Elements of Physical Biology

“Voilé un homme gui a fait son mieux pour ennuyer deux ou trois cents de ses concitoyens; mais son intention était bonne: il n'y a pas de quoi détruire Persépolis.” Composed and Printed at the By roy Winuams & Witxins Company Baltimore, Md., U. 8. A. The preface is that part of a book which is written last, placed first, and read least. AsI 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 summarized 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 circumstances that gave origin to the work, and the conditions under which it came into being. He may express his feelings as to its alleged purpose, 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 without 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. Reference 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 skeleton framework elaborated in the journal literature, was carried out at the Johns Hopkins University upon the invitation of the Department 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

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 encouragement 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 quotations. The somewhat extended excerpts from certain articles published 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 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 development 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 pertinent facts was in nowise aimed 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 consulted. 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, (whomI 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, X XXIII 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

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 trepidation, for I recall how Voltaire said of one: ‘Il fit une philosophie comme on fait un bon roman; tout parut vraisemblable, et rien ne fut vrai;’”’ and there comes to mind the language still plainer of du Maupassant—‘“‘Depuis qu’ils ont appris 4 lire et a écrire, la bétise latente se dégage.”’ I trust that the reader’s response to these pages may not be too fervent an Amen to the prayer of The Sceptical Chymist “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 ertinencies, we shall either by their books receive an advantage, or CuapTerR [| PUP MRLLA DP TELC LEI DLONIG 1. toon = ree ete attr rare a ain atk CREE Hed e ATA 3 Evolution Defined: The History of a System in the Course of Irreversible PiiraAmnCOriMAvi ODN ence freee oe tsi f ek hess 5 asebcech Shaw aceie ws watostens 20

CuHapTer IV Hyolution Conceived a8 & Redistribution. . 2.0.0.6. scows os ciniiesmecvneins 41 nese roerany Gr PE NyAIGAL BIOLOPY....6-5< >> >a cies Maat ache auisws oer sie ste 49 Cuapter VI The Fundamental Equations of the Kinetics of Evolving Systems. Gen- eR RE RE PCE EEG Oki arena eso kede ee sean es a he 57 Cuapter VII Chemical Equilibrium, as an Example of Evolution under a Known Law.. 152 ihe Parameters of State. <.c.isvin saseecne dc nnes seein bee eee 300

The Energy ‘Transformers of Nataredi{ Alivc.i<s cae codecs cesctene ee 325 The Relation of the Transformer to Available Sources.................. 336 CuHaptTer XXVI The Morrelating Anparatusictrias ess «oie. soe vss ne cee eee 362 Extension of the Sensuous World Picture... .......0..cccececccucecccuce 371 OO NEC IOUS ORE Mare ener aaa eran teat ats adoro alaicie a. og W' Caters areata’ Die Sreteco Re 388 Sow AI CLIO Of ONRCLOUSDESN 0 aa miamiwar tier ciara nv aisio ance oe Waainvs ala s¥ee eionie 394 The Origin of Consciousness in the Living Organism..................... 402 PP reom EDO Lan LONATOL (CONS CLOUSNEBAN. susie sce ble cn © cm vaio sas ns ca oe nee 406 CHapTer XXXIII inewiowsoletue Correlahing SAPParatUsy. ..c. cicada ndislccinlelsisiares wesietele v stetts 410

fennchuisions=Retrospech and Prospect: cece > <cocoud <0 4 sce dacuiags aca 417 Banonmorcuarnol physical, DIOLOP Ys 32c sec asc ayraiga cs bsaeise «aces cm eaales 435 Fig. 1. Graph of 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. 122........... Fic. 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......

Fig. 4. The law of population growth for the United States according to RPOPIEANCPRCE CMe E em ees ken cincae «tenet cco cre cane ene ree Fig. 5. Growth of a population of Drosophila (fruit flies) under controlled experimental conditions, according to Pearl and Parker............. Fig. 6. Growth of a bacterial colony (B. dendroides). according to IEG MERE TIE OTE RE er ese «coe ts eis ne oa ne Alas see inkns ie citiege siouere stoete Fic. 7. Growth of rat according to H. H. Donaldson and T. B. Robertson.

Fria. 8. Growth of sunflower seedlings according to H. 8. Reed and R. H. iolland* computed curve: by Li. J. Reed. iia. os. ee. so nmsiceecens Fig. 9. Growth of sunflower seedlings. The same data as in figure 8, but Pi Gtedita LOpaAritnmic CiseTaM...c., praca cues coe cee eerie Fic. 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..............cceeceececeessencreees

Fia. 11. Course of parasitic invasion of insect species according to W. R. That attire oS a ae ana rien Acar AR Annan Ips neniinpiinet enc Fra. 12. Increasing diffusion-in-time of successive generations in the progeny of a population element...............2--0eeeeeeee erence ees Fia. 13. Course of parasitic invasion of insect species, according to Lotka; PIGTIPHIATAUUIEATINCUT. corpo tachrr es ace esesce ates he eciee -rebingeen as Fia. 14. Course of parasitic invasion of insect species, according to Lotka; PORE NATD TUORLMICNY. utes foc cw wale dass 2o2 mae ap oe gine sisald seaiaiame

Fra. 19. Logarithmic survival curves for man, Drosophila, and Proales decipiens. Plotted according to centiles of life-span. After R. Pearl. . Fic. 20. Diagrams to illustrate proof of stability of normal age distribution. Reproduced from A. J. Lotka, Proc. Natl. Acad. Sci., vol. 8, Fic. 21. “Stable” age distribution, as exemplified by the population of England and Wales in the decade 1871-1880...............-.++2+2 eee 114 Fig. 22. Diagram of relation between birth rate per head b and death rate per head d in population with stable age distribution................ 117 Fia. 23. Diagrammatic illustration of influence of random and of selective slaughtering upon survival curve of biological species.............- 120 Fie. 24. Growth of favored type in mixed population of two phenotypes After J,. B.S. Haldane. «2 s.5:5..0 vosasctsane ese ae eee ee ae eee . 124 Fia. 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 Fic. 27. Some fundamental types of equilibrium, in a system with two dependent, Variablegs... ta. 2-5 tuc.cu ea eteies:tas alsae elekeielen eae een eee 148 Fia. 28. Map of integral curves for the Ross malaria equations. Reproduced from A. J. Lotka, Am. Jour. Hygiene, January Supplement,

Fia. 30. Age distribution in population of molecules of two substances in monomolecular chemical equilibrium. Reproduced from A. J. Lotka, Kalmbach. cc cn. sas anineae hota > 5 aeeeetin mei cadena 167 Fig. 32. Seasonal analysis of stomach contents of starling. After E. R. Kalmbach and I. N,.Gabrielgon. 2..is.«.e0ecasls oa nckoceee eee 167 Fra. 33. Comparative daily destruction of grasshoppers by several species Fia. 34. Seasonal food habits of the Meadow Lark. After H. C. Bryant. 168 Fia. 35. Stomach contents of a Brewer’s Blackbird. After E. R.

KalmBaoh... .<c...% ¢. ews ss p.ce ge alee humeaerte Semieteites aan ae 169 Fig. 36. Density of microorganisms (exclusive of bacteria) in sea water. After G. W. Martin, oo. sicaecewcsenad an buen hei 174 Fic. 37. Some of the important food-chains of animal life in the Kattegat. After Petersen and Martin., «<3... ...cccss<+ eee eee 175 Fra. 38. The varied diet of the Codfish. By courtesy of the Illustrated Landon New. ..-'cic teres os a obsinds vepeaseti nu ae ascii tee en 177 F16,.89, Kay to figure. 3865 cc an.siss ts 152s uel adv eney wee cues Se 179 Fra. 40. Cross section of the atmosphere showing some features characteristic of different altitudes. After W. J. Humpbhreys....d..0000uee ae 186 Fia. 41. Composition of the atmosphere at different levels. After W. J. Humphrey...» ss kWussadslt Aessiey nic ¢ eatacentn Sheik bern Muaetaiee aan 187 Fig. 42. Comparison of composition of Earth’s crust and human body... 196 Fira. 43. Comparison of sea water and blood serum..................... 202

Fra. 44, Correlation in the occurrence of Na, Fe and K, Mg in rocks. After H. 8. Washington. ..c:y cis <sass icc ciect obec eee 205 Fia. 45. Periodic classification of the elements, showing division into petrogenic elements and metallogenic elements. After H. S. ec emma oe Oe Ws Pee aero ON Fg ot dv kaa od eG ae abana Dee oe 254 Fia. 55. Uranium and its products of radioactive disintegration......... 263 Fig. 56. Equilibrium polygon for Radon (radium emanation) in contact

MIM se MINIT OOTALION PTOUUCHR 2-40.14 ees bd sos noua ee Soaderntulsiens 266 Fia. 57. Relative abundance of the elements. Diagram according to W. D. Harkins, based on analysis of meteorites. (Jour. Am. Chem. LUST et ee ee mo a sas toe sae eee ieee sb bae sees ae 271 Fia. 58. Equilibrium polygon for the human species and some of the species on which it depends for its food supply.................-.0-045 277 Fig. 59. The Yellow Shark and some of his relatives, as an example of DossIDiy orthogenctic development... sic. ia sc dees ores seed ecrecsess se 296 Pra oo Law of urban concentration, «. 2.6 icsss acs 5.54 secede s'gei ne ae 308 Fia. 6i. Relation between rate of reproduction in Drosophila (fruit fly) and density of mated population. After Pearl and Parker.......... 309 Fia. 62. Relation between mean length of life and population density in ieononuied, Alter Pearl and Parker... 22.5 26s; cbesSescniadeeeeeres 310 Fia. 63. Hyperbolic curves obtained by plotting as ordinates the number of general, 2,3. . . nspecies, and as abscissae the number n of such Po SESU TES) tA Be (a CLT a ae ek tea oe ee 314 Fia. 64. Relation between number and size of genera of all flowering plants, plotted logarithmically. After J. C. Willis................. 315 Fia. 65. Relation between number and size of Rubiaceae, plotted logarith- RTO ATUGET Dy Kore WV LLIN, «letters oe inne ad areca pvaieraigie Wie bisa eae pin sane 315 Fia. 66. Relation between number and size of genera of chrysomelid beetles, plotted logarithmically. After J. C. Willis.................++000- 316

Fia. 67. Solubility of carbon dioxide in water, expressed in volumes of CO; measured at normal temperature and pressure, per volume of water. PCCP Rta VV ee NE TUe sy epigas vals viavie sce as Caries eee tee ase euikesnminee 318 TGmOseel he Titlawheel- GL 16.70. 4c cence rds ac wd cae ode aadee shag smears ts 334 Fic. 69. Mechanical walking beetle, exhibiting the several characteristic Fig. 72. How the future enters into the determination of the motion of the walking mechanical beetle, thus imitating purposive action (tele- OLOR Wy) State hoe aaeaac’s payee a3 9 eee Oe Eanes naan s OFAC . 882

VEROUES TIC terre RNA ete RCD RI, occ S GSE A jo hae aih Crews Pom Lene 74 Table 5. Course of parasitic invasion of insect species, according to W. R. SNES TTOPTTS ONO ses Send, RE eS pach Ne Re pe ee be BM te ae 86 Table 6. Tabular survey of different modes of interdependence of biologi- (ont SPOTS ohn tls Ais pet cats are Has eR Os een fer 98 Table 7. Example of normal age distribution.............0..eeceeceseees 113 Table 8. Relation between birth rate per head b and death rate per head d

Table 26. Supply of plant foods in the soil..............0ee eee ee eee eeee 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- BYALION PTOdUcts........-.ccccrvcersccocsenccurversvrecernecsacsese 265 Table 29. Radioactive equilibrium of radon (radium emanation) in con- 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 Adjustors..... 413 Table 36. Classification of the sciences..........---+eeseeeereereseeeees

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 objective 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 supersaturated 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 reasons, 14—Due in part to convenient arbitrary restrictions, 15—Relation between growth, environment and structure, 15—The laws of chemical dynamics in structured systems will be the laws that govern the evolution of a system comprising living organisms, 16—Application to Biology: The organism as a structured physico-chemical system, 16—The travelling environment, milieu intérieur, 17—Increasing independen

ce of organism of its remote environment, 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—Abandonment of attempts to build perpetual motion machines was equivalent to recognizing the law of conservation of energy, 18—Abandonment of the attempt 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 evolution, 19.

Chapter II. Evolution Defined. Definition should conform as far as possible to common usage of the term, 20—Analysis of common conception of evolution, 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 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 definition 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 transformations 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 frictional force, 27—Inertia-free or completely damped systems, 28—Accelerations vanish with velocities, 29—Velocities are single-valued functions of configuration, 29.