University of Virginia Library

Chapter 13
Simple and Compound Evolution

§98. Where the only forces at work are those directly tending to produce aggregation or diffusion, the whole history of an aggregate will comprise no more than the approaches of its components towards their common centre and their recessions from their common centre. The process of evolution, including nothing beyond what was described at the outset of the last chapter, will be simple.

Again, where the forces which cause movements towards a common centre greatly exceed all other forces, any changes additional to those of aggregation will be comparatively insignificant: there will be integration slightly modified by further kinds of redistribution.

Or if because of the smallness of the mass, or because of the little motion it receives from without in return for the motion it loses, the integration proceeds rapidly; there will similarly be wrought but insignificant effects by secondary forces, even though these are considerable.

But when, conversely, the integration is slow. either, because the quantity of motion contained in the aggregate is relatively great; or because, though the quantity of motion which each part possesses is not relatively great, the large size of the aggregate prevents easy dissipation of the motion. or because, though motion is rapidly lost more motion is rapidly received; then, other forces will cause in the aggregate sensible modifications. Along with the change constituting integration, there will take place further changes. The Evolution, instead of being simple, will be compound.

These several propositions require some explanation.

§99. So long as a body moves freely through space, every force which acts on it produces an equivalent in the shape of some change in its motion. No matter how high its velocity the slightest lateral traction or resistance causes it to deviate from its line of movement; and the effect of the perturbing influence goes on accumulating in the ratio of the squares of the times during which its action continues uniform. But when this same body is held fast by gravitation or cohesion, small incident forces, instead of giving it some relative motion through space, are otherwise dissipated.

What thus holds of masses holds, in a qualified way, of the sensible parts of masses, and of molecules. As the sensible parts of a mass, and the molecules of a mass, are, by virtue of their aggregation, not perfectly free, it is not true of each of them, as of a body moving through space, that every incident force produces an equivalent change of position: part of the force goes in working other changes. But in proportion as the parts of the molecules are freely bound together, incident forces effect marked re-arrangements among them. Where the integration is so slight that the parts, sensible or insensible, are almost independent, they are almost completely amenable to every additional action; and along with the concentration going on there go on other re-distributions. Contrariwise, where the parts are so close that what we call the attraction of cohesion is great, additional actions, unless intense, have little power to cause secondary re-arrangements. The firmly-united parts do not change their relative positions in obedience to small perturbing forces; but each small perturbing force usually does nothing more than temporarily modify the insensible molecular motions.

How may we best express this difference in general terms? An aggregate that is widely diffused, or but little integrated, is an aggregate containing a large quantity of motion — actual or potential or both. An aggregate that has become completely integrated or dense, is one containing comparatively little motion: most of the motion its parts once had has been lost during the integration that has rendered it dense. Hence, other things equal, in proportion to the quantity of motion an aggregate contains will be the quantity of secondary change in the arrangement of its parts that accompanies the primary change in their arrangements. Hence also other things equal, in proportion to the time during which the internal motion is retained, will be the quantity of this secondary re-distribution. It matters not how these conditions are fulfilled. Whether the internal motion continues great because the components are of a kind that will not readily aggregate, or because surrounding conditions prevent them from parting with their motion, or because the loss of their motion is impeded by the size of the aggregate they form, or because they directly or indirectly obtain more motion in place of that which they lose; it throughout remains true that much retained internal motion renders secondary re-distributions facile, and that long retention of it makes possible an accumulation of such secondary re-distributions. Conversely, non-fulfilment of these conditions, however caused, entails opposite results. Be it that the components of the aggregate have special aptitudes to integrate quickly, or be it that the smallness of the aggregate permits easy escape of their motion, or be it that they receive little or no motion in exchange for that which they lose; it alike holds that but little secondary re-distribution can accompany the primary re-distribution constituting their integration.

Let us, before studying simple and compound Evolution as thus determined, contemplate a few cases in which the quantity of internal motion is artificially changed, and note the effects on the re-arrangement of parts.

§100. When a vessel has been filled to the brim with loose fragments, shaking it causes them to settle down into less space, so that more may be put in. And when among th e fragments there are some of much greater specific gravity than the rest, these, in the course of a prolonged shaking, find their way to the bottom. What are these results, expressed in general terms? We have a group of units acted on by an incident force — the attraction of the Earth. So long as these units are not agitated, this incident force cannot change their relative positions; agitate them, and their loose arrangement passes into a more compact arrangement. Again, so long as they are not agitated, the incident force cannot separate the heavier units from the lighter; agitate them, and the heavier units begin to segregate. Mechanical disturbances of more minute kinds, acting on the parts of much denser masses, produce analogous effects. A piece of iron which, when it leaves the workshop, is fibrous in structure, becomes crystalline if exposed to a perpetual jar. The polar forces mutually exercised by the atoms, fail to change their disorderly arrangement into an orderly arrangement while they are relatively quiescent; but these forces succeed in rearranging them when they are kept in a state of intestine motion. Similarly, the fact that a bar of steel suspended in the magnetic meridian and repeatedly struck, becomes magnetized, is ascribed to a re-arrangement of particles produced by the magnetic force of the Earth when vibrations are propagated through them. Now imperfectly as these cases parallel those we are considering. they yet serve roughly to illustrate the effect which adding to the quantity of motion an aggregate contains, has in facilitating re-distribution of its components.

More fully illustrative are the instances in which, by artificially adding to or substracting from the molecular motion called its heat, we give an aggregate increased or diminished facility of re-arranging its molecules. The process of tempering steel or annealing glass, shows us that internal re-distribution is aided by insensible vibrations, as we have just seen it to be by sensible vibrations. When some molten glass is dropped into water, and its outside is thus, by sudden solidification, prevented from participating in that contraction which subsequent cooling of the inside tends to produce; the units are left in such a state of tension, that the mass flies into fragments if a small portion be broken off. But if this mass be kept for a day or two at a considerable heat, though a heat not sufficient to alter its form, this extreme brittleness disappears: the component particles being thrown into greater agitation, the tensile forces are enabled to re-arrange them into a state of equilibrium. Much more conspicuous is the effect of heat where the re-arrangement of parts taking place is that of visible segregation. An instance is furnished by the subsidence of fine precipitates. These sink down very slowly from solutions which are cold; while warm solutions deposit them with comparative rapidity. That is to say, exalting the molecular oscillation throughout the mass, allows the suspended particles to separate more readily from the particles of fluid. The influence of heat on chemical changes is so familiar that examples are scarcely needed. Be the substances concerned gaseous, liquid, or solid, it equally holds that their chemical unions and disunions are aided by rise of temperature. Affinities which do not suffice to effect the re-arrangement of mixed units that are in a state of feeble agitation, suffice to effect it when the agitation is raised to a certain point. And so long as this molecular motion is not great enough to prevent those chemical cohesions which the affinities tend to produce, exalting it facilitates chemical re-arrangement.

Let us pass to illustrations of a different class. Other things equal, the liquid form of matter implies a greater quantity of contained motion than the solid form: the liquidity being itself a consequence of such greater quantity. Hence, an aggregate made up partly of liquid matter and partly of solid matter, contains more motion than one which, otherwise like it, is made up wholly of solid matter. It is inferable, then, that a liquid-solid aggregate, or, as we call it, a plastic aggregate, will admit of internal re-distribution with comparative facility; and the inference is verified by experience. While a magma of unlike substances ground up with water continues thin there goes on a settlement of its heavier components — a separation of them from the lighter. As the water evaporates this separation is impeded, and ceases when the magma becomes thick. But even when it has reached the semi-solid state in which gravitation fails to cause further segregation of its mixed components, other forces may still produce segregation: witness the fact that when the pasty mixture of ground flints and kaolin, prepared for making porcelain, is kept some time, it becomes gritty and unfit for use — the particles of silica separate themselves from the rest and unite into grains; or witness the fact known to every housewife, that in long-kept currant-jelly the sugar takes the shape of imbedded crystals.

No matter then under what form the motion contained by an aggregate exists — be it visible agitation, or such vibrations as produce sound, be it molecular motion absorbed from without, or the constitutional molecular motion of some component liquid, the same truth holds. Incident forces work secondary re-distributions easily when the contained motion is large in quantity; and work them with increasing difficulty as the contained motion diminishes.

§101. Yet another class of facts which fall within the same generalization must be named before proceeding. They are those presented by certain contrasts in chemical stability. Speaking generally, stable compounds contain but little molecular motion, and in proportion as the contained molecular motion is great the instability is great.

The most common and marked illustration of this, is that chemical stability decreases as temperature increases. Compounds of which the elements are strongly united and compounds of which the elements are feebly united, are alike in this, that heating them or adding to the quantities of their contained molecular motion, diminishes the strengths of the unions of their elements; and by continually augmenting the contained molecular motion, a point is in each case reached at which the union is destroyed. That is to say the re-distribution of matter which constitutes simple chemical decomposition, is easy in proportion as the quantity of contained motion is great. The like holds with double decompositions. Two compounds, A B and C D, mingled together and kept at a low temperature, may severally remain unchanged: the cross-affinities between their components may fail to cause re-distribution. Raise the heat of the mixture, and re-distribution takes place; ending in the formation of the compounds A C and B D.

Another truth having a like implication, is that chemical elements which, as they ordinarily exist, contain much motion, have combinations less stable than those of which the elements, as they ordinarily exist, contain little motion. The gaseous form of matter implies a relatively large amount of molecular motion, while the solid form implies a relatively small amount. What are the traits of their respective compounds? Those which the permanent gases form with one another, cannot resist high temperatures: most of them are easily decomposed by heat; and at a red heat, even the stronger ones yield up their components. On the other hand, the chemical unions between elements that are solid except at high temperatures, are very stable. In many, if not indeed in most, cases, such unions are not destroyed by any heat we can produce.

There is, again, the relation, which appears to have a kindred meaning, between instability and amount of composition. "In general, the molecular heat of a compound increases with the degree of complexity." With increase of complexity there also goes increased facility of decomposition. Whence it follows that molecules with contain much motion in virtue of their complexity, are those of which the components are most easily re-distributed. This holds not only of the complexity arising from the union of several unlike elements; it holds also of the complexity arising from the union of the same elements in higher multiples. Matter has two solid states, distinguished as crystalloid and colloid; of which the first is due to union of the individual atoms or molecules, and the second to the union of groups of such individual atoms or molecules; and of which the first is stable and the second unstable.

But the most conclusive illustration is furnished by the combinations into which nitrogen enters. These are specially unstable and contain specially great quantities of motion. A peculiarity of nitrogen is that, instead of giving out heat when it combines with other elements, it absorbs heat. Besides carrying with it into the liquid or solid compound it forms, the motion which previously constituted it a gas, it takes up additional motion; and where the other element with which it unites is gaseous, the molecular motion proper to this, also, is locked up in the compound. Now these nitrogen-compounds are unusually prone to decomposition; and the decompositions of many of them take place with extreme violence. All our explosive substances are nitrogenous — the most destructive of them all, chloride of nitrogen, being one which contains the immense quantity of motion proper to its component gases, plus a further quantity of motion.

Evidently these general chemical truths are parts of the more general physical truth we are tracing out. We see in them that what holds of sensible masses, holds also of the insensible masses we call molecules. Like the aggregates formed of them, these ultimate aggregates become more or less integrated according as they lose or gain motion; and like them also, according as they contain much or little motion, they are more or less liable to undergo secondary re-distributions along with the primary re-distribution.

§102. And now having brought this general principle clearly into view, let us observe how, in conformity with it, Evolution becomes, according to the conditions, either simple or compound.

If a little sal-ammoniac or other volatile solid be heated, it is disintegrated by the absorbed molecular motion and rises in gas. If this gas comes in contact with a cold surface, and loses it excess of molecular motion, integration takes place — the substance assumes the form of crystals. This is a case of simple evolution. The concentration of matter and dissipation of motion do not here proceed gradually — do not pass through stages; but the molecular motion which caused assumption of the gaseous state being dissipated, the matter passes suddenly to a solid state. The result is that along with this primary re-distribution there go on no appreciable secondary re-distributions. Substantially the same thing holds with crystals deposited from solutions. Loss of that molecular motion which, down to a certain point, keeps the molecules from uniting, and sudden solidification when the loss goes below that point, occur here as before; and here as before, the absence of a period during which the molecules are partially free and gradually losing their freedom, is accompanied by the absence of minor re-arrangements.

Mark, conversely, what happens when the concentration is slow. A gaseous mass losing its heat and undergoing a consequent decrease of bulk, undergoes also many simultaneous changes. The great quantity of molecular motion contained in it, giving great molecular freedom, renders every part sensitive to every incident force; and, as a result, its parts have various motions besides that implied by their progressing integration. Indeed these secondary motions which we know as currents, are so conspicuous as quite to subordinate the primary motion. Suppose that, presently, the loss of molecular motion has reached the point at which the gaseous state can no longer be maintained, and condensation follows. Under their more closely-united form, the parts of the aggregate display, to a considerable degree, the same phenomena as before. The molecular motion and accompanying molecular mobility implied by the liquid state, permit easy re-arrangement; and hence there go on rapid and marked changes in the relative positions of parts — local streams produced by slight disturbing forces. But now, if instead of a mobile liquid we take a sluggish one such as molten pitch or asphalte, what happens as the molecular motion decreases? The liquid thickens — its parts cease to be movable among one another with ease; and the transpositions caused by feeble incident forces become slow. Little by little the currents are stopped, but the mass still continues modifiable by stronger incident forces. Gravitation makes it bend or spread out when not supported on all sides, and it may easily be indented. As it cools, it continues to grow stiffer; and eventually, further loss of heat renders it quite hard: its parts are no longer appreciably re-arrangeable by any save violent actions.

Among inorganic aggregates, then, secondary redistributions accompany the primary re-distributions where this is gradual. During the gaseous and liquid stages, the secondary re-distributions, rapid and extensive as they are, leave no traces: the molecular mobility being such as to negative the fixed arrangement of parts we call structure. On approaching solidity we arrive at a plastic condition in which re-distributions can still be made, though much less easily; and in which they have a certain persistence — a persistence which can, however, become decided only where solidification stops further re-distribution.

Here we see what are the conditions under which Evolution becomes compound, while we see how the compounding of it can be carried far only in cases more special than any hitherto contemplated; since, on the one hand, extensive secondary re-distributions are possible only where there is a great quantity of contained motion, and, on the other hand, such re-distributions can have permanence only where the contained motion has become small: opposing conditions which seem to negative any large amount of permanent secondary re-distribution.

§103. And now we are in a position to see how these apparently contradictory conditions are reconciled. We shall appreciate the peculiarity of the aggregates classed as organic, in which Evolution becomes so high; and shall see that this peculiarity consists in the combination of matter into forms embodying enormous amounts of motion at the same time that they have a great degree of concentration.

For notwithstanding its semi-solid consistence, organic matter contains molecular motion locked up in each of the ways above contemplated separately. Let us note its distinctive traits. Three out of its four chief components are gaseous; and in their uncombined states these gases united in it have so much molecular motion that they are condensible only with extreme difficulty. Hence it is to be inferred that the proteid-molecule concentrates an immense amount of motion in a small space. And since many equivalents of these gaseous elements unite in one of these proteid-molecules, there must be in it a large quantity of relative motion in addition to that which the ultimate atoms possess. Moreover, organic matter has the peculiarity that its molecules are aggregated into the colloid and not into the crystalloid arrangement; forming, as is supposed, clusters of clusters which have movements in relation to one another. Here, then, is a further mode in which molecular motion is included. Yet again, these compounds of which the essential parts of organisms are built, are nitrogenous; and we have lately seen it to be a peculiarity of nitrogenous compounds that, instead of giving out heat during their formation, they absorb heat. To all the molecular motion possessed by gaseous nitrogen, is added more motion; and the whole is concentrated in semi-solid protein. Organic aggregates are very generally distinguished, too, by having much insensible motion in a free state — the motion we call heat. Though in many cases the quantity of this contained insensible motion is inconsiderable, in other cases a temperature much above that of the environment is constantly maintained. Once more, there is the vast quantity of motion embodied in the water that permeates organic matter. It is this which, giving to the water its high molecular mobility, gives mobility to the organic molecules partially suspended in it; and preserves that plastic state which so greatly facilitates re-distribution.

These several statements yield no adequate idea of the extent to which living organic substance is thus distinguished from other substances having like sensible forms of aggregation. But some approximation to such an idea may be obtained by contrasting the bulk occupied by this substance, with the bulk which its constituents would occupy if uncombined. An accurate comparison cannot be made in the present state of science. What expansion would occur if the constituents of the nitrogenous compounds could be divorced without adding motion from without, is too complex a question to be answered. But respecting the constituents of that which forms four-fifths of the weight of an ordinary animal — its water — a tolerably definite answer can be given. Were the oxygen and hydrogen of water to lose their affinities, and were no molecular motion supplied to them beyond that contained in water at blood-heat, they would assume a volume twenty times that of the water.

Whether protein under like conditions would expand in a greater or a less degree, must remain an open question; but remembering the gaseous nature of three out of its four chief components, remembering the above-named peculiarity of nitrogenous compounds, remembering the high multiples and the colloidal form, we may conclude that the expansion would be great. We shall not be wrong, therefore, in saying that the elements of the human body if suddenly disengaged from one another, would occupy far more than a score times the space they do: the movements of their molecules would compel this wide diffusion. Thus the essential characteristic of living organic matter, is that it unites this large quantity of contained motion with a degree of cohesion which permits temporary fixity of arrangement.

§104. Besides seeing that organic aggregates differ from other aggregates, alike in the quantity of motion they contain and the amount of re-arrangement of parts which accompanies the progressive integration; we shall see that among organic aggregates themselves, differences in the quantities of contained motion are accompanied by differences in the amounts of re-distribution.

The contrasts among organisms in chemical composition yield us the first illustration. Animals are distinguished from plants by their far greater amOunts of structure, as well as by far greater rapidity with which changes go on in them; and, in comparison with plants, animals contain immensely larger proportions of those nitrogenous molecules in which so much motion is locked up. So, too, is it with the contrasts between the different parts of each animal. Though certain nitrogenous parts, as cartilage, are stable and inert, yet the parts in which secondary re-distributions have gone on, and are ever going on, most actively, are those mainly formed of highly-compounded nitrogenous molecules; while parts which, like deposits of fat, consist of relatively-simple molecules, that are non-nitrogenous, are seats of but little structure and but little change.

We find proof, too, that the continuance of the secondary re-distributions by which organic aggregates are distinguished depends on the presence of that locked-up motion which gives mobility to the water diffused through them; and that, other things equal, there is a direct relation between the amount of re-distribution and the amount of contained water. The evidences may be put in three groups. There is the familiar fact that a plant has its formative changes arrested by cutting off the supply of water: the primary redistribution continues — it withers and shrinks or becomes more integrated — but the secondary re-distributions cease. There is the less familiar fact that the like result occurs in animals — occurs, indeed, after a relatively smaller diminution of water. Certain of the lower animals furnish additional proofs. The Rotifera may be rendered apparently lifeless by desiccation, and will yet revive if wetted. When the African rivers it inhabits are dried up the Lepidosiren remains torpid in the hardened mud until return of the rainy season brings water. Humboldt states that during the summer drought, the alligators of the Pampas lie buried in a state of suspended animation beneath the parched surface, and struggle up out of the earth as soon as it becomes humid. The history of each organism teaches the same thing. The young plant, just putting its head above the soil, is more succulent than the adult plant; and the amount of transformation going on in it is relatively greater. In that portion of an egg which displays the formative processes during the early stages of incubation, the changes of arrangement are more rapid than those which an equal portion of the body of a hatched chick undergoes. As may be inferred from their respective powers to acquire habits and aptitudes, the structural modifiability of a child is greater than that of an adult; and the structural modifiability of a young man is greater than that of an old man: contrasts which are associated with contrasts in the densities of the tissues; since the ratio of water to solid matter diminishes with advancing age. And then we have this relation repeated in the contrasts between parts of the same organism. In a tree, structural changes go on rapidly at the ends of shoots, where the ratio of water to solid matter is very great; while the changes are very slow in the dense and almost dry substance of the trunk. Similarly in animals, we have the contrast between the high rate of change going on in a soft tissue like the brain, and the low rate of change going on in dry non-vascular tissues — hairs, nails, horns, etc.

Other groups of facts prove that the quantity of secondary re-distribution in an organism varies, caeteris paribus, according to the contained quantity of the motion called heat. The contrasts between different organisms, and different states of the same organism, unite in showing this. Speaking generally, the amounts of structure and rates of structural change, are smaller throughout the vegetal kingdom than throughout the animal kingdom; and, speaking generally, the heat of plants is less than the heat of animals. Comparisons of the several divisions of the animal kingdom with one another, disclose parallel relations. Regarded as a whole, vertebrates are higher in temperature than invertebrates; and they are as a whole higher in activity and complexity. Between subdivisions of the Vertebrata themselves, like differences in the degrees of molecular vibration accompany like differences in the degrees of evolution. The least compounded of the Vertebrata are the fishes; and, usually, the heat of fishes is nearly the same as that of the water in which they swim: only some large ones being decidedly warmer. Though we habitually speak of reptiles as cold-blooded, and though they have not much more power than fishes of maintaining a temperature above that of their medium, yet since their medium (which is, in the majority of cases, the air of warm climates) is on the average warmer than the medium inhabited by fishes, the temperature of the class reptiles is higher than that of the class fishes; and we see in them a correspondingly higher complexity. The much more active molecular agitation in mammals and birds, goes along with a considerably greater multiformity of structure and a far greater vivacity. The most instructive contrasts, however, are those occurring in the same organic aggregates at different temperatures. Structural changes in plants vary in rate as the temperature varies. Though light effects those molecular changes causing vegetal growth, yet in the absence of heat, such changes are not effected: in winter there is enough light, but not enough heat. That this is the sole cause of the suspension of growth, is proved by the fact that at the same season, plants contained in hot-houses go on producing leaves and flowers. We see, too, that their seeds, to which light is not simply needless but detrimental, germinate only when the return of a warm season raises the rate of molecular agitation. In like manner the ova of animals, undergoing those changes which produce structure in them, must be kept more or less warm: in the absence of a certain amount of motion among their molecules, the re-arrangement of parts does not go on. Hybernating animals also supply proof that loss of heat carried far, retards extremely the vital transformations. In animals which do not hybernate, as in man, prolonged exposure to intense cold causes extreme sleepiness, which implies a lowered rate of organic changes; and if the loss of heat continues, there comes death, or stoppage of these changes.

Here, then, is an accumulation of proofs. Living aggregates are distinguished by the associated facts, that during integration they undergo remarkable secondary changes which other aggregates do not undergo to anything like the same extent; and that they contain (bulks being supposed equal) immensely greater quantities of motion, locked up in various ways.

§105. The last chapter closed with the remark that while Evolution is always an integration of Matter and dissipation of Motion, it is in most cases much more. And this chapter opened by specifying the conditions under which Evolution is integrative only, or remains simple, and the conditions under which it is something further than integrative, or becomes compound. In illustrating this contrast between simple and compound Evolution, and in explaining how the contrast arises, a vague idea of Evolution in general has been conveyed. Unavoidably, we have to some extent forestalled the full discussion of Evolution about to be commenced.

There is nothing in this to regret. A preliminary conception, indefinite but comprehensive, is needful as an introduction to a definite conception. A complex idea is not communicable directly, by giving one after another its component parts in their finished forms; since if no outline pre-exists in the mind of the recipient these component parts will not be rightly combined. Much labour has to be gone through which would have been saved had a general notion, however cloudy, been conveyed before the distinct and detailed delineation was commenced.

That which the reader has incidentally gathered respecting the nature of Evolution from the foregoing sections, he may thus advantageously use as a rude sketch. He will bear in mind that the total history of every sensible existence is included in its Evolution and Dissolution; which last process we leave for the present out of consideration. He will not forget that whatever aspect of it we are for the moment considering, Evolution is always to be regarded as an integration of Matter and dissipation of Motion, which may be, and usually is, accompanied by other transformations of Matter and Motion. And he will everywhere expect to find that the primary re-distribution ends in forming aggregates which are simple where it is rapid, but which become compound in proportion as its slowness allows the effects of secondary re-distributions to accumulate.

§106. There is much difficulty in tracing out transformations so vast, so varied, and so intricate as those now to be entered upon. Besides having to deal with concrete phenomena of all orders, we have to deal with each group of phenomena under several aspects, no one of which can be fully understood apart from the rest and no one of which can be studied simultaneously with the rest. Already we have seen that during Evolution two great classes of changes are going on together; and we shall presently see that the second of these great classes is re-divisible. Entangled with one another as all these changes are, explanation of any one class or order involves direct or indirect reference to others not yet explained. We can do no more than make the best compromise.

It will be most convenient to devote the next chapter to a detailed account of Evolution under its primary aspect; tacitly recognizing its secondary aspects only so far as the exposition necessitates.

The succeeding two chapters, occupied exclusively with secondary re-distributions, will make no reference to the primary re-distribution beyond that which is unavoidable: each being also limited to one particular trait of the secondary re-distributions.

In a further chapter will be treated a third, and still more distinct, character of the secondary re-distributions.

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