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. 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 perhaps 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.’ 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 we mine and spread on our field, so that this loop in the chain 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 the element is a closed circulation. Unfortunately the cycle is quantitatively quite incomplete. Wan Hise, quoting Whitson’s investigations, shows that, on a very conservative estimate, the soil of the United States loses annually some 2 million tons of P.O;, the equivalent 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 seen that the 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. ’¥For an excellent illustrated account of the part played by the Guanay bird in this cycle see R. C. Murphy, Natl. Geogr. Mag. Sept. 4, 1924,"p." 279, an 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, is largely due to the depletion of the soil in phosphorus. . . . . The work (at the Ohio Agricultural Experiment Station’) 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.!°

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 contains a moderate percentage of a substance it may be possible to utilize it commercially, whereas, if the percentage falls below this amount it is without value.

Phosphatic 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 secondary 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 constituent in steel) becomes segregated, and is thus eliminated, in the slag. This latter, by suitable processes, is converted into a very serviceable fertilizer.”

8 The Natural Wealth of the Land, and its Conservation. Paper given at the White House Conservation Conference, May 13, 1908. 12 For details regarding the use of phosphatic slags as fertilizer the reader may be referred to G. S. Robertson, Basic Slag and Rock Phosphates, Cambridge University Press, 1922. 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 Vinet.

The Circulation of Chlorine and the Alkalis. It will be convenient 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 prepare 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 bunsen 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 # 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 J until it reaches the top of the syphon, whereupon it drains back into the flask A and is reévaporated, 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. The action of this apparatus is closely analogous to the natural extraction of soluble constituents from the earth’s crust by the water in circulation through clouds, rain, rivers and the sea, under the influence of the sun’s heat.

@IOAD AAIMOTHD WOAIGOY AH, ‘aUOLVN NI SLNAWATOL GHL dO NOILVIOOUID “FG “OI 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?! It is a circumstance 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.”

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, Boel 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. 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 recovery 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.* 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 sulphur. 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.

The 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

role not only within the body of the organism, but also in the soll, where it hastens the oxidation of carbonaceous matter, thus conde 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 a characteristic stamp is placed on certain of the elementary cycles by the form in which

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 corn. 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). each element occurs or takes part in the circulation. Thus, the gases oxygen and carbon dioxide occur in nearly uniform distribution, 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 elements and those which like phosphorus, potash, ete., 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 te the phenomenon 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

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 réle in those secondary life phenomena which we commonly describe as commerce and trade. Two tables 26, and 27, are, finally appended, the one giving certain data of interest regarding the Supply of Plant Foods in the

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 perhaps that can be attained in the present state of our knowledge. As I’, W. Clarke’ remarks, “Such estimates may have slight numerical 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® once more: “In calculations of this sort there is a certain fascination, but their chief merit seems to lie in their Suggestiveness.”’

Aus dieser Untersuchung wird kein Dualismus hervorgehen, sondern eine Wissenschaft, welche Organisches und Anorganisches umfasst, und die den beiden Gebieten gemeinsamen Thatsachen darstellt.—E. Mach. 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 equilibrium. 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 ata temperature 6, it is commonly assumed that at every instant the quantities X, Y are such as correspond to equilibrium at the temperature @.

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 Po, the variables X, Y,. . . defining the state of the system have certain values Xo, Yo, . . . 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 variables X, Y will have nearly the value of Xo, Yo, . . - Or, in the notation of an earlier section, if

gives X; = Cj = constant (3) then we assume that with P= Pip (4) where P(t) is a slowly changing function of t, we shall have where C;(t) is a root of the system of equations It should be noted that, strictly speaking, this involves a contradiction. 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

The second approximation we obtain by differentiating (10), (11), so as to obtain the derivatives Xy’, Y1’, which, although not zero, are nevertheless small, according to our supposition of a slow change. Substituting these in (7), (8) we find And so on, for successive higher approximations. But this process can be contracted into a compact expression. We have from which it is seen that X.(t), Y2(¢) can be expressed directly as the solution of the system of equations

Special Case. Returning to the general case of n variables, suppose that for all values of Xi X.. . . differing appreciably from 3. Gat Om ie the equilibrium values, the velocities a Ta . . . are negligible dXr : as compared with some one of them, say a Then we can write, practically BCX Xa ce ey eee Xn) = FAX SXRG Mae a ee (25) JUNO Cp 2 Gyprs 5 He eh e X,) =0 where F; is excluded from the system (25). This defines Xi = C1(X,) etc. 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.

Moving equilibria play an important réle in evolutionary processes of the most varied type, as emphasized almost ad nauseam by Herbert Spencer,! 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 VILLA LALLA MALL A Ad dM AMAL MMM (Ra) UMIMMMLUMMIUMLMLTM YMA,

LLL (Po) VL LLLLLA hhh hh hhh Geo ) WILMMSSSSEE LA SLMMMMGLMTE STL he, Whhlllelitttss (Rab) ZL LLL LLAMA Rac) WULMMAIULMIUMIMILUMSSLSESALSEES A, Fic. 55. URANIUM AND Irs Propucts or RaproacTiIvE DISINTEGRATION (U = uranium; Io = ionium; Ra = radium; Rn = radon = radium emanation; 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.

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 typ‘cal series of radioactive transformation chains, and to state briefly the simple law of transformation of such elements by spontaneous atomic disintegration: The amount of a substance transformed per unit of time is directly proportional to the amount of that substance present, so that if S; is the 7 substance in a transformation chain

Si Sem. 2 w OS... a=? Sitio Be (31) and if we denote by X; the mass of S;, then we have a system of equation where the coefficients \ are constants, invariable under all conditions 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? 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 7‘ substance, being