Elements of Physical Biology

Among laboratory investigations of the influence of “climatic parameters,”’ under controlled conditions, may be reckoned the work of R. Pearl and §. Parker in their studies “On the Influence of Certain Environmental Factors on the Duration of Life in Drosophila.’’?? 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 cotton wool.

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 analytical conditions for equilibrium, as set forth in Chapter XII, these conditions must be read in the sense that they hold true when certain 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

vary according as pressure and temperature, or volume and temperature. 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, (see Chapter XII) is susceptible. Since certain parameters 71, po, . . . are to be held constant in the application of this condition, the addition of a set of terms P; dp: + P2 dp, + . . . to the expression 6Q’ for a small virtual displacement will in nowise alter its value. We may, then replace the condition (14) by the fully equivalent one

0 = (db), = dXe+...+Pidpit Podm.+... (15) where the subscript p denotes that the parameters pi, po, . . -., conjugate to the parameters P;, P2, . . . . 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! with the similar conditions for equilibrium which, as already pointed out, play an important rdle in thermodynamics. However, in the analogous equations of 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 ® (Xi, Xe, . . . Pi, Po, . . .) The question may, indeed be raised, whether by a suitable 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, Sechs Vorlesungen iiber das thermodynamische Potential, 1906, p. 43. This formal agreement seems to extend also to another feature. The thermodynamic condition for stable equilibrium demands that the second differential (d°)p shall be positive, and this in turn demands that . shall be negative. conjugate parameters of the type (1) of footnote 5, then ae <0. ential. But this is a separate problem, on which we shall not here expend further effort. Only this shall be noted in passing: Whereas, in the thermodynamical treatment of physico-chemical phenomena a function ® 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 thermodynamic potentials, in terms of which the behavior of the system can be concisely epitomized, after the manner of thermodynamics. 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 réle analogous to forces, without being in any sense identical with forces (or even with generalized forces); certain other conjugate parameters p would play a rdle analogous to displacements, and certain functions @ would resemble in their relations to certain events in the system, the energy functions @ (free energy, thermodynamic potentials) of thermodynamics.

That certain isolated portions of such a general system of quasidynamics 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 energetics, in the strict sense, as ordinarily understood, of life-bearing systems in the course of evolution.

Die Natur hat sich die Aufgabe gestellt das der Erde zustrémende Licht im Fluge zu erhaschen und die beweglichste aller Krifte, in die starre Form verwandelt, aufzuspeichern. Zur Erreichung dieses Zweckes hat sie die Erdkruste mit Organismen tiberzogen, welche lebend das Sonnenlicht in sich aufnehmen und unter Verwendung dieser Kraft eine fortlaufende Summe chemischer Differenzen erzeugen. Diese Organismen sind die Pflanzen. Die Pflanzenwelt bildet ein Reservoir, in welchem die fliichtigen Sonnenstrahlen fixiert und zur Nutzniessung geschickt, niedergelegt werden.—J. 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. 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 living 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 transformers, or engines.'

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 process, 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 inexorably 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 proportional to the quantity M (mass) of working substance and its frequency of circulation, n, per unit of time, through the cycle; thus

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 wpon the temperature of the source and that of the sink; with a suitably chosen temperature scale the law of the maximum output W can be put in the extremely simple form where Q is the energy drawn from the source, 7’, the (absolute) temperature of the source, and 7, that of the sink. The ratio a which measures the fraction of the energy Q converted into work is spoken of as the efficiency of the transformer.

The actual performance of a heat engine always falls short—and usually far short—of the theoretical maximum (3) attainable under ideal conditions of reversible operation, whereas all real processes, as has been pointed out in an earlier chapter, are zrreversible. The first service rendered by the laws of thermodynamics is thus a negative one, to save us from vain efforts to achieve the impossible. They tell us what we cannot do; they give us no guarantee as to what we can do, in this matter of engine efficiency. In other fields these same principles are, indeed, found competent to yield us information of most positive character, as the physicist and physical chemist knows from boundless wealth of example; the very fact that they hold independently of substance and form lends to their application a catholicity hardly equalled elsewhere in science, and at the same time gives 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 réle. Here thermodynamics may be found powerless to assist us greatly, and the need for new methods may be felt. The significance of this in our present concerns will be seen as the topic develops.

Composite and Coupled Transformers. The simplest type of transformer of the kind that here chiefly interests us would comprise one working substance fed from one source and discharging to one sink. Two or more such transformers may, however, work in parallel from one source, thus forming in the aggregate one composite transformer. Or, two or more may be coupled in series or cascade, the sink of one functioning as the source for the next of the series. So, for example, W. L. R. Emmett has constructed a composite engine consisting of two separate engines, the first operating with mercury

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” 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 chemical 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 transformer. For in that case, if a mass hM stores an amount of energy W, we have, according to (2) for a small interval of time dt 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 independent of the size of the transformer, we have by integration of (4)

The transformer under these conditions, grows according to the law of compound interest. 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 M and write 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/b 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 substance 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 drawn, 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 substance, but with a complex variety of such substances, a fact which has certain important consequences.

Plant and Animal as Coupled Transformers. Coupled transformers 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 interest 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 COs, 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 compound 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 functions 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. 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 aggregate one large transformer built up of many units functioning in parallel. * Hydra viridis, however, is probably not a single organism, but an organism of the animal type harboring in its body separate plant-like organisms with which it lives in symbiosis. 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,‘ ninety-eight million miles away from the working substance (the “‘boiler’’). From the engineer’s standpoint this would be an execrably bad design, if a high efficiency alone were the aimin 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 2,200,000,000 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’ not quite 2 gramcalories (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* 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’ all the energy taking part in the

4 The recognition of this fact is credited by Herbert Spencer (First Principles, § 172, footnote) to Herschel (Outlines of Astronomy, 1833). 6 Jour. Franklin Inst., 1920, p. 118. Compare also G. Ciamician, Die Photochemie der Zukunft (Sammlung Chemisther Vortriige, 1922, p. 429). Assuming 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 sunlife cycle must pass. And of this last amount only 24 per cent falls to plants cultivated for human needs.’ 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 adequate picture of the life cycle in its totality if we reflect that the total energy thus coursing through the system every year is of the order of 22 times’ 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. Ifthe 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 as could not very well be supposed to exist in the most primitive life forms. * H. A. Spoehr, Jour. Ind. and Eng. Chem., 1922, vol. 14, p. 1144. Regarding 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 thisenergy. 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 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. Washington 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 dissipated during the growth of the plant. See also C. L. Holsberg, Jour. Ind. Eng.

the winds represent some 5000 times that amount of coal.? 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" 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 billion 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" has calculated that if every 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” quotes an estimate by Engler of the world’s total water power as the equivalent of seventy billions of tons of coal. According to C. G. Gilbert and J. E. Pogue 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