and in the absence of analogous 
relations in the case of malaria. 

Extension of Scope of Rigorous Applicability. While the prime 
result of a searching analysis of the foundations of the Le 
Chatelier principle is to emphasize rather the restrictions of its 
scope, yet in certain respects such analysis does furnish a rigorous 
basis for a certain generalization of its applicability beyond those 
bounds where its warrant rests on the firm ground of thermo- 
dynamics. And this extension of the strict applicability of the 
principle takes place essentially in two directions. On the one hand 
the thermodynamic justification, at any rate in the form commonly 
presented, covers only true equilibria, and does not extend to 



DISPLACEMENT OF EQUILIBRIUM 287 

steady states maintained with constant dissipation of energy. 
This restriction does not appear in the demonstration of the prin- 
ciple on the broadest grounds that suffice for its establishment, 9 
Le Chatelier's principle applies, in certain cases, to steady states 
of the more general type, as well as to true equilibria. 

The second direction in which the analysis, on general grounds, of 
the principle, enlarges its field of warrant, is in the matter of the 
kinds of "factors" to which it is properly applicable. It has already 
been pointed out that, in its physico-chemical application, it must 
be used with proper discrimination as to the distinction between the 
capacity and the intensity factor of an energy, as, for example, 
volume and pressure. It is found, upon analysis, that the ap- 
plicability of the principle to the effect of a change in pressure, for 
example rests upon the following fundamental property of the 
pressure and volume of a system in stable equilibrium. 

1. For every value of v, the volume of the system, there is a 
definite value of p i} the pressure which it exerts, the internal pres- 
sure, as we may term it. 

2. The volume v increases or decreases according as the internal 
pressure p\ is greater or less than the external pressure p upon the 
enclosure, that is to say, 

dv > . > 

= according as pi =; p 6 . 

3. It can be shown that, given (1) and (2), stability demands that 
the curves representing the relative between p (ordinates) and v 
(abscissae) must slope from left to right downwards. For if such 
a curve slopes in the opposite direction, then the slightest displace- 
ment from equilibrium will immediately cause the system to travel 
with cumulative effect, avalanche -like, along the pv curve further 
and further away from the starting point. 10 

9 For justification of this and other statements made in those paragraphs 
the reader is referred to the author's paper already cited. It may be remarked 
that Ehrenfest (loc. cit.) expresses the belief that such broader scope belongs 
to the principle, but he does not support his impression with proof. 

10 It is interesting to note that an upward slope, from left to right,, occurs 
in the middle limb of the van der Waals' pv curve of a gas. But this limb 
represents an unstable state which is never realized, the gas, instead of follow- 
ing this part of the curve, partially condenses and traces a horizontal straight 
line for the pv relation. 



288 ELEMENTS OF PHYSICAL BIOLOGY 

Now these fundamental properties (1), (2) and (3), of a capacity 
and an intensity factor of an energy 11 are shared by certain para- 
meters that have no direct or simple relation to energy whatsoever; 
and since the applicability of the principle depends upon these 
properties, it will extend to such other parameters possessing them. 
As an example may be mentioned the relation between area a 
occupied by a population, and the rent per unit area RI that an 
(average) individual is willing to pay. If .Ri is greater than R e , 
the rent at market rate, the individual will move into a more 
spacious apartment, and a will increase, and vice versa; so that 

== according as Ri = R B 
at ~^~ < ~- 

On the other hand the curves representing, in rectangular coordi- 
nates, the relation between rent and area available per head, neces- 
sarily slope from left to right downward. If it were true, as some- 
times stated, that the more a man has, the more he wants, economic 
equilibrium would be an unstable condition. 

This example is presented here with reservation. There may be 
various complications in practice that may form obstacles to the 
simple application of the principle indicated. But it will serve 
to show how a perfectly rigorous justification may exist for the 
application of the principle of Le Chatelier outside the field of plain 
energetics and thermodynamics. Where, and only where such 
justification can be clearly shown to exist, there it will be permissible 
and useful to apply the principle. Applications made broadcast, 
without prior examination of the parameters involved, perhaps 
without any thought at all of reasonable parameters, are of little 
if any worth. 

One other word of caution must be said, for which the example of 
area and rent will furnish a suitable illustration. Before we apply 

11 Owing to the custom of counting heat absorbed by a system as positive, 
but work done upon it as negative, the relation analogous to that of (2) takes 
the form, in the case of heat energy, 

dQ <- n ,. < 

^ according as 9 j =0, 

Ql ^ 

where Q is the quantity of heat absorbed by the system at a temperature from 
a source at the temperature 0. Here the Qd curves slope upward from left to 
right. Cf. A. J. Lotka, loc. cit., p. 36. 



DISPLACEMENT OF EQUILIBBIUM 289 

the principle to any particular parameter, we must be sure that the 
contemplated change will modify this parameter alone, and not 
also at the same time others that are in principle, if not in physical 
fact, to be regarded as independent. So, for example, one reason 
why the example of area and rent was presented above with express 
reservation is that, ordinarily at any rate, it may be difficult or im- 
possible to modify the area of a population without modifying at the 
same time certain other features, such as the supply of nutriments 
furnished in the soil, etc. 

On the whole, so far, it must be said that the result of a careful 
analysis of the principle of Le Chatelier yields negative results, so 
far as practical application to biological systems is concerned. The 
chief conclusion is that great caution must be exercised in employing 
the principle. This result may be somewhat disappointing, but 
it is for that none the less important. Facts are stubborn things; 
it seems a pity to demolish the idol of a pretty generalization, but 
in such things we cannot permit the wish to be father to the thought. 
And the idol is not wholly demolished in fact his hitherto doubtful 
title to certain domains has been established on a clear basis. But 
his province must be recognized as very definitely bounded. 

DISCUSSION OF DISPLACEMENT OF EQUILIBRIUM INDEPENDENTLY 
OF LE CHATELIER'S PRINCIPLE 

In view of the limitations in the field of strict applicability of the 
principle of Le Chatelier, we are in general forced to consider 
separately each particular case of displacement of equilibrium. 
How such cases may be treated may be exemplified by the following 
two instances. 

Case 1. Displacement of Equilibrium between Food and Feed- 
ing Species. Consider a species $ 2 of mass X z , which requires 
for its (equilibrium) sustenance of a mass k 2 X z of food. Let this 
food be derived exclusively from the slain bodies, of total mass 
di XT,, of a species /Si. Let a fraction e of all the deaths in Si be 
those caused by S 2 feeding upon Si. Then 

k 2 X 2 = ediXi (1) 

-- 



290 ELEMENTS OF PHYSICAL BIOLOGY 

It is generally in the interest of the species $2 to reduce this ratio 
to a minimum, especially in such a case as that of a domestic 
species Si, kept by man ($ 2 ) to provide him with flesh food. For 
the species Si itself consumes food, and is thus directly or indirectly 
a tax upon the system. In fact, the species Si is merely a sort of 
food factory for S 2 , and the less of Si is required to produce the 
requisite amount of food k z X 2 , the more efficient is *Si as a food 
factory. 

We may therefore enquire what the formula (2) tells us regarding 
the efficiency of Si as a food producer. 

Xi h 

It will be observed that the ratio a = = may be reduced 

Jiz etti 

in two ways by operating upon the species Si (operating on S 2 , it 
might be reduced by diminishing 7e 2 ; but we will exclude this from 
consideration) ; an increase in either e or in di will bring about this 
result of reducing a. Now e would be increased if the species $ 2 
helped to protect S\ from its other enemies. This, of course, is one 
of the obvious expedients employed by man toward his domesticated 
sources of sustenance. 

X 

But the species $ 2 may also operate to reduce the ratio a. = 

As 

A* 

by increasing di, and it may do this in several ways, 
etti 

We may write 

(3) 

(4) 

where Ni is the number of the population of S i} mi the mass per 
head of this living population, TO/ the mass per head of the individ- 
uals slain by S Z) and j is a factor, namely -, Evidently dij is the 

TTt/]^ 

death rate per head in the population Si; to simplify matters 
we may assume that j is (nearly) unity, so that d\ represents directly 
the death rate per head in Si. 

It is evidently possible to increase d i} the death rate per head in 
Si, without disturbing the equilibrium, provided that the birth rate 
61 is increased in equal amount. There are several ways of ac- 
complishing this. The most obvious is systematic breeding. We 
may briefly consider the analysis of an ideally simple case in point. 



DISPLACEMENT OF EQUILIBRIUM 291 

Let bi be the natural birth rate per head and di the death rate 
per head, in a population of NI individuals of a food species Si. 

Of the total deaths, let pNi occur through various other causes, 
while qNiN 2 are clue to the destruction of Si by the species S 2 that 
feeds upon Si. 

In equilibrium, then, we have 

&i - di = bi - qN'2 - p = (5) 

N 2 = b ^2 (6) 

9 

Furthermore, let the species $ 2 , when in equilibrium, consume 
f Nz individuals of species NI, so that 

#2 = qNiNz (7) 

Ni = ^ (8) 

Now let $ 2 "cultivate" the species $1, so that the birth rate of the 
latter is raised from bi to bi + aN 2 . 
The conditions for equilibrium now are 

&i + ffN t ' - qNa' -p = (9) 

N z ' = ^ (10) 

q-a- 

NI = ' as before (llj 

The effect of this cultivation, then has been, in this case, to leave 
the population of Si, the food species, unchanged. But the feeding 

species S 2 has increased in the ratio 

q-a- 

This result could hardly have been foreseen by the aid of the 
principle of Le Chatelier. 

In this argument it has been supposed, as a first approximation, 
that q is a constant. In point of fact q will no doubt be somewhat 
modified when the species Si is "cultivated" by Sa. The effect of 
such modification of q would then be superimposed upon the effect 
derived in the argument set forth above. 



292 ELEMENTS OF PHYSICAL BIOLOGY 

Case 2. Change of Circulation through Moving Cycles. Among 
the moving equilibria in nature an important class are those which 
arise in systems traversed by matter in cyclic transformations. 

Consider a very simple example of a cyclic transformation chain, 
such as that in which, of three components Si, S z , S 3 , the first 
becomes converted into the second, the second into the third and 
the third returns to the first, after the pattern: 



7 \ 

$3 < - ' $2 

We may write the equations of the transformation 



_ _ _ ci (~y- y y \ n T" /-. Tf 

/'iv-ii, A, AS; ga^s g\A 
at 

dZ 2 = 
dt ' "' 



dt ' ' 

where in the most general case gi, g 2 , g s are each of them a function 
of Xi } X% } X$. 

When a steady state is established, so that the derivatives -7- 

Cvt 

vanish we have, evidently 

7? ~Y -V /1 o\ 

A-i-^-z-^-s (Id; 

from which it is seen that, in the steady state, that component is 
most abundant, which has the slowest proportional rate of decom- 
position, the smallest g. This smaller g acts as a "bottle neck" 12 
in the cycle, causing material to accumulate in front of it. It acts 
as a brake, as a limiting factor, upon the rate of circulation through 
the system. 

12 1 am borrowing this term from the language of efficiency engineers, who 
employ it to denote a point, in a consecutive series in industrial operations, at 
which the progress of work is arrested by a local "limiting capacity." 



DISPLACEMENT OF EQUILIBEIUM 293 

If the total mass of Si, $ and S s is in some way fixed, so that we 
put Xi + ^2 + Xa = M = const., we have, evidently, for a steady 
state 

jA. I ~~ . , ., , . _. . *' * * . ~~~ IrL \ 14:7 



Similarly 

Xz = *W M . (15) 



X 9 --M (16) 

f/l ~|- (72 + f/8 

The circulation I, i.e., the mass circulating through the system 
per unit of time, is evidently given by 



M (17) 

tfi -I- f/a + f/a 



and 

.^/^.ff^lM.) 

OH i (r/i H- r/z -I- <j*r 



'-"-'-- M approx,, if f/i IB smtill (19) 



Furthermore, 



Hence 



Hence, to increase the circulation, the best effect, other things 
equal, is obtained by seeking to increase the smallest g. 

This result, also, the Lo Chatelier's principle seems incompetent 
to predict, 



294 ELEMENTS OF PHYSICAL BIOLOGY 

Some Significant Cases of Instability. It lies in the nature 
of things that a special interest attaches to stable states and stable 
systems. They represent the lasting features in the changeful 
landscape of nature that is what we mean by stability. They are 
the survivors in the struggle for existence. 

But the class of unstable states and systems is not without a 
special interest of its own. Departures from stability, so far from 
forming insignificant exceptions, are found to play an important 
role both in normal and in pathological life processes. 

The body does not always react* in the direction of a restored 
equilibrium when exposed to a disturbing influence. The opposite 
type of reaction is sufficiently frequent to give occupation and means 
of livelihood to a distinct profession, whose business it is to prevent 
this adverse type of reaction from proceeding to the point where it 
sets a limit to life. A particularly pernicious form of this adverse 
reaction to influence tending to disturb the life equilibrium is that 
known among medical men as the vicious circle. A. departure from 
equilibrium, instead of stimulating a compensating response, pro- 
vokes a further departure in the same direction, with cumulative 
effect. If this process goes on only to a certain point and then 
stops, there may be little or no damage sustained. But conditions 
may arise which, by their very nature, produce a continued accumu- 
lation of deviations from the stable equilibrium position, until the 
limits compatible with the continua,tion of organized life processes 
are exceeded. So, for example, a person exposed to hardships 
through adverse economic conditions, suffers from malnutrition; 
this lowers his resistance to bacterial infection; he contracts tuber- 
culosis; there is a loss of appetite, and malnutrition not only is 
accentuated, but may become fixed even if better economic con- 
ditions are provided. And now a closed cycle, a "vicious circle," 
is established, and the disease grows like an avalanche tumbling 
down a slope, 13 gathering weight at each revolution of the cycle, on 
the downhill path to dissolution, thus 

13 A condition analogous to that represented by the middle (ascending) limb 
of the van der Waals' curve for the relation between pressure and volume of 
gas. 



niSPL.AOKMMNT Ol' 1 KQ'U I LI BRtUM 



205 



r 



loss of .'ippetile --- 



I 



lowered reKistance tc 
infection 




AfIB OUOUl' 

All agon 

Under 25 
2534 | 

H5 44, 
45 54 
55 and over 


\VHKli IT 

(a) 20 per c.enl, or more over- 
u'citrh 1, 


NMMHI'IK 
KXAM- 

2 OIW 


I'HOl'OKTION IN ISA 

II ' .: 

Oil MOIU'l AI1OVK N 


I'd' (HMll. 


Differ- 
ence 


15.7 
(i.l 

5 . 1 

1.1.2 
4.5 

10.7 
4,0 

22.4 
S,2 

32.0 
2 . 1. 


5) . (') 
-0.5 
6.7 
(5.7 
14.2 
S.O 


(h) N'orniid weight" 


'4,251 


fit ) 


(10 


47fi 

1,442 
4(iS 

21!) 
255 


(a,) . 


no , 




(b) 


(n,i 


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1 . 477 



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p. 8 and a forllioominff Htudy by Prof. I. V. Iliacook, Yule University. 
f Five per con I, above or below average weight for age and height. 



296 



KLEM1SNT8 OF 



Cumulative 




>f ><Z Mf #* a ^3 f 





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of a 

a 




- ',,,-v : .^-^ 

v v h i ST * 

> ' (/< l . 




'"*"''" co '"- rol 



reptiles 



DISPLACEMENT OF IIQUILIBRrUM 207 

were swept on upon a tidal wave of unremitting growth, until their 
cost of living exceeded their earning capacity, until their very (strength 
proved their fatal weakness; unable to gather, in a day's run, suffi- 
cient food to fill their .monstrous paunch, they became the victims 
of their colossal ambition; their carcases remained enshrouded in 
the rocks, monumental wrecks by the wayside, where, the caravan of 
evolution has passed on. . . . . 

But there is another view which may account for this chapter in 
Natural History, as lias boon pointed out to me by Mr. ,1. !. S. 
Haldanc in correspondence the gist of which is, briefly, as follows: 
The large reptiles of the secondary age had large, pituitary glands. 
It was probably the secretion of these that determined their large 
size. Now a large animal has a high blood pressure- -a fact which 
is exemplified, in a way, in statistics of clinical observations on 
human material, witness table 32 p. 295. With high blood pres- 
sure there would be a tendency for the capillaries to leak. The thing 
that stops them leaking is pituitrin. Thus selection will tend to 
increase the pituitary gland in large animals. Unless it is possible 
for variations to arise increasing the output of pituitrin but not that 
of the anterior lobe, successive generations will tend to become bigger 
and bigger, till they ultimately perish of hyperpituitarism. 1 ' 1 

Sometimes, it seems, the trend of evolution by a cumulative cydc 
may be grotesque rather than pernicious. This might well be the 
explanation of such singular vagaries as those observed, for example, 
in a group of fishes related to the shark. This series (fig. />{)) (to 
which my attention was drawn by Mr. J. T. Nichols of the American 
Museum of Natural History) exhibits progressive flattening of the 
body accompanied by thinning out of the tail, until the latter I'M 
reduced to a more lash.. Hero some gland controlling growth may 
have become increasingly active in response to selection operating 
on some useful quality, and meanwhile some secondary effect had 
to be taken into the bargain, regardless of utility. 

But cumulative cycles do not always work toward destruction or 
toward mere caprices devoid of utility. The effect of gathering 
momentum is equally potent in the constructive sphere. ' Perhaps' 
the most striking examples of this have occurred in the realm of 

14 Somewhat similar views have boon oxprosHod by A. I I. Hturtcvant. Science 
1924, vol. 59, p. 579. ' 



2 gg ELEMENTS OP PHYSICAL BIOLOGY 

mental phenomena. The oyc lfi and the hand have probably con- 
tributed more than any other single cireumstancn to the evolution of 
the human mind up to its present level. The possession of tin agile 
member gave opportunity for exercise of the menial faculties, this 
in turn reacted towards increased development, of the tactile sense 
and manipulative skill of the hand, and so on in a cumulative cycle. 

A similar "cumulative cycle" has probably had a, large part, in 
developing our faculty of speech. In the present stage of our 
development, we find it almost indispensable, in Ihinkiny, to use 
language, a vehicle whose primary function would seem to bo the 
transmission of thought from one individual to another, and which 
would seem wholly superfluous in the traffic of thought within the 
precincts of one mind, as money currency is needless in the give- 
and-take within the same household. Which, then came first, 
thought, or language? Neither, of course, can claim dear pre- 
cedence. They must have developed together, in mutual stimu- 
lation. The habit of communicating thoughts to others- must have 
reacted upon the thinker and made him more perfect, first as a 
thinker, and then again, in turn, as a communicator of thought, as 
a speaker; and so, in a species of cycle, not vicious but benign, 
thought promoted speech arid speech furthered thought,, in an 
endless chain of cause and effect, such as thai; which we witness in 
the somewhat useless but rather entertaining spectacle of a wit 
chasing its tail, or (to turn from, the fine to the useful arts), in the 
economically more significant performance of the donkey urged to 
unwonted productive effort by the hope of (witching up with that 
elusive wisp of hay dangled by the driven' before the poor beast's 
nose. Cause and effect are so intermingled in a chain of alterna- 
tions that they have become indistinguishable, 

To cite in third place a more modern instance, the mutually 
fertilizing influence upon each other of pure and applied science 
falls into the same class of benign cycles. Here also cau.se and 
effect are so intermingled that the relative merits of the two not 
very clearly separated branches of scientific endeavor are hardly 

1B Of. G. H. Parker, Proc. Am. Phil. Soc-.., 1022, vol. 01, p. 107; alno (1. Elliot, 
Nature, 1923, vol. 112, p. 443. 



DISPLACEMENT OF EQUILIBRIUM 299 

a subject for profitable debate. If, as some 18 bold, "the final justifi- 
cation of science is the power it creates for the use of mankind/' 
then we must call to remembrance that this "power must be 
created before it is used." 17 

The instances cited should be sufficient to demonstrate how 
effectively resourceful nature makes use, in her economy, of in- 
stability, with its cumulative potency, as a progressive force; as 
well as of stability, the essentially conservative element in evolution. 
Indeed, we, of the human race, have good reason to be mindful 
of this fact, for the wholly unparalleled rapidity of our scientific and 
industrial evolution in past decades is itself the most brilliant 
example of instability and its cumulative power as a factor in 
evolution. 

16 The writer is not among these, if by final justification is meant the only 
sufficient justification. No one would think of demanding such justification 
for art. Why require it of science? Such an attitude towards her is like that 
of the man who, having received repeated favors from his fellow, begins to 
acquire the habit, and to look upon such favors as due to him, and as the sole 
justification for the other's existence. 

17 C. S. Minot, Science, 1911, p. 119. 



CHAPTER 
THE PARAMETERS OF STATE 

In dealing with any natural phenomenon especially one of a vital nature, 
with all the complexity of living organisms in type and habit the math- 
ematician has to simplify the conditions until they reach the attenuated char- 
acter which lies within the power of his analysis. Karl Pearson. 

Little has been said, so far, of the parameters P employed to 
define the state of the systems under consideration. In the earlier 
chapters these parameters have, in fact, been largely eliminated 
from discussion by restricting the treatment to the case of evolu- 
tion under constant parameters P; subsequently the special cases 
of evolution with slowly changing P's, and the influence upon *| 

equilibrium alone of changes of unrestricted kind in the P's have 
been discussed; but all of this from a general standpoint, without 
giving much thought to the particular nature and properties of 
these parameters. It is desirable now to give some attention to 
this hitherto neglected phase of the subject. 

The simplest, and in many respects a very illuminating example 
of the nature and function of the parameters P is furnished in the 
thermodynamic treatment of physical systems. Here we are ac- 
customed to the use of such parameters as pressure, temperature, 
surface tension, etc., to define the state of the systems under con- 
sideration. 

Topographic Parameters. Obviously there is much latitude 
in the choice of such parameters; for if any parameter P can be 
employed to define the state of a given system, any single-valued 
function F (P) of that parameter will also serve, though certain 
selections of parameters may be found much more advantageous 
in practice than others. In particular, it is found, in systems 
amenable to thermodynamic treatment, that P's can be so selected 
that they appear as the intensity factors of an energy. 1 This 
selection has actually been made in the example cited above. Or, 
alternatively, any one of the P's so selected, can be replaced by 

1 Helmholtz, Die Thermodynamisch-chemischen Vorgange 1882 (Ges. < 

Abh., vol. 3, p. 958) ; P. Ehrenfest, Zeitschr. f . phys. Chemie, 1911, p. 234. \ 

300 



PAEAMETEES OF STATE 301 

the extensity factor of an energy. So, in place of the pressure p 
we can introduce the volume v, these two parameters being con- 
nected by a functional relation of the form. 

v = <p(p, Zi, Z a , . . . Z n > (1) 

The parameter v (volume) is almost the simplest type imaginable 
of a topographic parameter. In many systems commonly con- 
sidered in physical chemistry the only way in which the topography 
of the system plays any appreciable role in the processes going on 
therein is through the volume defined by the boundaries of the 
system. Even the shape of the boundary is in most cases immaterial. 

In the systems in which organic evolution is proceeding, the 
situation is very different. In one respect the topographic para- 
meters are often, in this case, even simpler than in the physico- 
chemical example, namely in this, that living organisms (except 
aquatic species) make their excursions, extend their activities, es- 
sentially in a space of two dimensions the earth's surface, or at 
least a rather thin shell near that surface. Hence we are interested 
in areas rather than volumes; in place of a parameter v, volume, we 
may expect to find figuring in the discussion a parameter a, area. 

But aside from this slight simplification (which does not always 
apply), the influence of topography in systems in the course of 
organic evolution is immeasurably more complex than in the sim- 
ple physico-chemical systems that form the chief subjects of study 
in the laboratory and in theory. Indeed, the conditions presented 
in nature are so complex that we can hardly hope to construct any 
systematic mathematical analysis of this phase of the subject, ex- 
cept by the expedient of dealing in somewhat radical abstractions, 
such as evolution "in a uniform environment" or, perhaps, in an 
environment reproducing in very greatly simplified form some of 
those principal geographic features that are typical of our globe. 

There is something unsatisfactory in such abstractions that seem 
rather far remote from conditions actually met in nature. But it 
must be remembered that such abstractions are a necessary, and, 
as experience has abundantly shown, a very effective aid to our 
limited mental powers, which are incompetent to deal directly with 
unexpurgated nature in all its complexity. Neither should it be 
forgotten that the worker in the laboratory, though he may seem 
to be nearer to nature, himself is dealing essentially in abstractions. 



302 ELEMENTS OF PHYSICAL BIOLOGY 

When the physical chemist investigates a chemical reaction in a 
constant temperature bath, he is not copying nature, where con- 
stant temperature is an exception, but is deliberately establishing 
an "unnatural" situation. He does this in order to separate the 
influence of one factor upon the course of events from that of a 
multitude of others; feeling confident that when he has gained an 
insight into the workings of such a simplified and, in a sense, un- 
natural system, he will be the better equipped to understand, or at 
least to make a further study of more complicated systems, approach- 
ing more and more nearly those occurring in nature. It is precisely 
the same principle which justifies us, in "substituting an ideal, upon 
which it is possible to operate, for intractable reality," 2 when we 
essay the systematic treatment of natural processes by mathematical 
analysis. So, for example, Karl Pearson in his memoir on Random 
Migration treats among others the case in which "breeding grounds 
and food supply are supposed to have an average uniform, distribu- 
tion over the district under consideration;" 3 and the simple case of 
"migration into a cleared rectangular area," etc. Somewhat similar 
topographic simplicity is assumed as the basis of studies of Brownlee 
on the Mathematical Theory of Random Migration and Epidemic 
Distribution. We shall have occasion to refer to these studies again 
in another connection. It is not intended to follow up this phase 
of the subject here. 

Neither will any attempt be made to sketch here even in outline 
the empirical side of the subject, our observational knowledge re- 
garding the dependence of life in its various forms upon the para- 
meters of state. There is a ripe and extensive literature available 
on this special phase of biology, which it is unnecessary to dupli- 
cate here. It will suffice to refer to standard works on geograph- 
ical biology and to general ecology. 4 

2 Nature, 1922, p. 764. 

3 Draper's Company Memoirs, Biometric Series III, 1906. 

4 The following may be mentioned: A. Engler and 0. Drude, Die Vegetation 
der Erde, Sammlung pflanzengeographischer Monographien (a cyclopedic 
work in many volumes). A. F. W. Schimper, Clarendon Press, 1903, Plant 
Geography. E. Warming, Clarendon Press, 1909, Oecology of Plants. A. R. 
Wallace, 1876, The Geographical Distribution of Animals. F. E. Beddard, 
1895, Textbook of Zoogeography. H. Gadow, Cambridge University Press, 
1913, The Wandering of Animals. E. L, Trouessart, 1922, La Distribution 
Geographique des Animaux, 



PARAMETERS OF STATE 303 

In physico-chemical systems the topographic parameter v (volume) 
is the capacity factor of an energy, as had already been noted; and 
associated with v is what may be termed a conjugate parameter 
Pi (pressure), which is the intensity factor of the energy in question, 
i.e., that factor which determines the direction of any change in 
the capacity factor v, according to the scheme 

= according as pi = p e (2) 

dt < ^ 

where p e is the external pressure. 5 

The Intensity Law in Organic and Economic Systems. Is 
there anything corresponding to the relation (2), the Intensity Law, 
as it has been termed, in the case of the topographic parameter a 
(area) which enters into the definition of the state of a system in 
the course of organic evolution? This matter has already been 
referred to, in a way, in discussing the Principle of Le Chatelier. 
It was there noted that, in the case of human population area and 
rent are related to each other in accordance with a scheme of the 
type (2). More generally, supply and demand in economics stand 
in a relation of this type, and accordingly present a certain analogy 
to the capacity and intensity factors of an energy an analogy which, 
by some writers, has been construed as actual identity in kind, 
prices having, by these writers, been identified with the intensity 
factor of an "economic energy." Now energy is a perfectly definite, 
measurable thing, of definite dimensions. Those who thus speak of 
a special form of "economic energy" should be prepared to give us 
at least some indication how this energy is to be measured, in the 
customary units of energy. No such indication is forthcoming. On 

6 The relation (2) is essentially the Helm-Ostwald Intensity Law. Although 
this law is not as universal as its sponsors would make it appear, yet it has a 
certain field of utility. For a critique of this law see M. Planck, Eight Lec- 
tures on Theoretical Physics, Columbia University Press, 1915, p. 11. The 
form of the relation (2) may be taken as the definition of a pair of conjugate 
parameters. However, the definition must be made a little more general to 
cover certain cases. We shall say that G, g are conjugate parameters if either 

dG ^ n > 

-5- < according as g t < g e (1) 

dG > . .. < 

-j- according as g. = g, (2) 



304 ELEMENTS OF PHYSICAL BIOLOGY 

the contrary, as we shall see in dealing with the dynamics of evolu- 
tion, the economic equivalent of a form of energy (which is some- 
thing quite different from its mechanical equivalent), is not con- 
stant but variable though it tends to approach, or to fluctuate 
about, a certain value. 

On the mistaken identification of prices and related economic 
quantities with the intensity factor of an energy, some authors have 
sought to build a system of biodynamics (social dynamics). 6 The 
analogy which certain conjugate parameters of the perfectly gen- 
eral kind bear to intensity and capacity factors of an energy present 
the opportunity for such efforts, which are, in themselves, well 
worth while. But it must not be forgotten that the result of such 
efforts can be only a species of quasi-dynamics, something analo- 
gous to, but not identical with, the dynamics of physical forces. 
Just what the relation between such quasi-dynamics and true dy- 
namics may be, is a separate problem, to which we shall have oc- 
casion to give some attention in the section devoted specifically to the 
dynamics of life-bearing systems. 

The paying of rent in coin of the realm is, of course, a phenom- 
enon peculiar to the human species. But the peculiarity is one of 
mode of manifestation rather than of inherent quality. We may 
speak of the rent per unit area that the representative individual 
is willing to pay as a measure or at least an index of the "popula- 
tion pressure." Now this population pressure this willingness to 
sacrifice effort for the sake of gaining elbowroom is present quite 
independently of our peculiar method of expressing it in terms of 
rent. It exists also among other species, though we may lack so 
convenient a gauge for it as we have, in our own case, in rent. We 
shall see later how at least a quantitative conception of such bio- 
physical (economic) entities as population pressure and the like can 
be gained on a general basis, which applies to species other than 
human. 

6 Compare G. Helm, Die Lehre von der Energie, 1887, pp. 72 et seq.; Ost- 
wald, W., Energetische Grundlagen der Kulturwissenschaften, Leipsic, 1909, 
p. 155. Die Philosophic der Werte, Leipsic, 1913, pp. 260, 314-317, 326, 328. 
Among other writers who touch on the subject of the relation of economic value 
and price to energy are : Budde, Energie und Recht, Leipsic, 1902, p. 56; Wini- 
arski, "Essai sur la Mecanique Sociale," Revue Philosophique, 1900, vol. 49, 
p. 113. See also J. Davidson, Qu. Jour. Economics, August, 1919, p. 717. 



PARAMETERS OF STATE 305 

For the present, without making here a closer analysis of the 
conjugate parameters a, p, (area, rent or population pressure) it 
will suffice to point out that the mere existence of the relation 

= according as p\ = p e (3) 

at < *^ 

may give into our hand the means of drawing certain conclusions 
regarding the behavior of the system, Quite independently of the 
intimate -nature of these quantities, a, p. In illustration of this it is 
only necessary to refer once more to the discussion of the principle 
of Le Chatelier in Chapter XXII. 

Distant Analogy to Gas Law. Again, still without any search- 
ing analysis of all the physical implications of the parameters a 
and p, we may note certain facts regarding the relation. 

a = $( P) Z lt X t , . . . X n ) (4) 

which connects the conjugate parameters a, p, just as pressure p 
and volume v, in physico-chemical systems, are connected by the 
relation 

v = p(p, XL, X a> . . .) (5) 

This latter, in the simple case of a gas takes the form 

v = m (6) 

P 

m. ,, , ., , 
or, since is the density d 



T = RT (7) 

d 

constant, at constant temperature 

Let N be the total number of a (human) population, a the area 
occupied by it, and Ni the total income of the population. Let p 
be the rent per unit area; and let the population spend a fraction 
R' of its income on rent. Then evidently 

pa = NR'i (8) 



306 ELEMENTS OF PHYSICAL BIOLOGY 

A. r 

Putting = population density = d' we have 
to a 

~^R'i (9) 

a 

It will be seen that there is a certain analogy between the formulae 
(8), (9) as applied to the relation between rent (population pressure) 
and area occupied by a population, on the one hand, and the formu- 
lae (6), (7) as applied to the relation between the pressure p and 
the volume v of a gas. The analogy is particularly close if the in- 
come per head i, and the factor R r are constant as a changes. The 
former may be true, approximately, if the inhabitants of area a 
derive their income from some extraneous source quite independent 
of this area. It will not be true, even in rough approximation, if 
the inhabitants derive their income from the produce of the area a 
itself. It is not the author's intention to emphasize unduly mere 
analogies. Nevertheless, the one here presented seems worthy of 
passing notice. Compare also E. Woodruff, Expansion of Races. 

The actual relation between population density and rent or land 
value is a subject of great economic interest. Research in this 
subject is in progress under the auspices of the Institute for Re- 
search in Land Economics, Madison, Wis., but has not, at this 
time of writing, matured to published results. 

Law of Urban Concentration. An empirical law of urban con- 
centration was pointed out some years ago by F. Auerbach (Peter- 
manns Mittheilungen, 1923, p. 74). Arranging in order of magni- 
tude the cities of a given country, he found that the product of 
population and ordinal number (rank) was approximately con- 
stant. Thus, plotting rank against population, he obtained a 
hyperbolic curve, or, plotting the product of these two quantities, 
he obtained, roughly speaking, a straight line. For some of his 
curves the reader must be referred to the original publication. 

The illustration (fig. 60) shows the graph obtained by plotting the 
logarithm of the population of the cities of the United States (1920) 
against the logarithm of their respective rank. In the higher ranks 
only every fifth city has been plotted. It will be seen that, excep- 
ting cities of rank 4, 5 and 6, the plot does approximate quite 
closely to a straight line. The slope of this line, however, is not 
exactly unity, as demanded by Auerbach's law, but 0.93, so that the 



PARAMETERS OF STATE 



307 



actual law of urban concentration in the United States, in 1920, 
was, within the limits indicated, given by 



where P denoted the population of the city of rank R. 



^ rOPULATiCFi 
(Tens of thoussndsj 



500 
400 

300 

200 

100 
90 

BQ 
"0 
6O 
50 

4O 

30 

20 

10 
9 
8 
1 
f> 


) 
















1 










\ 
















?d Largest Citis 
3 United Stsfes: 
lecordln^ to Ran 


3 




\ 














Hunc'rc 
in th 




X 


\ 












19 2O, f 






> 


\ 


\ 


\ 


















1 








f\ 


























. ^ 




























> 


>\ 




























~\ 


\ 




























"\ 




























\> 




























r ^ 






























> 










1Q$ P= lad 5,000,000 - 0.93 JO 

PR "3 = 5,030,000 


$* 


1 


N 


X 


X 


H 














car. 




























"/~ 




























^ 


























1 



3 4- 5 6 T 9 9 10 

RANK 



CO UO 40 50 GO TO 09(5 SM 



FIG. 60. LAW OF URBAN CONCENTRATION 

Graph obtained by plotting as ordinates, on logarithnic scale, Population of 
United States Cities, and as abscissae the corresponding Rank (in order of 
magnitude), also on logarithmic scale. 

It may be left an open question how much significance is to be 
attached to this empirical formula. We shall meet with a similar 
relation in Chapter XXIII in dealing with Willis' theory of Age and 
Area. 



308 ELEMENTS OP PHYSICAL BIOLOGY 

The Biological Background of Population Pressure. In the 
preceding paragraphs we have accepted it as a fact that there is 
at any rate some degree of relation between population density and 
the "desire for expansion" which finds expression, in the human 
species, in the willingness to spend a certain fraction of the income 
upon ground rent or its equivalent in interest and taxes upon real 
estate. It is not proposed to attempt here any searching analysis 
of the precise physical significance of this desire for expansion. But 
that it is ultimately referable to very cogent biological and physical 
factors is self-evident. The degree of crowding of a group of or- 
ganisms affects both its death rate (mean length of life) and also 
its rate of reproduction, as well as, no doubt other significant vital 
fimctions. As Pearl and Parker 7 remark, in their paper on the 
influence of population density upon rate of reproduction in Dro- 
sophila : 

It has long been known that degree of crowding of organisms in a given 
space, or the density of the population, has an influence upon various vital 
processes of the individuals composing the population. In the matter of 
growth Semper 8 and before him Jabez Hogg showed that volume of water 
apart from food and other conditions has an influence upon the rate. This 
subject has again been studied recently by Bilski. 10 Farr 11 showed that there 
is in man a definite relation between population and death rate. This old 
work of Farr has recently been gone over carefully and confirmed by Brown- 
lee. 12 Drzwina 13 and Bohn show that a particular concentration of a toxic 
substance, just lethal for a single individual in a given volume of water (work- 
ing with such organisms as infusoria, planarians, hydra, tadpoles, etc.), will 
be sub-lethal if several individuals are present in the same fixed volume of 
water. 

Influence of Population Density on Rate of Reproduction. Pearl 
and Parker 14 have determined experimentally the relation between 
rate of reproduction and the density of a population of Drosophila 
(fruit flies) in a universe of constant volume (glass bottle). This 

7 R. Pearl, and S. Parker, Proc. Natl. Acad. Sci., vol. 8, 1922, p. 212. 

8 K. Semper, Animal life as affected by the natural conditions of existence. 
Fourth Edition, London, 1890. 

9 Cited from Semper, loc. cit, 

10 F. Bilski, Pfliiger's Arch., vol. 188, 1921, p. 254. 

11 W. Farr, Decenn. Suppl. Reg. Gen., 1861-1870. 

12 J. Brownlee, Jour. Roy. Stat. Boo., vol. 82, 1919, pp. 34-77; vol. 83, 1920, 
pp. 280-283. 

13 A. Drzwina and G. Bohn, C. R. Soc. Biol. Paris, vol. 84, 1921, pp. 917-919. 
R. Pearl and S. Parker, Proc. Natl. Acad. Sci., vol. 8, 1922, p. 212. 



PARAMETERS OF STATE 



309 



relation is found to resemble in form Farr's law for the death rate 
D in a human population of density d: 

log D = log a + k log d (10) 

in which a and k are constants. Pearl and Parker found 

log y = 1.54 - O.OOSz - 0.658 log x (11) 



16 



cS 

Of 

I 



10 




10 SO 3O ^0 &0 SO 70 ffO 
fl/fS PER BOTTLE 



FIG. 61. RELATION BETWEEN RATE OF REPRODUCTION IN DROSOPHILA (FRUIT 
FLY) AND DENSITY OF MATED POPULATION 

The circles indicate observed values; the drawn-out curve is computed 
according to equation (11). After Pearl and Parker. 



310 



ELEMENTS OF PHYSICAL BIOLOGY 



where y denotes the number of imagoes per mated female per \ 
and x denotes the mean density of the mated population (measured a s 
flies per bottle) over a sixteen-day period. The results obtainea 
by Pearl and Parker are exhibited graphically in figure 61, the small 
circles denoting observed values, and the drawn-out curve values 
computed by the formula cited above. It should be noted, how- 
ever, that in Farr's law the coefficient k of log d is positive, where- 
as in the Pearl and Parker formula it is negative; death rate in- 




40 "60 ~60 100 /10" 14$ 160 180 

OF FLIES IN BOTTLE AT BBSfNMtf& 

FIG. 62. RELATION BETWEEN MEAN LENGTH OP LIFE AND POPULATION DENSITY 

IN DROSOPHILA 

The curve is a freehand smoothing of the observations indicated by the 
small circles. After Pearl and Parker. 

creases with population density, whereas rate of reproduction, in 
this series of experiments, was found to decrease as the density in- 
creases. 

Influence of Population Density on Duration of Life. The same 
authors have also investigated the relation between population 
density and duration of life in Drosophila. 15 Their results are 
shown graphically in figure 62. The smoothed curve exhibits a 
very interesting feature. While crowding unmistakably diminishes 

1S R. Pearl and S. Parker, Am. Jour. Hygiene, vol. 3, 1922, p. 94; Amer. 
Naturalist, vol. 56, 1922, p. 312. 



PARAMETERS OF STATE 311 

the average length of life, as one would naturally expect, the curve 
does not fall continuously from left to right, but has a maximum. 
The flies do not thrive best when they have the most ample space 
per individual; there is an optimum density which is best suited to 
their needs for company or for some other obscure factor supplied 
by a certain moderate amount of crowding. 

TOPOGRAPHIC PARAMETERS DURING PERIOD OF DIFFUSION 

Willis' Theory of Age and Area. As regards the influence of 
those topographic parameters which define the boundaries of the 
system, a special case arises during that period in the life of a body 
of organisms, when its spread has not yet extended to those bound- 
aries. Certain aspects of the phenomena presented during this 
period of diffusion have been made the subject of a painstaking 
study, conducted with much originality of view, by C. J. Willis. 16 
One may not agree in all points with Dr. Willis' conclusions, but 
the material of fact collated by him is in itself significant and of 
value. As Prof. W. Bateson in a review of this book remarks : "To 
have hit on a new method of investigating even a part of the theory of 
evolution is no common achievement, and that the author has done 
this cannot in fairness be denied." Dr. Willis' principal thesis is 
essentially this, that the area occupied by a biological species is a 
measure of its antiquity in evolution. To be more precise, and to 
quote the author's own words: 

' The area occupied at any given time, in any given country, by any group of 
allied species at least ten in number, depends chiefly, so long as conditions 
remain reasonably constant, upon the ages of the species of that group in that 
country, but may be enormously modified by the presence of barriers, such as 
seas, rivers, mountains, changes of climates from one region to the next, or 
other ecological boundaries, and the like, also by the action of man and other 



The thesis, thus stated, is "well hedged" with qualifications. 
Professor Bateson remarks: "Every evolutionist agrees that, apart 

16 Age and Area: A Study in Geographical Distribution and Origin of Spe- 
cies; Cambridge University Press, 1922. For review see Nature, 1923, p. 39; 
Science Progress, January, 1923, p. 474. 



312 ELEMENTS OF PHYSICAL BIOLOGY 

from disturbing elements, area is a measure of age. 17 .... We 
are, however, asked to believe that in practice this mode of esti- 
mating the age of a species is, on the whole, trustworthy; that 
endemic species and varieties in general can and must be for the 
most part accepted as new starters in evolution, and not as 
(remnants of) survivors." 

Dr. Willis supports his views by observations gathered chiefly in 
Ceylon and New Zealand. His evidence is not altogether convinc- 
ing. Professor Bateson in the review already quoted remarks point- 
edly: "On any theory of evolution endemics (and rare species) must 
be in part novelties and in part relics; but why, apart from the 
theory of Age and Area, we should believe that endemics are in 
such great majority novelties I do not clearly understand, for though 
we know little of origins, we are certain that myriads of species 
have become extinct. It is surely contrary to all expectation that 
the process of extinction should be in general so rapid, and the final 
endemic phase so short that the number of species in that final 
stage should be so insignificant." Referring to the same point A. 
G. Thacker remarks: "Species and genera do die out, and there- 
fore there are diminishing ranges as well as expanding ranges. . 
. , . Dr. Willis thinks that veiy few of the small range species 
are, in fact, decreasing. 55 For a further critique of the theory of 
Age and Area the reader may well be referred to the two reviews 
already cited, while Dr. Willis 5 own presentation of his case will be 
found expanded in detail in his book Age and Area, Cambridge 
University Press, 1922. Quite recently (I add this in correcting 
proof) Prof. G. V. Yule has lent his able advocacy to Willis 5 
theory in an extensive paper published in the Phil. Trans. Roy. 
Soc., 1924, vol. 213, Series B, pp. 21-87, Some of the assumptions 
underlying Professor Yule's argument do not seem to commend 
themselves to the critical reader, in particular his supposition that 

17 '"'Tor this and other reasons Dr. Willis 5 findings seem hardly competent 
to furnish a basis of attack against any otherwise established or suggested 
theory of evolution. On this point Dr. Willis himself does not seem wholly 
consistent, for though he advises in one place that it would be 'wiser to aban- 
don natural selection 5 as the general principle that has guided evolution, in 
another place he admits that 'nothing can come into lasting existence without 
its permission.' This admission is all that any thoughtful adherent of any 
theory of evolution asks. 55 A. G. Thacker, The Dynamics of Distribution, 
Science Progress, 1923, vol. 17, p. 474. 



PARAMETERS OF STATE 313 

the number of new species thrown is independent of the number of 
individuals. 

Turning from the theoretical and debatable portion of Dr. Willis' 
contribution, to the factual material presented by him, we are con- 
fronted by a number of very remarkable relations, such as those 
represented graphically in figure 63. In this drawing ordinates 
represent the number of genera in the several natural families of 
plants and animals indicated, and the corresponding abscissae 
represent the number of species in each genus plotted. So, for ex- 
ample (fig. 63), of the family Cornpositae 1143 genera were noted, 
as follows: 



446 genera of 1 species 
140 genera of 2 species 
97 genera of 3 species 
43 genera of 4 species 
55 genera of 5 species 
etc. 



An examination of these drawings clearly brings out the following 
facts: The rnonotypic genera, with one species each, are always the 
most numerous, commonly forming about one third of the whole 
group; the ditypics, with two species each, are next in frequency, 
genera with higher numbers of species becoming successively fewer. 
Set out graphically as in figure 63, the genera exhibit what Dr. 
Willis calls a "hollow curve" of frequency (in point of fact a hyper- 
bola of the generalized type), and, as Professor Bateson remarks, 
there is no gainsaying the fact that these curves, though collected 
from miscellaneous sources, have a remarkable similarity. Perhaps 
more striking still is the relation established in figures 64, 65, and 
66. The quantities plotted here are of the same character as in 
figure 63, but they are plotted on a doubly logarithmic scale, with 
the remarkable result that the graphs obtained are in close approx- 
imation straight lines. Thus if x denotes the number of species 
in a genus, and y denotes the number of genera comprising x species, 
we have 

log x + a log y b = (12) 

or 

x y = const* (13) 



314 



ELEMENTS OF PHYSICAL BIOLOGY 



that is to say, the variables x and y are connected by a hyperbolic 18 
relation. It should be noted that this relation covers a wide variety 
of cases, including both plants and animals. 



Monospecific Genenaal this end of curvs 



o 



Linepf Genera 
J of 
5spp. 




MIXED 
CURVES 



The large dots represent the Origins 



By courtesy of Nature 



dumber of species for size of area.) 

Mi T d h " OT CUrVeS ' ^^"-^" !?"? ^ Beginning of ea ch are the 



numbers of monotypes. 



FIG. 63. HYPEHBOLIC CORVES OBTAINED BY PLOTTING AS ORDINATES THE 
-\USIBBB OF GBKEBA HAvmc 1, 2, 3, . . . n SPECIES, AND AS ABSCXSSAE 

THE N0MBEE n OP SUCH SPECIES 

The last curve above shows as ordinates the number of species of endemic 
compositae in the Galapagos Islands, as abscissae the corresponding areas 
o\er which such species have spread. After J. C. Willis. 



**** 



**" ^ h ^ erbola *V = const, falls 



as a 



PARAMETERS OF STATE 



315 



Mumber of spacfes 

10 20 30 40 50 



100 



1-0 1-2 1-4 16 1-8 2-0 
log (N 9 of species) 



-2 -4 

JS# courtesy of Nature 

FIG. 64. RELATION BETWEEN NUMBER AND SIZE OF GENERA op ALL 



PLANTS, PLOTTED LOGARITHMICALLY 
After J. C. Willis 
NS of species 

10 30 



10.000 





100 



8 "Tb"~" 1-2 
log fN? of species) 
By eourttty of Natws 

FIG. 65. RELATION BETWEEN NTTMBEE AND SIZE OF RTOIACBAK Pr.OTran 

LOGAEITHMICALLT 

After J. C. Willis 



316 



ELEMENTS OP PHYSICAL BIOLOGY 



Dr. Willis' interpretation of the remarkable curves obtained by 
him may be quoted in his own words (Nature, February 9, 1924, 

p. 178): 

If species of very limited area and genera of one species (which also have 
usually small areas) are, with comparatively few exceptions, the young begin- 
ners in the race of life, and are descended in general from the species of wider 
dispersal and the larger genera, and if the number of species in a genus is, 
broadly speaking, a measure of its age, the idea at once suggests itself that a 




Number of species 

FIG. 68. RELATION BETWEEN NUMBER AND SIZE OF GENBEA OF 
BEETLES, PLOTTED LOGARITHMICALLY 

After J. C. Willis 



given stock may be regarded as "throwing" generic variations much as it 
throws offspring, so that the number of genera descended from one prime an- 
cestor may be expected to increase in geometric ratio or according to the law of 
compound interest. The number of species descended from one ancestor 
might be expected to follow the same form of law with a more rapid rate of 
growth. On such a very rough conception it is found that the form of fre- 
quency distribution for sizes of genera should follow the rule that the logarithm 
of the number of genera plotted to the logarithm of the number of species gives 
a straight line. 



PAEAMETBBS OF STATE 317 

It follows from the conception stated that the excess of the slope of the line 
over unity should measure the ratio of the rate of increase of genera to that of 
species. The slope should always, therefore, lie between the limits 1 and 2, for 
a slope of less than unity would have no meaning, and a slope exceeding 2 
would imply that generic variations were more frequent than specific varia- 
tions. Hitherto no exception has been found to the required rule. One group 
of fungi tested (Hymenomycetineae) gave a line with a slope very little 
exceeding unity (1.08), but the figures found for flowering plants lie between 
the narrow limits 1.38 and 1.64, with an average of about 1.43. Snakes and 
lizards both give a figure very near 1.50, and the Chrysomelidae about 1.37. 

For further details the reader must be referred to Dr. Willis' 
book Age and Area, and to a paper by E. S. Pearson, in Biometrika, 
August, 1923, vol. 15, of which the following passage, part of that 
author's conclusions, may be quoted: 

There is no doubt that these principles represent a certain aspect of the 
process of evolution, but I believe that Dr. Willis has stressed their importance 
beyond the limits which the evidence of observation will bear. They cannot 
explain everything, and we have seen that in many cases results which we are 
led to predict with their assistance are scarcely borne out, while in other cases 
recurrent distributions can also be accounted for on different hypotheses. 

Climatic Parameters. The state of a physico-chemical sys- 
tem is commonly described in terms of its temperature (in addition 
to pressure, etc.). Without attaching any deep significance to the 
analogy, it may be remarked that systems in which organic evolu- 
tion is under way commonly require, as essential parameters to 
define their state, the statement of sundry quantities that describe 
climatic conditions, such as temperature, humidity, precipitation, 
light, etc. The influence of these upon the course of events must 
form an essential part of the study of evolution in life-bearing 
systems. 

The investigations of the influence of temperature upon meta- 
bolic processes an approximate doubling of reaction velocities for 
every 10C. rise in temperature we shall here note only very briefly 
as belonging rather to the field of biochemistry than to the more 
strictly ecological studies in which we are here interested. More 
in the line of our immediate interests are certain data gathered in 
oceanographic researches, which have already furnished us with 
much illustrative material. The influence of light, temperature, and 



318 



ELEMENTS OF PHYSICAL BIOLOGY 



C0 2 concentration is discussed by G. W. Martin in his paper al- 
ready cited. 19 He remarks: 

Plants on land receive the full benefit of the sun's rays as we know them. 
Plants living under water receive only a portion of the rays that reach the land. 
Part of the light that strikes the water is reflected, and the part that penetrates 
the water is gradually absorbed in passing through that medium, the red and 
yellow rays first, the blue and violet last. This differential absorption is 
reflected in the curious and well-known distribution of marine algae according 
to color the green kind growing in shallow water, the brown in an inter- 
mediate zone, and the red in the deepest water, although there are, of course, 
numerous exceptions to this general rule of distribution. Another property 




FIG. 67. SOLUBILITY OP CARBON DIOXIDE IN WATER, EXPRESSED IN VOLUMES 

OF C0 2 MEASURED AT NORMAL TEMPERATURE AND PRESSURE, 

PER VOLUME OF WATER 

After G. W. Martin 

of light is that it is refracted by water, and the greater the angle at which the 
rays strike the water, the greater will be the refraction. In the tropics, where 
the rays are practically vertical, the amount of refraction is insignificant, but 
in high latitude, where the rays strike the water at a sharp angle, the refraction 
is marked, as a result of which the rays are bent into a more nearly vertical 
direction, thus increasing their penetration in depth, and partly compensating 
for the unfavorable angle at which they strike the water. Helland Hansen 
was able to show that in the Atlantic Ocean south of the Azores, on a bright 
summer's day, light is abundant at a depth of 100 meters, still including at that 
depth a few red rays. At 500 meters the red rays have completely disappeared 
but blue and ultra-violet rays are still plentiful, and may be detected at 1000 

19 G. W. Martin, Scientific Monthly, 1922, p. 456. 



PARAMETEKS OF STATE 319 

meters, but have completely disappeared at 1700 meters. It is not probable, 
however, that under the most favorable conditions photosynthesis may be 
carried on at depths greater than 200 meters. 

Temperature is less directly important in the sea than on the land since 
there is no great danger of injurious extremes being reached. Indirectly, its 
importance lies in the fact that carbon dioxide is much more soluble in cold 
water than in warm (see fig. 67) and it is probably this, rather than the direct 
influence of temperature, which accounts for the fact that the most luxurious 
development of plant life is in the colder waters of the earth. 

Among laboratory investigations of the influence of "climatic para- 
meters," under controlled conditions, may be reckoned the work of 
R. Pearl and S. Parker in their studies "On the Influence of Certain 
Environmental Factors on the Duration of Life in Drosophila." 20 
In these experiments it was found, for example, that certain species 
of flies, kept in bottles closed by a single layer of silk bolting cloth 
("ventilated bottles"), had 10 per cent longer life, on an average, 
than similar flies kept in bottles whose neck was plugged with cot- 
ton wool. 

PARAMETERS OF STATE AND THE ANALYTICAL CONDITION FOR 

EQUILIBRIUM 

In the fundamental equations both of the Kinetics and of the 
Statics of material transformations, as set forth in earlier chapters, 
the coefficients are in general functions of the parameters of state, 
and it is only on the supposition that evolution is proceeding under 
essentially constant conditions of topography, climate, etc., that 
these coefficients could be treated as constants. 

Furthermore, since these same coefficients enter into the analyti- 
cal conditions for equilibrium, as set forth in Chapter XII, these 
conditions must be read in the sense that they hold true when cer- 
tain specified parameters of state are held constant. If another set 
of parameters, instead, is held constant, the equilibrium conditions 
will retain the same form, but the values of the coefficients will 
change accordingly. This is precisely analogous to the state of 
affairs regarding the thermodynamic conditions for equilibrium 
Generally it can be said that in equilibrium the thermodynamic 
potential is a minimum, but the expression for this potential will 

80 Arner. Naturalist, vol. 56, 1922, p. 385. 



320 ELEMENTS OF PHYSICAL BIOLOGY 

vary according as pressure and temperature, or volume and temper- 
ature, for example, are held constant. 

In concluding this section it is desirable to call attention to a 
modification, in outward form, of which the analytical condition for 

equilibrium, 

Q' = minimum, dQ' = (14) 

(see Chapter XII) is susceptible. Since certain parameters pi, 
j?2, . . . are to be held constant in the application of this condi- 
tion, the addition of a set of terms PI dpi + P 2 dp z -f . . .to 
the expression 8Q' for a small virtual displacement will in nowise 
alter its value. We may, then replace the condition (14) by the 
fully equivalent one 

dO' dQ' 

= (d$) p = ^ dXi -f ^ dX s + . . . -f Pidpj. + P 2 dp, + . . . (15) 

where the subscript p denotes that the parameters pi, p 2 , . . . , 
conjugate to the parameters P 1} P 2 , , . . . are to be held constant 
in forming the expression (15). This statement of the condition 
(15) adds, of course, nothing new to the case. It is mentioned 
here only on account of its formal agreement 21 with the similar con- 
ditions for equilibrium which, as already pointed out, play an im- 
portant role in thermodynamics. However, in the analogous equa- 
tions erf thermodynamics the expression d $ is a complete differential. 
In the present instance we have no basis for the supposition that 
(15) is the true differential of a function $ (Zi, Z 2 , PI, P 2 , 

. . .) The question may, indeed be raised, whether by a suit- 
able choice of parameters and variables it can be achieved that 
(15), in the case here under consideration, is such a complete differ- 

21 Compare, for example, Van Laar, Seehs Vorlesungen iiber das thermo- 
dynamische Potential, 1906, p. 43. 

This formal agreement seems to extend also to another feature The ther- 
modynamic condition for stable equilibrium demands that the second differen- 
tial (d**) p shall be positive, and this in turn demands that ^ shall be negative. 
(See M. Planck, Thermodynamik, 1905, pp. 134, 190; Duhem, Traite d'Ener- 
g^tique 1911 vo . 1, p. 466; A. Winkelmann, Handbuch der Physik, 1906, vol. 
d, p. o90.) Similarly, in the general case, stability demands that if Q, g are 

conjugate parameters of the type (1) of footnote 5, then ^- < 0. 



PARAMETERS OF STATE 321 

ential. But this is a separate problem, on which we shall not here 
expend further effort. Only this shall be noted in passing: Where- 
as, in the thermodynamical treatment of physico-chemical phenom- 
ena a function <3? is given (essentially as the expression of the laws of 
thermodynamics), and whereas certain consequences are derived 
from this known function, the type of problems with which we 
are here concerned is of inverse nature. We are given certain data 
regarding the behavior of these systems, for example, the fact that 
their evolution follows more or less closely a system of equations of 
the type of the general equations (1) (Chapter VI) of the Kinetics 
of material transformation; and the problem may be raised, as to 
whether there exist functions $ analogous to the functions known as 
thennodynamic potentials, in terms of which the behavior of the 
system can be concisely epitomized, after the manner of thermo- 
dynamics. If such a plan could be successfully carried out, the 
result would be a species of quasi-dynamics of evolving systems, in 
which certain parameters P played a rdle analogous to forces, with- 
out being in any sense identical with forces (or even with generalized 
forces); certain other conjugate parameters p would play a role 
analogous to displacements, and certain functions <& would resemble 
in their relations to certain events in the system, the energy func- 
tions $ (free energy, thermodjrnamic potentials) of thermodynamics. 
That certain isolated portions of such a general system of quasi- 
dynamics have some degree of viability seems probable. Whether 
the general system is capable of development in a form possessing 
any considerable utility shall here be left an open question. For 
at this point we shall leave the path followed so far, and shall strike 
out in a new direction, with a view to sketching, not a system of 
quasi-dynamics or quasi-energetics, but the dynamics and ener- 
getics, in the strict sense, as ordinarily understood, of life-bearing 
systems in the course of evolution. 



PART IV 

DYNAMICS 



UK*. 



CHAPTER XXW 
THE ENERGY TRANSFORMERS OF NATURE 

Die Natur hat sich die Aufgabe gestellt das der Erde zustromende Licht im 
Fluge zu erhasehen und die beweglichste aller Krafte, in die starre Form 
verwandelt, aufzuspeiehern. Zur Erreichung dieses Zweckes hat sie die Erd- 
kruste mit Organismen iiberzogen,welche iebend das Sonnenlicht in sich auf- 
nehmen und unter Verwendung dieser Kraft eine fortlaufende Summe chem- 
ischer Differenzen erzeugen. Diese Organismen sind die Pflanzen. Die 
Pflanzenwelt bildet ein Reservoir, in welchem die fliichtigen Sonnenstrahlen 
fbdert und zur Nutzniessung geschickt, niedergelegt werden. /. R. Mayer. 

We approach now the third and last stage in our enquiry, toward 
which all that has gone before may be said, in a way, to have been in 
the nature of preparation. 

The fundamental equations of kinetics 

d ^=F i (X 1 ,X i , . . .;P,Q) (1) 

dt 

may appear at first sight to contain no hint of dynamical, of energetic 
implications. These can be read into the equations only by calling 
to mind the physical nature of certain of the components whose masses 
X appear in the equations : These components aggregates of liv- 
ing organisms are, in their physical relations, energy transformers. 
The evolution which we have been considering, and shall continue 
in this last phase to consider, is, then, essentially the evolution of a 
system of energy transformers; the progressive redistribution of the 
matter of the system among these transformers. The dynamics 
which we must develop is the dynamics of a system of energy trans- 
formers, or engines. 1 

Fundamental Characteristics of Energy Transformers. We shall 
do well to begin by calling to mind some of the fundamental elements 
or characteristics of energy transformers or engines, and of the manner 
of their working. An engine, such as a steam engine, for example, 
receives energy from a source such as a coal fire. This energy is 
absorbed by a working substance (water or steam), which, in the proc- 

1 See also A. J. Lotka, Jl. Wash. Acad. Sci., 1924, p. 352. 

325 



326 ELEMENTS OF PHYSICAL BIOLOGY 

ess, undergoes modification or change of state (in a general sense of 
the term) ; the working substance, at some stage in the operation of 
the engine, again gives out energy, of which a part in engines of 
human construction, commonly appears in a particular, selected 
form adapted to some end useful to and purposed by the maker or 
owner. Another fraction of the energy discharged by the working 
substance, is passed on to a sink or absorber of energy, which may be 
simply the surrounding air, or in the case of a naval engine it may be 
the sea water employed to cool the condensed steam before it returns 
to the boiler. This discharge of a portion of the energy from the 
source into a sink is practised, not designedly because any useful 
purpose is served thereby, but unavoidably because, in the case of 
all forms of heat engines, the second law of thermodynamics inexor- 
ably demands this payment of a tax to nature, as it were. 

Cyclic Working; Output and Efficiency. A finite change of the 
working substance, performed just once, can yield only a finite 
amount of work. Hence an engine of this type, in order to operate 
continuously so as to furnish a steady supply of energy of indefinite 
amount, must of necessity work in a cycle, returning periodically to 
its initial state many times. For a given engine, working under 
given conditions, the total output W/t per unit of time is propor- 
tional to the quantity M (mass) of working substance and its fre- 
quency of circulation, n, per unit of time, through the cycle; thus 

W 

~~kMn (2) 

Regarding the variation in the output for different engines, and for 
operation under different conditions, two fundamental laws of the 
greatest theoretical and practical importance, the very corner-stones 
of the edifice of thermodynamics, inform us that 

1. The maximum output of which a heat engine is capable under 
ideal conditions of working is independent of the nature of the working 
substance, and of the details of mechanism and construction of the 
engine. 

2. This maximum output obtainable under ideal conditions of 
operation depends solely upon the temperature of the source and that of 
the sink; with a suitably chosen temperature scale the law of the maxi- 
mum output W can be put in the extremely simple form 

W=Q~~ (3) 

-i a 



327 

ENERGY TRANSFORMERS OF NATURE 

where Q is the energy drawn from the source, T the (at).. ^ 
temperature of the source, and ^ that of the sink. The ratio -Q 

which measures the fraction of the energy Q converted into woi ^ 

spoken of as the efficiency of the transformer. ^ j 

The actual performance of a heat engine always falls shoit - ^ 
usually far short of the theoretical maximum (3) attainable 
ideal conditions of reversible operation, whereas all real pio "~ ' 

'77 I llO 

as has been pointed out in an earlier chapter, are irreversible. 
first service rendered by the laws of thermodynamics is thus a neg 

"lIlMPV 

live one, to save us from vain efforts to achieve the impossible, 
tell us what we cannot do; they give us no guarantee as to what we c( 
do, in this matter of engine efficiency. In other fields these same 
principles are, indeed, found competent to yield us information 
most positive character, as the physicist and physical chemist know> 
from boundless wealth of example; the very fact that they hold inde- 
pendently of substance and form lends to their application a catholic- 
ity hardly equalled elsewhere in science, and at the same time givfv 
into our hands an instrument of the most extreme economy of thought, 
since we are relieved, in such application, of the necessity of treating 
each particular case, with all its complication of detail, on its own 
merits, but can deal with it by the short cut of a general formula. 
Still, the austere virtue of this impartiality with respect to substance 
and form becomes something of a vice when information is sought' 
regarding certain systems in which mechanism plays, not an incidental, 
but the leading role. Here thermodynamics may be found power- 
less to assist us greatly, and the need for new methods may bo folk 
The significance of this in our present concerns will be seen as the 
topic develops. 

Composite and Coupled Transformers. The simplest typo of 
transformer of the kind that here chiefly interests us would comprise 
one working substance fed from one source and discharging to omi 
sink. 

Two or more such transformers may, however, work in paralln! 
from one source, thus forming in the aggregate one composite trariK" 
former. Or, two or more may be coupled in series or cascade, tho, 
sink of one functioning as the source for the next of the series. Ho, 
for example, W. L. R. Emmett has constructed a composite engine, 
consisting of two separate engines, the first operating with mercury 



328 ELEMENTS OF PHYSICAL BIOLOGY 

for its working substance, at a higher temperature, and the second 
operating with water at a lower temperature. It is to be observed 
that two such "coupled' 7 transformers again constitute a transformer, 
a compound transformer, which may possess certain special virtues, 
from the standpoint of the engineer, or in other respects. 

Accumulators. A special type of transformers is that in which the 
energy is transformed into a latent form, and is thus stored up for 
future use. A great variety of accumulators are in technical use. 
In the simplest case such an accumulator may consist of empounded 
water or a raised storage tank, ready upon the opening of a sluice 
or a valve to discharge its stored up energy. More closely akin to 
the systems in which we are here primarily interested is the lead 
accumulator or secondary battery, in which electrical energy is 
transformed into and stored as chemical energy, somewhat as the 
energy of sunlight is, in the leaves of plants, transformed into chemi- 
cal energy and stored up in the form of starch. 

This type of chemical storage is of very particular interest because 
of the remarkable phenomena to which it is competent to give rise 
through the circumstance that the substance in which the energy 
is stored in chemical form is itself the working substance of a trans- 
former. For in that case, if a mass TiM stores an amount of energy 
IT 7 , we have, according to (2) for a small interval of time dt 

dW hdM T 

IF" IT-** 71 (4) 

If the transformer functions at a constant rate (i.e., with a fixed 
number of cycles per unit of time) and if the coefficient k is independ- 
ent of the size of the transformer, we have by integration of (4) 

k n 

M = M Q e~h (5) 

The transformer under these conditions, grows according to the law 
of compound interest. 2 

For small ranges of size the assumption of a sensibly constant k 
is reasonable, and the law thus deduced may be expected to represent 
the facts tolerably well. For greater range we must regard k as a 
function of If and write 

k = a + b M + c M 2 + . . . (6) 

2 Compare L. J. Briggs, The Living Plant as a Physical System Jour 
Wash. Acad. Sc., 1917, vol. 7, p. 95. 



ENERGY TRANSFORMERS OF NATURE 329 

so that (4) becomes 

^=n(a+6M+. . .) (7) 

Mdt 

In second approximation, therefore, (breaking off the bracketed series 
at the second term) we find for the law of growth of the transformer 
the Verhulst-Pearl law (see Chapter VII). 



where m = M + a/6 and the subscript zero denotes the value of the 
variable at the instant t = 0. 

Anabions and Catabions. The living organism partakes of the 
functions both of an energy accumulator and of an energy dissipator. 
The former function is especially marked in plants and in the young 
growing organism. Biological terminology speaks of the process of 
energy accumulation by the growth (synthesis) of the working sub- 
stance as anabolism, and of the liberation of the stored energy with 
conversion into other forms as catabolism. Organisms in which 
anabolic processes predominate are conveniently classed together as 
anabions (plants), those in which catabolic processes predominate, 
as catabions (animals). The line of division cannot be sharply 
d) awn, a fact which was commented upon in some detail in the first 
chapter. But in the majority of cases organisms have a pronounced 
bias toward one or the other of the two forms, and no difficulty arises 
in classifying them. 

We may form the conception of a system of transformers comprising, 
in the most general case, individual single transformers, aggregates 
of composite transformers, and coupled transformers; some or all of 
which may partake in greater or less degree of the nature of 
accumulators. 

It is precisely such a system of transformers that is presented to us, 
on a vast scale, in nature, by the earth with its population of living 
organisms. Each individual organism is of the type of the simple 
transformer, though it does not operate with a single working sub- 
stance, but with a complex variety of such substances, a fact which has 
certain important consequences. 



330 ELEMENTS OF PHYSICAL BIOLOGY 

Plant and Animal as Coupled Transf ormers . Coupled trans- 
formers are presented to us in profuse abundance, wherever one 
species feeds on another, so that the energy sink of the one is the 
energy source of the other, 

A compound transformer of this kind which is of very special inter- 
est is that composed of a plant species and an animal species feeding 
upon the former. The special virtue of this combination is as follows. 
The animal (catabiotic) species alone could not exist at all, since 
animals cannot anabolise inorganic food. The plant species alone, 
on the other hand, would have a very slow working cycle, because the 
decomposition of dead plant matter, and its reconstitution into C0 2 , 
completing the cycle of its transformations, is very slow in the absence 
of animals, or at any rate very much slower than when the plant is 
consumed by animals and oxidized in their bodies. Thus the com- 
pound transformer (plant and animal) is very much more effective 
than the plant alone. We shall have occasion to refer to this matter 
again. 

It is, of course, conceivable that the anabolic and catabolic func- 
tions should, in their entirety of a complete cycle, be combined in one 
structure, one organism. Physically there is no reason why this 
should not be, and, in fact, nature has made some abortive attempts 
to develop the plant-animal type of organism; there are a limited 
number of plants that assimilate animal food, and there are a few 
animals, such as Hydra viridis, that assimilate carbon dioxide from 
the air by the aid of chlorophyll. 3 But these are exceptions, freaks of 
nature, so to speak. For some reason these mixed types have not 
gained for themselves a significant position in the scheme of nature. 
Selection, evolution, has altogether favored the compound type of 
transformer, splitting the anabolic and the catabolic functions, and 
assigning the major share of each to a separate organism. 

The several individual organisms of one species form in the aggre- 
gate one large transformer built up of many units functioning in 
parallel. 

3 Hydra viridis, however, is probably not a single organism, but an organ- 
ism of the animal type harboring in its body separate plant-like organisms 
with, which it lives in symbiosis. 



ENERGY TRANSFORMERS OF NATURE 331 

And lastly, the entire body of all these species of organisms, 
together with certain inorganic structures, constitute one great 
world-wide transformer. It is well to accustom the mind to think 
of this as one vast unit, one great empire. 

The "World Engine. The great world engine in which each of 
us is a most insignificant little wheel has its energy source, its 
firebox, so to speak in the sun, 4 ninety-eight million miles away from 
the working substance (the "boiler"). From the engineer's stand- 
point this would be an execrably bad design, if a high efficiency 
alone were the aim in view. For of the five hundred thousand million 
million million horsepower which the fiery orb radiates into space 

year in, year out, a ridiculously small fraction 2 is 

intercepted by the earth. It would take more than two billion, 
earths placed side by side to form a continuous shell around our sun 
at the earth's distance, and thus to receive the total output of solar 
heat. The other planets receive corresponding amounts. The 
remainder of the sun's disbursements sweeps past us into the depths 
of space, to unknown destiny. 

Of the energy that reaches the earth, 35 per cent is reflected 
(principally from the clouds), and 65 per cent is absorbed. The 
surface of the solid globe receives on an average 5 not quite 2 gram- 
calories (1.94) per square centimeter, placed normal to the beam, per 
minute, or enough heat to melt a layer of ice 424 feet thick every 
year. Arrhenius 8 quotes Schroeder to the effect that about 0.12 per 
cent of this energy is absorbed by the green vegetation, the gate of 
entrance through which practically 7 all the energy taking part in the 

4 The recognition of this fact is credited by Herbert Spencer (First Princi- 
ples, 172, footnote) to Herschel (Outlines of Astronomy, 1833). 

5 C. G. Abbot, The Sun, 1911, p. 298. In the tropics, at noon, a plot of 250 
acres receives energy at the rate of one million horsepower (W. W. Campbell, 
Science, 1920, vol. 52, p. 548). 

6 Jour. Franklin Inst., 1920, p. 118. Compare also G. Ciamician, Die 
Photochemie der Zukunft (Sammlung Chemischer Vortrage, 1922, p. 429). 
Asstiming an area of one hundred twenty-eight million square kilometers as 
inhabited by plants, Ciamician computes that thirty-two billion tons of dry 
matter per annum is produced, the equivalent of 17 times the world's annual 
coal production. 

7 Certain bacteria whose metabolism is based on iron, sulphur or selenium 
derive their energy from other sources. They are thus independent of sun- 



332 ELEMENTS OF PHYSICAL BIOLOGY 

life cycle must pass. And of this last amount only 24 per cent falls 
to plants cultivated for human needs. 8 The forests take the major 
share, 67 per cent; 7 per cent falls on the grass steppes, and 2 per 
cent on desert plants. If these figures leave the mind somewhat 
confused with detail, it may assist the imagination to form an ade- 
quate picture of the life cycle in its totality if we reflect that the total 
energy thus corn-sing through the system every year is of the order of 
22 times' 5 the world's annual coal production. Conversely this 
statistical fact may serve to form for us a correct estimate of the really 
cosmic magnitude of human interference with the course of nature. 

The organic circulation, the living part of the world engine, though 
to us of most direct interest, is quantitatively speaking only a small 
part of the whole. If the organic cycle gives occupation to an amount 
of energy of the order of 20 times the world's coal consumption, 

light a fact of the greatest significance in connection with the problem of the 
origin of terrestial life as we know it today. For green plants carry on their 
life business by the aid of chlorophyll, a substance representing a high degree 
of specialization, such ae could not very well be supposed to exist in the most 
primitive life forms. 

8 H. A. Spoehr, Jour. Ind. and Eng. Chem., 1922, vol. 14, p. 1144. Regard- 
ing the efficiency of cultivated plants in recovering solar energy for the use 
of man, the calculations of H. A. Spoehr are of interest. On the basis of 1.5 
gram calories per square centimeter per minute for the value of the solar 
radiation received at the earth's surface, he computes the daily energy income 
per square meter (six hours insolation) as 5400 kilogram calories. Figuring the 
heat of combustion of coal at 8000 kilogram calories, this gives the equivalent 
of 0.675 kilograms of coal per square meter, or 16.4 tons of coal per acre. For 
ninety days of insolation this represents the equivalent of 1476 . 63 tons of coal. 

Spoehr then proceeds to obtain a figure for the efficiency of a wheat crop 
in the utilization of this energy. Assuming a large yield of 50 bushels or 17 . 619 
hectoliters per acre, and considering this entirely as starch, we find an energy 
equivalent of 0.623 ton of coal. The efficiency here, then, is measured by the 

, - 0.623 
very low figure - = 0.0004 = 0.04 per cent. 

14/0 

It should be noted, however, that not all the heat absorbed by the plant 
appears stored up in the body of the plant. A large amount is used up in the 
work of evaporation (transpiration). According to L. J. Briggs (Jour. Wash- 
ington Acad., 1917, p. 92; Journal Agr. Research, 1914, pp. 1-63), the 
energy stored by the plant represents from 1 to 5 per cent of the energy dissi- 
pated during the growth of the plant. See also C. L. Holsberg, Jour. Ind. Eng 
Chem., 1924, vol. 6, pp. 524-525: Progress in Chemistry and the Theory of 
Population. 



ENERGY TBANSFORMERS OP NATURE 333 

the winds represent some 5000 times that amount of coal. 9 Ocean 
currents are another large item. Some idea of the magnitude of the 
energy here involved may be gathered from an estimate given by 
L. J. Henderson according to which the gulf stream alone conveys 10 
two-hundred million tons of water per second through the straits of 
Yukatan. If this body of water were cooled to arctic temperature we 
should have a transfer of energy at the rate of eight and a half bil- 
lion horsepower. Most important of all, in the inorganic cycle, is 
the circulation of water by evaporation, precipitation, and river flow 
(including waterfalls) back to the ocean. Of the masses involved 
a picture had been presented in Chapter XVI. As to the energy 
involved, Henderson estimates the horsepower of evaporation from. 
100 square kilometers of tropical ocean at over one-hundred million 
horsepower. 

C. P. Steinmetz 11 has calculated that if eveiy raindrop falling in 
the United States could be collected, and all the power recovered 
which it could produce in its descent to the ocean, this would yield 
about three-hundred million horsepower. G, Ciamician 12 quotes an 
estimate by Engler of the world's total water power as the equiva- 
lent of seventy billions of tons of coal. According to C. G. Gilbert 
and J. E. Pogue 13 the production of hydroelectricity in the United 
States in 1910 was the equivalent of forty-million tons of coal, 
whereas nearly ten times that amount went into the production of 
steam and carboelectric power. These authors further estimated 
that the water power developed at the date indicated represented 
about 10 per cent of that readily available, and 3 per cent of the total 
that might be open to development under elaborate arrangements 
for storage. 14 

9 For a discussion of the Atmosphere considered as an engine see Sir Napier 
Shaw's Rede Lecture, published in Nature, 1921, p. 653. This author arrives 
at the estimate that "the best you can expect from the steam-laden air of the 
equatorial region working between the surface and the stratosphere, under 
favorable conditions, is a brake-horsepower efficiency of 25 per cent." 

10 L. J. Henderson, The Fitness of the Environment, p. 182. 

11 Survey Graphic, 1922, vol. 1, p. 1035 (cited by H. A. Spoehr, Jour. Ind. 
Eng. Chem., 1922, vol. 14, p. 1143). 

12 Die Photochemie der Zukunft; Samml. Techn. Vortrage, 1914, p. 431. 

13 Power, its significance and needs; Smithsonian Institution Bulletin 102, 
Part 5. 

14 For a comprehensive survey of power development actual and potential 
see F. G. Baum, II. S. A. Power Industry. Also W. S. Murray, A Superpower 
System for the Region between Boston and Washington. United States 
Geological Survey Professional Paper 123 of 1921. 



334 ELEMENTS OF PHYSICAL BIOLOGY 

Relation of Transformer Cycle to Circulation of the Elements. 
The circulation of substance in the organic world and its inorganic 
background, which was considered in an earlier chapter in its purely 
material relations, now acquires a new significance. We recognize 
in it now a typical characteristic of the great world engine which, 
for continued operation, must of necessity work thus in cycles. The 
picture presented to our minds is that of a gigantic overshot mill 
wheel, receiving from above the stream of sunlight with its two 
hundred twenty-seven million gross horsepower though much of 
this is spilt without effect and discharging below its dissipated 
energy in the form of heat at the general temperature level. The 




FIG. 68. THE MILL-WHEEL OF LIFE 

main outstanding features of the wheel are represented dia- 
grammatically in figure 68. But in detail the engine is infinitely 
complex, and the main cycle contains within itself a maze of subsidi- 
ary cycles. And, since the parts of the engine are all interrelated, 
it may happen that the output of the great wheel is limited, or at 
least hampered, by the performance of one or more of the wheels 
within the wheel. For it must be remembered that the output of 
each transformer is determined both by its mass and by its rate of 
revolution. Hence if the working substance, or any ingredient of the 
working substance of any of the subsidiary transformers, reaches its 
limits, a limit may at the same time be set for the performance of the 
great transformer as a whole. Conversely, if any one of the subsidi- 



ENEBGY THANSFOBMEBS OF NATUBE 335 

ary transformers develops new activity, either by acquiring new 
resources of working substance, or by accelerating its rate of revolu- 
tion, the output of the entire system may be reflexly stimulated. 
As to the significance of this for the evolution of the system as a whole 
more will be said later, in the discussion of certain phases of the 
evolution of the human species in particular; for it is hardly necessary 
to remark that the case of man presents features of so remarkable 
character that it calls for special consideration, quite aside from the 
pardonable excess of interest which we personally feel in the 
creature. 

Evolution of the World Engine; The picture we must keep before 
us, then, is that of a great world engine or energy transformer com- 
posed of a multitude of subsidiary units, each separately, and all 
together as a whole, working in a cycle. It seems, in a way, a singu- 
larly futile engine, which, with a seriousness strangely out of keeping 
with the absurdity of the performance, carefully and thoroughly 
churns up ah 1 the energy gathered from the source. It spends all its 
work feeding itself and keeping itself in repair, so that no balance is 
left over for any imaginable residual purpose. Still, it accomplishes 
one very remarkable thing; it improves itself as it goes along, if we 
may employ this term to describe those progressive changes in its 
composition and construction which constitute the evolution of the 
system. For the statement will bear reiteration and emphasis 
this is the conception we must form of organic evolution: the evolu- 
tion of the great world engine as a whole, not merely that of any 
single species of organisms considered separately. What is the trend 
of this development? Toward what end does the great transformer 
shape and reshape itself? A provisional answer to the question will 
be suggested in due course. For a time we must now abandon our 
broad viewpoint, and turn from the consideration of the great trans- 
former as a whole, to a discussion of certain of its subsidiary engines 
which present points of special interest and importance. 



CHAPTER XXV 
RELATION OF THE TRANSFORMER TO AVAILABLE SOURCES 

As an enterprise, mathematics is characterized by its aim, and its aim is to 
think rigorously whatever is rigorously thinkable or whatever may become 
rigorously thinkable in course of the approved striving and refining evolution 
of ideas. C. J. Keyser. 

Distributed and Localized Sources of Energy. In Garnet's 
classical analysis of the operation of a heat engine the source of 
energy is taken for granted as one of the fundamental data of the 
problem. 

In nature sources of energy are not thus supplied unconditionally, 
and for our present purposes it becomes necessary to extend the 
analysis of transformer operation so as to take into its scope also 
some of the significant characteristics of the sources from which the 
engines of nature derive their supplies. And here a fundamental 
distinction is to be made between two lands of sources, namely, (1) 
evenly, or at least continuously distributed sources, and (2) localized 
sources, heterogeneously distributed. 

If the transformer draws its energy supply from a source uniformly 
distributed over a region R, at any point of which it can make contact 
with the source, then, evidently, within the region R the performance 
of the transformer is independent of its location. So, for example, 
plants derive their energy from sunlight falling upon them gratui- 
tously, and draw their suppli es of material partly from atmospheric car- 
bon dioxide and oxygen diffusing to them by a spontaneous process, 
and partly from dissolved salts seeping to their roots automatically, 
that is to say, by a process essentially independent of any intervention 
on the part of the plant. And quite in accord with this general dis- 
tribution of plant food, the typical plant is a sessile, passive organism. 

If, on the contrary, the transformer draws its supply from discon- 
tinuous, heterogeneously distributed sources, then continued 
operation demands at least some degree of relative motion between 
the transformer and the sources, so that the occasional collisions 
may occur between the transformer and a source. 

336 



RELATION OF TRANSFORMER TO AVAILABLE SOURCES 337 

Random and Aimed Collisions. Purely random collisions, such 
as those contemplated in the kinetic theory of gases, may suffice to 
bring an adequate supply to the transformer. 1 But evidently the 
output of the transformer will be enhanced if, instead of relying upon 
a precarious supply gleaned in fortuitous encounters, a suitable 
correlation is established between the motion of the transformer and 
the location of the sources. This may be accomplished in two ways, 
as follows: 

1. There may be actual mechanical union 2 positively connecting 
transformer and source, so that there is a functional relation (in the 
mathematical sense) between the motion of the transformer and the 
topography of the source. A simple instance in point is a trolley 
car. Here there is a definite relation between the topography of the 
system (track), the reaction of the transformer up it, and the distribu- 
tion of the source. The car is not free to move except along the track 
and along the trolley wire. 

2. Contact with the source may not be positively secured, but 
merely rendered more probably than in purely random collisions, by 
the occurrence of more or less accurately aimed collisions. Source and 
transformer are in this case mechanically independent, the motion of 
the source is not fully determined when the topography of the system 
is given; a certain freedom remains. There is, in this case, not func- 
tional relation, but only correlation between the motion of the trans- 
former and the topography of the system: no specific motion is 
determined, only certain motions are rendered more probable than 
others. 

Negative Correlation. It is to be noted, of course, that such correla- 
tion between the motion of a transformer and the location of features 

1 For an experimental investigation of the movements of lower organisms 
(Paramecium, Colpidium, Trachelomonas) see Przibram, Pftiigers Archlv, 
1913, vol. 153, pp. 401-405. The movements were found to follow the law de- 
duced by Einstein and Smoluchowski for Brownian movement (which, of 
course is random), namely that the mean square of the displacements of a 
particle in any direction in equal intervals of time t is proportional to t. The 
order of magnitude of the movements of the organisms, however, and the 
influence of temperature, were quite different in the case of Brownian 
movement. (For an account of the Einstein-Smoluchowski law see, for exam- 
ple, C. Schaefer, Einfiihrung in die theoretische Physik, 1921, vol. 2, p. 487.) 

2 Compare L. T. y Quevedo, Essai sur 1'automatique, Revue Ge'ne'rale des 
Sciences, 1915, vol. 26, p. 601. 



338 ELEMENTS OF PHYSICAL BIOLOGY 

of its environment is competent to bring other benefits aside from a 
a supply of energy and material (food). All transformers are more or 
less vulnerable. Exposed to an environment varying from point to 
point and from instant to instant, a transformer will in general sooner 
or later meet with an injurious stress, that is to say, a stress that will 
change its structure or constitution to a point where effective opera- 
tion is impaired or altogether abolished. If it is desirable, in the 
interest of increased output, that collisions with suitable energy 
sources be rendered more probable than in purely random motion, it is 
evidently equally desirable, in the interest of continued operation of 
the transformer, that collision with harmful features in the environ- 
ment be rendered less probable. In other words, in addition to 
apparatus establishing a positive correlation between the motion of the 
transformer and the location of sources, it is desirable that there be 
also provided apparatus establishing negative correlation between 
such motion and the location of injurious features of the environment. 
Collisions should, as far as possible, be aimed toward sources, and 
away from points of danger. The fate, the success of the transformer, 
will evidently depend both on the versatility of the aim, and on its 
accuracy; on the number and character of targets picked out for aim, 
and on the closeness with which the hits upon the target cluster around 
the bull's eye. 

The Correlating Apparatus. It is on the general plan indicated in 
the preceding paragraph that nature's mobile transformers, especially 
the typical animal organisms, operate. In the competition among 
these, for food and for safety, the accuracy and the versatility of 
aim characteristic of each species will evidently be most important 
determinants of relative success or failure, and hence of the trend of 
evolution. The dynamics of evolution thus appears essentially as 
the statistical dynamics of a system of energy transformers, each 
having a characteristic vulnerability, a characteristic versatility and 
accuracy of aim. It is here that the method of thermodynamics is 
inadequate. Its austere virtue of impartiality toward different 
mechanisms becomes a vice when information is sought regarding 
systems in which mechanism plays a leading r61e. The mechanism, 
or, to use a somewhat broader term free from mechanistic implications, 
the apparatus, by which the correlation is established between motion 
and environment, by which behavior is adapted to circumstances, is 
here not an incidental detail to be lightly dismissed as of secondary 



RELATION" OP TRANSFOEMEB TO AVAILABLE SOTJBCES 339 

importance, but must occupy the very center of attention. To a 
somewhat detailed consideration of this apparatus we now proceed; 
in the interest of vivid, realistic presentation of the subject it will, 
however, be desirable to abandon from this point on the veiy general 
treatment and, to speak now specifically in terms of biological units, 
organisms, rather than in terms of the broader physical concept of 
energy transformers. It should be constantly borne in mind, how- 
ever, that this change in attitude, or, it were better to say, in termi- 
nology, is chiefly a matter of convenience and effectiveness of pres- 
entation, and the fundamental physical principles involved, as set 
forth in the more general terms, should never be allowed to sink far 
below the surface of our immediate thought. 

The Component Elements of the correlating Apparatus. The 
continued existence of the organism, toward which his actions are 
aimed, demands that he shall direct his energies, his activities in 
accordance with the state of his environment, of the external world, 
avoiding unfavorable conditions, and seeking out those favorable or 
necessary to his maintenance. This includes the locating and seizing 
of food. 

But as a material, physical system, his actions are primarily deter- 
mined by his own state. Hence, in order that his actions, determined 
immediately by the state of the organism himself, may be mediately 
determined by the state of the external world, apparatus must be 
provided whereby the state of the organism becomes in a certain 
suitable manner a function of the state of the external world. The 
external world is depicted in the organism by a certain apparatus, 
a set of organs and faculties, which we may appropriately term the 
Depictors. 

The depictors include first the Receptors or Organs of Special Sense 
(eyes, ears, nose, etc.) ; and second the Elaborators, whose function is 
to combine and further elaborate the crude information furnished by 
the senses. The physical location and structure and mode of opera- 
tion of the elaborators is much less obvious than that of the receptors. 
In fact, we ordinarily recognize them rather as faculties (Memory, 
Reason) than as organs. 

Another set of organs and faculties, the Adjusters, determine the 
particular reactions, the behavior of the organism, in the light of the 
information brought in by the receptors and further elaborated by the 
elaborators. So the hungry bird, sighting a worm on the lawn, flies 



340 ELEMENTS OF PHYSICAL BIOLOGY 

down to the spot from the tree on which it is perched, and secures its 
prey. The sight of the worm, together perhaps with the memory of 
earlier meals collected near the same spot, acts as a stimulus or 
Drive to responsive action. This last step, action, commonly in- 
volves the use of members, or motor organs, Effectors, such as wings, 
feet, hands, etc. In complicated cases, as in human behavior, the 
elaborators may also play an important role in the effector step of 
the process by which motion is correlated to environment, behavior 
adapted to circumstance. So, for example, the traveller, before 
setting out on a journey, plans his itinerary, perhaps months or years 
in advance. 

Receptor-Effector Circuit Begins and Ends in Environment. It is 
a noteworthy fact that this process of correlating action to conditions 
is essentially cyclic in character: It has its origin in the external 
world, which becomes depicted in the organism, provokes a response, 
the terminal step of which is usually, if not always, a reaction upon 
the external world. The net result is, in a sense, that the external 
world has reacted upon itself. The organism has acted as an inter- 
mediary. There is something more than a mere surface significance 
in this fact. For it is true generally that animals function essentially 
as catalysers, as agents assisting in a change that is "trying" to take 
place on its own account. So the green grass is, in a sense, hungry 
for oxygen, namely in the sense that its oxidation is accompanied by 
a diminution of free energy. The animal consuming the grass and 
deriving from its oxidation the requisite energy for further activity 
has not initiated any revolutionary process, but has merely helped 
nature in its course, has merely rolled the ball downhill, so to speak. 
This is all that the animal organism is competent to do, and man is 
not exempt from this restriction: In all our doings, whether we will 
it or not, we are assisting in a fundamental natural process, we are 
obeying an inevitable law of energetics. 

Correlating Apparatus Not Peculiar to Living Organisms . It must 
not be supposed that the typical elements of the correlating appara- 
tus, the receptors, adjusters and effectors, are wholly peculiar to 
living organisms. They can be very clearly recognized also in cer- 
tain mechanisms of human construction. In fact, owing to the 
circumstance that the operation of such man-made mechanism is 
fully known to us, that they harbor no mysterious "vital" principle 
or ill-understood element of consciousness, such purely mechanical 



EELATION OP TKANSFOEMEB TO AVAILABLE SOUECES 341 

contrivances furnish particularly apt illustrations of the principles 
involved in the operation of the correlating apparatus. It is there- 
fore well worth while to consider here a simple example of this kind. 
Some time ago there appeared on the market an ingenious toy, 
primarily designed, no doubt, merely to amuse; but, in point of fact, 
highly instructive. Its general appearance and simple mechanism 
are illustrated in figure 69. The beetle "walks" on two toothed 
wheels, of which one is an idler, while the other is rotated by a spring 
whose gradual release is ensured by a simple escapement device. 
At its forward end reckoning in the direction of motion (at the 
"head") the toy is provided with a pair of antennae, of which one is 
a dummy, and rises clear of the table upon which the beetle is placed 
to exhibit its talents. The other antenna is operative and is so bent 
downward as to glide along the table top, in contact with it. A little 




FIG. 69. MECHANICAL WALKING BEETLE, EXHIBITING THE SEVERAL CHARAC- 
TEEISTIC ELEMENTS OP THE COERELATING APPARATUS 

in advance of the propelling wheel is another smaller toothed wheel, 
running idle, and disposed transversely to the direction of the driving 
wheel. This transverse wheel clears the table without contact in the 
normal working position of the beetle. The animal, if placed some- 
where near the center of the table, makes a straight track, apparently 
intent upon reaching the edge and seeking destruction in a species 
of mechanical suicide. But the moment the operative antenna 
clears the edge of the table, the body of the toy, till then held up by 
the contact of the antenna with the table surface, sinks down a frac- 
tion of an inch, and the transverse wheel now contacts with the 
table. In consequence the toy rotates until the running wheel 
is parallel with the table edge, and the insect continues its pere- 
grinations with the operative antenna hugging the side of the table top. 
Clearly here the antenna is a receptor, which "apprises" the insect 
of certain features in its environment, which depicts, in a crude but 



342 ELEMENTS OF PHYSICAL BIOLOGY 

sufficient manner the environment in the toy. The law of depiction 
is here extremely simple; a depression in the external world (table 
top) is translated into a downward tilt in the angle of repose of the 
toy. 

The adjuster, in this case, is the transverse wheel, about as simple 
an example of an adjuster as can well be imagined. It "construes" 
the information furnished by the receptor antenna, and modifies in 
accordance with this information the law of motion of the toy, in 
such manner as to preserve the beetle from a fall which might destroy 
that stability of form on which the continued operation, according to 
schedule, of the mechanism depends. 

It would be easy to cite a number of other examples of devices con- 
structed either as toys, scientific curiosities, or for actual technical 
use, which exhibit more or less prominently the typical correlating 
apparatus, with receptor, adjuster and effector. By far the most 
highly perfected of such automatic devices is the modern machine- 
switching apparatus for telephones, which eliminates the "oper- 
ator" at the central offices. This device, which fulfills an amazing 
multiplicity of functions, will be found briefly described in non-tech- 
nical language in the April number 1923 of The Bell System Tech- 
nical Journal. 

Perhaps more directly in line with our present interest here is a 
mechanical chess player that was designed some years ago by L. 
Torres y Quevedo; 3 this device successfully counters any move (with 
a limited number of pieces, merely as a matter of simplicity) that a 
living opponent may choose to make upon the board. The game of 
chess itself is so well conceived a conventionalization of the battle 
of life 4 that it is well worth the while to make a seeming digression to 
analyze the fundamental elements of this remarkable game. The 
bearing of this analysis upon certain problems of biological evolution 
will then become apparent. 

8 A description will be found in the Scientific American Supplement, 
November 6, 1915, p. 296. 

4 The aptness of this illustration has no doubt been remarked by many. 
I have recently noted the following pertinent references : F. L. Wells, Mental 
Adjustments, 1917, p. 6. Eddington, Time Space and Gravitation, 1920, p. 
184; T. H. Huxley, A Liberal Education and Where to Find it. Collected 
Essays, 1894, vol. 3, p. 81. A bibliography of the mathematical treatment of 
chess will be found in W. W. R. Ball, Mathematical Recreations, 1911, 
Chapter VI, p. 109. 



RELATION OF TRANSFORMER TO AVAILABLE SOURCES 343 

Chess as a Conventional Model of the Battlefield of Life. A 
game of chess is a succession of physical events. How is its course 
determined? 

The elements that determine this course are as follows : 

1. A topographic map, a chart of geometric constraints, the chess 
board. 

2. Movable upon this chart, a number of movable points (chess- 
men), each the center of & field of influence, defined for each movable 
point in relation to the geometric constraints. So, for example, the 
field of influence of a pawn extends to the two squares diagonally 
in front of the pawn. 

3. A law restricting the time-rate of advance of each moving point 
(moves alternate from white to black). 

4. A law defining the influence upon each other of two points in 
collision, i.e., two points whose fields of influence have interpenetrated 
to a prescribed extent. An example of this is the rule that a chessman 
arriving upon a square occupied by a hostile piece, throws the latter 
off the board. 

5. A law restricting the movements of the points when not in 
collision, i.e., when outside one another's field of influence. So, for 
example, a bishop may move only diagonally. 

6. The elements enumerated so far place restrictions upon permis- 
sible changes (moves). These elements alone cannot, evidently, 
determine any occurrence of any kind: Absolute immobility, for 
example, or any random move that did not violate the rules of the 
game, would equally satisfy the conditions enumerated. 

7. In addition to the elements, 1, 2, 3, 4, 5, there must therefore 
be in operation some positive principle (tropism) which not merely 
restricts possible occurrences, but which determines actual events. 
In chess this principle is furnished by the effort of each player to 
bring about checkmate. Each move is so aimed (with greater or less 
accuracy and breadth of view, versatility, according to the skill of the 
player) as ultimately to force a checkmate. 

From the battlefield of chess we now turn our eyes on the scene of 
the great biological contest: Before us is a topographic map, over 
which move those organisms that are by nature gifted with motion. 
We may think of each such organism as a moving point, the center 
of a field of influence. As the chessplayer must accustom his mind's 
eye to see, radiating out from each chessman, its field of influence- 



344 ELEMENTS OF PHYSICAL BIOLOGY 

upon the board, so we, in envisaging the battleground of organic 
evolution, must see each organism carrying around with it, as if 
rigidly attached to its body, a field, or a target, of zones, of the fol- 
lowing character. 

A. Zones of Influence, In general the motion of the individual 
will be determined by laws too complicated to be readily analyzed, and 
therefore will be described as random. But there will upon occasion 
be a rather abrupt break away from such random movement, according 
as a certain feature of the environment lies without or within certain 
zones. For example, the movements of a fly wandering about on a 
window pane are, presumably, in all cases physically determinate. 
But in a homogeneous field (uniform illumination etc.), the motion 
will assume, on the whole, a random character. We may suppose 
that, in first approximation at any rate, the migrations of the individ- 
ual will follow some such law as those developed, for example by 
Sir Ronald Ross, 5 by Pearson and Blakeman, 6 or by Brownlee 7 for 
random migration. But, bring some particle of food within the field 
of sensuous observation of the fly, and the law of motion instantly 
changes from random to more or less clearly directed. 

We may, then, construct about each individual a sort of target of 
zones of influence. The ideal would be to draw this target on a 
quantitative plan, according as a stimulus of strength s exerts a 
directing influence d at a distance r. In practice there may be diffi- 
culty in constructing these zones, but we may at least conceive them 
as drawn. 

We may say that a given organism is "in encounter" with a given 
point (e.g., a feature of the topographic chart) when that point falls 
within its field of influence. Similarly we may say that two organisms 
are in encounter when the one falls in the field of influence of the other. 
This encounter is mutual or one-sided according as each is within the 
other's field } or as only one is in the other's field, but not conversely, 
for example if A sees B, but B does not see A; or, to take an example 

5 Sir Ronald Ross, Prevention of Malaria, 1922, second edition, pp. 179, 700. 

6 K. Pearson and J. Blakeman, Drapers' Company Research Memoirs, 
III: XV, 1906. 

7 J. Brownlee, Proc. Roy. Soc. Edin., 1910-1911, vol. 31, pp. 262-289; of other 
references related to this subject the following have been noted: F. Y. Edge- 
worth, Entomological Statistics, Metron, 1920, vol. 1, p. 75; W. H. Cole, Sci- 
ence, 1922, vol. 55, p. 678; W. B. Hardy, Nature, December 30, 1922, p. 866 
(Twelfth Report of the Development Commissions 1922). 



345 

RELATION OP TRANSFORMER TO AVAILABLE SOUBCES 

from chess, a bishop may threaten a pawn, though the pawn does not 
threaten the bishop. Zones of influence may extend over millions of 
miles, as in the case of a traveller steering his course by the stars. 

B. Zones of Mobility. We may stake out around each organism 
a target of zones indicating the distance which it is physically capable 
of travelling in 1, 2, , . .n units of time. These zones also we shall 
think of as attached to the organism and carried round with it in 
its wanderings through the landscape. 

It is clear that the fate of the organism, and the history, the evolu- 
tion of the system as a whole, will depend, first, on the character of 
the zones of influence and the zones of mobility; and second, on the 
nature of the correlation, the law of the aimed movements,, established 
through these zones. We may seek to establish analytical expressions 
for this dependence. 

Let g be a parameter defining the character or "pattern" of a target 
of zones of influence or of mobility of the organisms of species S. 
Thus, for example, q might be parameter, or one of a set of parameters, 
defining visual acuity, measured on some suitable scale, at a distance 
of 5, 10, 15, . . . feet, under standard conditions. Or, g might be a 
parameter defining the minimum time required for the organism to 
reach a point 5, 10, 15, ... feet from his actual position, under 
standard conditions. 8 

Analytical Statement of Problem. We may now enquire: 

1. What will be the effect upon the rate of growth of the species 
if the parameter g is increased by a (small) amount dqf If r is the 
fractional rate of increase of the species S, can we establish an expres- 

d?* 

sion for the partial derivative ;? 

A glance at the chess analogy will help to make clear the nature of 
the question thus raised. In chess we might ask: What would be the 
effect upon the course of the game if, other things equal, we were to 
modify in some stated particular the rules limiting the permitted 
moves of a given piece, for instance by allowing a pawn to move two 
squares, instead of the conventional one? 

2, A second enquiry of peculiar interest relates, not to the character 
(pattern) of the zones of influence and mobility, but to the form of 

8 Isochrone charts of essentially this character, relating to travelling facili- 
ties, were, according to Darmstaedter, first suggested by K. Bichter in 1833 arid 
actually prepared by Sir Francis Galton in 1881 (L. Darmstaedter, Handbuch 
zur Geschichte der Naturwissenschaften und der Technik, 1908, p, 792). 



346 ELEMENTS OF PHYSICAL BIOLOGY 

relation established, through these zones, between the action of the 
organism and his environment. For it is hardly necessary for us to 
be reminded that two individuals or species with the same visual 
acuity, for example, may react in very different manner on seeing the 

same thing. 

Here again the chess analogy is helpful. The corresponding en- 
quiry with regard to chess is: What would be the effect upon the 
course of the game, if, with unchanged rules as to the moves of the 
pieces, a given change were made in the method, or the ability, of one 
of the players? 

To deal with these problems it is desirable to introduce two con- 
cepts, that of the Behavior Schedule, and that of Specific Productivity 
in a given activity. 

THE BEHAVIOR SCHEDULE 

It has been remarked 9 that "a living organism is both cause and 
effect of itself." We may say in somewhat more detailed statement, 
that the organism goes through a certain routine of motions or activi- 
ties which are rendered possible by ^& structure, and which, in turn, 
are a necessary condition for the continued existence of that structure. 
These activities in general involve the expenditure of certain quanti- 
ties of free energy, and a part of the energy so expended necessarily 
is spent in collecting (earning} a "replacement" amount equal to the 
total expenditure, to balance the account, to cover the cost of living. 
While this phenomenon is, in a general way, characteristic of all 
mobile forms of life, the particular method followed in this cyclic 
activity of gathering and spending free energy varies in the most 
multiform manner from one species or type of organism to another. 

Each type of organism may thus be said to possess a characteristic 
Behavior Schedule, which may be defined in terms of certain coeffi- 
cients as follows: Of its total expenditure E per unit of time, a repre- 
sentative individual of the population will spend, on an average a 
fraction Xj in a particular activity Aj, which may be defined as the 
maintaining of a parameter Uj at the value u$. So, for example, 10 
a human being may expend on an average, per day, 

9 Kant, Kritik of Judgment. Transl. Bernard, London, 1892, p. 274. 

10 The figures in this example are chosen arbitrarily, although an effort 
has been made to make them reasonably realistic. In view of the wide vari- 
ations in standards and cost of living in different countries, different social 



RELATION OF TRANSFORMER TO AVAILABLE SOURCES 347 

number of calories 

ISO external work (services sold) in 
maintaining his daily food sup- 
ply at 3,000 cal. 

2,500 internal work (physiological 
work) in maintaining his body 
temperature at 9SF. 

130 external work (services sold) in 
maintaining Ms house rent at, 

daily 2.00 

60 external work (services sold) in 
maintaining his dairy supply of 

clothing at SO , 75 

30 external work (services sold) in 
maintaining his daily supply of 
sundries at SO. 25 

100 external work (services sold) in 
maintaining the rate of in- 
crease of the population at 1 per cent per annum 



3,000 calories total expenditure and total earnings 
(Note: 1 calorie = 30S6 foot pounds.) 

SPECIFIC PRODUCTIVITY 

Consider some particular activity A j which results in maintaining 
a parameter Uj (e.g., food capture per head per unit of time) at the 
value Uj, then we will define P-, 3 the Specific Productivity of energy 
Ej spent in activity Aj by 

Pj = '' - (cj a constant) (1) 

and we note that 



strata, and at different epochs, close figuring, in such an example as this, would 
be out of place. Numerical data pertinent to this example will be found 
scattered widely in various sources, of which the following may here be men- 
tioned: J. Amar, Le Moteur Humain, 1914, p. 254; R. Hutchison, Food and 
Dietetics, 1902, p. 37:46; J. LeFevre, La Chaleur Animale, 1911; F. H. Streight- 
off, The Standard of Living, 1911. 



348 ELEMENTS OF PHYSICAL BIOLOGY 

EFFECT OP CHANGE IN ZONE PATTERN 
(Intra-Species Evolution) 

We are now prepared to consider the analytical representation of 
the influence of changes in the pattern of the zones of influence and 
the zones of mobility, on the one hand, and, on the other, of a change 
in the behavior schedule, on the proportional rate of increase r of 
the species of organisms under discussion. 

This proportional rate of increase, r = -777 , is in general a func- 

.Arft 

tion of the parameters U (food capture, shelter, etc.), so that we may 
write 

r = r(ui, u 2 , . . . Uj, . . . ) ( 3 ) 

and 

-^L^-^L^i (4) 



Now the specific productivity P- t in activity A$ itself depends upon 
the character of the zone pattern. For, the more perfectly the in- 
dividual is apprised of the relevant features of its environment (i.e., 
the more perfectly developed its zones of influence), the better, other 
things, equal, will it be able to direct its activities to the ends de- 
fined by the parameters U; and a similar remark evidently applies 
to the zones of mobility. If, then, q is a parameter denning the 
character of these zones, we may write 

Pi = Pj(g) (6) 

and 

| r JL |p (7) 

-1^*1 (8) 

Ouj Oq 

or, more generally, since a change in q may affect not only a single 
productivity P j} but also others, PI, P 2 , . . . P n 



RELATION OF TRANSFORMER TO AVAILABLE SOURCES 349 

the summation being extended over all the activities AI, A z , . . 
A- } , . . , A a in so far as they are affected by the parameter q. 
(It is immaterial whether those not so affected are included in the 
summation or not, since they will contribute a zero term.) 
It lends a certain interest to the relation (9) if we observe that such 

dr dr 

partial derivatives as ;r , ^ possess a concrete signification, as 

follows : 

Consider two small increments Agi and Aq z in two parameters 
QI and go. (To make matters concrete, suppose qi measures visual 
acuity, q z auditory acuity.) If Aqi and Ag- 2 are such that 

dr . dr , 

_A 3l -g--Ag 2 = (10) 

i.e., such that 

Agi _ dr / dr 

A^ = d^/d^ (11) 

then it will be indifferent for the rate of the increase of the species 
whether visual acuity is increased by Agi or auditory acuity by Ag 2 . 
We might say, in this sense, that the increments Agi and Ag 2 are, in 
this event, equivalent, or that that they have the same total value 
(in exchange against each other) for the species. Moreover, from 
(10) it is evident, on this same understanding, that the partial deriva- 

dr 
tive ^ measures the value (in exchange) per unit, 11 to the species, of 

dr 

the parameters gi, and similarly measures the value (in exchange) 

per unit of the parameters g z . We may symbolize these facts by 
writing 

dr 

dS-** < 12) 

dr 

d^. = ^ <* 

The relation (9) then appears in the form 



y-i 



u An arbitrary proportionality factor enters, which is conveniently made 
unity by suitable choice of units. 



350 ELEMENTS OF PHYSICAL BIOLOGY 

Certain steps in the development set forth above are reminiscent of 
the hedonistic calculus of Jevons and his school of economists. One 
is thus naturally led to look for a relation between value (in exchange) 
as here defined, and economic value in exchange, as conceived by those 
authors. It should be expressly noted, however, that the reasoning 
here followed, and the conclusions reached, are quite independent of 
any economic theory. As for the relation of the present reflections 
to economic theory, this will become apparent in the paragraphs that 
follow. 

EFFECT OF CHANGE IF BEHAVIOR SCHEDULE 

We may note, first of all, that 

drj _ dr C)j _ 5?- , 

dlpd^jdipd^ j 

where p- } = ^77 defines what we may term the marginal productivity 

OIL j 

of energy expended upon the parameter Uj. This marginal pro- 
ductivity p; will, in general, differ from the total productivity Pj 
defined by equation (1). 

It is, however, desirable, to express the relation between r and the 
behavior schedule in another way, with the following considerations 
in mind. 

Rigid or Automaton Type and Elastic Type of Behavior 
Schedule. The apparatus by which the coefficients X defining the 
behavior pattern are determined varies widely in different species 
of organisms. At one extreme we may suppose that we have an 
organism, with a rigid, inelastic behavior schedule, the coefficients X 
being determined explicitly, once for all, by the properties of the 
individual. The extreme case of this kind is to be found, presumably, 
in plants, where, for example, the amount of energy expended in 
anabolism to replace wear and tear (e.g., annual leaf-fall) may be 
taken as a comparatively simple function of the leaf area. Many 
of the lowest forms of animals, actuated by simple tropisms, no doubt 
also approximate closely to such a rigid behavior schedule, what might 
be termed the automaton type of behavior schedule. 

But in the higher animals, and most particularly in man, we have 
an elastic behavior-schedule. Here the A's are not fixed in simple 
explicit manner by the physical character of the organism. We 



BELATIOX OF TBANSFOKMER TO AVAILABLE SOURCES 351 

encounter here the phenomenon which we experience in ourselves 
subjectively as free choice between alternative courses of action, 
alternative values of the X's open to us to choose from. 

This cannot mean, of course, that the X's are wholly arbitrary, or 
physically indeterminate. Some action is and must be taken. But 
the natural principle which operates in the determination of the X's, 
of the behavior schedule, is not immediately obvious. 

The avenue of approach which seems to give most promise of 
lending us an insight into the relations here involved, is the following: 

The elastic type of behavior schedule, the free-choice schedule, as 
distinguished from the automaton type, is essentially a characteristic 
of the more highly organized among the mobile (animal) organisms. 
This fact is so prominently displayed to us in our own selves, that 
the adaptive superiority of the elastic type over the automaton type 
is commonly (and perhaps in a measure unjustly) taken for granted. 
If this assumption of such superiority be true, then the principle 
which operates in determining the coefficients X's must be that they 
tend, on the whole, to be adjusted, in the operation of free choice, 
toward values favorable to the growth of the species. In the ideal 
case of perfect adaptation the X's would, according to this view, be 
such as make r, the proportional rate of increase of the species, a 
maximum. Let us see what this would imply. 

In reacting upon its environment to influence the parameter Uj, 
the organism itself necessarily undergoes some modification, since 
it gives up energy Ej, (subjectively this modification is commonly 
felt as fatigue). In other words, if the state of the individual is 
defined by the values of certain (internal) parameters /i, /a . > 
then the expenditure of an element of energy 8 E- } by the individual, 
if not accompanied by other effects, is accompanied by a change 
5/i,5/ 2 . . . in the parameters /. At the same time the (external) 
parameter Uj is modified by ou- } . 

The effect of these modifications upon r is given by 



where, for brevity, the contracted notation has been employed 
* *' drd/ k 



352 ELEMENTS OF PHYSICAL BIOLOGY 

If r is to be a maximum, (5r) must vanish for any arbitrary small 
value of 5 Ej, so that we must have for every subscript j, according 
to (16) 

dr dj dr d/ . 

(18j 



or, adopting the notation of (12), (13), (15) 

t'uiPj + t'fpt = (19) 

Relation between Ideal and Actual Organism. We have thus 
far considered an ideal type of organism of the free choice type of 
behavior schedule, constructed on the principle that the X's shall be 
so chosen as to make the proportional rate of increase r a maximum. 

It remains to consider the relation between this ideal type of or- 
ganism and the actual organism. The actual organism is not con- 
sciously guided by any consideration of the effect of his actions upon 
the rate of increase of his species. At least the instances in which 
such considerations are operative are so exceptional that we may well 
leave them out of account. What guides a human being, for example, 
in the selection of his activities, are his tastes, his desires, his pleasures 
and pains, actual or prospective. This is true, at least, of some of 
his actions, those which are embraced in his free-choice type of be- 
havior schedule. That the human behavior schedule 12 also contains 
an element of the non-elastic (automaton) type may be admitted in 
deference to those who have leveled their destructive criticism at the 
hedonistic account of human behavior. We may, however, restrict 
our discussion here to that portion or phase of conduct which is 
determined by hedonistic influences. In this case, then, we are dealing 
with an organism which seeks to make, not r, but 0, its total pleasure 
("ophelimity" in Pareto's terminology) a maximum. Argument 
precisely similar to that developed above here leads to the condition. 

dQ 5uj dO r d/ 

+ = C20) 



12 In a modern civilized community we cannot very well speak of one typical 
behavior schedule of the individual, owing to the division of labor, with 
specialization of individuals in different pursuits. This matter will be found 
discussed more particularly, in Chapter XXVIII dealing with the adjusters 



HELATION OP TRANSFORMER TO AVAILABLE SOURCES 353 

ft is immediately seen that (18) and (20) will lead to the same 
adjustment of the activities of the individual if, and only if the 

50 
marginal ophelmiities r are proportional to the corresponding 



A *' ' 

derivatives ;r~ i.e. 

OUj 



- 

__ _ c 
OUj UMj 



We see then, that an organism actuated by pleasure and pain will 
so distribute its activities as to make r a maximum, if, and only if, its 
marginal ophelimities are proportional to the corresponding deriva- 

br 

tives r~ . 

OUj 

Effect of Small Departure from Perfect Adjustment. If we 
look upon the sense of pleasure and pain as an adjunct serving the 
express purpose of directing the activities of the organism towards 
ends beneficial to the growth of the species, then a species for which 
condition (21) were satisfied would represent perfect adaptation in 
this respect. 

This leads us to a somewhat different setting of our problem regard- 
ing the influence of a change in the behavior pattern upon the rate of 

or 

increase of the species. Instead of enquiring after :^7 , we may seek 

OHij 

information regarding the influence, upon r, of a change in the tastes 

50 

or desires of the species as defined by the derivatives r . An 

J OUj 

answer can be given at any rate in the neighborhood of the "perfect" 
adjustment of tastes defined by (21), i.e., for a species whose behavior 
schedule does not depart materially from that defined by (18). 
Consider a species for which the ideal (perfect) adjustment is given by 

ujpj + fp f = (22) 

Suppose that this species actually adjusts its activities according to 
the plan (23) departing slightly (by an "error of valuation" 5e) from 
the perfect adjustment, namely 

(uj + 8e)pj + vfpt = (23) 



354 ELEMENTS OF PHYSICAL BIOLOGY 

Then it can readily be shown 13 that 

<. / ?> 

7^- = ~ V;Pi ?T- (SujPj + WfPf) (24) 

O6j y ouj j 

which is the required analytical expression for the influence of a small 
"error of valuation" upon the rate of increase of the species. 

The utility which such formulae as here developed may possess 
must be sought, not so much in their application to numerical 
examples data for this are now and may long remain unavailable 
as in the light they throw, quantitatively, upon the biological 
foundations of economics, in the relations which they reveal between 
certain biological and certain economic quantities. It must be 
remembered that the mathematical method is concerned, not only, 
and indeed not primarily, with the calculation of numbers, but also, 
and more particularly, with establishment of relations between mag- 
nitudes. 14 

Relation of Economic Value to Physical Energy. The behavior 
schedule has been quantitatively defined in terms of energy. 
This, if not the only possible definition, is at any rate a convenient 
one, and has also the advantage of emphasizing the important rela- 
tion of the organism to the energy sources of his environment. His 
correlating apparatus is primarily an energy capturing device its 
other functions are undoubtedly secondary. Evidence of this is 
manifold. The close association of the principal sense organs, eyes, 
ears, nose, taste buds, tactile papillae of the finger tips, with the 
anterior (head) end of the body, the mouth end, all point the same 
lesson, 15 which is further confirmed by the absence of any well 
developed sense organs in plants. 16 Exceptions here do indeed prove 
the rule, for sensitive plants, with a well-defined correlating appa- 
ratus, are just those which have departed so far from norm as to 
consume flesh food. And contrariwise, we ourselves are "blind" 
toward the one food that is omnipresent and which we consume by 

" A. J. Lotka, Jour. Washington Acad. ScL, 1915, vol. 5, p. 397. 

14 Compare A. Cournot, Researches into the Mathematical Theory of 
Wealth, English translation by Irving Fisher, 1897, p. 3. 

16 Herbert Spencer, Principles of Biology, vol. 2, p. 166; E. H. Starling, Sci- 
ence, 1909, p. 394; A. J. Lotka, Annalen der Naturphilosophie, 1910, p. 67. 

16 For a resume of "plant psychology," see C. H. Farr, Atlantic Monthly, 
December, 1922; also Sir Frederick Keehle, The Plant Commonwealth and 
Its Mode of Government, Nature, 1924, vol. 144, pp. 13, 55. 



RELATION OF TRANSFORMER TO AVAILABLE SOURCES 355 

an almost unconscious, vegetative process, namely oxygen. If we 
seek an insight into the "psychology of plants/' it may be well to 
begin by imagining what our mental state would be if, in all our food 
quest, we remained as passive and indifferent as in the function of 
breathing. 

The life contest, then is primarily a competition for available 
energy, as has been pointed out by Boltzmann. 17 Energy in this 
sense and for this reason has value for the organism which is a very 
different thing from saying (as some have said or implied) that 
economic value is a form of energy. It is true that different 
kinds of energy are in a certain sense interconvertible into each 
other at fairly definite rates by exchange upon the market, in a 
human population. But the conversion factors here involved are of 
a totally different character from those that enter into the analytical 
expression of the law of conservation of energy. 

This must be immediately apparent from the fact alone that the 
'mechanical equivalents" of the several forms of energy are absolute 
constants, whereas the economic conversion factors are somewhat 
variable, though they have often a species of approximate constancy, 
a fact which calls for explanation. 

Economic Conversion Factors of Energy, A simple example 
may help to clarify the view; the case of the automatic vending 
machine, the penny-in-the-slot chocolate dispenser, for instance. 

The salient facts here are : 

1. A definite amount of money brings in exchange a definite amount 
of commodity (and of energy). 

2. The physical process is a typical case of "trigger action," in 
which the ratio of energy set free to energy applied is subject to no 
restricting general law whatever (e.g., a touch of the finger upon a 
switch may set off tons of dynamite). 

3. In contrast with the case of thermodynamic conversion factors, 
the proportionality factor is here determined by the particular 
mechanism employed. 

Reflection shows that all transformation of money or of economic 
assets of any kind into energy by exchange upon the market is of 

17 Der zweite Hauptsatz der mechanischen Warmetheorie, 1886 (Gerold, 
Vienna), p. 210; Populate Schriften, No. 3, Leipsic, 1905; Nernst, Theoretische 
Chemie, 1913, p. 819; Burns and Paton, Biophysics, 1921, p. 8; H. F. Osborn, 
The Origin and Evolution of Life, 1918, p. XV. 



356 ELEMENTS OP PHYSICAL BIOLOGY 

this character. It is always a case of trigger action. Somewhere 
there is a store of available energy, which can be tapped with an 
expenditure of greater or less effort. The payment of the price sets 
in motion the requisite machinery for the release of that energy (or 
for its transfer of ownership, the release being delayed at the discre- 
tion of the buyer). 

In view of the entire absence of any general law regulating the 
ratio of energy released to energy applied in such cases of trigger 
action, we may ask the question, how does it come about that eco- 
nomic conversion factors, economic ratios-in-exchange of different 
forms of energy, display any regularity whatever? The answer is 
not far to seek. The approximate constancy of the economic con- 
version factors is traceable to the approximate constancy in type 
of the mechanism involved, namely the human organism and its 
social aggregations. Just as one particular slot machine will always 
deliver a certain package of chocolate, so a certain social organization 
under similar conditions will render (approximately) the same 
amount of selected form of energy in return for a stated sum of money. 
As to the circumstances that quantitatively determine these economic 
conversion factors, for a discussion of these the reader must be re- 
ferred to the literature; 18 only this may be remarked here, that the 
conception advanced by Ostwald, 19 for example, that the determining 
feature is the (physical) availability of the particular form of energy, 
is inadequate. 

Collective Effect of Individual Struggle for Energy Capture. Our 
reflections so far have been directed to the selfish efforts of each 
organism and species to divert to itself as much as possible of the 
stream of available energy. But if we recall once more the admoni- 
tion of Bunge Nature must be considered as a whole if she is to be 
understood in detail we shall be led to enquire: What must be the 

18 A. J. Lotka, Proc. Natl. Acad. Sei., 1921, vol. 7, p. 192. 

19 W. Ostwald, Die Energie, 1908, p. 164. Of other literature more or less 
pertinent to the subject the following may be mentioned: G. Helm, Die Lehre 
von der Energie, Leipsic, 1887, pp. 72 et seq. W. Ostwald, Energetische 
Grundlagen der Kulturwissenschaften, Leipsic, 1909, p. 155. Die Philosophic 
der Werte, Leipsic, 1913, pp. 260 ; 314-317, 326, 328; Budde., Energie und Recht, 
Leipsic, 1902, p. 56; Winiarski, Essai sur la M<eanique Sociale, Revue Philo- 
sophique, 1900, vol. 49, p. 113; J. Davidson, Qu. Jour. Economics, August, 1919, 
p. 717. 



RELATION OF TRANSFORMER TO AVAILABLE SOURCES 357 

effect, upon the world-as-a-whole, of the general scrimmage for 
available energy? 

It has already been pointed out that the operation of the correlating 
apparatus is of the nature of a cycle beginning and terminating in the 
external world; that the grazing cow is able to subsist because the 
grass is "hungry for oxygen," that animals are essentially catalysers, 
oiling the machinery, as it were and assisting energy in its downhill 
path to levels of lower availability (higher entropy). If we had only 
the animal kingdom to consider we should in the first instance be 
disposed to conclude that the cosmic effect of the scrimmage for 
available energy would be to increase the total energy flux, the rate of 
degradation of the energy received from the sun. But plants work 
in the opposite direction. And even among animals, greater 
efficiency in utilizing energy, a better husbanding of resources, and 
hence a less rapid drain upon them, must work to the advantage of 
a species talented in that direction. ao There are thus two opposing 
tendencies in operation, and it is difficult to see how any general 
principle can be applied to determine just where the balance will be 
struck. 

The Law of Evolution Adumbrated as a Law of Maximum 
Energy Flux. This at least seems probable, that so long as there is 
an abundant surplus of available energy running "to waste" over the 
sides of the mill wheel, so to speak, so long will a marked advantage be 
gained by any species that may develop talents to utilize this "lost 
portion of the stream." Such a species will therefore, other things 
equal, tend to grow in extent (numbers) and this growth will further 
increase the flux of energy through the system. It is to be observed 
that in this argument the principle of the survival of the fittest yields 
us information beyond that attainable by the reasoning of thermo- 
dynamics. 21 

As to the other aspect of the matter, the problem of economy in 
husbanding resources will not rise to its full importance until the 
available resources are more completely tapped than they are today. 
Every indication is that man will learn to utilize some of the sunlight 
that now goes to waste. The general effect will be to increase the rate 

20 Compare JrJohnstone, The Mechanism of Life, 1921, p. 220. 

21 This fact has been recognized independently by the writer and also by 
H. Guilleminot. For details see A. J. Lotka, Proc. Natl. Acad. Sci., 1922, p. 
153. 



508 ELEMENTS OF PHYSICAL BIOLOGY 

of energy flux through the system of organic nature, with a parallel 
increase in the total mass of the great world transformer, of its rate of 
circulation, or both. 22 

One is tempted to see in this one of those maximum laws which are 
so commonly found to be apt expressions of the course of nature. 23 
But historical recollections here bid us to exercise caution; a prema- 
turely enunciated maximum principle is liable to share the fate of 
Thomsen and Berthelot's chemical "principle of maximum work." 

STATISTICAL MECHANICS OF SYSTEMS OF ORGANISMS 

Let us call to mind once more the picture of the life conflict viewed 
as the interplay of organisms moving over a topographic chart and 
suffering a succession of collisions with each other and with features 
of their environment. 

We might seek to develop, for such a system, a discipline of 
statistical mechanics similar to that which the physicist has developed 
to deal with the kinetic theory of gases and allied problems. 

No attempt will be made here to carry out this project in any degree 
of completeness, or to carry it to such ultimate conclusions as it may 
be competent to furnish. But it may not be out of place to indicate 
at least a few points, in addition to the pertinent matter contained 
in the preceding paragraph, that can be offered as first steps toward 
the development of such a discipline. 

Mean Free Path. In the elementary kinetic theory of gases it 
is shown that the mean free path I of a molecule in a gas is given by 24 

(25) 



Mrs* 



For a more detailed discussion of this point see A. J. Lotka, Proc. Natl. 
Acad. SeL, 1922, p. 147. 

23 Compare J. Larmor, Proc. London Math. Soc., 1883-1884, vol. 15, p. 159; 
Petzoldt, Maxima and Minima und Okonomie. 

2 * See, for example, Winkelmann, Handbuch der Physik, 1906, vol. 3, p. 696. 
This elementary result is based on the simplifying assumption that the velocity 
of all the moving molecules is the same. Taking into account the velocities 

ranging according to the Maxwellian law, it is found that I = < ,, ~" But 

for our purposes it is quite sufficient to accept the simple elementary method 

and its result. 



RELATION OP TRANSFORMER TO AVAILABLE SOURCES 359 

where A r is the number of molecule per unit volume, and s their 
diameter. This, of course, relates to motion in three dimensions. 

We may apply similar methods to the case of two species, Ni 
individuals of Si and A T 2 individuals of S, operating on a square 
mile, say, of ground. If the field of influence of Si is a circular field of 
diameter s it is easily shown that (according to the elementary 
theory) the mean free path for the individuals of Si is, expressed in 
miles, 

Z=- (26) 

Nzs 

Frequency of Collisions and of Capture. If v is the average 
velocity of the individuals of Si, the frequency collision will be, 
approximately at any rate, 

F = vNiN z s (27) 

In general not all collisions, but only a certain fraction c, will result 
in capture. The total captures per unit of time, per square mile, will 
then be 

C = cvNiNts (28) 

It may be noted in passing that the expression thus found represents, 
in certain cases at any rate, the term k Ni N z which appears in 
equation (38) of Chapter VIII, where it was introduced without 
analyzing its precise physical significance. 

Influence of Size of Organism. It is interesting to observe the 
influence of size of the predatory organism on the frequency of 
capture. Suppose, leaving all other factors the same, we halve the 
size of the predatory organisms, so that the new value of Ni, which 
we may designate by a prime, is given by 

Ni' = mi (29) 

If the velocity of the smaller organisms is unchanged, we shall have 
for the new frequency of capture 

F r = 2NiNicvs (30) 



More appropriate, perhaps, is the supposition that the new velocity 
v f is related to the old v in the proportion of the linear dimensions, 

i.e., as W' = -\/2 = 1.26 We should then have 



360 ELEMENTS OF PHYSICAL BIOLOGY 



F ' = 



= 1.6 NiN 2 cvs (32) 

= 1.6 F (33) 

There is then, other things equal, an advantage for predatory species 
in small size. In nature, presumably, there is a tendency to strike 
a compromise between the advantage thus gained, and certain disad- 
vantages, such as relative defencelessness, incurred by decreased 
stature. 

Curves of Pursuit. The coefficient c which occurs in (28) is 
open to further discussion and analysis. A collision is characterized 
by the fact that through its duration the law of motion differs essen- 
tially and discontinuous^ from the law of motion between collisions. 
The coefficient c evidently depends on the law of motion during 
collision. During collision the two individuals follow a course of 
the type known as a curve of pursuit. For a discussion of these 
curves so far as they have been studied, the reader must be referred 
to the pertinent literature. 25 The mathematical theory of problems 
in pursuit and conflict generally has hitherto been developed princi- 
pally, if not exclusively, in connection with warfare. In any effort 
to deal with the more general theory of conflict between biological 
species it may be well to have an eye open to the methods followed 
in the treatment of problems of military and naval tactics. Here, 
however, this mere hint must suffice. 

Random Motion under a Bias. Various problems relating to 
the motion of a point following in part a random course, but at the 
same time controlled by some kind of directing influence, have been 
dealt with by L. Baehelier in his Calcul des Probabilites, 1912, to which 
the reader may be referred. Chapter XX, on Probabilites Cinema- 
tigues, may be found suggestive in connection with the type of motion 
presented by living organisms, a motion that can be regarded as 
containing both a systematically directed and also a random element. 

Use of Models. Another point shall be passed over here with a 
mere suggestion. The mathematical treatment of the statistical 
mechanics of the kind of systems here taken in view may appear to 
threaten formidable difficulties. It is to be hoped that this will not 

25 See, for example, Boole, Differential Equations, fourth edition, p. 251. 



BELATIOX OF TBANSFORMEB TO AVAILABLE SOURCES 361 

altogether prevent its attack, even if at first sweeping simplifications 
must be made in the fundamental assumptions. But the writer 
wishes to draw particular attention to one method that in the past 
has not been used to any considerable extent, and which may be 
found serviceable where ordinary analytical methods become for- 
bidding. The method to which I refer is a special form of the graphic 
method, namely the method of working models. It is well worth 
considering whether interesting light may not be thrown on various 
problems of biological conflict, by the use of models designed to imi- 
tate the biological warfare somewhat after the manner in which the 
war game imitates the armed conflict of nations. 



CHAPTER XXVI 
THE CORRELATING APPARATUS 

Let us now consider the character of the material Nature whose necessary 
results have been made available .... for a final cause. Aristotle, 

In preceding pages we have dealt with the correlating apparatus, 
and its functions, in the gross, without paying more than passing 
attention to the details of its constitution and operation. It is 
desirable now to fill in some of these omitted details; we shall con- 
sider in turn the depictors, elaborators, effectors and adjusters, with 
especial attention to the case of the human species. For it goes 
without saying that a particular interest attaches to the study of the 
correlating apparatus in man, if only because in no other creature 
has it developed such singular excrescences as that which prompts, for 
example, the writing of this book and furnishes the means for the 
accomplishment of the task. Man thus stands out, if not as a 
superior being, at any rate as a highly peculiar creature. One might 
perhaps dispute the propriety of the study so unhesitatingly advo- 
cated by Pope; but one cannot truthfully deny the fundamental 
fact of man's inordinate interest in himself. Moreover, there are 
certain very important phenomena that play a prominent rdle 
in the operation of the correlating apparatus, phenomena for the 
study of which our chief source, indeed our only altogether indis- 
putable source of data, lies in our own self: that group of phe- 
nomena briefly summarized under the term consciousness. In- 
evitably therefore, a study of the correlating apparatus, if carried out 
in any detail,, will center largely about the manifestation of this 
apparatus in the human species. 

In dealing with the several elements of the correlating apparatus 
it will be convenient to depart somewhat from what might appear the 
most natural order. Receptors and effectors, though functionally 
separated at the two extreme ends of the operative cycle, are in cer- 
tain respects rather closely related in practice. Similarly there is in 
certain respects an approach between the elaborators and the ad- 
justers. We shall, accordingly, consider the several elements in 
the order Receptors, Effectors, Elaborators, Adjusters. 

362 



CORRELATING APPARATUS 363 

THE RECEPTORS 

The receptors, as lias already been noted, are one of the two classes 
of organs or faculties concerned with the depiction of the environment 
in the organism (the other class being the elaborators) . A typical 
receptor is the eye, which, in the most literal sense, depicts the 
external world upon the retina. The law of depiction, in this case, 
is given by the principles of geometrical optics, and is most easily 
expressed in terms of two systems or reference frames of coordinates, 
the one fixed with regard to suitably chosen features in the external 
world, the other fixed with regard to the eye that forms the image. 
So, for example, the impression my eye received at noon today was 
determined by the fact that it was located at the N.W. corner of 
Monument Square and was pointed upward at an angle of about 45 
degrees, and turned in the E. S.E. direction. The tip of the Wash- 
ington Monument, whose coordinates in the "external world" 
system are x, y z, say, was thus depicted upon my retina 3 by a point 
with the coordinates x', y' , z'. This appearance in the analytical, 
expression of the depicting process, of two coordinate reference 
frames, or at least something equivalent, is very characteristic and 
should be particularly noted. We shah 1 have occasion to refer to 
this matter again. 

But the picture formed by the eye, typical as it is of the process 
of depiction, is nevertheless essentially incomplete. We know our 
own world picture as something much more expansive, much more 
intimate and profuse in detail. When I view a landscape I have not 
merely in my eye a dead photograph of the rolling hills and placid 
valleys, in their garb of green, and stirring with life. These things 
I see; but at the same time I hear the bells of the grazing herd, and 
all those familiar noises that belong to the tout ensemble of the rustic 
scene; while the fragrance of the sun-scorched woods, or perhaps the 
perfume of flowers, enters to fill out another aspect of the picture. 
So all our receptors or sense organs are, in a larger sense, depicting 
organs, each supplying its special share toward that composite world 
picture into which their several contributions are united and further 

1 Strictly speaking this is an inverted statement of the facts. We are 
directly cognizant of sense impressions x' y' z', as our prime data, and we 
infer, or hypothecate, as secondary data, corresponding coordinates x, y, z, 
of an external world. See Chapter XXXIV, footnote 2. But for our pres- 
ent purpose the more usual ("naive) viewpoint will serve. 



364 ELEMENTS OF PHYSICAL BIOLOGY 

developed by certain special faculties, the Elaborators, notably the 
Memory and Imagination. 

Artificial Receptors, A detailed discussion of the natural 
receptors with which our body is supplied by the physiological 
processes of embryological development and growth is unnecessary 
here, since these things are fully discussed in special works devoted 
to these subjects, such as for example, Ladd and Woodworth's Ele- 
ments of Physiological Psychology (Scribner's, 1915). But a special 
development of the receptors in man, which has had, and is destined 
still to have, an altogether superlative importance in the evolution 
of the world is passed over in total silence in most works of the 
character cited, and calls for discussion here in some proportion to 
the importance of this phase of the subject: the artificial aids and 
adjuncts to our senses which the ingenuity of man has pressed into 
his service. With prophetic eye Robert Hooke in 1665 foresaw no 
doubt very imperfectly what these aids were destined to ac- 
complish for the human race. 

The next care to be taken, in respect to the senses, is a supplying of their 
infirmities with instruments, and, as it were, the adding of artificial organs to 
the natural; this .... has been of late years accomplished with prodi- 
gious benefit to all sorts of useful knowledge It seems not im- 
probable, but that by these helps the subtility of the composition of bodies, 
the structure of their parts, the various texture of their matter, the instru- 
ments and manner of their inward motions, and all the other possible appear- 
ances of things, may come to be more fully discovered 

That the artificial adjuncts to our correlation apparatus are subject 
to a process of evolution by selection, by trial and error, was clearly 
recognized by David Hume, 2 who in this, as in other important points, 
anticipated the conceptions of Darwin and Spencer. The last 
mentioned was the first to realize fully and to point out clearly the 
role of man-made contrivances, as artificial sense organs on the one 
hand, and as artificial members (effectors) on the other. 3 As we 

- Dialogues concerning Natural Religion, 1757, Edition of 1907, pp. 189-190. 
Hume's reflections relate particularly to the artificial effectors (as represented 
by^a ship, for example), but the underlying principle is, of course, the same. 

3 Compare Herbert Spencer, Principle of Psychology, Chapter VII, Section 
164; Emerson, The Conduct of Life, Everyman's Library Edition, pp. 159-190 
(original edition, 1860); Wiener, Die Erweiterung unserer Sinne, Leipzig 1900; 
Lehmann, Die Kinematographie, Leipzig, 1911, p. 1. 



CORRELATING APPARATUS 365 

look back today upon the progress In recent centuries, it is plain 
beyond ail possible misunderstanding that the ushering in of the 
era of the man-made adjuncts to his natural body has given not only 
a new direction to the process of evolution, but has speeded up its prog- 
ress to an extent without the remotest parallel in the history of our 
globe. How long it may have taken man to develop his organ of sight 
by the slow processes of physiological evolution we are quite unable to 
say, but this is certain, that the time is reckoned in many millions of 
years. Contrast with this the following brief historical record: The 
use of spectacles was introduced about 1350. 4 The invention of the 
microscope is credited to the Dutch optician Janssen, 1590. A mod- 
ern microscope is capable of a magnification of several thousand diam- 
eters. (This, however, does not indicate its "separating'' power, which 
in point of fact, is only about 200 times greater than that of the 
naked eye.) Particles too small to be formed into a distinct image 
by the microscope can still be detected by the ultra microscope, 
invented by Zsigmondy in 1903. By the method of X-ray photog- 
raphy developed chiefly by Laue 1912 and Bragg 1915, direct 
optical evidence of the arrangements of atoms in a crystal is ob- 
tained, and the distance between the layers, of the order of 
T,u~o,tfoTr of an inch, is measured. This represents, in effect, a 
million-fold improvement on the separating power of the eye. The 
method of C. T. R. Wilson 5 1912 renders visible to the eye the track 
of an electron, whose diameter is of the order of one ten-million- 
niillionth of an inch. The power of the natural vision is, in such case 
as this, virtually multiplied by two hundred billion. The step from 
the use of a crude pair of spectacles in 1300 to this was taken in the 
space of about six centuries and much of the progress is condensed 
within a space of less than three decades. The evolution of man's 
artincal sense organs has proceeded at a pace so utterly out of scale 
with that of his natural equipment that the aid of diagrammatic 
representation quite forsakes us here. Any attempt to plot such. 
progress as this on a single scale in rectangular coordinates could 

4 Darmstaedter in his Handbueh der Gechichte der Naturwissensehaftem 
states that the Emperor Nero in A.D. 63 employed a cut emerald to view the 
gladiator contests. Roger Bacon in A.D. 1250 recommended the use of lenses 
for persons of weak sight. The chronicle of St. Catherine's Convent at Pisa 
mentions Alessandro de Soina as maker of spectacles. 

s Proc. Roy. Soc. Ser. A., vol. 87 (1912), p. 277. 



306 ELEMENTS OF PHYSICAL BIOLOGY 

merely result in two limbs of a curve, the first essentially coinciding 
with the time axis, the second rising abruptly, at an angle indis- 
tinguishable from a right angle. 8 

The historical sketch thus drawn represents but a diminutive 
fragment of the total development of man's artificial correlating 
apparatus. It is out of the question to cover here in any exhaustive 
manner even the aids to vision alone. We must pass by with a mere 
mention the astronomical telescope, which opens the pupils of our 
eyes one hundred inches wide; 7 or that fantastic application of the 
stereoscope to astronomical objects, which enables us to see the 
universe as it would appear to a gigantic being with his eyes many 
millions of miles apart. As for a general survey of the entire field of 
our artificial sense organs, to give this would amount to nothing less 
than the writing of a work, in several volumes, on general observa- 
tional methodology. For our purpose here these hints must suffice. 

THE EFFECTORS 

The natural effectors, like the natural receptors, have received 
their full share of attention, and it is not proposed to add here to the 
existing literature 8 on this special phase of the subject. As to the 
artificial aids to the effectors, these are plainly evident on every 
hand, and do indeed give a stamp altogether its own to this unpre- 
cedented industrial era in which we live. Gilbert and Pogue in 
their memoir on Power 9 estimate that the use of power derived from 
coal and other extraneous sources (i.e., not from the human body) 
gives to each man, woman and child the service equivalent of 30 
servants. But in point of fact this figure, based merely on the total 
horsepower developed, gives an altogether inadequate picture of the 
real facts. Machinery has not only increased our energy output, 
it has immensely multiplied the speed of production. One extreme 

s Compare also H. Heath Balden, The Evolution of Behavior, Psychol. 
Eev., 1919, p. 247. 

7 Or more than double this, with the aid of Michelson's interference device. 

s The following may here be mentioned: J. Amar, Le Moteur Humain, 1914; 
A. Keith, Engines of the Human Body, 1920; 0. Fisher (Teubner), 1906 
Grundlagen fiir eine Mechanik der lebenden K5rper; C. Bell, Animal Mechan- 
ics, 1838 (Library of Useful Knowledge); W. M. Feldmann, Biomathematics, 
Lippincott 1923: L. L. Burlingame, General Biology, (Jonathan Cape) 1923. 

* Smithsonian Institution Bulletin, 102, Part 5. 



CORRELATING APPARATUS 



367 



example of this is seen in the printing plant. A modern newspaper 
press, with a crew of 6 to 10 men, can turn out 80,000 complete 
16-page papers per hour, all folded, counted and delivered ready for 
the carrier boys. It may be left to the reader to make some kind of 
estimate of the time that would be required to write the same matter 
out in longhand, to say nothing of the folding and counting. 




SOO miles. 



FIG. 70. THE EVOLUTION OF MAN'S MEANS OF TRANSPORTATION 
Distance travelled in one nour by different means of conveyance 

Artificial Effectors; Industrial Evolution. In the develop- 
ment of our artificial effectors, as with the receptors, the progress 
of evolution has been a rocket-like ascent. To take a simple and 
very moderate example, the evolution of means of personal trans- 
portation is exhibited diagrammatically in figure 70, which, is in 



368 



ELEMENTS OP PHYSICAL BIOLOGY 



essence a target of zones of operation of the kind referred to in 
Chapter XXV, The figures on which the diagram, are based, some 
of which may very well have been superseded, are the following: 

TABLE 33 
Distance travelled in one hour by different modes of conveyance 



MEA3T5 OP TBA.XSPO STATION 


MILES 




YEAR 


Man walking. 


8 


G. E. Lamer 


1905 


Man running 


11 


J. Bouin 


1913 


Man on bicvcle 


50 


H. Caldwell 


1903 


Man on motorcycle 


100 


O. Walker 


1915 


Alan on aeroplane. 


200 


About 


1920 











It has already been noted that the evolution of man's artificial 
aids to his effectors, by a process of "survival of the fittest" was recog- 
nized as early as 1757 by David Hume. We can now add, from the 
modern quantitative viewpoint, that this resemblance between the 
development of our inorganic accessories and that of organic popula- 
tions extends also, in a number of instances, to the growth curves. 
So, for example, figure 71 exhibits the curve of growth of American 
Railways (United States). 19 It will be recognized as the typical 
S-shaped Yerhulst-Pearl curve of growth. 

Singular Effects of Industrial Evolution. Aside from its ob- 
vious result of greatly enhancing the effectiveness of the cor- 
relating apparatus, the modern development of its artificial aids has 
had certain other less obvious and in some respects rather singular 
effects. For the artificial portion of our correlating apparatus differs 
in several important respects from our native endowment. My 
microscope does not die with my body, but passes on to my heirs. 
There is thus a certain permanence about many portions at least of 
the artificial apparatus. And for that very reason the development 
of this artificial equipment of human society has a cumulative force 
that is unparalleled in ordinary organic evolution. This cumulative 
effect is most of all marked in the artificial aids to our elaborators. 

"Figures for 1840 Sci. Am. Reference Book, 1914, p. 235; 1850 to 1910; 
World Almanac. 1921, p. 277; figure for 1918, Statistical Abstracts, 1920, p. 814. 
Compare also E. Pearl. The Population Problem, Geogr. Rev., October, 1922 

p. 83S. 



CORRELATING APPARATUS 



369 



The most singular feature of the artificial extension of our natural 
body is that they are shared in common by a number of individuals. 
When the sick man consults the physician, who, we will say, makes 
a microscopic examination, for example, the patient is virtually hiring 
a pair of high-power eyes. When you drop a nickel into the telephone 
box, you are hiring the use of an ear to listen to your friend's voice 
five or ten miles distant. When the workingman accepts a wage 
of forty dollars for his weekly labor, he is in fact paying to his em- 




1830 



10 I9SO 



FIG. 71. GEOWTH OF AMEBICAN RAILWAYS 



plovers an undetermined amount for the privilege of using his 
machines as artificial members to manufacture marketable wares. 11 

The modern development of artificial aids to our organs and 
faculties has exerted tw r o opposing influences. 

On the one hand it has in a most real way bound men together into 
one body: so very real and material is the bond that modern society 
might aptly be described as one huge multiple Siamese Twin. 

On the other hand, since the control over certain portions of this 
common body is unevenly distributed among the separate individ- 

11 In certain, branches of industry (e.g., shoemaking) a rental is actually paid 
by the worker for the use of machines. 



370 ELEMENTS OP PHYSICAL BIOLOGY 

uals, certain of them may be said in a measure to own parts of the 
bodies of others, holding them, in a species of refined slavery; and 
though neither of the two parties concerned may be clearly conscious 
of the fact, it is often resented in a more or less vague way by the one 
less favored. Herein lies one source of much of the social unrest 
that has accompanied the development of modern industrialism. 
The more optimistic among us may entertain a hope that in tune the 
unifying influence of our ever growing common body may outweigh 
the disruptive forces that ever and again manifest themselves too 
plainly for our comfort. That a species of "slavery," that is to say 
of ownership of one person's body by another or by others, should 
prevail, is in the last analysis an absolutely unavoidable situation, 
once we recognize that no sharp lines are drawn to separate the 
individual from his fellow; willy-nilly we must accept the fact. We 
ma}', however, seek to control the distribution of this ownership in 
the way most advantageous to the general welfare. That is the 
pin-pose of our property laws, such as they are and such as they 
will be. 



CHAPTER XXVII 
EXTENSION OF THE SENSUOUS WORLD PICTURE 

. . . bodily eyes 
Were utterly forgotten, and what I saw 
Appeared like something in myself, a dream, 
A prospect of the mind." 

Wordsworth. 

The Elab orators. While the sense organs (receptors) are the 
prime agents in the formation of our world picture, they are not the 
sole agents that contribute. The further elaboration of this picture 
is largely the work of our mental faculties: memory, which stores 
impressions and makes our picture a chronological album or file rather 
than a single snapshot : and imagination, 1 which fills in those features 
of the landscape that are hidden from view by intervening obstacles. 
This process of filling in hidden features may be either arbitrary, as 
in the demonistic interpretation of nature current among savages 
and surviving among us in many superstitions, in the play of the 
child, and in the fancy of the poet; or, the process of filling in may 
be more or less rigorously directed by certain rules which long experi- 
ence has taught us to be productive of a realistic picture, a picture 
which, when comparison with actuality becomes possible, is found to 
be "in accord with facts;" one that may safely be made a basis for 
zwechmassig action. 2 The realistic type of thinking, the kind which 
"works," has perhaps been evolved by a process of survival of the 
fittest from the other kind (termed autistic thinking). 8 The body 
of rules which realistic thinking follows constitutes the science of 
logic. The constructive exercise of the imagination within the limits 
prescribed by logic is what we call the process of reasoning. When 

1 It should be noted in passing that the word imagination itself means 
image-formation or depiction. 

2 It is deserving of emphasis that the function of imagination is not merely 
the conception of mythical creations, but also, and quite particularly, the 
presentation, to the mind, of realities. Hence imagination plays an impor- 
tant role in the exact Sciences. 

3 See F. L. Wells, Mental Adjustments, 1917, p. 46. 

371 



372 ELEMENTS OF PHYSICAL BIOLOGY 

its premises are suitably chosen, for instance, on the basis of sense 
perceptions, the product is a contribution to a realistic world picture. 
The Scientific "World Picture: Coordinate Systems. The last 
refinement in world depiction is the scientific world picture. In 
the exact sciences this assumes the numerical form. So, for example, 
the position of a particular object in space is identified, in the simplest 
case (namely, if the object is sufficiently described as a point) by 
the statement of three numbers, the space coordinates of that point. 
The motion of the point is then described or represented (pictured) 
by a set of equations 



=/.(*) 

where x, y, z are the coordinates of the moving point at instant t, 
this last being also identified by means of a number. 

Now an infinite number of equally appropriate pictures of this 
kind can be given for the motion of the point, for the coordinates 
z, y, z can be chosen in an infinite number of ways. They may be 
rectangular coordinates, or polar coordinates; their reference frames 
may be fixed on the earth, or on the sun, or in any other suitable 
manner. But each choice of a system of coordinates will furnish its 
own particular set of functions /; each picture will in this respect 
differ from every other such picture. Not a little of the success of 
the scientific investigator depends on his judgment in choosing a 
suitable system of coordinates, such as will furnish the simplest 
and most convenient picture, the most convenient functions /. So, 
for example, the motion of the planets is most simply described 
with reference to a frame of coordinates fixed to the sun, and not, 
for example, one fixed to the earth. The discovery of a particularly 
convenient reference frame, though in a sense it adds nothing to 
our knowledge of concrete facts, may nevertheless constitute one of 
the major events in the progress of human knowledge. For, such 
discoveries "'make the Universe anew within the minds of men." 4 

The Ego as a Coordinate Reference Frame. It is a matter 
of very particular interest that the first rudiments of this numerical 
world picture, in terms of coordinates, is to be discerned in one of 

4 W. C. Curtis, Science and Human Affairs, 1922, p. 186. ^' 



EXTENSION OF SENSUOUS WORLD PICTURE 373 

the most fundamental traits of the human mind, one of the most 
elementary, irresistible, na'ive intuitions to which we are all subject, 
namely, the distinction between a self and an external world. If 
we wished to express mathematically the relations between the ap- 
pearance upon the ground glass screen of a photographic camera, 
and the "external world" about the camera moving through that 
world, we should undoubtedly find that the simplest expression 
would be obtained in terms of a reference frame fixedly attached 
to the more solid features of the external world, and a second ref- 
erence frame fixedly attached to the camera. 

So we find it most convenient to express the infinite variety of 
sense perceptions (the totality of our world-picture) and the rela- 
tions between them in terms of a self and an external world. This 
naive intuitional view may be taken to be the rough unanalyzed raw 
material out of which, by a process of attenuation and abstraction, 
the scientific method has finally peeled the kernel of the two systems 
of coordinates the one in which the external world is described, and 
the second, privately owned by the individual as it were, in which 
his world picture is recorded. The self thus appears as something of 
the nature of a (somewhat blurred) reference frame of coordinates, 
or rather, a set of several such frames, for the individual is 
quite accustomed to a multiple entry system of bookkeeping, in 
which the same object is entered both as seen and as felt, for 
example. 5 

The Ego Immaterial. This conception of the self as something 
of the nature of a system of coordinate reference frames will be found 
rather helpful in several connections. So, for example, it instantly 
makes clear why we cannot conceive of the self as something material. 

5 It is no doubt this double entry system that is largely responsible for our 
construct of an external world compounded of what are at bottom nothing more 
than complexes of sensations. As E. B: Holt remarks, "even two reflexes 
acting within one organism bring it about that the organism's behavior is no 
longer describable in terms of the immediate sensory stimulus, but as a func- 
tion of objects and situations in the environment" (The Freudian Wish, 
1916, p. 76). Those complexes of sensations which we refer or ascribe to 
objects are characterized by a greater or less degree of permanence. It is this 
permanence of association of certain sensations that induces us to postulate 
an object as their carrier. Such relative permanence lends a peculiar interest 
to the sensation complex, so that it has truly been said that the aim of science 
is the search for the invariants of Nature (E. W. Brown, Scientific Monthly, 
1921, p. 408). 



374 ELEMENTS OF PHYSICAL BIOLOGY 

When I say that / (the ego) was at Grand Central Station yesterday 
at noon, it is true that from the nature of things a certain object which 
I speak of as my body, i.e., the body of the ego, was there at the 
time stated. But this is merely an implication, it is not a simple 
identification of the ego with the body, otherwise the phrase my 
body would be pointless. Once I become accustomed to think of 
the ego as something of the nature of a coordinate reference frame, 
the matter is perfectly clear. The thing that counts, in the depic- 
tion of the world in me, is the position of my reference frame relative 
to the external world. To say that J was at the station yesterday 
at noon is to say that this reference frame was thus situated. The 
body attached to this reference frame is in that sense my body. 
And clearly, the ego so denned is something immaterial. 

Interpenetration of Egos. Then again, it is a notorious fact 
that the boundaries between the self and the external world cannot 
be clearly drawn. 6 The objective significance of this has already 
been noted, in the discussion of our artificial receptors and effectors, 
which are largely '''shared' 3 by a number of persons. The concep- 
tion of the self indicated above makes it immediately clear that 
any attempt to establish boundaries between the self and the external 
world, or, for the matter of that, between two selves, is not only use- 
less but meaningless. Coordinate reference frames have no boun- 
daries, and freely interpenetrate each other, being merely immaterial 
aids to fix our ideas. So the overlapping of many egos in fields com- 
mon to them, their essential unity with one another and with the 
universe, ceases to appear as a strange thought entertained by 
peculiarly minded people, and becomes an obvious truth. 

6 Compare F. B. Sumner, Scientific Monthly, 1922, vol. 14, p. 233. "The 
organism and the environment interpenetrate one another through and 
through the distinction between them is only a matter of convenience." 
Also C. J. Iveyser, Mathematical Philosophy, "How blind our familiar assump- 
tions make us! Among the animals, man, at least, has long been wont to 
regard himself as a being quite apart from and not as part of the cosmos round 
about him. From this he has detached himself in thought, he has estranged 
and objectified the world, and lost the sense that he is of it. And this age-long 
habit and point of view, which has fashioned his life and controlled his thought, 
lending its characteristic mark and color to his whole philosophy and art and 
learning, is still maintained, partly because of its convenience, no doubt, and 
partly by force of inertia and sheer conservatism, in the very teeth of the 
strongest probabilities of biological science. Probably no other single hy- 
pothesis has less to recommend it, and yet no other so completely dominates 
the human mind." 



orrK 
EXTENSION OP SENSUOUS WORLD PICTUBE 

Where Is Mind? 7 The question which has sometimes been raised, 
as to location of the mind, is also seen in a better light. The thing 
that counts, in the affairs of the individual, is the relative position 
of the several reference frames, his own and that of the ex- 
ternal world. Where the adjusters, even their concrete, ^ material 
apparatus, are located, is inconsequential. We may bo in doubt 
whether the expression "the location of the mind" has any meaning; 
but there can be no doubt that such location is of no practical con- 
sequence. If it can in any sense be said that mind perceives the world 
of physical phenomena, this at least is certain, that it does ^ so 
exclusively through the channels of our sense organs. The mind 
looks into the physical world through the pupils of our eyes as t.ii 
small boy watches the ball game through a knothole in the fence;; 
the position of the knothole determines how much he shall sec or 
the game, and in what perspective. And the mind plays upon 
the physical events in our world as the organist plays upon 
the pipes of a modern organ, from a keyboard whose location in 
immaterial. The question "Where is the mind?" or "Whom in 
the ego?" might, if we rightly understood all the pertinent facts, 
appear as absurd as the tourist's request to be shown the equator 
These terms are merely symbols of reference by the aid of which wo 
describe relations between things. 8 

And quite in accord with this, we see in death not so much ovon 
as the dissolution of a system of coordinates, but merely the IONH of 
their pragmatic significance: 



7 Compare Bertrand Russell, The Analysis of Mind, 1921, pp. 141-MB. 
"The subject appears to be a logical fiction, like mathematical poinfcH and 
instants. It is introduced, not because observation reveals it, but bocauw) it in 
linguistically convenient, and apparently demanded by grammar. Nominal 
entities of this sort may or may not exist, but there is no good ground for 
assuming that they do. 

"If we are to avoid a perfectly gratuitous assumption we must diupcmw 
with the subject as one of the actual ingredients of the world." 

s From this point of view one is scarcely disposed to agree altogether with 
the proposition of Sir C. S. Sherrington in his Providential Address before Urn 
British Association at Hull (1922) : "The how of the mind's oonnnctiou \vilh Itn 
bodily place seems still utterly enigma." Nature, 1922, vol. 110, p. ,'Hil. Fur 
a presentation of a point of view somewhat opposed to the one hero Hot forth, 
the reader may be referred to an article The Group Mind and the Mineral ll'ill 
by J. Laird, in the Moaist, 1923, p. 453. 



376 ELEMENTS OF PHYSICAL BIOLOGY 

And then so slight, so delicate is death 
That there is but the end of a leaf's fall, 
A moment of no consequence at all. 

Mark Swann. 

Fundamental Premises and Implicit Assumptions. It has been 
noted in passing that the practical adequacy (Zweckmassigkeit) of 
the world picture formed by the aid of the elaborators depends on 
the judicious choice of the premises upon which the further elaboration 
is based. This, of course, is a very important condition. In so far 
as the premises are direct data of observation, the condition resolves 
itself into a demand for care and accuracy in taking observation, 
and for judgment in weighing evidence, especially where the data are 
presented in statistical form, with perhaps a considerable margin of 
doubt attached to each individual report. 

But there are other less obvious cases, in which a scrutiny of the 
fundamental assumptions is needful and presents no little cliffi- 
culty. For some of these premises relate, not to observational data 
but to conceptual structures peculiar to the world picture into which 
these data are fitted. Such premises are the fundamental postulates 
and axioms of geometry. By a stroke of genial intuition the founder 
of Euclidian geometry set down among his fundamental premises 
the parallel axiom, which states, in effect, that through a given 
point one and only one straight line can be drawn parallel to a given 
straight line. The true character of this fundamental premise re- 
mained hidden from the understanding of geometricians for many 
centuries. So difficult is it sometimes for us to become clearly aware 
of the nature of fundamental assumptions underlying our reasoning. 
Not till the end of the eighteenth century (Gauss 1792) was it realized 
that the parallel axiom, so far from being a "necessary truth," is essen- 
tially of the nature of an arbitrary assumption, and is only one of 
several alternatives each of which can claim equal legitimacy, each 
of which leads to a separate system of geometry. The Euclidian 
system was, until recently, the one in terms of which the world pic- 
ture of the physicist found most convenient description. But in 
recent years, observations of electrons moving with velocities ap- 
proaching that of light, and a number of other phenomena harmon- 
iously comprehended in Einstein's theory of relatively, have given 
us a new world picture that finds its most convenient representation 
in terms of non-Euclidian geometries. 



EXTENSION OF SENSUOUS WOBLD PICTURE 377 

Difficulty of Shaking off Preconceived Premises. The examination, 

and, where need be, revision of our fundamental premises is a task 
of a wholly different order from that of rearing upon these premises 
a structure of logical argumentation. It is a task that often demands 
the efforts of giant intellects, of men of altogether unusual indepen- 
dence of thought. Most of us are held back by our preconceived, 
intuitive judgments, which, blindly entertained, blind us also against 
the recognition of possible alternatives. "The main reason for 
the painfully slow progress of the human race is to be found in the 
inability of the great mass of people to establish correctly the premises 
of an argument." Nor is it only the great mass of the people, the 
average minds, that suffer from this ineptitude. Of Dr. Johnson, 
MacAuley remarks 

How it chanced that one who reasoned on his premises so ably should assume 
his premises so foolishly is one of the great mysteries of human nature. The 
same inconsistency may be observed in the schoolmen of the middle ages. 
These writers show so much acuteness and force of mind that the modern 
reader is perpetually at a loss to comprehend how such minds came by such 
data. 

As a matter of fact our innate perversity in this matter, our in- 
veterate conservatism in all that concerns some of those "implicit 
and unrecognized assumptions out of which sophistry is bred," 
is not due to negative influences, to sloth of mind, alone. There is 
a strong positive misguiding influence at work also: The wish 
is father to the thought. 10 

The fact is, we are confronted here with a species of aberration 
of our adjusters; an aberration which our race must outgrow if it 
is to come into its full inheritance under the sway of evolution. 
For, as Simpson remarks, "the stabilization of our institutions 
rests ultimately upon our ability to know and to test assumptions, 

8 Elliott, Am. Math. Monthly, 1922, p. 331. 

10 There is, fortunately, a natural corrective for our inclination to allow 
likes and dislikes to influence our reason. This corrective is found in the 
instinct of curiosity, the faculty that impels men to seek the truth, even if it be 
unpalatable. In fact, a certain type of mind seems to take a particular satis- 
faction in digging up such otherwise displeasing revelations; the cynic and 
even the muckraker thus has his useful function. It is probably safe to say, 
too, that curiosity a desire to know life in all its phases, to "experience real- 
ity" is fundamentally the motive that impels some individuals to taste of the 
less savory phases of life. 



378 ELFMENTS OF PHYSICAL BIOLOGY 

and upon a willingness to revise them without partisanship, or bitter- 
ness, or distress." 11 

One direction in which we may be called upon to make such a re- 
vision is our conception of the self or ego } along the lines already 
indicated. The old intuitive conception of the self, which narrows 
it clown and fences it off rigorously from the rest of the world, may 
have to give place to a broader conception. This may require the 
breaking through of inhibitions that obstruct our view and prevent 
us from gaining a full and lively realization of our essential unity with 
the universe; it may involve in some degree a retracing of our steps 
in past evolution; a retrenchment of our overdeveloped self-con- 
sciousness, to make room for a more comprehensive world-conscious- 
ness. 

THE COMMUNICATORS 

Aside from the ordinary receptors and elaborators, there is an- 
other avenue, a highly specialized type of receptors, by which the 
world picture acquires further detail and extension, namely by com- 
munication from, one individual to another. How far the faculty 
of such communication may be developed in species other than our 
own is today an open question; nor is this of much consequence for 
us here, as we are concerned with principles rather than with con- 
crete examples, and a single indubitable instance, such as we have 
in ourselves, suffices for the establishment and exemplification of 
the principle. 

Orthogenesis in Human Evolution. In the human species the 
communication of information from one to another takes place 
chiefly through speech, tradition and carved, written or printed 
records. The incalculable significance of these aids to the indi- 
vidual's elaboration of his world-picture needs no emphasis. In 
a recent number of Nature there appeared Professor Bohr's address 
on the structure of the atom, delivered on the occasion of the award 
to him of the Nobel prize for 1922. In this historical survey of the 
development of his theory he mentions nearly fifty names of inves- 
tigators who directly or indirectly contributed to this part of our 
world-picture. A person intelligently reading this lecture, making 
the picture part of his own mental stock-in-trade, is thus virtually 

11 Simpson, Am. Math. Monthly, 1922, p. 331. 



EXTENSION OP SENSUOUS WORLD PICTURE 379 

endowed with fifty pairs of eyes and hands, and has the benefit of 
the workings of fifty brains, for the most part master brains of the 
first rank, for the list includes such names as, Faraday, Maxwell, 
J. J. Thomson, Rutherford, Hertz, Lorentz, Planck, Einstein, to 
mention only a few. It is this thought-transmitting propensity of 
the human species, more than any other, that gives it a superlative 
lead over all the other creatures of the globe. 12 Man is the only 
animal who in any considerable measure bequeaths to his descendants 
the accumulated wisdom of past generations. Evolution in this 
case proceeds not merely by the slow process of selection, but is 
immensely hastened by the cumulative and continuous growth of 
a body of knowledge exempt from those laws of mortality which set a 
term to the life of the individual. Such evolution by a process not 
directly dependent upon (although subject to) selection is what biolo- 
gists have termed orthogenesis the direct genesis of a trait or species 
by the pursuit of an inherent trend or bias, irrespective of selective 
influences. Such orthogenesis (of the functional, not the physiologi- 
cal kind noted in Chapter XXII) is exhibited not only in the cumu- 
lative effect of tradition and printed records, but even more strik- 
ingly in the basic process itself by which the scientific world picture 
is developed. This development has not been wholly an evolution by 
selection, by survival of the fittest, at least not if we take the word sur- 
vival in its literal sense. On the contrary, this is perhaps the clearest 
example extant of evolution b}" orthogenesis, by the unfolding of an in- 
herent trend independently of any selecting influences. Our Galileos, 
our Newtons, our Thomsons, our Einsteins, have not been singled out 
by a process of lethal selection from among others less fit to survive. 
The process by which viable, pragmatically competent systems of 
thought (or world-depiction) are evolved is quite other than this. 
The Copernican system has survived over the Ptolemaic, not be- 
cause the originators and the supporters of the former were better 
adapted to life under the then existing conditions rather the re- 
verse was true. It is not even a mere principle of economy of thought 
that gave victory to the Copernican system. The decisive factor 

12 The importance of the accumulation of human knowledge through tradi- 
tion, permanent records, and lasting technical installations has been empha- 
sized by A. Korzibski (Manhood of Humanity, Dutton, 1921) to whose central 
thesis the existence of a fundamental hiatus between man and the rest of 
creation I cannot, however, subscribe. 



380 ELEMENTS OF PHYSICAL BIOLOGY 

was that the comparative simplicity of the Copernican system eased 
the further advance of knowledge, which had been very effectively 
checked by the intricacies of the epicycles. It is not so much that 
the human niind has a bias for simplicity -though that may be true 
as that, with its finite limitations, the mind progresses faster and 
farther as soon as a simpler system is substituted in place of a more 
complicated, even when both systems are otherwise competent truly 
to represent facts. 

Orthogenesis does not, of course, suspend selection. Of two 
species, that one will most survive, whose orthogenesis, if any, 
leads it in a favorable direction. Presumably, destructive ortho- 
genesis may occur, as well as constructive. Indeed, it has been sug- 
gested that some of the extinct monster species were thus drawn 
to their doom by an orthogenesis, controlled perhaps by endocrine 
glands, that swelled their dimensions beyond all bounds of propriety. 
What is most significant is that orthogenesis, whether constructive 
or destructive, must accelerate the pace of evolution. No more 
telling demonstration of this could be asked than the prodigious 
advance made by man in recent centuries and decades, advances 
traceable directly to the orthogenetic character of the evolution of 
his mental furniture. The provocative agent in this orthogenesis 
is curiosity, the faculty that anticipates needs, that solves problems 
before they become burning issues; that inspires research in pure 
science, and throws in for good measure practical applications, as 
gifts that are often only too truly gratuitous. And coupled with 
this curiosity, a native impulse that induces men to impart their 
findings to others. 

Meanwhile orthogenesis continues. 13 Man has travelled far, 
from the crude intuitive recognition of the ego and the non-ego, the 
first dim realization of a depiction of one system of coordinates upon 
another; to our latest conception of the part played by coordinate 
reference frames in our intercourse with nature. The most modern 
world-picture, as drawn for us by Einstein and his followers, seems 
to outstrip, for the time being, not only our needs, but our immediate 
opportunities for practical application. But that is the virtue of 
orthogenesis. 

13 For a somewhat detailed presentation of the case of orthogenesis in man 
see the author's article Biassed Evolution in Harper's Magazine, May, 1924. 



CHAPTER XXVIII 
THE ADJUSTORS 

Was wir Willen nennen 1st niehts anderes als die Gesammtheit der teilweise 
bewussten und mit Voraussicht des Erfolges verbundenen Bedingungen einer 

Bewegung In der bewussten Willenshandlung fallen Ursache und 

Zweck Zusammen. E. Mack. 

From the nature of things the adjusters are more recondite, both 
in their material substance and in their operation, than either the 
receptors or the effectors. It has already been remarked that the 
location of the adjusters is inconsequential; partly for this reason, 
and partly because their concrete material apparatus does not need 
to be external (as must be that of the receptors and effectors), we 
have at most a very imperfect consciousness of the location of the 
adjusters. It is chiefly from hearsay that the man in the street 
associates the brain with mental processes. 

It is, then, not greatly surprising, that the functioning of the ad- 
justors should be shrouded in a good deal of mystery, which even 
introspection into our own experience does not by any means dispel. 
If unsatisfied curiosity is the fans et origo of human interest, such 
interest should certainly not be lacking in this phase of our present 
enquiry. 

Mechanistic and Teleological Interpretation of Adjusters. We 
have seen, from the example of a simple toy, that typical and fully 
competent adjusters can very well be provided in and by purely 
mechanical structures. In the toy beetle anticipatory correlation 
between the reaction of the beetle and untoward variations of the 
environment is established as follows: The beetle is progressing 
along the straight line AB, (see fig. 72) . Its law of motion is that 
of uniform progression along this straight line. Suppose a scale of 
centimeters is laid along AB. Successively higher scale divisions 
along A B are reached at successively later intervals. In fact, this 
scale, with the beetle moving along it (at constant velocity, we may 
suppose, to simplify the argument) constitutes a clock. If at the 
time t the driving wheel of the beetle is at the zero mark, scale 

381 



382 ELEMENTS OF PHYSICAL BIOLOGY 

divisions to the left correspond to and represent past instants, and 
those to the right represent future instants. Suppose the antenna 
is 5 divisions long, and that the table edge is at division mark 15. 
If for any reason the adjuster apparatus failed to function, at time 
t = 15 the driving wheel of the beetle would pass the table edge and 
fall over. When the adjuster apparatus is functioning, five time 
units in anticipation of the threatened catastrophe the antenna 
"senses" the danger, and the creature turns aside into the path of 
safety. Note that this anticipatory reaction depends upon the 
correspondence between points forward upon the line of advance, and 
future instants of time. A supposititious future, & future that may be, 
is depicted, instant by instant, by successive points in the line of 
advance of the beetle on the supposition that its law of motion 

i 

I 

J Q J J U ' t ~^ J -_-_j-.^__^ 

I 

,1 

I 

FIG. 72. How THE FUTURE ENTERS INTO THE DETERMINATION OF THE MOTION 

op THE WALKING MECHANICAL BEETLE, THUS IMITATING PURPOSIVE 

ACTION (TELEOLOGY). 

continues unchanged. The behavior of the beetle is determined in 
terms of this depiction of a supposititious future. 1 

1 This conception of a future that may be is found both in A. N. Whitehead, 
Principles of Natural Knowledge, and also in E. Mach's Analyse der Emp- 
findungen (1903, p. 78). The expression seems to raise a question as to just 
what meaning may justly be ascribed to it in a determinate universe. One 
admissible meaning is indicated in the test above: The future that may be 
is that computed by extrapolation according to a law of motion that in fact 
does not hold up to the instant under consideration. Another construction 
that suggests itself is that the future that may be is one compatible with cer- 
tain differential equations, but not necessarily with the integration constants. 
The toy beetle shows very clearly how a future that may be can, seemingly, 
influence the course of events. It is interesting to note that there is another 
circumstance which also is competent to explain the apparent influence of this 
fictitious future upon the present course of events. Mach points out, with 
especial reference to the seemingly miraculous foresight displayed by certain 



THE ADJUSTOES 383 

The depiction in this case is plainly mechanical or geometric. 
We, as living, conscious organisms, in certain circumstances exhibit 
a precisely analogous behavior; our action is determined by a picture 
(psychic in this case) of the future that we seek to avoid or to attain. 2 
"In human purpose the result to be attained is first pictured in 
consciousness, and the thinker then proceeds by a series of acts to 
fulfill his preconceived aim." The law of "preconceiving" Is pre- 
cisely the same in both cases, at any rate in the simple case in which 
the reaction is one of avoidance of an unfavorable condition. An 
image of the future of the system is constructed on the supposition 
that the mechanism or organism does not interfere. This is the future 
that may be. Interference, financed from the fund of free energy, 
then takes place accordingly, thus modifying the course of events 
and determining the future that will be. 

Little doubt enters our mind in construing the course of events in 
these two cases. We are directly conscious of our own volition 
(whatever its precise physical significance may be.) We hesitate 
not at all in describing our action as purposive, as directed to and 
determined by an end, by a final cause. As to the tin beetle, we have 
dissected him and fully understand his mechanism. We would think 
it foolish, with our peep behind the scenes, to impute to him volition 
or purpose; we describe his action as mechanical, as fully determined 
by an efficient cause. 

The Doubtful Cases. But what shall we do when confronted with 
a case that falls into neither of these categories? An amoeba, for 
example? We cannot enter the amoeba in spirit and become parties 
to its conscious experience; we do not even know whether it has any 
such experience. On the other hand its mechanism is not com- 
pletely known to us. To class it among purposive, teleological 
beings so long as we are ignorant of its working, and to be prepared 

instinctive actions, that the life process is essentially periodic in character, 
repeated over and over in successive generations, and that it may not be so 
much the future of individual A that influences its action, as the past of its 
progenitors A', A", . . . who were placed in similar circumstances on 
earlier occasions. "Es ist dann micht eine mogliche Zukunft die wirken 
konnte, sondern eine unzahlige Mai dagewesene Vergangenheit, die gewiss 
gewirkt hat." 

2 H. C. Warren, Journal of Philos. Psych, and Sci. Method, 1916, vol. 13, 
p. 5. 



384 ELEMENTS OF PHYSICAL BIOLOGY 

to reclassify it among "purely mechanical" structures 3 us buun as we 
come to understand its physical operation, seenis hardly a very 
commendable way to marshal our mental stock-in-trade. There is 
here involved something of those mysteries to which reference has 

3 "Die Vitalisten begehen nun den Fehler, die Zielstrebigheit dort zu leug- 
nen, wo ikre Ursache durch physikalische Gesetze erklarbar ist, da sie eben 
diese Zielstrebigkeit als rait den physikalischen Gesetzen nicht zusarnmen- 
hangend betrachten." (C. Doelter, Aus dem Grenzgebiete des Organischen 
und Anorganisehen, 1906, p. 13.) It is a singular fact possessing a certain psy- 
chological interest, that as soon as we understand the modus operandi of a tel- 
eological mechanism we are disposed to reject its interpretation in terms of 
"final causes." Why this preference for the mechanistic view? There is an- 
other closely analogous case. So long as we remain in ignorance of the precise 
working of our nervous system in the phenomenon of memory, we are forced 
to contemplate this faculty as being p ,rhaps wholly psychic in character. To 
quote Bertrand Russell (Analysis of Mind, 1921, p. 92), "I am inclined to . . . . 
hold that past experience only affects present behavior through modifications 
of physiological structure. But the evidence seems so far from conclusive 
that I do not think we ought to reject entirely the possibility that mnemic 
causation may be the ultimate explanation of mneinic phenomena.'' Here 
also we feel that just as soon as a physical basis of memory were made mani- 
fest, we should discard the hypothesis of a purely psychic mneme. A certain 
light is perhaps thrown on this curious psychological bias when we consider 
the matter from the point of view of the equations of motion of a mechanical 
system. We noted in Chapter IV (pp. 47, 48) that conceivably the equations 
representing the course of events might contain a lag or a lead, that is to say, 
the motion at time t might, for example, depend explicitly upon the condition 
of the system at time (t - a) or perhaps at time ( + &), or both. We also 
noted in passing that something of this sort seems actually to be the case in 
systems comprising living organisms, since the reaction of these upon their 
environment is a function of their previous history through the intervention 
of memory, and a function of the future through the intervention of volition. 
But we also noted particularly that the appearance of a lag or lead in the 
equations might be spurious. So for example the rate of incidence of new ma- 
laria cases today may be expressed as a function of the number of persons 
bitten by infected mosquitoes nine days ago (period of incubation). But 
this is merely a short way of describing the state of these persons today ; so that 
the equation could also be written without the lag term. Why do we, in 
mechanical systems, give preference to an equation free from a lag term, when- 
ever such can be framed? The first thought that suggests itself, perhaps, is 
that we do this from a bias for simplicity. But this is probably not the true 
explanation. More likely we make this selection because there is something 
arbitrary about the lag term. It does not give a unique representation of the 
process. The differential equation free from a lag or lead, on the contrary, is 
more free from arbitrary features, and is presumably in some sense unique. 



THE ADJUSTORS 385 

been made. The mystery may be in part of our own making. The 
difficulty in answering a question sometimes arises from the fact 
that the question has been badly put. Certainly no harm can come 
from an effort to make a survey of some of the relevant facts and 
their relations. To such a survey we shall proceed forthwith. Here 
it may be well to summarize briefly three cardinal points in our 
observations so far: 

1. Mechanisms teleological in their operation can be constructed, 
which we would not in any ordinary sense of the word describe as 
conscious. 

2. The active types of teleological mechanisms in nature (animals) 
impress us as being in some sense conscious, though in the case of the 
lower rungs on the scale we feel very doubtful as to just what mean- 
ing to assign to this statement. 

3. In our own selves we feel that consciousness (volition) plays a 
dominant role in the teleological operation of our bodies, and, in 
particular, in the operation of the adjusters. 

Adaptive Adjustment of Tastes. In all that has been said so far 
the individualistic character of tastes has been emphasized. A 
man's likes and dislikes are essentially his own personal affair. 
As Pareto 4 remarks, if a man dislikes spinach, it is useless trying to 
prove to him, as one would demonstrate a proposition in geometry, 
that spinach tastes good. Judgments of this kind are typically not 
of that class in which "universal assent" can be attained, the class 
with which the worker in physical science is mainly concerned. 5 

Now this does not mean, as might perhaps at first sight appear, 
that tastes of different individuals are wholly random collections of 
likes and dislikes, dealt out purely haphazard, like the cards from a 
well shuffled pack. However erratic human desires may appear in 
detail, in the gross they display a species of uniformity, of law, of 
constancy; a fact recognized long ago by Adam Smith, who "con- 
sidered a science of economics possible because of a few outstanding 
traits of man which guaranteed self-preservation, while also promot- 
ing the welfare of society at large." 6 The same constancy in the 

4 Manuel d'Economie Politique, 1909, p. 62. 

5 Compare N. Campbell, The Elements of Physics, J. W. N. Sullivan, 
Aspects of Science, 1923, p. 30. 

6 0. F. Boucke, Am. EC. Review, 1922, p. 599. 



386 ELEMENTS OF PHYSICAL BIOLOGY 

average performance (symptomatic of desires) of men was again noted 
by Quetelet, and more particularly by Herbert Spencer, 7 who was 
presumably the first to recognize the full significance, in the evolution 
of the race, of that "adjustment of feelings to actions" which has 
made "pains .... the correlatives of actions injurious to 
the organism, and pleasures .... the correlatives of actions 
conducive to its welfare." This, as Spencer points out, is the 
inevitable outcome of natural selection, since "there must ever have 
been, other things equal, the most numerous and long-continued 
survivals among those races in which these adjustments of feelings 
to actions were the best, tending ever to bring about perfect adjust- 
ment. 3 ' 

Genuine Utility for Social Service. And what is the "perfect 
adjustment?" A hint of the quantitative method of approach to 
this question has been given in Chapter XXV. The argument there 
set forth suggests something of the nature of an absolute standard 
of value, to which actual standards established in the community 
must approach, however imperfectly. Without attempting any 
quantitative definition, or, indeed, any definition at all, such an 
absolute standard has been directly or implicitly mooted by many. 
Irving Fisher 8 thus speaks of a genuine utility for social service, a 
concept which is evidently intended to be purified from the caprice 
of the individual. The question is, remarks T. N. Carver, 9 "not 
what men are actually like, but what men fit best into the cosmos. 
What are the earmarks of a good man, that is, of a man who adds 
strength to the community or nation? It is not enough if we study 
the variations of human institutions, habits, morals, etc. We want 
to know what institutions, habits and moral systems work well, 
what kind of a nation or social organization fits into the cosmos and 
grows strong under the conditions of the Universe. Similarly, as to 
; individual motives, it is not simply a question as to what motives 

'/_ ' actually govern human behavior, though it is important that we 

f should know that. It is of equal importance that we know what 

motives or combinations of motives work well." Jusfc as man has 

7 Herbert Spencer, Principles of Psychology, section 124; Data of Ethics, 
section 34. 

8 Irving Fisher, Am. Econ. Review, June, 1918, vol. 8. 

9 T. N. Carver, Qu. Jour. Econ., November, 1918, p. 197. 



THE ADJUSTOES 



387 



learned, in the progress of ages, to think logically, to think in accord 
with reality, so he must yet learn to will rightly, that is, in harmony 
with Nature's scheme. We have here a thought that seems funda- 
mental for a natural system of ethics. I will not follow it up further 
at this point, but shall take occasion to return to it in the closing 
chapter. 



CHAPTER XXIX 
CONSCIOUSNESS 

Vous connalssez, n'est-ce pas, cette jolie griserie de I'&me? On ne pense 
pas, on ne reve pas non plus. Tout votre etre vous echappe, s'envole, s'epar- 
pille. On est la mouette qui plonge, la poussiere d'e"cume qui flotte au soleil en- 
tre deux vagues, la fumee blanche de ce paquetbot qui s'eloigne, ce petit corail- 
leur a voile rouge, cette perle d'eau, ce flocon de brume, tout excepte soi meme. 

Alphonse Daudet. 

Intimately involved, both, in the process of world depiction, and in 
the operation of the adjusters, as we know them in ourselves, is the 
phenomenon of conscious-ness. In preceding pages this has been 
taken for granted. But our study would be incomplete indeed if we 
did not give some separate consideration to a phenomenon that is of 
so superlative importance in the shaping of the world's events. 

Consciousness is a natural phenomenon which we know directly 
in ourselves, and whose existence we infer in others from their be- 
havior in view of its greater or less resemblance, in type, to ours. 

Relation of Consciousness to Physical Conditions. What mainly 
interests us here, regarding this phenomenon, is its relation to physi- 
cal processes and structures. 

These relations are presented to us in two aspects, and we may 
accordingly distinguish them as (1) conditional, and (2) operative 
relations; that is to say, first relations between consciousness and the 
physical conditions necessary for its manifestation; and second, 
relations between consciousness and physical events that seem to be 
dependent upon consciousness for their occurrence, in the operation 
of the correlating apparatus. The enquiry into these latter relations 
must cover (a) the function of consciousness in directing the course of 
events, and (5) the origin of conscious mechanism or apparatus which 
so directs that course; the reasons that can be assigned, if any, why 
organic evolution should have seized upon consciousness as a tool to 
secure adaptive (zweckmassig) behavior in the organism. 

CONDITIONAL RELATIONS 

It is frequently pointed out with critical emphasis that mechanistic 
attempts to explain consciousness are philosophically unsound. 

388 



CONSCIOUSNESS 389 

Such, strictures are based upon a misconception of the function of 
science, mechanistic or other. Science does not explain anything, 
consciousness occupies in this respect a position in no wise peculiar. 
Science does not explain electricity, for example. Science is less 
pretentious. All that falls within its mission is to observe phenomena 
and to describe them and the relations between them. It is true that 
in loose parlance such statements are commonly made as: The 
inertia of matter is explained by the electron theory. But all this 
means is that certain relations have been established between the 
properties of an electric charge, and those of amass of gross "matter;" 
that the laws of motion of matter can be comprehended in the laws of 
motion of an electron. If explanation means the making comprehensible 
in this sense, then this is explanation. But who should say that 
the attempt to establish relations between consciousness and other 
phenomena is philosophically unsound? One would be disposed to 
retaliate by questioning the soundness of his philosophy. 

Quite on the contrary, the study of the relations between conscious- 
ness and other phenomena is not only legitimate, but altogether allur- 
ing and full of promise. 

Here, however, a difficulty confronts us at the outset. Strictly 
speaking, the only consciousness I can ever know (unless altogether 
revolutionary developments in our sources of knowledge should 
follow) is my own. This seems to impose most serious restrictions 
upon the investigations. 

A Fundamental Hypothesis Admitted. However, there is general 
assent that, in this study, we shall admit the fundamental hypothesis 
that the consciousness of my fellowmen exists and is sufficiently like 
my own to constitute a proper subject for study as a type phenome- 
non. We even go farther, and quite willingly admit the propriety 
of investigations regarding the consciousness of dogs, cats, apes, mice, 
sparrows, and so forth, as manifested by their behavior. All this is 
well enough, until some one begins to ask impertinent questions. 
Just where we are to stop in hypothecating consciousness? And 
what do you mean by saying that Jones's consciousness is like Smith's? 
or like that of a dog? or of an amoeba? These questions are embar- 
rassing. But so long as we deal with restricted material and restricted 
enquiries regarding the relations between consciousness and other 
phenomena, we find in practice we can ignore these fine points. And 
then certain basic propositions find at least provisional acceptance. 
The first of these we may enunciate as follows: 



390 ELEMENTS OF PHYSICAL BIOLOGY 

Consciousness is Closely Bound Up with Life Processes and 
Structures. The statement hardly requires exemplification. Starve 
a man, and he becomes unconscious. The same may happen after 
a blow on the head, and so on. 

Unfortunately, however, our proposition is not so proof against 
criticism as it appears. For it is admitted that we observe con- 
sciousness only by its manifestations similar to those which we know 
directly in ourselves. The inference that consciousness is absent in 
non-living matter reminds one somewhat of the assumption commonly 
made by ignorant persons that insects or similar voiceless creatures 
feel no pain. Since non-living matter lacks the familiar means of mani- 
festing any consciousness which it might possess, it is evidently not 
permissible to base, upon the absence of such familiar manifestation, 
any conclusion as to the absence of consciousness. We are really 
arguing in a circle: First we agree to postulate consciousness where 
certain manifestations are observed. Then we turn around and say 
that the presense of these manifestations is characteristic of conscious- 
ness, and their absence of its absence. 

The truth is, all we can state with any degree of confidence is that, 
if non-living matter possesses any kind of consciousness, this must be 
of a character so radically different from our own as wholly to trans- 
cend our powers of imagination. This may appear at first sight a 
rather pointless observation. But it must be remembered that the 
statement holds true with almost equal force with regard to living 
matter in the case of such elementary forms as amoeba, for example. 
The importance of such reflections as this is that it draws our atten- 
tion to the significance of forms or modes of consciousness. The gen- 
eral scheme of nature is more readily understood if we contemplate 
the several material objects as gifted with graded modes of conscious- 
ness, than if we suppose them sharply divided into conscious and 
unconscious. It is true that this point of view commits us to 
admit the existence of modes of consciousness utterly inaccessible to 
human experience. But this admission is not as damaging as it may 
appear, for, in a restricted measure at least, we are forced to make it 
in any case as soon as we hypothecate consciousness in a dog or a 
flea, for example. 

Allowing, however, for these finer distinctions, the statement may 
stand that consciousness of the character familiar to us in ourselves, 
or of a character approaching to this, is closely bound up with life 
processes, in the way indicated. 



CONSCIOUSNESS 391 

Consciousness Dependent on Metabolism. The Personal Element. 
This suggests that the continued conscious state of matter requires 
constant excitation by the metabolic processes, somewhat as the con- 
tinued maintenance of a magnetic field in the neighborhood of a 
conductor requires constant excitation by the passage of a current. 
And since metabolism is essentially a state of chemical flux, or chemi- 
cal reaction in progress, one is led to suspect that the conscious state 
may be in some way correlated to that, transitional state through 
which matter must pass on its way from one stable molecular com- 
bination to another 1 a state regarding which our knowledge today is 
extremely fragmentary. Almost the only direct evidence we have of 
matter actually in that state is the observation by Sir J. J. Thomson 
and by F. W. Aston of such molecular debris as CH 3 and the like, by 
a method capable of detecting these fugaceous aggregations of atoms 
even though their life period be only a few millionths of a second. 
Meanwhile it must be borne in mind that in the case of the highly 
complex and bulky molecules characteristic of organic matter, the 
"intermediate" state between two compounds may be something 
more lasting. It is even conceivable that "open" molecules may, in 
this realm of chemistry, be the more stable configuration; the mole- 
cules may perhaps be more or less in a state of oscillation, in a species 
of tautomerism, between two "closed" compounds. This would, 
in a way, harmonize with the continuity of consciousness, as known 
to us, if consciousness be indeed typically associated with the "open" 
state of molecules. On the other hand it may give us at least some 
distant idea of the meaning of consciousness as applied to so-called 
non-living inorganic matter. Such consciousness as may here occur 
would be, it seems, of the nature of flashes of almost infinitesimally 
short duration. If this conception appears fantastic, it must be borne 
in mind that brevity of time is altogether a relative concept; by geo- 
logical standards human life itself is merely a flash of lightning in the 
eternal darkness; and though to most of us the altogether impersonal 
species of consciousness which seems to be here implied must appear 
inconceivable, those who have observantly come through the experi- 
ence of syncope may not find the thought so unreasonable. 

Pendant la syncope, dit un auteur qui a pu e'tudisur sur lui m&rae ce phe"- 
nomene, c'est le n6ant psychique absolu, 1' absence de toute conscience, puis on 

1 Compare Sehonbein, Jl. f . prakt. Chemie, vol. 40, p. 152. 



gg 2 ELEMENTS OF PHYSICAL BIOLOGY 

commence a avoir un sentiment vague, illimite, infini, un sentiment d'exis- 
tence generate sans ancune delimitation, sans la moindre trace de distinction 
entre le moi et le non moi; on est alors une partie organique de la nature ayant 
conscience du fait de son existence, mais n'en ayant aucune du fait de son 
unite organique; on a, en deux mots, une conscience impersonelle. . . . 
On a des sensations stupides, si je puis m'exprimer ainsi, c'est a dire, des 
sensations qui, justement parcequ'elles restent isolees, ne peuvent pas etre 
connues, mais seulement senties. 2 

In an entirely normal state, too, certain persons seem to have 
realized the experience of a species of impersonal consciousness. An 
example of this is to be seen in the quotation from Daudet's Lettres de 
man Moulin that has been placed at the head of this chapter. 3 Thus 
the phenomenon of the ego is neither as fundamental nor as simple 
as it may appear to the naive observer. The occurrence of primitive 
consciousness of a kind, which does not recognize an ego, is not only - 
possible, for ought we know, but should be regarded as decidedly 
probable. It may indeed, be argued with much plausibility (as we 
have already had occasion to note) that the ego is a mere artifice, an 
aid to thought (just as a frame of rectangular coordinates is a mere 
figment, convenient for the purpose of defining the position and con- 
figuration of geometrical structures), but has no objective existence, 
and forms no indispensable element of the more general phenomenon 
of consciousness. 

The separation of "chemical" processes from other physical proc- 
esses is almost certainly merely a matter of convenience. If, then 
we tentatively associate consciousness with certain states of chemical 
strain in molecules, we are forced to contemplate the possible extension 
of out- conception to matter under physical strain generally. Space 
does not permit us to follow up in detail the implications of such a 
point of view. It must suffice to indicate that it leads us to question 

- Herzen, Le cerveau et Pactivite c6re"brale, 1887, p. 236; quoted by Janet, 
L'automatisme psychologique, 1889, p. 43. 

3 A very similar thought is expressed by Theodor Dreiser in Proteus (Amer- 
ican Mercury, 1924, vol. 1, p. 9) : 

"And I am the birds flying in the air over the river, 



The sun, the shade, 
The warmth, the grass, 
And myself 
And not myself 
Dreaming in the grass." 



CONSCIOUSNESS 393 

whether a much frowned upon species of anthropomorphism may not, 
after all, be in some sense legitimate. When we say that a soap bubble, 
for example, tends to contract under surface tension, or perhaps when 
we use even less guarded language and say that it is trying to con- 
tract, our terms are commonly thought reprehensible as being more 
picturesque than scientific. Yet we ought to be prepared for the 
conception that the straining of the bubble to contract may not be 
so fundamentally different a thing from the straining of an amoeba 
to engulf a food particle, or the straining of a Newton to assimilate 
a new conception or to solve a problem in philosophy. The two 
phenomena may be far separated, indeed, upon the scale of evolution, 
yet they may be two rungs upon the same scale. 



CHAPTER XXX 
THE FUNCTION OF CONSCIOUSNESS 

In the last chapter we have considered some of the reflections 
that suggest themselves In connection with the first fundamental 
proposition, namely that consciousness, as we know it in ourselves, 
is closely bound up with life processes and structures. 

A second basic proposition regarding consciousness, which will 
find at least provisional acceptance, is that consciousness, as known 
to ourselves, is of variable content, and that its content is a function 1 
of our past and present bodily states. The form of the functional 
relation 2 is in part known, but only in part. It is, of course, by 
virtue of this functional relation that consciousness plays a part 
in the receptor-adjustor-effector apparatus. 

This leads us to the second aspect of the relation between con- 
sciousness and physical structures and events, namely, the function 
which consciousness fulfills in the organism, and the problem as to 
how it has come about that living organisms have appropriated to 
themselves, in the course of evolution, the property of consciousness, 
or, to be more precise, of that particular type of consciousness 
which is characteristic of them. 

OPERATIVE RELATIONS 

One function of consciousness in the operation of the receptor- 
adjustor-effector apparatus has already been considered, namely 
the part which it plays in elaborating further the crude data for the 
world-picture supplied by the special senses. 

But consciousness plays an equally fundamental role in the 
operation of the adjusters. It is quite evident that no amount of 
cold, intellectual information, pure and simple, can in itself ever 

1 In the mathematical sense. 

2 For a discussion of the metaphysical aspect of this functional relation 
the reader must be referred to the special literature. Attention is particularly 
directed to a paper by L. T. Troland in the Jour. Washington Academy, 1922, 
vol. 12, p. 141. See also H. C. Warren, Jour. Phil. Psych, and Sci. Method' 
pp. 20-21, footnote. ' 

394 



FUNCTION OF CONSCIOUSNESS 395 

determine an action. If I am standing at a street crossing, and my 
senses inform me that, should I start to walk across at this moment, 
I should be killed by a passing car, this information in itself can 
" 4 nave no effect one way or the other upon my action. In addition 
to the cold knowledge, there must be something of the nature of 
motive, which gives me an interest, on the one hand in the act of 
crossing (as for example to reach the restaurant across the street 
and satisfy my hunger), and on the other in avoiding collision with 
with the street car (the anticipatory image in my mind, of the 
suffering which this would cause). 

In the lower organisms motivation appears to us almost wholly 
mechanical and fatalistic. The tropisms of a moth apparently 
draw it toward a light with the same mechanical inevitableness as 
the gears of the toy beetle constrain it to follow the table ,edge. 
The opposite extreme, the highest refinement and complexity in 
motivation, we observe in our own selves. 

In human purpose the result to be attained is first pictured in conscious- 
ness, and the thinker then proceeds by a series of acts to fulfill his preconceived 

aim The typical purposive experience consists in a thought of 

some future occurrence followed by a series of actions -which culminate in the 
very situation which the original idea represented. 3 

But what determines "the result to be attained," which is thus 
pictured in the consciousness? The matter has been well expressed 
by Veblen in a passage which at the same time brings out clearly the 
relation of the purely intellectual functions of consciousness to the 
emotional (motivating) functions: 

The ends of life, the purposes to be achieved, are assigned by man's instinc- 
tive proclivities; but the ways and means of accomplishing those things which 
the instinctive proclivities make worth while are a matter of intelligence. 
Men take thought, but the human spirit, that is to say, 
the racial endowment of instinctive proclivities, decides what they shall take 
thought of, and how, and to what effect. 

3 H. C. Warren, Jour. Phil. Psych, and Scientific Method, 1916, vol. 13, 
p. 5. Compare also F. L. Wells, Mental Adjustments, 1917, p. 11. "The free 
imagination of wished-for things results well for the mind through painting 
in more glowing colors the excellence of what is wished for, and firing the am- 
bition to strive for it more intensely." For a rather different viewpoint see 
B. Russell, Analysis of Mind, 1921, pp. 75-76. 



ELEMENTS OF PHYSICAL BIOLOGY 



Dynamic Psychology; Instinctive Drives to Action. Thus, in 
our analysis of the operation of the correlating apparatus, we are 
led to a consideration of the fundamental instincts that furnish 
the driving power behind the activities of the organism. The study*' 
of these instincts has been organized into a definite branch 
Dynamic Psychology of which we can here note only a few of the 
outstanding features. We are treading upon ground not alto- 
gether cleared, at this date, from controversial entanglements. 

Certain psychologists, notably Freud and his followers, have 
taken the view that the really fundamental drives for action can 
be reduced to a very few, such as hunger, the sex call, and the 
gregarious instinct. 4 From these the less elementary motives are, 
according to this school, derived by a process of "sublimation." 
In contrast with this R. S. Wood worth regards as separate and 
independent sources of action those drives which are operative in v 
the course of creative activities: 

The various creative proclivities which (Freud) refers to the redirected 
energy of the sex instinct as their sole driving force, have in Professor Wood- 
worth's opinion driving forces of their own. Of sublimation he holds that when 
an intellectual interest, say, is made to supplant a sex impulse, the latter is 
not drawn into service, but resisted. 5 

Individual Traits. Instinct of Workmanship and Self-Expres- 
sion. We may well leave it to the psychologists to settle their 

4 McDougall in his Introduction to Social Psychology, lists twelve "simple 
instincts" as follows: 



INSTINCT 


CORRESPOND- 
ING AFFECT 


INSTINCT 


CORRESPOND- 
ING AFFECT 


Flight 


Fear 


Parenthood 


Tenderness 


Pugnacity 


Anger 


Reproduction 


Sex 


Repulsion 


Disgust 


Feeding 


(Appetite) 


Curiosity 


Wonder 


Gregariousness 




Self-assertion 




Acquisition 




Self-abasement 




Construction 













Such lists as this seem rather arbitrary, and in some degree dependent on the 
whim of their author. Compare for example F. W. Taussig, Inventors and 
Money-Makers, 1915, p. 7; Irving Fisher, The Survey, March, 1919, p. 937. 

6 M. F. Washburn reviewing Woodworth's Dynamic Psychology, 1918, in 
Science, 1918, vol. 48, p. 373. 



FUNCTION OF CONSCIOUSNESS 397 

difference of opinion in this field. For our purposes it is 
enough to know that these drives to action are operative, that some 
ends to men are "instinctively worth while." And if we ask: 
What are those ends that are instinctively worth while, we find 
that a mere list of primitive instincts is at most only a very in- 
adequate answer to our question. In their broad fundamental 
instincts men are, indeed, essentially alike. But that adjustment 
of the relative intensity of their several instinctive proclivities, 
which finds its material expression in the behavior-schedule, in 
the coefficients X (Chapter XXV) is capable of infinite variation. 
What is "worth while" is after all a matter of taste, and de gustibus 
non est disputandum "people of radically different temperaments 
cannot come to any understanding by intellectual means/' 6 their 
vain efforts to do so lead only to mutual repugnance, for "differences 
of taste produce greater exasperation than differences on points of 
Science." 7 This divergence of tastes among men, responsible as 
we must no doubt hold it for many bitter feuds between individuals 
and between nations, is not without its useful aspect. In the present 
state of the human race, with its divisions of labor and its specializa- 
tion, there is room for all sorts and conditions of men, and this 
statement applies not only as regards their abilities, but also, and 
perhaps more particularly, as regards the channels into which 
each seeks by preference to divert the stream of his energies, the 
sphere in which he most willingly applies his abilities. Much could 
be said in support of the proposition that differences in temperament, 
rather than differences in intellectual endowment, determine the 
place that each man is fitted to occupy in the social scheme. For, 
as Young has said, "With the talents of an angel, a man may be a 
fool." It is not enough to be able, there must be a strong impulse 
to do. "Not only to know, but according to thy knowledge to do, 
is thy vocation," says Fichte. A study of motivation in exceptional 
men, men of genius, is both instructive and inspiring. The dominat- 

6 Rosa Mayreder, quoted in the The Lancet 1913, p. 1006. Compare also 
William James, On a Certain Blindness in Human Beings. 

7 MacAuley, Critical Essays, p. 501. The contrast has been drawn particu- 
larly between introverts and extroverts "who find it so difficult to understand 
each other, and so easy to despise," Compare also Nature, July 21, 1923, p. 
88: "In actual life the want of rapport between these types is a matter of 
daily observation." 



398 ELEMENTS OF PHYSICAL BIOLOGY 

ing drive in the life of such a man is undoubtedly the imperative 
impulse to translate into outward expression, into concrete reality, 
that inward image which, as Warren very aptly observes, is the 
first essential element in human purposive action. Creative minds 
have borne their own eloquent testimony: 

As the sculptor must dream the statue prisoned in the marble, as the artist 
must dream the picture to come from the brilliant unmeaning of his palette 
. . . . , so he who writes must have a vision of his finished work 8 . . . 

An attribute which may be taken for granted in every artist is passionate 
intensity of vision. Unless vision is passionately intense, the artist will not 
be moved to transmit it, . . . . 9 

Lowell, consulted by a young author as to the royal road to good 
style, advises him that the first requirement is to have something 
that "will not stay unsaid." The same intentness upon outward 
expression of the inner vision speaks in the words of Carlyle: 

A certain inarticulate self-consciousness dwells dimly in us, which only our 
works can render articulate and decisively discernible. Our works are the 
mirror wherein the spirit first sees its natural lineaments. Hence, too, the 
fallacy of that impossible precept, Know thyself; till it can be translated into 
this partially possible one : Know what thou canst work at. 

Blessed is the man who has found his work: let him ask no other blessedness. 
Know thy work, and do it; and work at it like Hercules. 

This imperative impulse to materialize a mental conception is 
by no means the monopoly of the artist. In this bantering style 
Arnold Bennett says of the amateur inventors "They have glimpsed 
perfection; they have the gleam of perfection in their souls." This 
is the goad that drives them on to unrelenting effort: the vision of 
their finished work. 

The race of contrivers and inventors does obey an inborn and irresistible 
impulse. Schemes and experiments begin in childhood and persist as long as 
life and strength hold. It matters not whether a fortune is made or pecuniary 
distress is chronic : there is increasing interest in new dodges, unceasing trial 

of new devices And it would seem that no satisfaction from 

pecuniary success or worldly recognition equals the absorbed interest of trial, 
experiment, novel problems, happy solutions. 10 

8 M. K,. S. Andrews in The Perfect Tribute, 1907, p. 6. 

9 Arnold Bennett. 

10 Taussig, Inventors and Money-Makers, 1915, p. 21 ; see also A. J. Lotka, 
Independent, July 12, 1919, p. 54. 



FUNCTION OF CONSCIOUSNESS 399 

Influence of Special Attitudes. There is undoubtedy a relation 
between the intensity of development of the instinct of work- 
manship and the natural endowment, the talents of the individual. 
The two things do not run altogether parallel, unfortunately, as 
evidenced by the well-known crank type of individual, who has 
something of the enthusiasm of genius, but lacks judgment in 
directing his energies into worth while channels. There are 
too, men lacking the impulse to put to competent use great 
natural gifts that they possess. But the general rule holds that: 
"Special aptitudes clamor for the opportunity of asserting them- 
selves. The tasks which are their fit occasion of self-expression are 
the supreme joy of the man of genius, who will suffer every earthly 
privation rather than brook the thwarting of his talents." 11 

It might be supposed that such exceptional development of the 
instinct of workmanship and self-expression as speaks in the words 
cited can play but a subordinate r61e in a world peopled for the most 
part with "ordinary" individuals. But this is a misconception on 
several counts. How effective may be the inspiration which we can 
all draw from the testimony of our betters is perhaps an open ques- 
tion. But it must be remembered that in the shaping of the world's 
events men of genius play a part proportionate to their greatness. 
It has been remarked that the world's history could be written as a 
series of biographies of great men. The general average of excellence 
in a community is upheld and advanced by the exceptional few, the 
leaders in thought and deed. 

But perhaps our chief interest in the manifestation of the instinct 
of workmanship and self-expression in its superlative measure, as 
we see it in the life and works of men of genius, lies in the fact that, 
after all, these men were human, even as we are; and that the trait 
which in them is developed to this high degree, is shared in some 
measure also by the rest of mankind. Here the instinct may not 
rise to such pitch as to be clearly felt and recognized by the individ- 
ual; he may be only dimly conscious of a vague unsatisfied want 
when he fails to find a normal outlet for it. Psychiatrists and 
economists tell us that the individual thus thwarted is apt to ascribe 
his vague feeling of discomfort to any but the true cause, and that 
social unrest in our present industrial system is due in no small 

11 H. T. Moore, The Sense of Pain and Pleasure. 



400 ELEMENTS OP PHYSICAL BIOLOGY 

measure to the want of an adequate outlet for the instinct of work- 
manship and self-expression. "A human being whose instincts are 
balked becomes tin enemy of society/' for "primitive instincts can 
be guided but not suppressed, If they become pent up the danger 
of unrestrained outbreak is great." 12 And referring to the same 
matter Taussig remarks: 

It Is obvious that the sum of human happiness would be greater if 
. . . , all commonly took direct satisfaction in the activities of earning a 
living. , . , The satisfaction of instinct conduces pro tanto to happiness, 

the balking of it to unhappiness Among those instincts to which 

it seems possible to give wide scope, without danger of satiation or remorse, 
is that of contrivance (workmanship). And yet the modern organization 
of industry smothers it in a great and probably growing proportion of men. 

If it is indeed true that the proportion of men so cramped in their 
creative efforts is growing, we have here a most regrettable condi- 
tion, for the words of Emerson remain true: 

In every variety of human employment .... there are among the 
numbers that do their task perfunctorily, as we say, or just to pass, as badly 
as they dare there are the working men on whom the burden of the busines 
falls those who love the work and love to see it rightly done, who finish their 
task for its own. sake; and the state and the world is happy that has most of such 
finishers. 

The Industrial and the Social Problem. The instinct of work- 
manship thus gives rise to a twofold problem in human affairs. 
On the one hand, considering the modern human community in the 
gross, so far as the development of social conditions are or can be 
brought under intelligent control, it is evidently desirable to provide 
for the healthy satisfaction of this eminently desirable trait of human 
character: "We have here too valuable and creative a tendency to 
allow it to be longer neglected, thwarted and dissipated." 13 

On the other hand each individual, if life is to bring him a good 
share of that satisfaction which it potentially holds for him., must 
order his affairs (so far as circumstance permit) with his eyes open 
to the demand of this instinct of workmanship. Failure to do this 
may rob him of his just heritage; he may find, too late, that he has 
sold his birthright for a mess of pottage, that, in the words of Arnold 

12 Irving Fisher. 

13 Ordway Tead. 



FUNCTION OP CONSCIOUSNESS 401 

Bennett, "his existence is a vast and poisonous regret." But even 
if he is spared this extreme, it holds true in any case that "better 
self-understanding means better self-control, and a wiser ordering 
of one's actions along the normal paths of happiness." 14 

14 F. L. Wells, Mental Adjustments, 1917, p. vii. 



CHAPTER XXXI 
THE ORIGIN OF CONSCIOUSNESS IN LIVING ORGANISMS 

Die eigenartigen Ziige der Organismen sind als provisorische Leitfaden auf- 
zufassen. E. Mack. 

We have had occasion to note that "behavior" very similar, in 
certain characteristics, to that of living organisms can be secured 
in a purely mechanical structure, such as that of the toy beetle. 

This raises the question why nature should have resorted to con- 
sciousness as a means for bringing about those reactions so charac- 
teristic of the Irving organism. The most obvious answer that sug- 
gests itself is that, for some reason beyond our present ken, the 
conscious organism is simpler than any purely mechanical structure 
that could be built to perform even approximately the same divers- 
ity of tasks with the same degree of effectiveness. But certain dif- 
ficulties arise if we accept (as is commonly done) the plausible 
hypothesis that to eveiy state of consciousness there corresponds 
a definite state of the material structure of the conscious organism. 

The Problem of Psycho-physical Parallelism. There is first 
of all the classical problem of psycho-physical parallelism. If the 
events in the physical world are wholly determinate, and if every 
conscious experience is in turn determined point by point by the 
physical substratum of the organism, what can be the utility of 
consciousness? For on this supposition my willing to perform a 
certain act is a mere incidental accompaniment of the physical 
circumstances that inevitably must bring about the object of iny 
act. To quote H. C. Warren: 1 

In denying directive selection to forethought we reduce consciousness to 
the role of an epiphenomenon. If purposive thought is not effective in pro- 
ducing mental or muscular activity, of what value is consciousness in the uni- 
verse? Is it anything more than a spectator of the physical changes which 
constitute real activity and form the basis of history? 

1 Jour. Phil. Psych. andSei. Method, 1916, v. 13, p. 20. 

402 




OEIGIN OF CONSCIOUSNESS IN LIVING OHGANISMS 403 

Professor Warren finds the answer to this question in the "double- 
aspect" theory of consciousness. 2 

, The objection (stated in the preceding paragraph) may hold against the 
traditional parallelistic world-view, but it loses force if we adopt the double- 
aspect standpoint. According to this interpretation our thoughts and pur- 
poses are only our way of experiencing what an independent observer might 
perceive as physiological activity. One set of occurrences is as "real" as 
the other. 

So, for example, my feeling of "hunger," would appear to a suitably 
equipped outside observer as a contraction of my stomach, the pres- 
ence in it of an accumulation of certain digestive fluids; a particular 
disposition of the molecules of certain nerves and certain portions of 
the brain, etc. 

Physical Analogies . Such dual aspect of a phenomenon is known 
to us also outside of the particular case of consciousness. So, for 
example, the magnetic force (intensity) at a certain point is one aspect 
of the same phenomenon which could also be described by a state- 
ment of the position of the molecules of the permanent magnet, say, 
to which the field is due. The "problem" of psycho-physical paral- 
lelism is probably due to an inadequate statement of the case. It is 
probably, in this sense, of the nature of a pseudo-problem. To say 
that a necessary condition for the wilting of these words is the willing 
of the author to write them, and to say that a necessary condition for 
the writing of them is a certain state and configuration of the material 
of his brain, these two statements are probably merely two ways 
of saying the same thing. A state of consciousness can be described 
either in terms of its "contents," or in terms of the disposition of the 
molecules, etc. of the brain, just as a magnetic field might be described 
either in terms of an intensity chart or in terms of the position of a 
number of magnets. 

But, evidently, the double-aspect conception of consciousness helps 
us not at all to recognize, in the intervention of consciousness, any 
plausible reason for simplification of mechanisms to be gained by this 
means. For fruitful suggestions we must look elsewhere, and it is in 

2 For a discussion of this theory, originated independently by a number of 
authors (Fechner, 1863; Clifford, 1878; Bourrat, 1883; Prince, 1885; Strong, 
1903; Heymans, 1905) see Tolman, Jour. Washington Acad. Sci., 1922, vol. 
12, p. 153. 



404 ELEMENTS OF PHYSICAL BIOLOGY 

this difficulty that the theory of consciousness sketched in Chapter 
XXIX gives promise of assistance. For on the one hand the appear- 
ance upon the field of action of molecules in the a opened-up" state 
furnishes a whole range of states of matter that do not play a signifi- 
cant role in the ' operation of ordinary mechanism. With this extra 
material the conscious mechanisms may conceivably accomplish 
what the mechanic, working with matter in its ordinary states, is 
powerless to do without complications of structure altogether prohibi- 
tive. Again, our conception of the physics of conscious matter reveals 
to our view an interplay of forces, to effect purposive adjustment, 
within the molecule; whereas the mechanic, in his constructions, must 
bring contending forces to bear and to produce their resultants through 
separate material members, gross masses. Here, then, may be found 
the opportunity for that economy of parts which is characteristic of 
living, conscious mechanisms. 3 

In some such manner as this it seems possible to account with 
reasonable plausibility at least for the fact that in the evolution of 
the animal type of organism, the type equipped with a correlating 
apparatus, consciousness has been seized upon as an effective means 
to secure adaptive behavior. 

Origin of Consciousness. One question remains as yet unanswered. 
Whence did the organisms derive this consciousness? Where and how 
did consciousness come into being: In a living organism? Then was 
the organism unconscious prior to the event? Or else, did conscious- 
ness arise outside the organism? Then consciousness would not be 
tied inseparably to life. 

The answer to these questions has already been foreshadowed. 
It is not consciousness that has been evolved an elementary flash 
of consciousness may be a native property of matter but a particular 
kind of integrated consciousness, a consciousness spun into a continu- 
ous thread by a faculty of memory, a consciousness embroidered as 
upon a canvas, whose function is to hold in place and in their proper 
relation the components of the picture. This background, this refer- 
ence frame, in the state of development in which we observe it in 
ourselves, is the ego, to whom all experiences are referred. The mate- 
rial organs to which this integrating function is entrusted is the nerv- 
ous system, including the brain. 

3 For a somewhat detailed discussion of this and related phases of the 
subject the author's article The Intervention of Consciousness in Mechanics 
maybe consulted. See Science Progress, 1924, p. 407. 



OEIGIN OF CONSCIOUSNESS IN LIVING ORGANISMS 405 

The nervous system is that bodily system, the special office of which, from 
its earliest appearance onward throughout evolutionary history, has been 
more and more to weld together the body's component parts into one con- 
a -=^solidated mechanism reacting as a unity to the world about it. More than any 
other system it has constructed out of a collection of organs an individual of 
unified act and experience. It represents the acme of integration of the animal 
organism As such it has spelt biological success to its possessor. 4 

4 Sir C. S. Sherrington, Presidential Address at British Association Meeting, 
1922. Nature, 1922, vol. 110, p. 350. Compare also A. G. Tansley, The New 
Psychology, 1916, p. 20, referring to Holt, The Freudian Wish, 1916, pp. 76-94. 
Tansley summarizes Holt's view in the words: "Professor Holt very clearly 
expounds the view that mind is merely the 'integration' of the organism's 
motor responses to stimuli. Professor Holt's position is that 'even two reflexes 
acting within one organism bring it about that the organism's behavior is no 
longer describable in terms of the immediate sensory stimulus, but as a function 
of objects and situations in the environment.' The secret of the connection 
>-, of mind, and brain remains as dark as ever. Professor Holt does, indeed, 
admit that mind is a 'synthetic novelty' 'the advent of specific response 
. . . . is the "birth of awareness and therefore of psychology itself.' But 
even if the integration of 'reflex responses' to become 'specific response' (i.e. 
response to an object or situation rather than to a mere stimulus) is rightly 
described as 'awareness,' and this is by no means self-evident, we are not 
thereby in the least degree helped to understand awareness or cognition in 
terms of anything else. We are still absolutely bound to interpret mind in terms 
of our own mind the only mind of which we have direct knowledge, though we may 
learn much about the conditions of its evolution." 

"The behavior of an organism adapted to its surroundings is related rather 
to the objects and situations of those surroundings than to physical and 
chemical stimuli as such, and this takes place by integration (i.e., the putting 
together to make a new whole) of simple motor responses to form complex 
ones. Thus the specific responses of an organism may be regarded as 'func- 
tions' (in the mathematical sense) of the objects and situations of its environ- 
ment, and the history of the evolution of response to environment, i.e., of 
behavior, and of mind itself, is the history of successive integrations of these 
'functions' to more and more complex purposes." 



ENERGY RELATIONS OF CONSCIOUSNESS 

Die Physik wird in der Biologie viel mehr leisten wenn sie erst noch durch 
die letztere gewachsen sein wird. E. Mach. 

To the naive observer, at any rate, consciousness appears to exert 
a directive action upon the course of events. If we regard the 
physical world as a determinate system, the events in which are com- 
pletely determined by the physical laws to which matter and energy 
are subject, a question thus arises: Where, in such a scheme as this, 
is there any opportunity for the agency of consciousness to bring its 
influence to bear? Several alternative answers to this question seem 
compatible with our limited knowledge. 

First Alternative: Possible Inaccuracy of Laws of Dynamics. 
First, the laws of physics as known to us may be an inaccurate repre- 
sentation of facts. Indeed, we know that they must be thus inac- 
curate, for we are far from having completely solved the problem of the 
Universe. It is therefore possible that something omitted from 
oui' formulation of dynamics and energetics is the origin of our per- 
plexity. That such an eventuality as this cannot be wholly ignored 
is demonstrated, for example, by certain features of the Bohr theoiy 
of the atom. "The quantum, conditions determining the permissible 
Bohr orbits can be explained physically only by attributing to the 
electrons a knowledge of the future." 1 This is a case in which the 
equations of motion contain a term with a lead, not a spurious lead 
that can be eliminated by suitable substitutes, but a real, essential 
lead that must of necessity appear in the equations. Let there be 
no misunderstanding. It is not intended to suggest that there is a 
direct relation between this circumstance and consciousness. The 
example is cited merely to show that the conceptions of classical dy- 
namics are far from exhausting the types of conceptions, in such 
matters, that we must be prepared to contemplate. At the same 
time it is only fair to observe that it seems hardly logical for a 
being composed of electrons to affect great surprise at the fact 

1 C. G. Darwin, Nature, 1923, vol. Ill, p. 771, vol. 112, p. 279. 

406 



ENERGY RELATIONS OF CONSCIOUSNESS 407 

that these electrons display certain properties reminiscent of 
consciousness. 

Second Alternative : Singular Orbits with Indeterminate Motion. 
~But, in point of fact, without going so far afield, we can 
see in the domain of classical dynamics opportunity for the 
entrance of consciousness as a directive agent upon the field of 
physical events. For there are certain cases in which the course of 
these events is not fully determinate in classical dynamics. Every 
case of unstable equilibrium is an instance in point. What do we 
know regarding the future fate of a cone set up and exactly balanced 
on its point? Any infinitesimally small force applied to it at any 
time will decide its fall in one direction or another. The history of 
such a system as this depends on infinitesimals, that is to say, on 
data of an order of magnitude that must escape the observation of 
our senses. To state the matter in more general terms, the orbits of a 
system moving in accordance with the laws of classical dynamics are 
of two kinds. Stable orbits are characterized by the fact that a small 
change in the conditions of the systems will bring about a small 
change in the orbit. Such is the orbit of a ball rolling down an 
inclined plane, after being started at an angle 6 with a velocity v. 
If we slightly change the angle 6 or the velocity v, or both, the orbit 
also will be but slightly changed. 

But there 'are other, unstable orbits, such as that of a bah 1 rolling 
along the ridge of a straight watershed. Such orbits correspond to 
singular integrals, or contain singular points. Here, if the angle of 
the initial velocity deviates ever so little from the orientation of 
the ridge, the ball will proceed along an orbit totally different from 
that following the ridge it will descend into one or other of the 
valleys on the two sides of the ridge. 

Here again, infinitesimal interference will produce finite, and, it 
may be, very fundamental changes in the result. 

This, essentially, is the nature of the conception suggested years 
ago by Clerk Maxwell, 2 and independently, it seems, by J. 
Boussinesq. 3 It is to be noted that such unstable equilibria and 

2 Life of Clerk Maxwell, by Lewis Campbell and William Garnett, 1882, 
p. 434. L. J. Henderson, The Order of Nature, 1917, p. 213; J. W. N. Sullivan, 
Aspects of Science, 1923, p. 156. 

^ 3 Cours de Physique Mathematique ; Conciliation du veritable de'terminisme 
me'ehanique avec 1'existence de la vie, etc. Originally published 1S78, repub- 
lished 1922, Gauthier-Villars, Paris. 



408 ELEMENTS OF PHYSICAL BIOLOGY 

orbits as exemplified by the cone precariously balanced on its point 
and by the ball performing its tight-rope trick along the ridge of a 
watershed are typical of systems disposing of a fund of ''available" 
energy. Such a fund of free energy, in turn, is typical of living*-, 
organisms. To quote again Clerk Maxwell: 

In all such cases there is one common circumstance, the system has a 
quantity of potential energy, which is being transformed into motion, but 
which cannot begin to be so transformed until the system has reached a certain 
configuration, to attain which requires an expenditure of work which in cer- 
tain cases may be infinitesimally small, and in general bears no definite pro- 
portion to the energy developed in consequence thereof Every 

existence above a certain rank has its singular points, the higher the rank, 
the more of them. At these points influences too small to be taken into account 
by a finite being may produce results of the greatest importance. All great 
results produced by human endeavor depend on taking advantage of these 
singular states when they occur. 4 

In the course of this our mortal life we more or less frequently find our- 
selves on a physical or moral watershed, where an imperceptible deviation 
is sufficient to determine into which of two valleys we shall descend. 5 

This conception makes the interference of consciousness (will) 
in physical events an exceptional occurrence: 

It appears that in our own nature there are more singular points' where 
prediction, except from absolutely perfect data, and guided by omniscience of 
contingency, becomes impossible than there are in any lower organization. 
But singular points are by their very nature isolated and form no appreciable 
fraction of the continuous course of our existence. 6 

Third Alternative: Possible Influence of Factors Eliminated 
from Equations of Dynamics. As to the last quotation, perhaps, 
one feels disposed to hesitate in adopting the standpoint suggested 
by the great physicist. For it seems that even the most trivial 
voluntary action involves the interference of consciousness in the 
course of physical events, and of such more or less trivial voluntary 
acts our waking consciousness is filled to the brim. A certain 
interest may therefore attach to an alternative point of view which 
has been developed by the writer elsewhere, and which is based on 
the following consideration: 

4 Clerk Maxwell, loc. cit., p. 443. 
B Clerk Maxwell, loc. cit., p. 441. 
6 Clerk Maxwell, loc. cit., p. 444. 



ENERGY EELATIONS OF CONSCIOUSNESS 409 

A. quantity which does not appear in the working equation de- 
scribing the laws of action of a physical system may nevertheless 
play a significant role in the world's events. So, for example, a 
mathematical theory of wealth, covering at any rate certain aspects 
of economics, can be built up in terms of prices and sales alone, 
without pushing the analysis of fundamentals beyond this point; 
that is to say, without examining the human emotions and motives 
that, presumably, find their numerical expression in prices. On such 
basis as this, for example, Cournot founded his admirable "Re- 
searches into the Mathematical Theory of Wealth." 

But to most of us it will appear quite evident that such a treat- 
ment as this is necessarily a very incomplete presentation of the 
actual events, however exactly it may represent the resultant effects 
observed. For it wholly ignores our desires and purposes, which to 
us appear very real and important constituents of the course of 
nature. 

This example should open our eyes to the possibility, with which 
we must be prepared to reckon, that the equations of dynamics, 
however perfectly they may picture the course of certain physical 
events, may fail entirely to reveal or to give expression to under- 
lying agency that may, in fact, be of fundamental significance. The 
interference of consciousness in mechanics may be very real, and 
yet the course of events may appear fully determined by the laws 
of dynamics. 7 

Energetics of Aimed Collisions. Aimed collisions imply a 
correlation between a present state or event and a future occurrence 
or eventuality (a future that will be or a future that may be). 
Psychologically this correlation is apprehended as purposive fore- 
thought. Physically it implies the disposal of a fund of free energy, 
since the energy for bringing about (or for avoiding) a future en- 
counter cannot itself be derived from that encounter. There is thus 
of necessity a fundamental connection between purposive action and 
the disposal of a fund of free energy. Purposive behavior can and 
does occur only in material structures disposing of such a fund. 

7 For a more detailed presentation of this viewpoint the reader must be 
referred to ths author's article The Intervention of Consciousness in Mechanics, 
Science Progress, January, 1924. 



1"" 



CHAPTER 
REVIEW OP THE CORRELATING APPARATUS 

Man. is the arch machine, of which all these shifts drawn from himself are 

toy models. Emerson. 

Some of the outstanding features of our reflections and observations 
in the chapters immediately preceding are summarized in tables 
34 and 35, which at the same time bring out a number of other 
significant facts. 

Table 34 sets forth systematically the main facts regarding the 
receptors and effectors, as exhibited particularly in the case of man. 
(A few entries shown in parentheses relate to species other than man, 
in cases in which man lacks the feature to be exemplified). 

In this tabulation Depictors or Informants are shown as divided up 
into Receptors, Elaborators, Relators, and Communicators. The 
Receptors are further subdivided into Internal Ceptors, Contact 
Ceptors and Distance Ceptors. These terms hardly require explana- 
tion, especially in view of the other entries on the table, which will 
serve to elucidate them. In every case represented, the name of 
the corresponding faculty, the native or natural organs, and the 
artificial organ or organs are shown. The list of the latter is far from 
exhaustive. 

The imagination, the faculty by the aid of which we hold before our 
mind's eye the material upon which we operate in the process of 
thinking, is shown divided into autistic and realistic imagination. 
The term autistic thinking has been introduced by psychologists 
to denote that type of thought in which the fancy is given free reins, 
unchecked by any demand for correspondence with reality; the thought 
of the savage, the child, the dreamer, the poet. 1 Realistic thinking, 
on the contrary, is constrained by the laws of Logic, which assure a 
due correspondence between the products of cogitation and the 
features of the external world to which they relate. 

1 "Les poetes se consolent, comme les enfants, avec des images." Anatole 
Prance , Le Jardin d'JEpicure. 

410 



EEVIEW OF COEEELATENG APPAEATUS 411 

The item "semi-realistic imagination" calls for special notice. 
It was suggested primarily by the case of the so-called realistic novel. 
Such a novel is realistic as to the types presented, though the specific 
. instances may have no counterpart in reality. Such semi-realistic 
thinking plays an important part in Science. Every physical 
formula is, in a sense, an instance of this type of thinking. When 
I say that the area of a rectangular surface measuring 2 by 4 feet is 
8 square feet, this does not impty that any such rectangle exists 
in reality. It may exist or not, the statement has a certain quality of 
truth independent of the reality of such a rectangle; the statement 
relates to a type rather than to a specific instance. 

The terms "Sense of Time" and "Spatial Sense" are self-explana- 
tory. They are suggested without prejudice as to their metaphysical 
significance. We must accept it as a. fact that we distinguish experience 
as having a definite sequence in time, and that we are able, unaided 
by artificial adjuncts, to gage with very fair accuracy equality of 
time intervals within certain somewhat narrow limits. Similar 
remarks apply to the entry Spatial Sense. Such entries are needed 
to make the table complete. If the reader, on metaphysical or other 
grounds dislikes these terms, others may be substituted at his 
discretion. 

The item Communicators calls for little comment. These are, in a 
sense, receptors and effectors set apart for or employed in a partic- 
ular, and a highly important use. 

Just as the Depictors or Informants throw a picture of the external 
world upon or into the organism, so the Epictors or Transformants 
translate into material reality the plans conceived, the pictures 
formed in the mind. The Brooklyn Bridge, for example, is a material 
representation or picture of the plans that once were in the designer's 
mind. 

These transformants include once again the elaborators, relators 
and communicators, for these fulfill a double function; the trans- 
formants further include the Internal and the External Effectors, 
whose nature and significance is apparent from the table. 

If time had permitted, the writer would much have liked to give 
to this table a quantitative cast by adding columns showing persons 
employed, production, consumption, imports, exports, and capitals 
invested in the arts and industries corresponding to the several items 
shown in the table, adding, in other words, a quantitative descrip- 



412 ELEMEXTS OF PHYSICAL BIOLOGY 

tion of the behavior schedule of human society. The table would 
thus give a coherent, biologically founded, picture of the life activities 
of the Body Politic. The behavior of this body as a whole, no less 
than that of its constituent organisms, is conditioned by its ana- 
tomical constitution and its biological needs. The substitution of 
artificial for natural organs in nowise alters this fact. 

The adjusters could not very conveniently be accommodated in 
the scheme of table 34. They have been separately systematized in 
table 35, 

The adjusters are here shown divided into two groups. The 
Internal Adjusters are those that control the distribution of effort in 
different pursuits in one organism, within the organism, so to speak. 
The External Adjusters, on the other hand, control the distribution 
of effort among the several organisms or groups of organisms com- 
prised in one species. 

Internal Adjusters. The internal adjusters operate through the 
faculty of choice (wish, will, etc.). Such choice may be made without 
any conscious reference to any objective principle, purely according 
to the dictates of instinctive impulse or tastes. No attempt is 
made to enumerate such instincts in any degree of completeness. 
They are shown classified according to the principal beneficiary into 
egoistic and altruistic instincts. The agent is not always conscious 
of the relation of his actions to the beneficiary. Thus, for example, 
the scientific investigator, working under the stress of the instincts 
of curiosity, workmanship, and self-expression, may have little or 
no thought of conferring a benefit on society. Such benefit never- 
theless follows. 

The choice may not be made simply in response to instinctive 
impulse. It may be more or less consciously guided by "principles," 
such as may be given either empirically, on the word of an accepted 
authority, the Church for example; or as worked out systematically 
by the agent himself (philosophy of conduct, ethics). 

These two types of choice may be respectively termed instinctive 
and reflective, or, in analogy with the terms employed with regard 
to thought, the instinctive may also be classed ag autistic, the 
reflective as realistic, since the former seeks no basis outside the 
individual himself, the latter tends to seek an objective basis. The 
discipline of Ethics here appears as a regulator of conduct in close 
analogy to the manner in which logic functions as a regulator of 
thought. 



REVIEW OF CORKELATING APPARATUS 



413 



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414 ELEMENTS OF PHYSICAL BIOLOGY 

This analogy is brought out with the greatest clarity in the follow- 
ing quotations, which should be read in parallel: 

Logic: C. J. Keyser, Mathematical Ethics: Clerk Maxwell 

Philosophy. 1922, p. 136. 

"Logic is the muse of thought, ". . . . an abandonment of 

When I violate it I am erratic; if I wilfulness without extinction of will, 

hate it, I am licentious or dissolute; but rather by means of a great devel- 

if I love it, I am free the highest opment of will, whereby, instead of 

blessing the austere rouse can give." being consciously free and really in 

Compare also the saying of Seneca: subjection to unknown laws, it be- 

"Si tibi vis oinnia subjicere, te subjice comes consciously acting by law, and 

rationi." really free from the interference of 

unknown laws." 

In the development of ethics, as in that of logic, the influence of 
natural selection must be to favor those habits of thought and action 
which are conducive to the welfare of the species. And. just as we 
have reached the point where at least the rudiments of logic are 
unassailably fixed in the healthy adult mind, so we may expect that 
socially sound principles of conduct will in time be more and more 
accepted as inevitable truths, their converse as "unthinkable," at 
least to the naive mind. Indeed, in very appreciable measure this 
is the case even now. Theft, for example, is to the normal person 
utterly unthinkable. The philosophic mind will of course, still, at 
all times, be able to conceive of unethical conduct as a possible 
alternative, just as today the philosopher can, as a sort of tour de 
force, of mental gymnastics, overcome his native faith in an external 
world, and assume temporarily the role of the solipsist. 

External Adjusters. The external adjusters, those that govern 
the distribution of effort among the several individuals of the species, 
present several points of much interest. Their operation is, of 
course, essentially restricted to species living in organized communi- 
ties, such as the bee, the ant, and, quite particularly, man. 

Xature has developed two entirely distinct methods of adjusting 
the distribution of activities among the several members of such a 
social group. The individual may be born into the world or nurtured 
to adolescence with a definitely specialized endowment of anatomical 
equipment and physiological and psychological faculties and predilec- 
tions. So the queen bee is fitted for her very particular part, the 
drone for his, and the working bee for its task. Each is capable only 



BEVIEW OF COKKELATING APPAEATUS 415 

of playing the part assigned, and presumably each is perfectly con- 
tent, wholly innocent of the joys and sorrows characteristic of the 
other's calling. In our own human species this condition is nearly 
approached as regards the special tasks of sex, at least in their 
primary forms. 

The second method adopted by nature is really a very singular, 
and one feels tempted to say, a highly ingenious one. Here the 
individual may have little or no natural disposition to specialize in 
a blind obedience to the call of social expediency. Nature, as it 
were, gives the reins into his hands, and only demands the right to 
impose a tax on all his profits. Smith and Jones get together, 
Smith offers Jones a pound of bread, and Jones accepts it in return 
for six ounces of beef. Each is satisfied. Each has driven a purely 
selfish bargain, without the least thought of the good of the com- 
munity. But the community has already collected its tax the 
exchange, on the whole, is to its benefit. 

Now this method has its advantages and disadvantages. One 
feels an unpleasant suspicion that c if Smith and Jones, instead of 
driving a mutually selfish bargain, instead of working in a measure 
against each other, could be brought to combine their forces in the 
definite purpose of serving the community, the latter would collect, 
not only a residual tax, but a more complete benefit. In the simple 
example of the loaf and the steak this is hardly apparent, but there 
can be little doubt that in human affairs much is lost by internal 
friction, by men pulling this way and that, instead of pulling together. 

The other disadvantage is that this method of division of labor 
frequently must fail to satisfy those working instincts which man still 
possesses, useless as they may appear in the circumstances. Now 
unsatisfied instincts are painful things. 

But this method, in spite of such disadvantages as it may have, has 
established itself very firmly among us. It must possess fundamental 
advantages. And it is not difficult to point out where these enter 
into the scheme of things. The tasks of the beehive, the anthill, 
are comparatively simple and few. Two, three, perhaps four 
sets of instincts serve the required ends. But to quote Veblen, 2 
<f the higher the degree of intelligence and the larger the available 
body of knowledge current in any given community, .... the 

2 T. Veblen, The Instinct of Workmanship, 1914, p. 6. 



416 ELEMENTS OP PHYSICAL BIOLOGY 

more complicated will be the apparatus of expedients and resources 
employed to compass those ends that are instinctively worth while/' 
So, in our own community, the list of different gainful occupations 
takes up over ten closely printed pages of the Statistical Abstracts 
of the United States. A behavior schedule of such complexity as 
this can hardly be taken care of by an assortment of as many in- 
stinctive proclivities. What is happening today is that the instinct 
of workmanship, so far as it plays a part in the working day of 
mankind, is sufficiently broad and plastic to adapt itself, with 
reasonable success, to a variety of tasks. Misfits there are, and some 
degree of heartache in consequence. But perfect adaptation is 
found in no department of life, neither can we expect it here. 



CHAPTER XXXIV 
CONCLUSION RETROSPECT AND PROSPECT 

Esperons dans ces etres inconcevables qui sortiront de 1'homme, comme 
1'homme est sorti de la brute. Anatole France. 

The Life Straggle in the Modern Community, It is not wholly 
from, partiality, nor from self-complacency alone, that we are led to 
view the evolution of man, and especially of modern man, with a 
peculiar interest. An impartial judge, if such could be produced, 
would doubtless concede to the'human species, as it stands today, an 
unique and predominant position in the scheme of Nature. For, 
civilized man has achieved the distinction of practically clearing the 
board of all foes of a stature in any way comparable with his own. 
This has resulted for him in a very special form of the struggle for 
existence. With the conflict against other species relegated to the 
background, man's combat with his own kind has been forced to the 
center of the stage. Increasing population pressure and continued 
success in the control of disease can only add to this effect, which is 
furthermore enhanced, while the struggle is at the same time forced 
into a very particular mold, by the industrial regime which has 
bonded the body politic into one organic whole. Under this regime 
we enter the battle of life en bloc. The activities of any one single 
individual are as a rule wholly incompetent to keep him or anyone else 
alive. The product of a day's work of a stenographer, for example, 
is a pile of papers covered with black marks. Taken out of its setting 
this is an entirely useless product, totally unfit to support the life 
of the producer. And much the same is true of the work of the 
bookkeeper, the draftsman, even the skiEed engineer or chemist. 
The race as a whole, indeed, still contends with external opposing 
forces. But the individual, in a large proportion of cases, is con- 
scious only of competition with his fellows. This competition takes 
the form of an intricate system of bargains to purchase the least 
intolerable form of dependence that the individual can secure, or to 
achieve such approach to independence as may be had. Whoever 
fails entirely in this struggle is Nature's convicted delinquent, the 

417 



4jg ELEMENTS OP PHYSICAL BIOLOGY 

unfit unable to draw to himself the needful share of the necessities 
of life, out of the general fund from which the body politic as a whole 
is supplied. 

A new and characteristic form of the struggle for existence thus 
arises the trend and presumptive outcome of which is for us a matter 
of evident interest. 

Organization of Motive Lags behind Industrial Organization. 
While the human species, as a mechanical going concern, has become 
organized into a social whole, the motivation that keeps it going 
has not undergone the same thoroughgoing organization, but con- 
tinues to be in great measure individualistic in type. Social ends are 
achieved through appeal to individualistic instincts. Our present 
industrial system operates by way of the mutually selfish bargain, in 
which each party to the transaction seeks his own advantage, regard- 
"ass of the gain or loss to society as a whole. The system works toler- 
ably well, beyond reasonable expectation perhaps; at least so it seems 
to those accustomed to the system. The competitive element which 
it introduces is not without salutory action. But, making proper 
allowance for this, one is left to ponder whether there may not, in 
due course, be evolved a superior system, that shall secure the inter- 
ests of the community more directly, and with less loss by internal 
friction in the social machinery. There are certain difficulties in the 
way of achieving this in man by those instinctive methods which 
operate effectively in insect societies, as has already been pointed 
out. Human activities are too multifarious to permit of simple 
adjustment by a stereotyped set of instinctive proclivities that pre- 
destine each infant at birth for his own particular sphere of activity 
through life. Nevertheless, we are not left wholly without en- 
couragement that the future evolution of our race may proceed in a 
direction that shall ultimately ease the conflict between man and 
man, and between man and the world at large. 

Philosophy as a Necessary Part of Scientific Enquiry, We have 
already had occasion to refer to the importance of attaining a clear 
realization of the nature of our fundamental assumptions. The 
scientific investigator has, in the past, not given to this phase, the 
philosophic phase, of human enquiry, the attention which it sooner 
or later must demand as a necessary condition of unimpeded progress. 
For if we define philosophy as the critical examination of the funda- 



CONCLUSION 419 

mental data of experience, 1 it is seen that philosophy is not something 
apart from science, but must form, an integral and essential part of 
every science. No science can be said to have reached the adult 
stage until critical examination of its fundamental concepts has at 
least begun. 

Classification of the Sciences in Relation to Self and External 
World. Of all fundamental assumptions in our thinking there is 
probably none so basic, so all pervading, as that of the division of the 
universe (that is to say, of the totality of experience) into an ego 
and a non-ego, a self and an external world, a knower and the known, 
an observer and a thing observed, a subject and an object, mind and 
matter; all of these pairs of terms are, as commonly employed, more 
or less close synonyms. 

Both unsophisticated thought and scientific thought accepts this 
division as axiomatic, and the physical sciences propose to study the 
external world, while psychology proposes to study mind, or the ego. 

Philosophy does not accept this division as axiomatic, but pro- 
poses, among other things, to inquire into the nature and significance 
of the distinction. The philosopher asks : What is ego, and what is 
non-ego? Where is the line drawn, and how do I come by this 
distinction? Thus philosophy studies the relations between the ego and 
the non-ego? According to the point of view that has been here 

1 This definition contains an implicit assumption, namely, that there are 
fundamental data of experience. This is not necessarily true. It may be that, 
no matter how far the analysis be carried, the data arrived at as the most fun- 
damental can always be resolved by further analysis into others more funda- 
mental. Thus the characteristic feature of philosophic enquiry, which dis- 
tinguishes it from scientific enquiry, is perhaps rather one of direction than 
one of result. "While science builds up from axiomatic data, philosophy works 
from these axiomatic data downward in the opposite direction. This is the 
view proposed by Bertrand Russell in his work Our Knowledge of the External 
World. 

2 This statement evidently holds true quite independently of the reality or 
objective existence of the ego and the non-ego or external world. Disputes as 
to such objective existence seem rather pointless. The fundamental data of 

'"- our experience are sense impressions. When certain relations obtain between 
certain sense impressions, we ascribe the latter to an external object. Thus, 
if I see a cat, and proceed to go through certain movements which I speak of 
as stroking the cat, I may presently have the sensation of soft fur against my 
hand, and a purring noise at my ear. In that case I say that the cat is real. 
Or, going through the same motions, I may feel the impact of my hand against 



420 ELEMENTS OF PHYSICAL BIOLOGY 

presented the ego is not a concrete thing, but is of the nature of a 
system of reference, in relation to which experience is described, 
somewhat as the geographical location of a city is defined in terms of 
longitude and latitude. Just as longitude may be reckoned from the 
meridian of Paris or from that of Greenwich or from any other con- 
venient datum circle, so experience is describable with reference to a 
number of different egos. 

The relation between the ego and the external object is brought 
out with great clarity by Bertrand Russell in his Analysis of Mind 
(1921, p. 100), after this manner: Sets of photographs of the stars 
might be made, first by taking all kinds of views, in different direc- 
tions, from one point in space. The collection thus brought to- 
gether would give the appearance of different stars in a certain place, 
or, as we may say, would be a catalogue of the world of stars as it 
appears from a certain center of perspective. But another collection 
might be made by photographing the same star from all kinds of 
different points in space. TKs collection would give us all the ap- 

a hard surface, etc. In that case I say that the supposed cat is merely the 
image, in a mirror, of a cat. Fundamentally the so-called real cat is merely a 
convenient hypothetical construct, convenient because it greatly simplifies 
language and thought. It would be possible to express in terms of sense 
impressions alone everything that is ordinarily expressed in terms of an 
external world. For that very reason it is quite impossible to prove that 
this external world has a real or objective existence, or, for the matter of 
that, that it has not. That the external world is a hypothetical construct is 
not ordinarily realised, because that construct is formed by an instinctive 
and unconscious process, so far as ordinary experience is concerned. In ex- 
traordinary circumstances, that call for the exercise of intense conscious 
reflection, the hypothetical nature of the construct is immediately apparent, 
as for example in the case of the Bohr atom, or the Einstein space-time 
continuum. But at bottom the real cat is just as hypothetical as the theo- 
retical Bohr atom, although perhaps less subject to revision as to its precise 
description. 

If we continue to employ the terms external world, object, etc., this must not 
be taken to imply that we are oblivious of the hypothetical character of these 
constructs, but only that we resort to the usual expedient, for the sake of 
grammatical simplicity. No harm will result from this use of the conventional 
terminology so long as we bear in mind its character, and do not allow our- 
selves to be drawn into the discussion of pseudo-problems arising out of that 
terminology and not out of the fundamental facts. Thus, for instance, to 
enquire whether mind has an objective existence is a question based on a mis- 
conception, not only of the term mind, but of the general character of all the 
data of our knowledge. 



CONCLUSION 

pearances of a certain star in different places, or, as we may say, 
they would be a catalogue of the different aspects of one object. 3 

The essential difference between the ego and the non-ego is, in 
this sense, merely a difference in the system of filing, so to speak, a 
collection of data. Arranged as a collection of observations from 
one perspective, they are the experiences of an ego. Arranged as a 
collection of aspects of the world from different perspectives, they 
are, in their totality, the appearances of the external world. 

This double system of filing or cataloguing our experiences is 
responsible for certain of the divisions of science. This is indicated 
diagrammatically in the chart table 36, which exhibits, for example, 
the position of the Physical Sciences, in the general scheme of human 
enquiries, as the study of the external world, or of that set of data 
which by common consent we ascribe to an external world; certain 
other data we associate more particularly with the self, whom we 
regard as equipped with a body, and gifted with consciousness. This 
twofold aspect of the self gives rise to a corresponding twofold 
development of the science of living beings. Biology, with its 
branches, studies more particularly the body of the organism, while 
Psychology busies itself with the phenomena of consciousness, as 
such. The relation of consciousness to the prevailing state of the 
body is perhaps to be regarded as par excellence the sphere of study 
of Psychophysics. 

With regard to the present and past the Self is a Knower. With 
regard to the future he is a Witter. That is to say, he has direct 
cognizance of certain past and present events through sensation 
and memory; he has direct cognizance of certain future events through 
his will. 4 In accordance with this twofold aspect of the Self, psychol- 

3 Compare also the ontograms and phanograms of K. Gerhards, Naturwissen- 
schaften, 1922, pp. 423-430, 446-452. 

4 Indirectly, i.e., by inference, he may have other knowledge regarding past, 
present and future. But as to direct knowledge the statement made above 
applies. It is very commonly overlooked that we have knowledge of the 
future through our will. This oversight is partly due to the fact that we sense 
this kind of future in a particular way, unlike our sensing of the past and 
present. It is partly also due to the masking of this kind of knowledge of the 
future through uncertainties surrounding the actual realization of our inten- 
tions. Upon reflection it will be found not unnatural that there should be an 
appearance of fundamental distinction between our knowledge of the past 
through memory, and our knowledge of the future through will. For, if for 



422 ELEMENTS OF PHYSICAL BIOLOGY 

ogy may be regarded as divided into two main branches, dealing 
respectively with the Self as a Knower and with the Self as a Wilier. 
Some of the principal subdivisions of these two main branches are 
indicated on the chart. Thus the first branch comprises first of all 
the study of the avenues by which we enter into possession of knowl- 
edge, i.e., the study of the special senses, including both the natural 
senses, and their artificial auxiliaries; furthermore the general theory 
of knowledge (Episternology, Ei'kenntnisstheorie, Scientific Method- 
ology); and the sciences of thought, both autistic and realistic or 
logical. 

The second major branch is shown as divided into Dynamic 
Psychology or Psychology of Motivation (including, for example, 
the study of instincts); Esthetics and the Theory of Values; and 
Ethics. 

brevity we may be allowed to speak in the customary terms of unsophisticated 
speech, we are, through memory, cognizant of the past state of the external 
world, in so far as there are effects (engrams) in our bodies of those past states; 
whereas, conversely, we are, through will cognizant of the future state of the 
external world, in so far as there are causes in us of those future states. This 
consciousness of causes within us of certain future (external) states, is just 
what we call will. Will is our subjective realization of what to an objective 
observer would appear as (plrreical) causes of the events "willed." Bertrand 
Russell's provisional definition of memory as "that way of knowing about the 
past, which has no analogue in our knowledge of the future," seems, in this light, 
unwarranted (Analysis of Mind, 1923, p. 165). We have here oily one par- 
ticular phase of the double-aspect theory of consciousness that has been noted 
ia^Chapter XXXI. From this point of view the question that is sometimes 
raised, as to whether our sense of willing (free will), our desires, are illusions, 
logical constructs, fictions, or the like (see B. Russell, Analysis of Mind, 1923, 
p. 32) seems pointless. The question whether we strike a man because we are 
angry, or whether as William James has put it, we are angry because we strike 
a man, seems to fall into this category. There are certain conditions in us that 
are tending to bring about, and that presently do bring about, the blow. 
Our own particular way of sensing these conditions is that which we express by 
saying that we entertain the emotion of anger, that we have forethought and 
intent to hit the man. From this "double-aspect" point of view there seems no 
room for any essential conflict between the standpoint taken, for example, 
by fiertrand Russell (Analysis of Mind, pp. 32, 280) that desires like forces are 
fictitious; and, on the other hand, the standpoint taken of the present writer, 
in Science Progress, January, 1924, pp. 417, 418, that forces, like desires, may, 
after all, not be purely fictitious. They may be the subj eetive, i.e., immediate 
or directly sensed aspect of certain states that can also become topics of 
objective, Le., indirect observation. 






a 



53 o o 

CC rC! W 

&q EH H 



3 .9 

>*"i b) CQ 

a o .g 



J 



& o 



a3 rt 

-2 B 



1-8 o 



H 






to 

"S "^ 
'o 03 

"S * 



423 



424 ELEMENTS OF PHYSICAL BIOLOGY 

This chart is not of course put forward as in any sense complete, 
but rather as suggestive of a natural classification, and as setting 
forth certain relations of somewhat fundamental character. 

REACTION OF KNOWLEDGE UPON EMOTIONS 

The feature in this chart that chiefly interests us in our present 
considerations is that division of the topics which arises from the 
twofold aspect of the Self, the Knower and the Wilier. 

Fundamentally the world of knowledge and the world of will, of 
desire, are wholly apart, as we have already had occasion to observe. 
Logic has nothing whatever to do with motives as such, though it 
may, of course, busy -itself with the consequences of motives. Con- 
trariwise, motives are in themselves unrelated to or independent of 
knowledge. The knowledge that if I cross the street at this moment 
I shall be killed or maimed does not in itself determine my action nor 
even my intent; this depends on my emotional bias, whether I am 
bent on suicide, or desirous of maintaining as nearly as possible a 
pleasant existence. 

Nevertheless a connection is established between knowledge and 
will, though the fact that the Knower and the Wilier are united in 
one physical body, so that physical reactions do occur between 
knowing and willing. That the recognition of a truth is attended 
with an emotional affect we well know, not only from our own experi- 
ence, but also from the fervid expression of some of the great pioneers 
of science. So Kepler, upon completion of the evidence establishing 
his third law of planetary motion, exclaims jubilantly: "Nothing 
holds me; I will indulge in my sacred fury." Or we may recall the 
words of Poincare: 

Science puts us in constant relation with something greater than ourselves; 
it presents to us a spectacle always renewed and always more vast. Behind 
what it shows us so grand it makes us divine something still more grand; 
this spectacle is a joy for us, but it is a joy in which we forget ourselves, and 
this is morally healthful. 

Quotations exhibiting this spirit, this connection in men's minds 
between the contemplation of the intellect and the affections of the 
emotional sphere, could be multiplied almost without limit. 

What result may we, then, expect to flow in the emotional sphere, 
from that phenomenal expansion of man's intellectual horizon which 



CONCLUSION 425 

modern science has brought, and the still greater revelations that are 
undoubtdly-yet to come? Men have gained much knowledge, but 
as yet they have scarcely had time to realize what they know, and the 
grandeur of the new truths. It is not enough to know; there must be 
a vivid imagination presenting to the mind's eye for contemplation 
at once the many facets of the glittering gem. When men shall have 
learned not only to know but to appraise the esthetic value of their 
knowledge, when they shall be filled with the glory of it all, surely a 
new era must dawn for the poetic arts. Wordsworth says : 

Poetry is the breath and finer spirit of all knowledge ; it is the impassioned 

expression which is in the countenance of all Science If the time 

should ever corne when what is now called Science .... shall be ready 
to put on, as it were, a form of flesh and blood, the poet will lend his divine 
spirit to aid the transfiguration, and will welcome the Being thus produced 
as a dear and genuine inmate of the household of man. 

It is, presumably, with such thoughts as this, that he writes in 
his Prelude 

. . . . The song would speak 
Of that interminable building reared 
By observation of affinities 
In objects where no brotherhood exists 
To passive minds .... 

And Renan, in L'Avenir de la Science, shows similar sentiment: 

Disons done sans crainte que, si le merveilleux de la fiction a pu jusqu'ici 
sembler necessaire a la poesie, le merveilleux de la nature, quand il sera devoile' 
dans toute sa splendeur, constituera une poesie mille fois plus sublime, une 
poe"sie qui sera la reality meme, qui sera fi, la fois science et poesie. 

We may well ask : If the simple Hebraic myth was competent to 
inspire a Haydn to compose an Oratorio of the Creation, what tone 
poem shall adequately celebrate the new meaning, in the mind of the 
modern astronomer, of the words 

The Heavens declare the Glory of God 

The Wonders of His power proclaims the firmament. 

Thus we are not left wholly without indication as to what may be 
the fundamental trend of the future evolution of our race. That the 
evolution of our intellectual capital is subject to a certain particular 
kind of orthogenesis we have observed in an earlier chapter. The 



426 ELEMENTS OF PHYSICAL BIOLOGY 

esthetic reaction of the new knowledge upon the race should bring 
with it a corresponding quasi-orthogenetic development in the 
sphere of esthetics, and through its mediation, also in the closely 
allied sphere of ethics. "When souls reach a certain clearness of 
perception, they accept a knowledge and motive above selfishness." We 
have noted elsewhere that, physically, no clear line of division can be 
drawn between the body and the environment. Psychologically too, 
we saw that the ego is not something that divides the world into 
separate fields, but is rather of the nature of a standard of reference 
in terms of which we find it most convenient to describe experience. 
But our system of coordinate reference frames, from a good servant, 
has threatened to become a bad master. As Keyser remarks, 
we have "estranged and objectified the world, and lost the sense that 
we are of it." It is as if evolution had overshot the mark, as if the 
race must in some degree retrace its step, and regain something of 
that impersonal consciousness that now seems to be only the occa- 
sional property of a few, who, like Wordsworth, are at times "unable 
to think of external things as having external existence, and who 
commune with all that they see as something not apart from, but 
inherent in their own immaterial nature." 5 Perhaps this transfigura- 
tion cannot be achieved but by the race passing through some great 
purging cataclysm, out of which a remnant may evolve toward a 
higher goal. It is familiar fact in geology that the species which pass 
on the stock to later eras of evolution are commonly not the main 
branches nor the most highly developed members of the evolutionary 
tree. So, also, it may not be the descendants of the now dominant 
divisions of our species that shall carry on the torch to light the new 
era, when "the world shall no longer be beheld as an alien thing, 
beheld by eyes that are not its own." 5 But this uncertainty cannot 
be allowed to deter us in such efforts as we may see fit to make to 
further by our own initiative the progress of the species, according 

_ * Compare E. Maeh, Die Analyse der Empfindungen, 1903, p. 24; "An 
einem lieiteren Sommertage im Freien ersehien mir einmal die Welt sammt 
meinem leh als eine zusammenhangende Masse von Empfindungen, nur im 
Ich starker zusammenMngend." Also Emerson: "... the sense of 
being which in calm hours rises, we know not how, in the soul, is not diverse 
from things, but one with them .... We first share the life by which 
things exist, and afterward see them as appearances in nature, and forget 
that we have shared their cause." 

8 C. J. Keyser, The Human Worth of Rigorous Thinking, 1916, p. 126. 



CONCLUSION 427 

to our best lights. It is not the least of our privileges that there seem 
to have been given into our hands the means whereby we may in a 
measure ourselves influence and control the fate and future of our 
species. It must be admitted that the fraction of the population is 
small that recognizes or cares anything about this great and golden 
opportunity for man to have a significant voice in the shaping of the 
world's destiny. But history has given us cause to be optimistic 
as to the possibilities of achievement by a small minority of perfervid 
men. "A little leaven leaveneth the whole lump." In our own day 
we have seen this principle only too effective in various propaganda 
not of the most desirable type. If men respond thus readily to 
guidance of very doubtful competence, those better qualified have 
at least no prima fade grounds for despairing utterly of establishing 
a body of followers. If enlightened men refuse to exert their influence 
toward the guidance of affairs according to their best knowledge, they 
certainly have no right to complain when they see the crowds follow- 
ing after leaders less hesitant, if also less competent. Even sheep 
have a bellwether. Leadership does not necessarily require in- 
telligence of a high type. To say that the populace does not want 
the highest type of leader is beside the point. The populace does 
not pick its leader; it is the leader that picks the populace. However, 
the writer does not mean to suggest that the man of science, should 
at the present epoch, proffer his services as a leader in spiritual 
affairs. His reluctance to do anything of this kind is wholly to be 
commended. But it would seem that the time is ripe for scientific 
men at least to consider some degree of concerted action, some degree 
of systematic communion among those who continue to feel a proper 
interest in the ethical issue, now that the mythological trappings 
with which this issue is commonly encumbered, 'have been fairly 
effectively relegated to the background in well appointed minds. 
Such concerted action seems needful, not so much for the virtue of 
that strength which is in union, as on account of that weakness which 
is the failing of the isolated individual: 

"Tis meet 

That noble minds keep ever with their likes 
For who so firm that cannot be seduced? 

The writer believes that he is expressing a feeling entertained by 
many, though not perhaps always clearly apprehended, if he states 



428 ELEMENTS OF PHYSICAL BIOLOGY 

that the world is ripe for some sort of concerted effort, a binding 
together in one form or other, of men possessing the scientific outlook 
and method of thought, combined with a sincere interest in the ful- 
filment of the great World Purpose. It is perhaps well to call to 
mind that the face of science is not turned squarely and unhesitatingly 
in this direction. Not only has the World War shown us all too 
clearly that the weapons of science are as keen for internecine warfare 
as for the campaign in the conquest of truth; more than this, there is a 
certain fashionable cynicism abroad which affects a scientific pose. 
There are those who, having hitched their wagon to a hog, fare forth 
proclaiming that the world is nothing but a dung heap; and those who 
advocate a humoring of the elementary man in us as a health measure. 
From the standpoint of mental hygiene, stupidity, too, is a rather 
healthy condition. Yet somehow, even for the sake of our health 
most of us would hardly elect to be stupid that is, if we had any 
choice in the matter. Cynicism has its uses. But in the end no 
one, not even the cynic himself, takes it very seriously. The pessi- 
mist spends his energy in jeremiads while the optimist is covering 
the ground with his forward stride. Let us endorse the stand taken 
by L. Witmer: 7 

What the world needs today is more of the optimism of the progressive and 
a little less of the pathological fear of the standpatter, more faith in creative 
evolution, more hope of reaching yet higher levels of achievement, and more 
of that freedom from prejudice called charity, another name for love the 
productive passion. 

Evolutionary Value of Nurture and Tradition. One form in 
which the demon of pessimism puts forth its head is in an overloud 
emphasis on the futility of the effects of nurture as opposed to the 
elemental force of nature* Without committing ourselves to in- 
defensible extremes in the opposite direction, we may put in a strong 
plea in support of the merits of nurture, merits so plain that their 
very obviousness has made us in some degree blind to them, and has 
thus given a weapon into the hands of the type of pessimist of which 

7 What is Intelligence, Scientific Monthly, 1922, p. 67. 

iQol To a / e ^' Jeimillgs > Hered % and Environment," Sci. Monthly, Sept., 
19.4, p. 225: What has gotten into the popular consciousness as Mendelism 
still presented in the conventional biological gospels-has been grotesquely 
inadequate and misleading; its seeming implications as to the trivial r61e of 
the environment has become null and void." 



CONCLUSION 429 

we speak. Those who so glibly discourse on the futility of efforts to 
improve man's nature, would they be satisfied to spend their lives 
among untutored savages? Would they relish the company of 
unclean slatterns and the vermin-ridden denizen of the slums? 
Would they care to live under the same roof with persons innocent 
of the rudiments of propriety in ministering to the natural needs 
of their bodies? If the benefits of nurture in these lesser occasions 
are so welcome, why make light of them in their relation to the more 
serious affairs of life? Such inconsistency is surely inconsistent also 
with the scientific spirit. In point of fact, tradition, so far from 
being a negligible factor in shaping the world of men, is one of the 
most powerful influences for evil, as for good, known to history. 
The tradition most easily within control is family tradition. In it 
we have a powerful lever competent to stir great masses into motion 
slow, perhaps, but none the less effective. 

Another reflection which is submitted to the attention of those who 
make light of the potency of nurture is this: Suppose we took this 
attitude of laisser faire in the realm, of science. Suppose we said : 
"What is the use of teaching the young generation the accumulated 
wisdom of scientific lore at bottom they will still remain essentially 
savages." Can we picture to ourselves with any degree of satisfac- 
tion the inevitable effect of such a policy upon the advance of science? 
The fact is, there is a fundamental error in this emphasis upon the 
alleged futility of nurture. It is based upon a disregard of the 
organic unity of the social body. It narrowly views the evolution 
of man as that of an individual "contained in his skin." The evolu- 
tion of our race today is something very different from this, as we 
have had ample opportunity to observe in preceding chapters. It 
is man plus his "artificial" aids to his life activities that evolves as 
one unit. These artificial aids most assuredly include traditions of 
all sorts, whether handed down by word of mouth, deposited in the 
archives of learned societies, or perpetuated in any other way. And 
there is no reason that can claim even a show of validity why we 
should attempt to draw a line of division, and say: "Here, in the 
province of science, industry and so forth, tradition is one of the 
processes essentially forming part of the evolution of man; but here, 
in ethics, tradition merely lends him a superficial veneer at bottom 
he remains a savage." Our varied institutions of industry, com- 
merce, law, etc., are no doubt subject to change and even to occa- 



430 ELEMENTS OF PHYSICAL BIOLOGY 

sional upheaval. Yet they have a considerable degree of stability, 
quite comparable with that of the somatic substance of our race; it 
also is neither unalterable nor wholly immune from danger of extinc- 
tion in some world-wide cataclysm. 

We have every reason, then, not only to anticipate, but to en- 
courage a development of man's emotional and ethical being along- 
side with and in the light of the advances made in the intellectual 
sphere. And indications are not lacking that in the emotional sphere, 
as in the intellectual, an orthogenetic bias is ready to anticipate 
selective evolution. The trend of selection in the realm of emotions, 
of instinctive proclivities, of tastes we have already ''noted: it follows 
Spencer's hedonistic principle, according to which those races are 
best adapted for survival, in whom adjustment of agreeable 
feelings to beneficial action is most perfect. And the principle 
admits of extension. Not only is it advantageous that we should 
desire those things that profit us and our species, but it is evidently 
equally essential that we should not set our hearts upon things 
impossible of attainment. The man who is forever crying for the 
moon is not well adapted for existence in this practical world. Thus 
the things we purpose, we who have stood the test of survival, must, 
on the whole, or at least in reasonable net balance, be things that 
corne to pass. Evidently the statement can be turned about: the 
things that come to pass are, in many instances at any rate, things 
we purpose; what is more important, they are the general type of 
things that we purpose. They have, accordingly, to us a character- 
istic appearance of purposefulness. And the human mind, con- 
templating the spectacle of the world's events, is impressed with this 
appearance of purposefulness, and finds itself constrained, by an 
inborn bias, by an instinctive intuition, to construe this appear- 
ance as the outcome of design. 

The fact seems to be that the operation of a fundamental purpose 
or design in Nature is one of those things that can neither be proved 
nor disproved. We are, therefore, at liberty, if we so choose to, 
believe in such a purpose. This is an occasion for the legitimate 
exercise of faith. 

We may, if we will, embrace this purpose for our own. Such will 
spells ultimate survival. No better guarantee for the welfare of the 
race could be furnished, than its essential harmony with Nature. 
Selection, then, would seem to point the way toward a will in con- 



CONCLUSION 



431 



formity with, that general principle which, for want of a better term, 
we may describe as the Supreme Purpose of the Universe. 

But selection alone does not determine the path of evolution. Just 
as the purchaser in a store is dependent upon the bias of the store- 
keeper who lays in a stock of assorted goods, so evolution must humor 
any bias there may be in the variety of types presented for selection. 
Are men's wills changing? Is there a drift in the general average? 
If so, whither does it tend? Toward a merging with the Supreme 
Purpose, or away from it? Have we any instrument competent to 
discover as much as a hint of an answer to these questions? 

Perhaps we have. It is true that the recent world cataclysm has 
reminded us all too clearly of the potency of knowledge to destroy; 
of the danger that our orthogenesis be of the fatal type; that man,, 
having grown too clever, may perish by the very perfection of his own 
weapons. But if the proverbial cat has nine lives, the human race 
at present has some seventeen hundred million, and the presumption 
is that even the most disastrous conflict would leave some remnant 
to carry on. Meanwhile there are not lacking signs on which the 
optimist may hang his hopes of a happier issue of our orthogenesis. 
He will point out that since our evolution has been upward in the- 
past, it is reasonable to expect it to continue so in the future. He will 
point to the rude ancestors, more beast than man, from whom we have 
ascended. Then, he will say, if you wish to form a conception of tha 
future of our race, consider the foremost, the most enlightened spirits 
of today, and reflect that these will represent the average of a clay 
that is coming. These men, looking out upon the world, are im- 
pressed above all with the essential unity of Nature, and of man with 
her. For "man is part of Nature, the part that studies the whole." 
Therefore, as man's eyes are opened by modern science to view the 
intricacies of atomic architecture, or to fathom the secret places of 
the stars, what is it but the Universe awakening, like some great 
giant, to a consciousness of his remoter members? 9 To the cold 
intellectual realization of this unity of man with the Universe there 
is an emotional counterpart. A full and intensely vivid realization 

9 This -was sensed by Hegel, who held that "the course of history is the proc- 
ess, not simply by which man comes to a consciousness of God, but that by 
which God comes to a consciousness of himself." (A. K. Rogers, A Student's 
History of Philosophy, 1921, p. 448). Compare also H. G. Wells, God the 
Invisible King; and M. Lembat, Science Progress, 1923, p. 112. 



432 ELEMENTS OF PHYSICAL BIOLOGY 

of the Inspiring truth is undoubtedly accompanied by feeling of 
high exaltation. To this we have, among many others, the testi- 
mony of Wordsworth 

I felt the sentiment of Being spread 

O'er all that moves and all that seemeth still; 

O'er all that, lost beyond the reach of thought 

And human knowledge; to the human eye 

Invisible, yet liveth to the heart. 

. . . . Wonder not 

If high, the transport, great the joy I felt 

Communing of this sort through earth and heaven 

With every sort of creature. 

It seems inevitable that a lively sense of this merging of the Self with 
the Universe shall hold as one of its constituents a fusion of personal 
desires with the Supreme Purpose of the Universe. "No man," 
says Emerson "has a right perception of a truth, who has not been 
reacted on by it, so as to be ready to be its martyr." 

The relation of knowledge and of ignorance to will is discussed, 
from a somewhat different angle, by Bertrand Russell in his book 
Our Knowledge of the External World (1914, p. 234). He remarks: 

The apparent indeterminateness of the future .... is merely a 
result of our ignorance. It is plain that no desirable kind of free will can be 

dependent simply upon ignorance Let us therefore imagine a set 

of beings who know the whole future with absolute certainty, and let us ask 
ourselves whether they could have anything that we should call free will. 
. . . . The beings we are imagining would easily come to know the causal 
connections of volitions and therefore their volitions would be better calculated 
to satisfy their desires than ours are. 

If the extension of Spencer's hedonistic principle, as sketched 
above, applies, and if through orthogenetic bias or otherwise the 
human race shall provide the requisite material for selection to 
operate upon, then these beings which Bertrand Russell "imagines" 
for the sake of his argument, will become something of an actuality 
as our evolution culminates. To them the words of Emerson will 
appry, that they will be "made of the same stuff of which events are 

made The mind that is parallel with the laws of nature 

will be in the current of events, and strong with their strength." 
Their attitude will be biologically sound, for, as Claude Bernard has 
said: 



CONCLUSION 433 

It is not by struggling against cosmic conditions that the organism develops 
and maintains its place ; on the contrary, it is by an adaptation to, and agree- 
ment with, these conditions. So, the living being does not form an exception 
to the great natural harmony which makes things adapt themselves to one 
another: it breaks no concord; it is neither in contradiction to nor struggling 
against general cosmic forces ; far from that, it forms a member of the universal 
concert of things, and the life of the animal, for example, is only a fragment of 
the total life of the universe. 

Or, to quote a spokesman of our own generation, the closing words 
of Sir Charles Sherrington's Presidential Address still ring in our 
ears : 

One privilege open to the human intellect is to attempt to comprehend 
.... the how of the living creature as a whole. In the biological synthesis 
of the individual this problem is concerned with mind. It includes examina- 
tion of man himself as acting under a biological trend and process which is 
combining individuals into a multi-individual organization, a social organism 
surely new to the world. Man, viewing this great supra-individual process, 
can shape his course conformably with it even as an individual, feeling that 
. . . . to rebel would be to sink lower rather to continue his own evolu- 
tion upward. 

Thus, in the light of modern knowledge, man is beginning to discern 
more clearly what wise men of all ages have intuitively felt his essen- 
tial unity with the Universe; and the unity of his puny efforts with the 
great trend of all Nature. A race with desires all opposed to Nature 
could not long endure; he that survives must, for that very fact, be 
in some measure a collaborator with Nature. With extending 
knowledge must come awakening consciousness of active partnership 
with the Cosmos "When souls reach a certain clearness of per- 
ception, they accept a knowledge above selfishness;" and "he that 
sees through the design must will that which must be." This is no 
mere resignation of a man to his fate, though the saying of Anatole 
France be true "Les grandes arnes se resignent avec une sainte joie." 
Not even joyful resignation is adequate; the state of the fully 
awakened consciousness is better described by the great physicist 
Clerk Maxwell, as "an abandoment of wilfulness without extinction 
of will, but rather by a great development of will whereby, instead 
of being consciously free and really in subjection to an unknown law, 
it becomes consciously acting by law, and really free from inter- 
ference of unrecognized laws." 



434 



ELEMENTS OF PHYSICAL BIOLOGY 



Such. Is the outlook to which the development of modern Science 
seems inevitably to be leading the thoughts of men. This is the goal 
of evolution, the perfect adjustment of feelings to actions, which 
guarantees survival: To say with the great Stoic "0 Universe, 
whatsoever is in harmony with thee, is in harmony with me." The 
being whose will is so adjusted is Fortune's favorite; all things must 
bend to his will as they bend to Nature's law. For his will is 
Nature's law. 




SYNOPTIC CHART 

OF PHYSICAL BIOLOGY AND ALLIED DISCIPLINES AS TREATED IN 

THIS WORK 

"Ce mage divisa en plusieurs parties ce qui n'avait pas besom d'etre divise"; 
il prouva m^thodiquement tout ce qui e"tait *clair; il enseigna tout ce qu'on 
savait; il se passionna froidement, et sortit suant et hors d'haleine. Toute 
1'assemble'e alors se r6veilla et crut avoir assist^ a une instruction." 
Voltaire. 



435 



SYNOPTIC CHARTS 



Guide to References. The numerals prefixed to the several items on 
Charts I, II. Ill, IV refer to the following list, which indicates some of the 
principal references to such items in this book. In a few instances of points 
not otherwise covered in this book supplementary references to the litera- 
ture are given. 







1 




ITEM 


PAGE 


ITEM 


PAGE 


CHART I 


32 


108, 109. 


1 


28, 29 


33 


108, 109. 


2 


28, 29 


34 


103 et seq. 


3 


28, 29 


35 


106, 152. 


4 


28, 29 


36 


42, 106, 152. 


5 


28, 29 


37 


57 et seq. 


6 


57 


38 


143 et seq. 


7 


58, 64 


39 


325 et seq. 


8 


58 






9 


57 

4"* { O 


CHAET II 


10 
11 


/ , 48 
48; Am. Jl. Hygiene vol. 3 


40 


45, 51. 




Jan. Suppl. p. 96. 


41 


46, 51. 


12 


57 


42 


46, 51. 


13 


100, 12S 


43 


See items 44 to 56. 


14 


130 


44 


Not discussed in this work. 


15 


130 


45 


See items 46 to 56 


16 


101, 130 et seq. ; Ann. Natur- 


46 


Proc. Natl. Acad. Sci. vol. 




phil. 1910 vol. 10 p. 65. 




7 1921 p. 169. 


17 


ISO, 132 et seq. 


47 


143, 259, 276. See also items 


18 


101, 115, 117 et seq. 




48 to 56. 


19 


87, 117 et seq. 


48 


261 (Special Case) 262, 265 


20 


Not discussed in this work. 




(Radioactive equilib- 


21 


110 et seq.; 115 




rium). Proc. Natl. 


22 


110 et seq. 




Acad. Sci. vol. 7 1921 p. 


23 


110 et seq. 




170. 


24 


115, 117. 


49 


259 et seq. 


25 


Not treated in this work. 


50 


See items 53 to 56. 


26 


128 


51 


See item 48. 


27 


103 et seq. ; 153, 155. 


52 


97, 212, 229. 


28 


103 et seq. 


53 


44, 45. 


29 


See items 30 to 34. 


54 


46, 122 et seq. 


30 


106, 152 et seq. 


55 


345 et seq. 


31 


69 et seq.; see also C. 


56 


122 et seq. 




Eijkman, Proc. Amster- 


57 


280 et seq. 




dam Acad. Sci. 1912 p. 


58 


45, 58, 59. 




629; Reichenbach, Zeit- 


59 


See items 60, 61, 62. 




schr. f. Hygiene und 
Infektions-krankheiten 


60 


Am. Jl. Hygiene vol. 3 Jan. 
Supply. 1923 p. 8. 




1911 vol. 69 p. 171. 


61 


60 et seq. 



436 



SYNOPTIC CHAETS 



437 



Am. Jl. Hygiene vol. 3 Jan 

Suppl. 1923 p. 25. 
See items 64 to 76. 
64 et seq. 
152 et seq. 
64 et seq. 
77 et seq. 
79, 82; Am. Jl. Hygiene 

loc. cit. 

83 et seq., 88 et seq. 
94. 
266, 296, 297; see also items 

72 to 76. 
61, 146 to 149. 
Not treated in this work. 
63. 
63. 
Not treated in this work. 



CHART III 



59, 145. 

59. 

146, 148, 149. 

See items 81 to 125. 

See items 82 and 84. 

See item 83. 

152 et seq.; 155, 157. 

144. 

280 et seq. 

259 et seq. 

276 et seq. 

161 et seq. 

163. 

95, 163. 

See items 92 to 96. 

See items 93, 94. 

164, 171 et seq., 175, 177 

Not treated in this work. 

166 et seq. 

See items 97 to 122. 

277; see also items 98, 99. 

173 et seq.; 181. 

181. 



100 



101 
102 
103 
104 
105 
106 
107 
108 
109 
110 
111 
112 
113 
114 
115 
116 
117 
118 
119 
120 
121 
122 

123 
124 
125 



126 
127 
128 
12Q 
130 
131 
132 
133 
134 
135 
136 



Not specifically treated in 
this work. For incidental 
references see items 105, 
106, 107, 117 to 119. 

See items 102 to 119. 

209, 215, 333. 

218, 226, 334. 

225; see also item 103 

229 to 232, 236. 

246, 247. 

252 et seq. ; 254. 

256. 

See items 110 to 119. 

188. 

225 to 228. 

See item 111. 

232 et seq. 

248 et seq.; 250. 

255. 

Not treated in this work. 

232 to 255. 

234, 248. 

239 to 242. 

Not treated in this work. 

See item 122. 

180, 238, 279; see also item 
119. 

280 et seq. 

300 et seq. 

321. 



CHAKT IV 



331 et seq. 

See items 128 and 129. 

345 et seq., 358. 

Not treated in this work. 

See items 131, 132. 

336 to 345. 

Not treated in this work. 

See items 134 et seq. 

328 to 330, 336. 

336 et seq. 

See item 137 et seq. 



438 



ELEMENTS OP PHYSICAL BIOLOGY 



137 
138 
139 
140 
141 
142 
143 
144 

145 

146 

147 
148 



See Item 138 et seq. 

317, 

300, 311. 

363, 370. 

45, 46, 122, 345, 348. 

Jl. Washington Acad. Sci. 

vol. 2 1912 p. 69. 

17, 336 et seq.; 362 et seq.; 
410 et seq. 

339, 371 et seq.; 410 et seq. 

339, 347 et teq. ; 363 et seq. 

371 et seq.; 410 et seq. 

Indirectly referred to in the 
substance of pages 383, 
394, 395, 398, 402, 407. 
For the general energetics 
of nutrition and related 



149 

150 
151 
152 

153 

154 

155 

156 

to 

163 



topics see special works on 
the subject, as, for ex- 
ample, Lefevre, La 
Chaleur Animale et Bio- 
energe'tique, 1911. 

410 (Table); see also item 
ISO. 

340, 347, 366, 411. 

See items 153, 154. 

339, 346, 381, 412, 414, 415, 
472. 

350. 

See item 155. 

350, 353, 416. 

See Table 34, page 412, and 
text relating thereto. 



ADDENDA 

The following references and notes, which have been omitted 
from the text through inadvertence or because they came to the 
author's notice too late, are here appended as a supplement. As 
stated in the Preface, no attempt at completeness of bibliography 
has been made. Perhaps, however, the material presented in these 
pages may be found, by anyone sufficiently interested, to furnish a 
serviceable base of departure for the gathering of a more exhaustive 
collation. 

Chapter I, page 9, footnote 10. See also L. A. Herrera, Royal Academy of 
the Lincei, June 15, 1924. Imitation of nervous and cellular tissue, by means 
of potassium hydroxide, silica and alcohol. 

Chapter II, page 36. Compare also A. J. Lotka, Irreversibility, Cosmic and 
Microcosmic, Jour. Washington Acad. Sci., August, 1924, pp. 352-3. It should 
perhaps be pointed out that the dissipative processes of nature, as discussed 
in this chapter, include, of course, both processes irreversible with regard to 
macroscopic operations, and also processes irreversible in the usual sense, 
that is, thermodynamically irreversible. 

Chapter II, page 44. Intra-group Evolution. If the composition or con- 
stitution of a group or species of organisms is described in terms of a frequency 
function, intra-group evolution is exhibited by the fact that the characteristic 
coefficients in such a function are functions of the time. This point has been 
referred to by Arne Fisher in Amer. Math. Monthly. March-April issue, 
1923, p. 97. Fisher thus writes the normal frequency function in the form 



(t) 

Chapter V, page 49 Compare also G. Bohn, La Forme et le Mouvement, 
Flammarion, 1921, p. 161. 

Chapter VII, Growth of Individual Organism, page 71. In this connection 
reference may also be made to the work of Lecomte de Nouy, of the Rocke- 
feller Institute for Medical Research, on the rate of cicatrization of wounds. 

Page 72, footnote 9, add the following reference: H. C. Bastian, Th.3 Nature 
and Origin of Living Matter, p. 47. 

Chapter VIII. For further discussion of the mathematical analysis of 
epidemiology and related topics see alsoR. Ross, Proc. Royal Soc., Ser. A, 
vol. 92, 1916, p. 204; vol. 93, 1917, pp. 212, 225, also; J. Brownlee, Proc. Royal 
Medical Soc., May, 1918, p. 115. 

439 



440 ADDENDA 

Chapter XV, Composition of Terrestrial Matter, page 194. See also V. M. 
Goldschrnidt, Geochemische Verteilungsgesetze der Elemente, Vitenskaps- 
seiskapets Skrifter I Mat.- Naturv. Klasse, 1923, no. 3, 1924, nos. 4 and 5; H. S. 
Washington, Jour. Washington Acad. Sci., 1924, p. 435; L. H. Adams, ibid., 
p. 459; J. H. Jeans, Nature, vol. 114, 1924, p. 828; H. Jeffreys, The Earth, 
Cambridge University Press, 1924. 

Chapter XV, page 203. Reference should have been made to Macallum's 
paper in the Trans. Roy. Soc. Canada, 1908, ii, p. 145. The marine origin of 
terrestrial animals was taught in remote antiquity, by Anaximander (610- 
540 B.C.) 

Chapter XXII, page 298. The role of the hands in the evolution of man's 
intelligence seems to have been clearly recognized by the Greek philosopher 
Anaxagoras (500-428 B.C.) "He explained man's intelligence by the power 
of manipulation that came when the forelimbs were freed from the tasks of 
locomotion" (W. Durant). 

Chapter XXIII, page 300. Compare also 0. Matousek, Geological Laws of 
Population, Amer. Jour. Physical Anthropology, 1924, vol. 7, p. 389. 

Chapter XXV, page 342. For further details regarding automatic telphone 
exchanges see also F. A. Ellson, Automatic Telephones (Pitman's Technical 
Primers, London, 1924); W. Aitken, Automatic Telephone Systems (Ernst 
Benn, London, 1924) 

Page 354. The influence of diet upon the mode of life was remarked by 
Aristotle (384-322 B.C.): "Of beasts some are gregarious, and others are 
solitary they live in the way which is best adapted to obtain the food of their 
choice." Very clearly the characteristics of animals and plants are referred 
to their respective food sources by La Mettrie in his little book L'Homme 
Plante (1748). He remarks very pointedly: "Les etres sans besoins sont 
aussisans esprit." (See .-.].-.;, ]v !: jo-: 211) M -id 301 in Chapters XVII and XXVI.) 
Chapter XXVI, pages >';.".. <-.- .!., : 5:<vir :; l data on the introduction of 
eyeglasses see, for example, R. Greef, Die Erfindung der Augenglaser, (A 
Ehrlich, Berlin, 1921). 

Page 366. Regarding the modern industrial development, with the use of 
machinery and, incidentally, with reference to the phonograph and radio 
concerts of today, the following words of Aristotle have acquired a strangely 
prophetic significance: "If every instrument should accomplish its own work, 
obeying or anticipating the will of others, . . . . if the shuttle should 
weave, or the plectrum touch the lyre, without a hand to guide them, then 
chief workmen would not need assistants, nor masters slaves." 

Chapter XXVII, page 374. Regarding the delimitation of the self, and 
related matters see also E. Mach, Analyse der Empfindungen; K. Pearson, 
Grammar of Science, 1900, p. 63; B. Bavink, Ergebnisse und Probleme der 
Naturwissenschaften, pp. 313, 320 et seq. 

Page 375. Add to footnote 7: Compare also the saying of Lamartine: 
"It is not I who think, but my ideas which think for me." And a modern 
writer has remarked that "it is not we who think, thinking is rather something 
that happens to us." Accordingly it would be grammatically better advised 
to employ an impersonal form of verb, and to say, instead of I think, rather 



ADDENDA 441 

it thinks, just as we say it thunders. Language is not altogether devoid of 
evidence of a vague realization of this. Especially in describing dreams and 
visions, with their characteristic submergence of the ego, we use such terms 
as methought, es dunkte mich, etc. 

Chapter XXX, page 395. Poets are good psychologists, in part, no doubt, 
because by nature introspective; in part, also, because keenly interested in 
human nature. The relation of emotions and of reason to action is well stated 
by Pope 

"On life's vast ocean diversely we sail, 
Reason the card, but passion is the gale." 

And La Fontaine has it 

"O douce volupte sans qui des notre enfance 
Le vivre et le mourir nous deviendraient egaux " 

General references. The following references, some of them guides to 
bibliographic sources, may be regarded essentially as an extension of the 
footnote 8 on page 366. 

Chapter XXVI. M. Schips, Mathematik und Biologie, Teubner, 1922. 
Contains a bibliography. 

H. Przibram, Anwendung Elementarer Mathematik auf Biologische Prob- 
leme, Engelmann, Leipzig, 1908. Contains a bibliography. 

G. Bohn, La forme et le mouvement, essai de dynamique de la vie. Flam- 
marion, Paris, 1921. Contains a bibliography. 

O. Fischer, Physiologische Mechanik, in Encyklopaedie der Mathema- 
tischen Wissenschaften, vol. IV, I, II, Heft I, pp. 62-126. The index on the 
literature of the subject contains a list of 21 textbooks and 421 monographs. 



OF 



Abbott, C. G., 331. 

Adams, L. H., 194. 

Adams, F. D., 274. 

Aitken, W., 440. 

Allen, E. J., 173. 

Amar, J., 347, 366. 

Anaxagoras, 440. 

Anaximander, 440. 

Andrews, M. R. S., 397. 

Aristotle, 362, 440. 

Arrhenius, S., 224, 227, 228, 234, 243, 

331. 

Aston, F. W., 156, 270, 391. 
Atkins, W. R. G., 223. 
Auerbach, F., 306. 
Aurelius, Marcus, 434. 



B 



Bachelier, L., 360. 

Bacon, R., 3, 365. 

Ball, W. W. R., 342. 

Baly, E. C., 155, 157, 221. 

Bancroft, W. D., 283. 

Barrell, J., 272. 

Bateson, W., 311. 

Baudisch, 0., 221. 

Baum, F. G., 333. 

Bavink, B., 440. 

Bawden, H. Heath, 366. 

Bayliss, W., 14, 19. 

Bell, C., 366. 

Benedicks, G., 40, 285. 

Bennett, A., 398. 

Bernard, G., 8, 17, 18, 203, 432. 

Bilski, F., 307. 

Biot, J. B., 41. 

Birkeland and Eyde, 239. 

Blackwelder, E., 245, 249. 



Blakeman, J., 344. 

Blondel, 61. 

Boas, 72. 

Bohn, G., 307, 439. 

Bohr, N., 378, 406. 

Boltzmann, L., 355. 

Bolyai, 18. 

Boole, 360. 

Bortkiewitch, 116. 

Bose, J. G., 221. 

Boucke, 0. F., 385. 

Bourrat, 403. 

Boussinesq., 407. 

Braham, J. M., 243. 

Bragg, 270, 365. 

Bridgeman, P. W., 274. 

Briggs, L. J., 7, 212, 332. 

Braun (and Le Chatelier), 283. 

Brown, E. W., 373. 

Brownlee, J., 81, 115, 307, 344, 439. 

Bucher, 239. 

Buckingham, E., 29. 

Buckle, P., 83. 

Budde, 304, 356. 

Bunge, G., 13, 201, 203, 204, 228, 257. 

Burlingame, L. L., 366. 

Burns, D., 9. 

Burns and Paton, 355. 

G 

Campbell, L., 407. 
Campbell, N., 385. 
Campbell, W. W., 331. 
Carlyle, 398. 
Carver, T. N., 386. 
Chamberlin, 272. 
Chatelier, Le, 281, 305. 
Chodat, 72. 

Christiansen, J. A., 157. 
Chwolson, 26, 283. 



443 



444 



INDEX OF NAMES 



Ciamician, G., 331, 333. 

Clarke, F. W., 185, 191, 192, 197, 

220, 223, 224, 226, 227, 235, 250, 

255, 258, 274. 

Clerk, Maxwell, 35, 379, 407, 433. 
Clifford, 403. 
Cole, W. H., 344. 
Conklin, E. G., 11. 
Cook, E. H., 223. 
Cooke, M. T., 166. 
Copernicus, 379. 
Cournot, A., 57, 409. 
Curtis, W. C., 372. 

D 

Dantec, Le, 285. 

Darmstaedter, L., 345, 365. 

Darwin, C., 165. 

Darwin, C. G., 193, 406. 

Dastre, 8. 

Daudefc, A., 388, 392. 

Davidson, L, 304, 356. 

Debierne, 264. 

Dodd, L. W., 21. 

Doelter, C., 384. 

Doering, C. R., 108. 

Donaldson, H. H., 72, 73, 132. 

Dreiser, T., 392. 

Driesch, 11. 

Drzwina, A., 307. 

Duhem, P., 160, 282, 320. 

Durant, W., 440. 

Dyk, v., 147. 

Dyson, F., 272. 

E 

East, E. M., 7, 66. 

Eddington, A. 8., 272, 342. 

Edgeworth, F. Y., 344. 

Ehrenfest, 282, 287, 300. 

Eijkman, C., 115. 

Einstein, A., 18, 337, 376, 379. 

Elliot, G., 298, 377. 

Ellson, F. A., 440. 

Emerson, R. W., 21, 364, 400, 426, 432. 

Emmetfc. W. L. R., 327. 



Empedocles, 185, 246. 
Encyclopedia Britanniea, 22. 
Engler, 227. 
Errera, L., 72. 
Euclid, 376. 
Euler, L., 112. 



Fajans, 270. 
Faraday, M., 379. 
Farr, G. H., 354. 
Farr, W., 115, 307. 
Fechner, 6, 403. 
Feldmann, W. M., 366. 
Fevre, J. Le, 347. 
Fiehte, 397. 
Fischer, 0., 441. 
Fisher, A., 439. 
Fisher, H. E., 239. 
Fisher, I., 386, 400. 
Fisher, O., 366. 
Forbes, A., 49. 
France, A., 410. 
Franck and Caro, 239. 
Franklin, W. S., 39. 
Fredericq, L., 203, 284. 

G 

Gadow, H., 165. 

Galton, F., 345. 

Garnett, W., 407. 

Gauss, 376. 

Gilbert, C. G., 333, 366. 

Glaser, O. C., 16. 

Glaser, R. W., 6. 

Glover, 103, 104, 105. 

Goethe, 4. 

Goldschmidt, V. M., 440. 

Gould, G. M., 12. 

Goursat, E., 159, 280. 

Greef, R. ; 440. 

Grinnell, Jones, 229, 237, 238, 239, 

241. 

Guilleminot, 357. 
Gumbel, E. T., 112. 



INDEX OF NAMES 



445 



H 



Haber, 234, 239. 

Haecker, L., 136. 

Haigh, L. D., 133. 

Haldane, J. B. S., 52, 122 et seq., 

170, 297. 
Hammick, 157. 
Hardy, G. H,, 124, 170. 
Hardy, W. B., 344. 
Harkins, W. D., 270, 271. 
Haydn, 425. 

Heath, Bawden H., 366. 
Hegel, 431. 
Heilbron, I. M., 221. 
Helm, G., 303, 304, 356. 
Helmholtz, 300. 
Henderson, L. J., 17, 203, 211, 217, 

333. 

Henson, 173. 
Heracleitus, 209. 
Herdman, W. A., 171, 181. 
Herrera, 439. 
Herrick, G. J., 7. 
Herschel, J., 331. 
Hertz, 379. 
Herzen, 391, 392. 
Heymans, 403. 
Hill, J. J., 251. 
Hiscock, I. V., 295. 
Hise, van, 251. 
Hogbom, A. G., 223, 224. 
Hogg, J., 307. 
Holland, B. H., 72, 74, 75. 
Hopkins, C. J., 257, 258. 
Holsberg, C. L., 332. 
Holt, E. B., 373. 
Hooke, E., 364. 
Howard, L. O., 90, 91. 
Huber, B., 231. 
Hume, D., 364. 
Humphreys, W. J., 186, 192. 
Hunt, S., 224. 
Hurwitz, 61. 
Hutchison, B., 347. 
Huxley, T. H., 342. 



James, (St.), 218. 
Janet, 392. 
Janssen, 365. 
Jeans, J. H., 189, 190. 
Jennings, H. S., 428. 
Jevons, F. B., 43. 
Johnson, 282, 377. 
Johnstone, J., 181, 357. 
Joly, J., 275. 
Jones, J. E., 190. 

K 

Kalmbach, E. E., 170. 

Kant, 13, 346. 

Keehle, F., 354. 

Keith, A., 366. 

Kelvin, 227, 274. 

Kepler, 424. 

Kesava, Pai M., 69. 

Keyser, C. J., 336, 374, 414, 426. 

Kirk, 211. 

Koehne, C. J., 227. 

Korzibski, 379. 



Laar, Van, 320. 

La Fontaine, 441. 

Laird, J., 375. 

Lamartine, 440. 

Lambert, W. D,, 274. 

Lane, A. C., 245, 365. 

Langmuir, I., 156, 157. 

Lascaux, E., 245. 

Le Chatelier, 52. 

Le Fevre, J., 347. 

Lehmann, 364. 

Lembat, M., 431. 

Lemberg, J., 227. 

Liebig, J., 97, 179, 223, 236, 246. 

Liebmann, H., 147, 151. 

Linck, 191, 220, 227, 235. 

Lindgren, W., 245, 249. 

Lipman, C. B., 232. 



446 



INDEX OF NAMES 



Lobatchewski, 78. 

Loeb, J., 9, 10. 

Lohmann, 173, 

Lorentz, 379. 

Lotka, A. J., 31, 33, 34, 39, 48, 60, 
62, 63, SO, 81, 82, 90, 91, 92, 110, 
115, 149, 150, 151, 154, 155, 245, 
268, 267, 285, 288, 325, 354, 356, 
357^ 3S0 3 398, 404, 409, 439. 

Lowell, 398. 

Louy, J., 283. 

Lowry, 157. 

M 

Maeallum, 440. 

MaeAuley, 282, 377, 397. 

MeOiendon, 9. 

McGee, W. J., 212, 216. 

McKendrick, A. G., 69. 

McLennan, J, G., 187. 

Mach. E., 259, 280, 381, 382, 383, 402, 

406, 426, 440. 
Marcus Aurelius, 434. 
Martin, G. W., 172, 173, 181, 229, 318. 
Martini, 79. 
Mathews, J. H., 221. 
Matousek, 0., 440. 
Maxwell, Clerk, 35, 379, 407, 414, 

433. 

Mayer, J. H., 325. 
Mayreder, R., 397. 
Meilor, J., 157, 281. 
Mettrie, La., 440. 
Miehaud, F., 160, 281. 
Michelson, 366. 
Milne, E. A., 190. 
Minot, C. S., 132, 299. 
Mitchell, 175, 266. 
Monnier, A., 72. 
Moore, 223. 
Moore, H. T., 399. 
Moritz, 275. 
Morley, J., 184. 
Moulton, 134, 272. 
Murphy, R. C., 250. 
Murray, J., 213. 
Murray, W. S., 333. 



N 

National Research Council, 136. 
Nernst, W., 8, 282, 355. 
Nero, 365. 
Newton, I., 379. 
Nichols, J. T., 108, 297. 
Norton, T. H., 229. 
Nouy, L. de, 439. 
Noyes, B., 108. 



Osborn, H. F., 17, 355. 

Ostwald, W., 72, 76, 235, 240, 274, 

303, 304, 356. 
Owen, S. P., 157. 



Pai, M. K, 69. 

Palitzsch, S., 17, 203. 

Pareto, W., 385. 

Parker, G. H., 12, 298. 

Parker, S. L., 69, 108, 164, 307, 308, 

319. 

Parsons, C., 273. 
Parsons and Petit, 237. 
Partington, J. E., 243. 
Paton, D. N., 9, 355. 
Pearce, A. S., 181. 
Pearl, E., 66, 68, 69, 108, 109, 162, 

278, 279, 307, 308, 319, 329, 368. 
Pearson, K., 25, 124, 300, 317, 344, 

440. 

Pennock, J. D., 233, 236. 
Perrin, J., 21, 26, 157. 
Pfeffer, 226. 
Phipson, T. L., 227. 
Picard, E., 59, 147, 280. 
Petersen, 175, 176, 181. 
Petronievics, 21. 
Petzoldt, 157. 
Planck, M., 303, 320, 379. 
Plato, 64. 

Pogue, J. E., 333, 366. 
Poincare", H., 28, 30, 92, 424. 
Poinsot, 19. 



INDEX OF NAMES 



447 



Pope, 441. 
Porstmann, 49. 
Poynting, J. H., 193. 
Prince, M., 403. 
Przibram, 337, 441. 
Ptolemy, 379. 
Punnett, E. C., 170. 
Putter, 174. 
Pyle, W. L., 12. 

Q 

Queredo, L. J., 337, 342. 

R 

Reed s H. S., 74. 

Reed, L. J., 66, 68, 72, 74, 75. 

Renan, 425. 

Rew, R. H., 162. 

Richter, K., 345. 

Riemann, 18. 

Robertson, G. S., 251. 

Robertson, T. B., 72, 73. 

Rodebush, W. H., 157.- 

Rogers, A. K., 331. 

Ross, R., 48, 81, 84, 147, 149, 150, 344, 

439. 

Royce, J., 26, 35. 
Russell, B., 4, 20, 22, 375, 395, 419, 

420, 422, 432. 
Russell, J. C., 245. 
Rutherford, E., 268, 269. 
Rydberg, J. R., 40. 

S 

Sachs, S., 6. 

Sala, G. A., 77. 

Sehaefer, C., 337. 

Schafer, E., 8. 

Schips, M., 441. ' 

Sehonbein, 156, 235, 391. 

Schroeder, 331. 

Schuchert, C., 224, 225, 269, 273. 

Seligmann, R. A., 219. 

Sempelowski, 249. 

Semper, K., 307. 

Seneca, 414. 



Shakespeare, W., 128, 427. 

Sharpe, F. R., 110. 

Sharp, D., 165. 

Shaw, N., 333. 

Sherrington, C. S., 375, 405, 433. 

Simpson, 377, 378. 

Slator, A., 69. 

Smith, A., 385. 

Smith, S., 8. 

Smoluchowski, 337. 

Smyth, C. H., 228. 

Soina, A. de, 365. 

Solvay, 239. 

Spencer, H., 7, 61, 283, 331, 354, 364, 

386. 

Spoehr, H. A,., 332, 333. 
Steinmetz, C., 333. 
Stevenson, J., 227. 
Streightoff, F. H., 347. 
Strong, 403. 
Strutt, 274. 

Sturtevant, A. H., 297. 
Sullivan, J. W. N., 20. 
Sumner, F. B., 374. 
Swann, M., 376. 



T 



Taussig, F. W., 396, 398. 
Taylor, J. T., 232. 
Tead, 0., 400. 
Thacker, G., 312. 
Tiffany, L. H., 171. 
Thomson, J. A., 132, 165. 
Thomson, J. J., 156, 379, 391. 
Thompson, D'Arcy W., 17, 203. 
Thompson, W. F., 173, 
Thompson, W. R., 83, 85, 86, 

91, 118. 

Thornton, H. G., 69, 70, 71, 164. 
Todd, G. W., 157. 
Tolman, R. C., 156, 403. 
Trowbridge, R. C., 133. 



U 



Uexktill, 16. 



INDEX OP NAMES 



Van Orsfcrand, 274, 

Veblen, T,, 395, 415. 

Vega, 236. 

Vegard, 187, 

Verhulst, 66, 368. 

Vernadsky, 201. 

Verne, J., 189. 

Vinci, Leonardo da, 252, 255. 

Voltaire, 435. 

W 

Waals, van der, 287, 294. 

Warren, H. C., 11, 383, 394 ; 395, 398, 

402. 

Washburn, M. F., 396. 
Washington, H. S., 197, 205, 206, 207. 
Watson, G. I\ T ., 81. 
Wegener, 186. 
Wells, H. G., 4, 431. 
Wells, F. L., 342, 371, 395, 401. 
Whitehead, A, N., 4, 100, 382. 



Whitney, M., 204, 255. 
Wiener, 364. 
Wilson, C. T. K., 365. 
Williamson, E. D., 194. 
Willis, C. J., 311 et seq. 
Willis, J. C., 307. 
Winiarski, 304, 356. 
Winkelmann, A., 320. 
Witmer, L., 428. 
Wohler, 8. 

Woodruff, L. L., 218. 
Wordsworth, 5, 184, 209, 371, 425, 
426, 432. 



Yost, 223. 
Young, 397. 
Yule, G. V., 312, 



Zsigmondy, 365 



OF SUBJECTS 



A 



Abbildung, 363. 

Accelerations vanishing with veloci- 
ties, 29. 

Accessibility of raw materials, 206- 
207. 

Accumulators, 328. 

Adaptation purely relative, 63. 

Adjusters, 339, 381 ; evolution of, 346; 
location of, 381; chart, 412; phy- 
siological or anatomical, 414; exter- 
nal, 414; economic, 415; internal, 
472. 

Age and Area theory, 311. 

Age distribution, influence on growth, 
109; "normal", 110, 114; "stable", 
110, 112, 113, 114. 

Agriculture, evolution of, 180. 

Aggregates, growth, 100; of constant 
units, 129; of variable units, 130. 

Aim, accuracy and versatility of, 338. 

Aimed collisions, 337, 409. 

Alfalfa weevil, 166. 

Anabions, 329. 

Animal and plant, distinction, 4-5. 

Animals characteristically active, 
mobile, 336; as catabions, 329. 

Annihilation, see extermination, also, 
extinction of species. 

Approximate expression for equilib- 
rium proportions, 267-268. 

Aptitudes, influence of special, upon 
motivation, 399. 

Aquatic, life, interspecies equilibrium, 
171; aquatic atmosphere, 193. 

Aquiculture, 173-181. 

Area and rent, 288-305; area as 
topographic parameter, 301; area 
and age, see age. 



Artificial receptors, 364, 440, corre- 
lating apparatus, 410, 440. 

Assumptions, implicit, 376-377. 

Asymmetry of time, 30 et seq., 37. 

Atmosphere, 185; losses from, 188; 
accessions to, 192; aquatic, 193. 

Autistic thinking, 410. 

Autocatalysis, 72. 

Automatic telephone exchange, 342, 
440. 

Automaton type of behavior 
schedule, 350. 



B 



Bacteria, growth of, 69. 

Bargain, mutually selfish, 415. 

Beef production, 132 et seq; effi- 
ciency, 136. 

Behavior schedule, 346; rigid or 
automaton type, 350; elastic type, 
350; effect of change in, 350; regula- 
tion according to maximum princi- 
ple, 351; of ideal organism, relation 
to that of actual, 352; effect of small 
departure from perfect adjustment, 
353; gainful occupations, 416. 

Behavior types, 7. 

Benign circles, 298, 440. 

Biassed movement, exemplified by 
chess, 343; biassed evolution, 380. 

Biochemistry, 317. 

Biological basis of economics, 163, 
164; surveys, 164. 

Biophysics, program of, 49. 

Birthrate and deathrate, relation 
between, 115; in "normal" popula- 
tion, 115; adjustment to optimum, 
128; economical and lavish, 131, 132 
et seq., 135. 



449 



450 



INDEX OF SUBJECTS 



Births, ratio of total, in successive 

generations, 87. 
Blood pressure and size of organism, 

295, 297. 
Blood serum, composition, compared 

with sea water, 201, 202. 
Body limits not clearly drawn, 374. 
Body, relation to ego, 374. 
Body fluids, 17. 

Body politic, essential unity of, 369. 
Body politic, 412. 
Boreholes, deep, 273. 
"Bottlenecks" in cycles of nature, 

292. 

Brownian movement, 337. 
Bulk mechanics, 50. 



C 



Capacity factors of energy, 282-303. 

Capture, frequency of, 359. 

Carbon dioxide, absorption in 

weathering of rocks, 223-224. 
Carbon (dioxide) cycle, 218-226; 

energetics of, 334. 

Carbon dioxide, origin of atmos- 
pheric, 227; solubility at different 
temperatures, 318. 
Carp, productivity, 173. 
Cartilage, sodium chloride content, 
in relation to marine origin of 
terrestrial species, 204. 
Catabions, 329. 
Catastrophic theory of earth's crust 

(Joly), 275. 

Cause and effect intermingled, 298. 
Cause, effective and final (Mach), 

381. 
Census of flora and fauna, 165-166; of 

aquatic species, 173. 
Centrifuge, use of, in making biologi- 
cal survery, 173. 
Changeful Sequence, 21. 
Characteristic Equation, 60. 
Chatelier, Le (principle of), 281, 293, 
305. 



Chemical reaction as an example of 

evolution, 152; theory of, 155, 156. 
Chemical Elements. See Elements. 
Chess, 342-343 et seq. 
Chess player, Mechanical, 342. 
Chili saltpeter, 235 et seq., 237. 
Choice, instinctive and reflective, 

412. 
Circulation of the elements in nature, 

209; tends to increase, 245. 
Circulation through moving cycles, 

change of, 292. 
Circulation, increase of, and law of 

evolution, 357-358. 
Cities, law of rank in size, 306. 
Classification of sciences, 419. 
Climatic parameters, 317. 
Clocks, radioactive chains as cosmic, 

268. 

Coal, exhaustion of, 222. 
Coal consumption, compared with 

solar energy, 332. 
Codfish, varied diet of, 177. 
Coefficients of transformation and 
their economic significance, 137 et 
seq. 

Coke ovens, losses of nitrogen from, 
233; by-product, replacing beehive 
type, 233. 

Collision frequency, 359. 
Collisions, random and aimed, 337. 
Collisions, energetics of, 409. 
Communicators, 378, 411. 
Competition of man with man, 417. 
Complete differential, 320. 
Completely damped systems, 28; 
characterized by single-valued 
growth function, 47. 
Composite transformers, 327. 
Concentration of natural resources 

208. 

Concentration, processes in nature, 
245-250; economic and energetic 
significance, 243; law of urban, 306. 
Conclusion, 417. 
Conduct, regulators of, 412. 



INDEX OP SUBJECTS 



451 



Conjugate parameters, 287-288, 303, 
320; See also parameters, topo- 
graphic. 

Consciousness, 388 et seq. ; mechanis- 
tic explanations, 388; relation to 
physical conditions, 388; condi- 
tional relations to physical condi- 
tions, 388; fundamental hypothesis 
of consciousness other than my 
own, 389; difficulty of attaching 
definite meaning to term con- 
sciousness as applied to lower 
organisms, etc., 389; bound up 
with life processes and structures, 
390; not separated sharply from 
unconsciousness, 390; forms or 
modes, of 390; impersonal, 388 
(Daudet), 391, 392; personal, 391; 

""-dependent on metabolism, 391; 
physico-chemical theory of, 391; 
evolution of, 393; operative rela- 
tions of, 394; function of, 394; a 
function of bodily state, 394; origin 
of, 402 et seq. 404; physical analogy, 
403; double aspect theory of, 403; 
physico-chemical theory of, 404; 
intervention in mechanics, 404; 
possible bearing of quantum theory 
on, 406; energy relations of, 406 et 
seq. ; intervention of, in mechanics, 
404, 407, 408; universe awakening 
to consciousness of itself, 431. 

Constraints, 58, 64. 

Continuity, principle of, 259. 

Convenience, in selection of coor- 
dinate reference frames, 372. 

Conversion factors of energy, 
economic, 355. 

Coordinate systems, 372; reference 
frames, 372. 

Correlating apparatus, 17, 336 et seq. 
338, 362 et seq.; elements of, 339; 
not peculiar to living organisms, 
340; evolution of, 345; perfect 
adjustment, 353; review, 410; chart, 
410; see also under its separate 
elements, such as Receptors, Ef- 



fectors, Adjusters, Elaborators, 
Communicators, Depictors, In- 
formants, Transformants, etc. 
Correlation, between movement of 
organism and the environment, 336 
et seq.; negative, between move- 
ment of organism and danger 
points, 337. 

Cosmic consciousness, 431. 
Cosmic irreversibility, 36. 
Cosmic mind, 375. 
Cosmogony, 272, 
Coupled transformers, 327. 
Cumulative cycles simulating ortho- 
genesis, 296. 
Curves of pursuit, 360. 
Cycles, benign, 298. 
Cycles in nature, 183, 209, 252; 
summary, 257; rate of participation 
of elements in cycles of nature, 258; 
law of increasing circulation, 357, 
358. 

Cycle of life, 334. 

Cyclic working of transformers, 326. 
Cyanamide process, 239. 



D 



Damped systems, 28. 

Data, methods of gathering, 52. 

Death, 185; Deathrate, see also birth- 
rate. 

"Death" of molecules in chemical 
reaction, 157. 

Definite quadratic form, condition 
for, 159. 

Definitions, 3; in biology, 5; of life, 7, 
18, 19; quantitative, 19; of evolu- 
tion, 19, 20. 

Delayed development theory of re- 
production, 12. 

Delayed twin, 12. 

Demographic functions, 101. 

Demographic relations in "normal" 
population, 115. 

Demology, general, 164. 

Density of aquatic population, 174. 



INDEX OF SUBJECTS 



Depiction (Abbildung) 339, 363; 

realistic, 371. 
Depictors, 339, 
Determinism and free will, seeming 

conflict, 406, 407. 

Dextrose, assimilated by oyster, 175. 
Diffusion of species, 311. 
Dilution culture method of making 

census of aquatic species, 173. 
Direction of evolution, 21 et seq. 26, 

37. 

Direction in time, 37. 
Discontinuities introduced by the 

senses, 5. 

Displacement of equilibrium, 280. 
Displacement of cycles, change in 

circulation resulting from, 292. 
Dissipative effects, 22, 24. 
Domestic animals kept for produce, 

1S2. 
Double aspect theory of consciousness, 

403. 
Double entry bookkeeping, in world 

depiction, 373. 
Drama of life, 183. 
Drives (motives), 396, 399. 
Drosophila, 69, 108 3 307, 309, 310, 319. 
Dynamic psychology, 396; as applied 

to industrial and social problem, 

400. 

Dynamics of evolving systems, 325. 
Dynamics of life-bearing systems, 

121, 122. 



E 



Earth's crust, composition, 194, 195, 
196, 439; thickness, 273; periodic 
melting of (Joly's theory), 275. 

Economic systems, intensity law ap- 
plied to, 303. 

Economic energy (alleged) 303. 

Economic significance of transforma- 
tion factorSj 137; conversion factors 
"of energy, 355; value and general 
utility for social service, 386. 



Economics, biological basis, 163, 164, 
244, 304; relation to energetics, 303, 
304; system of, developed without 
explicit reference to human desires, 
409. 

Eel grass as fundamental food of 
aquatic life, 176. 

Effectors, 340; evolution of, 347; arti- 
ficial, 366; internal and external, 
411. 

Efficiency of milk and beef produc- 
tion, 136; of plants in utilizing 
sunlight, 332. 

Ego, as coordinate reference frame, 
372; immaterial, 373; boundaries of, 
374; need of broader conception, 
378; as a particular development in 
general consciousness, 404; as a 
product of integration of con- 
sciousness, 405; classification of 
sciences in relation to distinction 
between ego and external world, 
419; as ICnower and as Wilier, 421. 

Egos, interpenetration of, 374, 440. 

Elaborators, 339, 370. 

Elements, relative abundance, 195, 
204, 206, 207, 270, 271; correlation 
of occurrence, 205; metallogenic 
and petrogenic, 207-208; circulation 
tends to increase, 245; immobile, 
246; circulation in nature, rate of, 
258; origin of, 269. 

Emotions, reaction of knowledge 
upon, 424. 

Encounters, see collisions. 

Energetics of aimed collisions and 
purposive behavior, 409. 

Energy, See also waterpower, wind- 
power, sun. 

Energy transformers of nature, 325 et 
seq. ; transformers, fundamental 
characteristics, 325; sources, dis- 
tributed and localized, 336; relation 
of economic value to, 354, 355; 
economic conversion factors of, 
355; law of evolution, 357; relations 
of consciousness, 406 et seq. 



INDEX OF SUBJECTS 



Engine, the world as an, 331. 
3pictors or transformants, 411. 
Spidemiology, 77, 79, 439. 
Equation, fundamental, of kinetics 
of evolving systems, 57, 77; charac- 
teristic, 60; of constraint, 58, 64; of 
kinetics, exceptional case, 89; case 
of three dependent variables, 94; of 
dynamics, possible significance of 
factors eliminated therefrom, 408. 
Eqiiilibria, number and character of, 
59; relations between several 
equilibria, 147. 

Equilibrium, 51; moving 51; displace- 
ment of 51, 143, 280, 289; conditions 
for, 59; equation, 59; mode of ap- 
proach, 61; equation, zero roots, 62; 
roots, 63; population, stability, 67; 
moving, 143; kinetic, dynamic and 
energetic conception, 143; general 
principles, 143; condition for sta- 
bility, 144; general condition for, 
145; equations, 145; character of 
146; different types, 146, 148; 
malaria, 147, 149, 150; model surface 
147, 149, 150; metastable, 151; 
chemical,, 154, 155; chemical, deter- 
mined in accordance with laws of 
thermodynamics, 157; condition in 
particular form, 161; interspecies, 
161, 171; first approximate expres- 
sion for, 259, 267, 268; moving, 259; 
second and higher approximations, 
260; radioactive, 262; polygon, 266, 
277; displacement of, between food 
and feeding species, 289; influence 
of parameters of state, 319; ther- 
modynamic conditions, 319; de- 
fined in terms of minimum law, 320; 
metastable and voluntary action, 
408. 

Equivalent increments, 349. 

Esthetics, 422. 

Ethics, 387; as regulator of conduct 
along "realistic" lines, 412. 

Ethnological bearing of advances in 
agriculture, 180. 



Euclidian and non-Euclidian geome- 
try, in the world picture, 376. 
Evolution of system as a whole, 16; 
definition, 19, 20, 24, 25; and his- 
tory, 20; and progress, 21 ; direction 
of, 21, 22; and probability, 25; and 
irreversibility, 26; second law of 
thermodynamics as the law of 
evolution, 26; passage to more 
probable state, 34, 35; redistribu- 
tion 41 et seq.; intra-group and in- 
ter-group, 44, 45; general mechanics 
of, 49; macro- or bulk mechanics, 
and micro mechanics, 50; dynamics 
or energetics, 50; second law of 
thermodynamics as the law of 
physico-chemical evolution, 157; 
of man's exploitation of natural 
resources, 180; of elements, 269; 
under changing parameters, 280; 
law of maximum energy flux, 357; 
industrial, 367; of the ego, 378; 
biassed (orthogenesis), 380; value 
of nurture and tradition for evolu- 
tion, 428. 

Exhaustion of coal resources, 222. 

Expediency, in definitions, 3, 5. 

Exponential series, 60. 

Extermination of one species by 
another, 87, 92. 

External world, 373; as hypothetical 
construct, 419-420; see also ego. 

Extinct species, 266, 296, 297, see also 
extermination. 

Extraction of rocks and soil by rain- 
fall, 252 et seq. 



F 



Farr's rule connecting birthrate, 
deathrate and mean length of life, 
115. 

Fatigue, 351. 

Feeding our foods, 180. 

Fetus in fetu, 12. 

Fitness a relative term, 63. 



454 



INDEX OF SUBJECTS 



Flame, analogy to living organism, 

218. 

Fly population, equilibrium, 59. 
Food chains, 136; 176 aquatic, 175, 

180. 
Food, influence on psychology, 219, 

354, 440. 

Food and Feeding species, displace- 
ments of equilibrium between, 289. 
Foods, primary, secondary and 

tertiary, 181. 

Foods, moisture contents, 211. 
Foods, supply of plant foods in soil, 

257. 

Force of mortality, 102. 
Force of mortality in chemical reac- 
tions, 153, 155. 
Fossil fuel, exhaustion, 222. 
Free energy, 321; relation to volun- 
tary action, 408. 
Frequency of collision and capture, 

359. 

Friction, 22, 24. 
Fruit fly, see Drosophila, 
Fundamental equations of kinetics of 
evolving systems, 57 et seq.; 
general case, 57 et seq.; solution, 
60; case of single dependent varia- 
ble, 64; two dependent variables, 
77. 

Future "that may be," 382; influence 
of, on course of events, 382, 383; 
role of, in purposive action, 395, 
398, 409; knowledge of the, through 
will, 421. 



G 



Gas law, analogy of population 
pressure, 305. 

Genera and species, Willis' theory 
(age and area), 313. 

Generation, rate of increase of popu- 
lation per generation, 118. 

Generations, diffusion in time of suc- 
cessive, 86; ratio of successive, 87. 

Genesis, ultimate of organism, 269. 



Genius, motivation in men of, 399. 
Genuine utility for social service, 

386. 

Geochemistry, 274. See also geo- 
physics, and numerous references 

under Clarke, F. W. 
Geophysics, 273. See also geo- 
chemistry. 
Grasshoppers destroyed by birds 

168. 
Growth, 9, 14, 43; law of population, 

64; in diminishing population, 70; 

determination of constants, 73. 
Growth function, single-valued, 47. 
Growth, of bacteria 69; of individual, 

71, 439 ; determination of constants, 

73. 

Growth of aggregates, 100. 
Growth of population, influence of 

age distribution, 109. 
Growth in population with Mendeliam 

inheritance, 122. 
Growth in man, 132; of industries, 

278; of world's population, 278; of 

transformers, 328. 
Growth, Verhulst-Pearl law, 368. 
Guanay (bird), 250. 
Guano, 236. 



H 



Half-decay period (of radio-active 

substance), 268. 

Hand, r61e of, in evolution, 298, 440. 
Hedonistic principle of Spencer, 

extension of 430, 432. 
Higher forms, 21. 
Human body, composition, compared 

with earth's crust, 196, 197. 
Hydrosphere, 192. 



Ideal Organism, relation to actual, 

352. 

Imagination, 371. 
Immobile constituents of soil, 179. 



INDEX OF SUBJECTS 



Immunising diseases, Martini's equa- 
tions, 79. 

Indifferent increments, 349. 
Indispensable components, 95. 
Industrial evolution, 307, 368. 
Industrial psychology, 400. 
Industrial organization, imperfection 
of adjustment of human motives to, 
418. 

Inertia-free systems, 28 et soq. 
Informants, 339; 410. 
Instability, significant cases of, 294. 
Instinctive arid reflective choice, 412. 
Instinct as determinant of action, 

395. 

Instinct of workmanship and self- 
expression, 396; 416. 
Instincts, list of, 396; danger of 
suppressed, 400; egoistic and 
altruistic, 412; inadequacy as ex- 
ternal adjusters in human com- 
munity, 415. 

Integration of nervous system, 405. 
Intelligence as discriminating agency, 

120. 

Intensity factor of energy, 282, 303. 
Intensity law (of energy), 303. 
Interpendence of species, 77; chart, 98, 
99; network of chains, 136; methods 
of gathering data, 164. 
Interfacial forces, 14. 
Intra-group evolution, 44; kinetics, 

122, 439. 
Inter-group evolution, see intraspecie 

evolution. 

Interspecies equilibrium, 161. 
Intra-species evolution, 44, 122, 348; 
analytical statement of problem, 
345. 

Invariants of nature, 373. 
Iron, circulation in nature, 256. 
Irreplaceable components, 65; see 

also replaceable components. 
Irreversibility, 21 et seq. 23; statisti- 
cal meaning, 30; macroscopic, 36, 
439. 
Irreversibility and evolution, 26. 



Jabberwock, 4, 7. 

K 

Kinetics of Evolution, fundamental 
equation, 44, 51. 

Kinetics of evolving systems, 57 et 
seq. 

Knowledge, reaction of, upon emo- 
tions, 424. 

L 

Lag, 23. 

Lag and lead in equations of kinetics, 
47; lag and lead, spurious, 48. 

Law of urban concentration, 306 

Le Chatelier's principle, 281; condi- 
tions of validity, 284, 286. 

Length of life of molecules in chemi- 
cal reaction, 155. 

Liebig's law of limiting factor, 97; 
229. 

Life, definition, 7, 18; origin of, 218; 
cycle of, 334; curve, 102 et seq.; 
table, 102 et seq.; life and oxida- 
tion, 218; life struggle in modern 
community, 417. 

Light, influence on biochemical reac- 
tions, 317, 318; influence on marine 
life, 318; penetration into sea water, 
318. 

Limiting factors, 97, 229; water, 212. 

Liparis dispar, 87. 

Lithosphere, 193; composition, 194; 
accessions to, 195. 

Living matter, characteristics, 8; 
origin of, 218. 

Logic, 371; 410. 

Logic and ethics, parallelism, 414. 

Losses from atmosphere, 188. 



M 



Machines, 7, 11; rent on, paid by 

worker, 369. 
Macro-mechanics, 50. 



456 



INDEX OF SUBJECTS 



Malaria, 79, 81 ; equilibrium, 147, 149, 

150. 
Marine origin of terrestrial species, 

203. 

Mass action, law, and its generaliza- 
tion, 42. 

Maximum and minimum laws, 157. 
Maximum energy flux, law of evolu- 
tion, 357. 

Maxwell's demon, 35, 121. 
Meadowlark in relation to species on 

which it feeds, 167. 
Mean free path, 358. 
Mean length of life, 114, 115, 267; of 
molecules in chemical reaction, 155. 
Mechanical imitations of correlating 

apparatus, 340, 342. 
Mechanical model of function of 

correlating apparatus, 381. 
Mechanical properties in relation to 

growth, 12. 
Mechanics, macro- and micro-, 50; 

bulk, 50; statistical, 50. 
Mechanistic conception, 48. 
Mechanistic and teleological inter- 
pretation of adjusters, 381, 382, 383, 
384. 

Memory, 48; 339. 
Mendelian inheritance, 122. 
Metastable equilibrium, 10, 151, 
Metastability and voluntary action, 

407. 

Methods of biological census of 

aquatic species, 173; summary, 176. 

Methods of gathering data regarding 

interdependence of species, 164. 
Micro-mechanics, 50. 
Migration, see random. 
Milieu interieur, 17, 203. 
Milk Production, record, 136. 
Mill wheel of life, 334. 
Mind, cosmic, 375; group mind, 375; 

location of, 375. 
Mind merely a symbol t>f reference. 

375. 

Minimum law of equilibrium, 320. 
Minimum laws. 157. 



Models, use of, for attacking refrac- 
tory problems in mathematical 
analysis, 360. 

Moisture contents of foods, 211. 

Monomolecular reactions, 106. 

Mortality and survival, 103 et seq. 

Mortality, force of in chemical reac- 
tion, 153, 155. 

Motion of organisms, laws of, as 
exemplified by chess, 343. 

Motivation, 395; in genius, 399. 

Movement, see also migration. 

Moving equilibria, 143, 259; organic, 
276. 

Moving equilibrium, special case; 
pace set by the slowest transforma- 
tion in a chain, 261, 265; 267 (foot- 
note 5) ; example of radioactive chain 
of transformations, 262. 
Mutually selfish bargain, 415. 

N 

Nannoplankton, 173. 

Nerve energy, 13. 

Nitrebeds, origin, 238; exhaustion 
238. 

Nitrogen, nomadic, 229. 

Nitrogen cycle, 229, 236; diagram, 230, 
231; gate of entry, 232; human inter- 
ference, 236; as limiting factor, 229; 
losses, 232; direct assimilation by 
plants, 233; accessory sources of 
234; oxidation process, 241; fixation 
processes, 239; industry, 240, 241, 
242. 

Nomadic nitrogen, 229. 

"Normal" population, 115. 

Nurture and tradition, evolutionary 
value of, 428. 

Nutrition of marine animals from 
dissolved organic matter, 175. 



Object and subject, see ego. 
Objective world, origin of concept, 
405. 



INDEX OF SUBJECTS 



457 



Ocean, composition, 191; ocean, 192; 

origin of salt in, 255. 
Oceanography, 181. 
Ontograms and phanograms, 421. 
Optimum birthrate, 128. 
Organic cycle, energetics of, 334. 
Organic matter, composition, 197, 

198, 199, 200. 
Organisms as composite transformers, 

329; as coupled transformers, 330. 
Orthogenesis, 296. 
Orthogenesis in human evolution, 

378. 

Oscillations, 61. 
Oscillatory approach to equilibrium, 

79. 

Oxidation as typical life process, 218. 
Oxygen as food, 219. 
Oxygen cycle, 225. 
Oyster culture, 181. 



Parameters of state P, 43; 300; influ- 
ence on equilibrium, 319. 

Parameters Q defining character of 
species, 46. 

Parameters, evolution under chang- 
ing, 280; conjugate, 287, 288, 303; 
topographic 300, 440; relations be- 
tween, 301 ; climatic, 317. 

Parasitology, 83. 

Passive character of plants, 336. 

Peat formation, 224. 

Pedogenesis, 12. 

Pendulum as example of simple 
mechanical motion, 27. 

Perfect adjustment of correlating 
apparatus, 353. 

Period of Diffusion, 311. 

Periodic processes, 22, 24. 

Periodicity in seemingly random 
series, 32. 

Phanograms and ontograms, 421. 

Phenotypes (Mendelian) 122. 

Philosophy as part of scientific 
enquiry, 418. 



Phosphate rock, 248. 

Phosphatic slag (as fertilizer) 251. 

Phosphorus, natural supply in soils, 
246; migration of, 248; losses of, 
248, 250. 

Phosphorus cycle, 246; diagram, 247. 

Physical Biology, Program of, 49. 

Physical chemistry of structured 
systems, 13. 

Physico-chemical evolution ? law of, 
14, 15, 16; physico-chemical evolu- 
tion, 152, 155; second law of ther- 
modynamics as the law of evolu- 
tion, 157. 

Physico-chemical systems, struc- 
tured, 15. 

Plaice, 173. 

Plant and animal, distinction, 4. 

Plant "psychology," 219, 355. 

Plant characters, in man, 219, 355. 

Plant foods in soil, supply of 257. 

Plant and animal as coupled trans- 
formers, 330. 

Plants as accumulators (anabions), 
329. 

Plants, efficiency in utilization of 
sunlight, 332; absence of correlating 
apparatus in, 355. 

Plants, characteristically passive, 
sessile 336. 

Population, law of growth, 64; 
United States, 5 66; experimental, 
69; Drosophila 69; diminishing, 70; 
bacterial colony, 71 ; determination 
of constants, 73; saturation point, 
67; rate of increase per generation 
118; census of flora and fauna, 
165, 166; growth of world's, 278; 
law of urban concentration, 306. 

Population equilibrium, stability, 67. 

Population element, progeny of, 86. 

Population with "normal' 1 age dis- 
tribution, 110. 

Population density, 307, 308, 309; 
equatic, 174. 

Population pressure, 288, 304, 305, 
307. 



458 



INDEX OF SUBJECTS 



Potassium in relation to life, 255, 
Potential) 10, 157; thermodynamic, 

319. 
Power, see energy, also waterpower, 

windpower, sun, coal. 
Preconceived premises, difficulty of 

shaking off, 377. 
Premises, fundamental, 376. 

Pressure-volume relation, 287. 

Prices, analogy to intensity factor of 
energy, 303. 

Primary foods, 181. 

Principle of continuity, 259. 

Principle of Le Ghatelier, 281; condi- 
tions for validity, 284. 

Proales decipiens, 108. 

Product I vit}* of carp, 173. 

Productivity, specific, 347. 

Program of physical biology, chart, 
53. 

Progress and evolution, 21. 

Pseudo-problems, 3, 4, 7. 

Psychology, dynamic, 396. 

Psycho-physical parallelism, 402. 

Purposive action, 395; relation to free 
energy, 409. 

Pursuit, curves of, 360. 

Q 

Quadratic forms, 158. 

Quantum theory and the asymmetry 
of time, 39. 

Quantum theory, possible relation to 
phenomena of will and conscious- 
ness, 406. 

Quasi-dynamics, 52. 

R 

Radioactive transformations 58, 62, 
83, 106. 

Radioactive equilibrium, 262; ap- 
proximate expression for, 267, 268. 

Radioactive substances as cosmic 
clocks, 208. 

Radioactivity, periodic melting of 
earth's crust (Joly's theory), 275. 



Radium, 263, 265. 

Railways, growth of American, 36 
Rainfall, 214. 
Random collisions, 337. 
Random migration, 337, 344; undt 
bias, exemplified by chess, 34? 
random movement under a bias 
360. 
Reaction constant regarded as fore 

of mortality, 153. 

Realistic world picture, 371 et seq. 
Reasoning, 371 et seq. 
Realistic thinking, 410. 
Reason, 339. 

Receptor-effector circuit, 340. 
Receptors, 339, 363 et seq.; evolutioi 

of 347, 348; artificial, 364. 
Record milk production, 136. 
Reflective and instinctive choice, 412, 
Rent and area, 288, 305. 
Rent on machinery, paid by worker, 

369. 

Replaceable components, 95; 163. 
Representation (Abbildung), 363. 
Reproduction, 8, 11, 12; extravagance 

in 132, 135. 

Resignation, policy of, in science, 19. 
Rigid type of behavior schedule, 350. 
Rivers, discharge of world's, 214. 
Rocks, weathering, 223, 224. 



S 



Salt of ocean, origin, 255. 

Saltpeter industry, 235, 236. 

Saturation point of population, 67. 

Science, pure and applied, mutual 
stimulation of, 298, 299. 

Sciences, classification 419, 421, 422; 
chart, 423. 

Scientific world picture, 372. 

Sea water and body fluids, 17; com- 
position, 191; composition com- 
pared with blood serum, 201, 202. 

Secondary foods, 181. 

Selective slaughtering, effect on rate 
of increase of species, 119. 



458 



INDEX OF SUBJECTS 



Potassium in relation to life, 255. 
Potential, 10, 157; thermodynamic, 

319. 
Power, see energy, also waterpower, 

windpower, sun, coal. 
Preconceived premises, difficulty of 

shaking off, 377. 
Premises, fundamental, 376. 
Pressure-volume relation, 287. 
Prices, analogy to intensity factor of 

energy, 303. 
Primary foods, 181. 
Principle of continuity, 259. 
Principle of Le Ghatelier, 2S1; condi- 
tions for validity, 284. 
Proales decipiens, 108. 
Productivity of carp, 173. 
Productivity, specific, 347. 
Program of physical biology, chart, 

53. 

Progress and evolution, 21. 
Pseudo-problems, 3, 4, 7. 
Psychology, dynamic, 396. 
Psycho-physical parallelism, 402. 
Purposive action, 395; relation to free 

energy, 409. 
Pursuit, curves of, 360. 



Quadratic forms, 158. 

Quantum theory and the asymmetry 
of time, 39. 

Quantum theory, possible relation to 
phenomena of will and conscious- 
ness, 406. 

Quasi-dynamics, 52. 

R 

Eadioactive transformations 58, 62, 
63, 106. 

Radioactive equilibrium, 262; ap- 
proximate expression for, 267, 268. 

Radioactive substances as cosmic 
clocks, 268. 

Radioactivity, periodic melting of 
earth's crust (Joly's theory), 275. 



Radium, 263, 265. 

Railways, growth of American, 369. 
Rainfall, 214. 
Random collisions, 337. 
Random migration, 337, 344; under 
bias, exemplified by chess, 343; 
random movement under a bias, 
360. 
Reaction constant regarded as force 

of mortality, 153. 

Realistic world picture, 371 et seq. 
Reasoning, 371 et seq. 
Realistic thinking, 410. 
Reason, 339. 

Receptor-effector circuit, 340. 
Receptors, 339, 363 et seq. ; evolution 

of 347, 348; artificial, 364. 
Record milk production, 136. 
Reflective and instinctive choice, 412. 
Rent and area, 288, 305. 
Rent on machinery, paid by worker, 

369. 

Replaceable components, 95; 163. 
Representation (Abbildung), 363. 
Reproduction, 8, 11, 12; extravagance 

in 132, 135. 

Resignation, policy of, in science, 19. 
Rigid type of behavior schedule, 350. 
Rivers, discharge of world's, 214. 
Rocks, weathering, 223, 224. 



Salt of ocean, origin, 255. 

Saltpeter industry, 235, 236. 

Saturation point of population, 67. 

Science, pure and applied, mutual 
stimulation of, 298, 299. 

Sciences, classification 419, 421, 422; 
chart, 423. 

Scientific world picture, 372. 

Sea water and body fluids, 17; com- 
position, 191; composition com- 
pared with blood serum, 201, 202. 

Secondary foods, 181. 

Selective slaughtering, effect on rate 
of increase of species, 119. 



INDEX OF SUBJECTS 



459 



Self consciousness as a particular 
mode of general consciousness, 404, 

Self-expression, instinct, of, 396. 

Self, see ego. 

Series solution of fundamental equa- 
tion of kinetics, 60. 

Sex, in reproduction, 13. 

Shark series of fishes, possible ortho- 
genesis in, 296. 

Siamese twin, the body politic as a 
multiple, 369. 

Simulacra vitae, 9, 439. 

Single-valued growth function, 47. 

Singular orbits, and the intervention 
of consciousness in mechanics, 407. 

Slavery, 370. 

Social psychology, 400. 

Social utility, 386. 

Sodium chloride cycle, 252; diagram, 
254. 

Soil, supply of plant foods in, 257. 

Solar energy, See Sun. 

Sophistry, bred out of unrecognized 
assumptions, 377. 

Soxhlet extractor, 253. 

Spacial sense, 411. 

Specific productivity, 347. 

Speech and thought, cumulative 
evolution of, 298. 

Spencer's hedonistic principle, an 
extension of, 430, 432. 

Spread of species, 311. 

Stability of age distribution, 11, 113. 

Stage of the life drama, 183, 185. 

Stars, evolution, 272. 

Statics, 51. 

Statistical mechanics, 24; of life- 
bearing systems, 121 ; of systems of 
energy transformers, 325, 345, 358; 
of systems of organisms, 358, 

Statistical models of irreversible 
processes, 30. 

Steady states, 51, 59, 143. 

Steers, growth of, 133 et seq. 

Stoichiometry, 50. 

Stomach contents, analysis of, 166. 

Stream of substance through the form 
of the organism, 130. 



Structured systems, 13. 

Subject, see ego. 

Subjective sense of direction in time, 

37. 

Sulphur, circulation in nature, 256. 
Sun, energy intercepted by plants, 

331 ; energy received by earth from, 

331; energy radiated by, 331. 
Sun's energy, compared with coal 

consumption, 332. 
Surveys, biological, 164; surveys of 

marine life, 173. 
Survival factor, 102. 
Survival curve, 103, 104, 105, 107. 
Survival curves for experimental 

populations, 108. 



Tastes, adaptive adjustments of 385; 
divergence of, 397. 

Teleological interpretation, and 
mechanistic, of adjustors, 381, 382, 
383, 384. 

Teleological mechanisms, 342, 440. 

Temperature, influence on biochemi- 
cal reactions, 317. 

Terrestrial species, marine origin, 
203. 

Tertiary foods, 181. 

Thermodynamic potential, 10, 157. 

Thermodynamics, second law, and 
evolution, 26; second law of, as law 
of evolution in physico-chemical 
transformations, 157. 

Thinking: autistic and realistic, 410; 
semi-realistic, 411. 

Tidal dissipation, 22, 24. 

Time, 22; positive and negative in 
mechanics, 27, 37; subjective sense 
of, 37; direction in, 37, 411; geologic, 
as indicated by radioactive sub- 
stances, 268, 269. 

Topographic parameters, 300, 311. 

Toy beetle, 341, 381. 

Tradition, evolutionary value of, 428. 

Transformants or epictors, 411. 

Transformation factors, their eco- 
nomic signficance, 137. 



OF SUBJECTS 



Transformer cycles, 326, 
Transformers, composite and 

coupled, 327, 330; growth, of, 328. 
Transportation, evolution of 367. 
Travelling environment, 16. 
Twin, 12. 
Types of organisms, economical and 

lavish birthrate, 131, 132 et seq. 



U 



Unadapted species, 266. 

Unfit species, 266. 

Unity of man with cosmos, 426. 

Universe awakening to consciousness 
of itself, 431. 

Universe, man's unity with 433. 

Uranium chain of radioactive ele- 
ments, 263. 

Urban concentration, law of, 306. 

Urea, 8. 

Utility, genuine, for social service, 
386. 



Value in exchange (of small incre- 
ments of two sensori-motor param- 
eters), 349, 

Value, economic, relation to physical 
energy, 354, 355; absolute standard 
of 353, 386; and genuine utility for 
social service, 386; theory of, 422. 

Verbal problems, 4, 7. 

Verfmlst-Pearl law, 329, 36S. 

Vestal flame, 219. 

Vicious circles, 294, 295. 

Vital processes, 8. 



Vital force, 13. 
Volcanic discharges, 222. 
Voluntary action and determinism, 

406 et seq. 
Volvox, 6. 

W 

War game, 361. 

Water circulation, fraction taking 
part in life cycle, 216. 

Water cycle, 209; diagram, 215; 
energetics of, 333; water require- 
ments of organisms, 210, 211, 212; 
supply, 213. 

Waterpower, 333. 

Watershed, moral, and voluntary 
action, 408. 

Wealth, mathematical theory of, 409. 

Weathering of rocks, 223, 224. 

Windpower, 333. 

Will, 48; general, 375. 

Working substance, 325 et seq. 

Workmanship, instinct of, 396. 

World Engine, 331; evolution of, 335. 

World picture, scientific, 372, double 
entry bookkeeping, 373. 

World Purpose, 428, 430. 

Z 

Zero roots of equilibrium equation, 

62. 
Zone pattern, effect of change upon 

rate of increase of species, 348. 
Zones of influence, 344. 
Zones of mobility, 345. 
Zostera (eel grass), 176. 
Zweckmassig action, 371. 



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