to Homer (1795) announced new modes of attack. Historical investigation was soon transformed by the elaboration of new methods.
5. "Progress" involves a judgment of value, which is not involved in the conception of history as a genetic process. It is also an idea distinct from that of evolution. Nevertheless it is closely related to the ideas which revolutionised history at the beginning of the last century; it swam into men"s ken simultaneously; and it helped effectively to establish the notion of history as a continuous process and to emphasise the significance of time. Pa.s.sing over earlier antic.i.p.ations, I may point to a "Discours" of Turgot (1750), where history is presented as a process in which "the total ma.s.s of the human race" "marches continually though sometimes slowly to an ever increasing perfection." That is a clear statement of the conception which Turgot"s friend Condorcet elaborated in the famous work, published in 1795, "Esquisse d"un tableau historique des progres de l"esprit humain". This work first treated with explicit fulness the idea to which a leading role was to fall in the ideology of the nineteenth century. Condorcet"s book reflects the triumphs of the Tiers etat, whose growing importance had also inspired Turgot; it was the political changes in the eighteenth century which led to the doctrine, emphatically formulated by Condorcet, that the ma.s.ses are the most important element in the historical process. I dwell on this because, though Condorcet had no idea of evolution, the pre-dominant importance of the ma.s.ses was the a.s.sumption which made it possible to apply evolutional principles to history. And it enabled Condorcet himself to maintain that the history of civilisation, a progress still far from being complete, was a development conditioned by general laws.
6. The a.s.similation of society to an organism, which was a governing notion in the school of Savigny, and the conception of progress, combined to produce the idea of an organic development, in which the historian has to determine the central principle or leading character.
This is ill.u.s.trated by the apotheosis of democracy in Tocqueville"s "Democratie en Amerique", where the theory is maintained that "the gradual and progressive development of equality is at once the past and the future of the history of men." The same two principles are combined in the doctrine of Spencer (who held that society is an organism, though he also contemplated its being what he calls a "super-organic aggregate") (A society presents suggestive a.n.a.logies with an organism, but it certainly is not an organism, and sociologists who draw inferences from the a.s.sumption of its organic nature must fall into error. A vital organism and a society are radically distinguished by the fact that the individual components of the former, namely the cells, are morphologically as well as functionally differentiated, whereas the individuals which compose a society are morphologically h.o.m.ogeneous and only functionally differentiated. The resemblances and the differences are worked out in E. de Majewski"s striking book "La Science de la Civilisation", Paris, 1908.), that social evolution is a progressive change from militarism to industrialism.
7. the idea of development a.s.sumed another form in the speculations of German idealism. Hegel conceived the successive periods of history as corresponding to the ascending phases or ideas in the self-evolution of his Absolute Being. His "Lectures on the Philosophy of History" were published in 1837 after his death. His philosophy had a considerable effect, direct and indirect, on the treatment of history by historians, and although he was superficial and unscientific himself in dealing with historical phenomena, he contributed much towards making the idea of historical development familiar. Ranke was influenced, if not by Hegel himself, at least by the Idealistic philosophies of which Hegel"s was the greatest. He was inclined to conceive the stages in the process of history as marked by incarnations, as it were, of ideas, and sometimes speaks as if the ideas were independent forces, with hands and feet. But while Hegel determined his ideas by a priori logic, Ranke obtained his by induction--by a strict investigation of the phenomena; so that he was scientific in his method and work, and was influenced by Hegelian prepossessions only in the kind of significance which he was disposed to ascribe to his results. It is to be noted that the theory of Hegel implied a judgment of value; the movement was a progress towards perfection.
8. In France, Comte approached the subject from a different side, and exercised, outside Germany, a far wider influence than Hegel. The 4th volume of his "Cours de philosophie positive", which appeared in 1839, created sociology and treated history as a part of this new science, namely as "social dynamics." Comte sought the key for unfolding historical development, in what he called the social-psychological point of view, and he worked out the two ideas which had been enunciated by Condorcet: that the historian"s attention should be directed not, as. .h.i.therto, princ.i.p.ally to eminent individuals, but to the collective behaviour of the ma.s.ses, as being the most important element in the process; and that, as in nature, so in history, there are general laws, necessary and constant, which condition the development. The two points are intimately connected, for it is only when the ma.s.ses are moved into the foreground that regularity, uniformity, and law can be conceived as applicable. To determine the social-psychological laws which have controlled the development is, according to Comte, the task of sociologists and historians.
9. The hypothesis of general laws operative in history was carried further in a book which appeared in England twenty years later and exercised an influence in Europe far beyond its intrinsic merit, Buckle"s "History of Civilisation in England" (1857-61). Buckle owed much to Comte, and followed him, or rather outdid him, in regarding intellect as the most important factor conditioning the upward development of man, so that progress, according to him, consisted in the victory of the intellectual over the moral laws.
10. The tendency of Comte and Buckle to a.s.similate history to the sciences of nature by reducing it to general "laws," derived stimulus and plausibility from the vista offered by the study of statistics, in which the Belgian Quetelet, whose book "Sur l"homme" appeared in 1835, discerned endless possibilities. The astonishing uniformities which statistical inquiry disclosed led to the belief that it was only a question of collecting a sufficient amount of statistical material, to enable us to predict how a given social group will act in a particular case. Bourdeau, a disciple of this school, looks forward to the time when historical science will become entirely quant.i.tative. The actions of prominent individuals, which are generally considered to have altered or determined the course of things, are obviously not amenable to statistical computation or explicable by general laws. Thinkers like Buckle sought to minimise their importance or explain them away.
11. These indications may suffice to show that the new efforts to interpret history which marked the first half of the nineteenth century were governed by conceptions closely related to those which were current in the field of natural science and which resulted in the doctrine of evolution. The genetic principle, progressive development, general laws, the significance of time, the conception of society as an organic aggregate, the metaphysical theory of history as the self-evolution of spirit,--all these ideas show that historical inquiry had been advancing independently on somewhat parallel lines to the sciences of nature. It was necessary to bring this out in order to appreciate the influence of Darwinism.
12. In the course of the dozen years which elapsed between the appearances of "The Origin of Species" (observe that the first volume of Buckle"s work was published just two years before) and of "The Descent of Man" (1871), the hypothesis of Lamarck that man is the co-descendant with other species of some lower extinct form was admitted to have been raised to the rank of an established fact by most thinkers whose brains were not working under the constraint of theological authority.
One important effect of the discovery of this fact (I am not speaking now of the Darwinian explanation) was to a.s.sign to history a definite place in the coordinated whole of knowledge, and relate it more closely to other sciences. It had indeed a defined logical place in systems such as Hegel"s and Comte"s; but Darwinism certified its standing convincingly and without more ado. The prevailing doctrine that man was created ex abrupto had placed history in an isolated position, disconnected with the sciences of nature. Anthropology, which deals with the animal anthropos, now comes into line with zoology, and brings it into relation with history. (It is to be observed that history is not only different in scope but) not coextensive with anthropology IN TIME.
For it deals only with the development of man in societies, whereas anthropology includes in its definition the proto-anthropic period when anthropos was still non-social, whether he lived in herds like the chimpanzee, or alone like the male ourang-outang. (It has been well shown by Majewski that congregations--herds, flocks, packs, etc.--of animals are not SOCIETIES; the characteristic of a society is differentiation of function. Bee hives, ant hills, may be called quasi-societies; but in their case the cla.s.ses which perform distinct functions are morphologically different.) Man"s condition at the present day is the result of a series of transformations, going back to the most primitive phase of society, which is the ideal (unattainable) beginning of history. But that beginning had emerged without any breach of continuity from a development which carries us back to a quadrimane ancestor, still further back (according to Darwin"s conjecture) to a marine animal of the ascidian type, and then through remoter periods to the lowest form of organism. It is essential in this theory that though links have been lost there was no break in the gradual development; and this conception of a continuous progress in the evolution of life, resulting in the appearance of uncivilised Anthropos, helped to reinforce, and increase a belief in, the conception of the history of civilised Anthropos as itself also a continuous progressive development.
13. Thus the diffusion of the Darwinian theory of the origin of man, by emphasising the idea of continuity and breaking down the barriers between the human and animal kingdoms, has had an important effect in establishing the position of history among the sciences which deal with telluric development. The perspective of history is merged in a larger perspective of development. As one of the objects of biology is to find the exact steps in the genealogy of man from the lowest organic form, so the scope of history is to determine the stages in the unique causal series from the most rudimentary to the present state of human civilisation.
It is to be observed that the interest in historical research implied by this conception need not be that of Comte. In the Positive Philosophy history is part of sociology; the interest in it is to discover the sociological laws. In the view of which I have just spoken, history is permitted to be an end in itself; the reconstruction of the genetic process is an independent interest. For the purpose of the reconstruction, sociology, as well as physical geography, biology, psychology, is necessary; the sociologist and the historian play into each other"s hands; but the object of the former is to establish generalisations; the aim of the latter is to trace in detail a singular causal sequence.
14. The success of the evolutional theory helped to discredit the a.s.sumption or at least the invocation of transcendent causes.
Philosophically of course it is compatible with theism, but historians have for the most part desisted from invoking the naive conception of a "G.o.d in history" to explain historical movements. A historian may be a theist; but, so far as his work is concerned, this particular belief is otiose. Otherwise indeed (as was remarked above) history could not be a science; for with a deus ex machina who can be brought on the stage to solve difficulties scientific treatment is a farce. The transcendent element had appeared in a more subtle form through the influence of German philosophy. I noticed how Ranke is p.r.o.ne to refer to ideas as if they were transcendent existences manifesting themselves in the successive movements of history. It is intelligible to speak of certain ideas as controlling, in a given period,--for instance, the idea of nationality; but from the scientific point of view, such ideas have no existence outside the minds of individuals and are purely psychical forces; and a historical "idea," if it does not exist in this form, is merely a way of expressing a synthesis of the historian himself.
15. From the more general influence of Darwinism on the place of history in the system of human knowledge, we may turn to the influence of the principles and methods by which Darwin explained development. It had been recognised even by ancient writers (such as Aristotle and Polybius) that physical circ.u.mstances (geography, climate) were factors conditioning the character and history of a race or society. In the sixteenth century Bodin emphasised these factors, and many subsequent writers took them into account. The investigations of Darwin, which brought them into the foreground, naturally promoted attempts to discover in them the chief key to the growth of civilisation. Comte had expressly denounced the notion that the biological methods of Lamarck could be applied to social man. Buckle had taken account of natural influences, but had relegated them to a secondary plane, compared with psychological factors. But the Darwinian theory made it tempting to explain the development of civilisation in terms of "adaptation to environment," "struggle for existence," "natural selection," "survival of the fittest," etc. (Recently O. Seeck has applied these principles to the decline of Graeco-Roman civilisation in his "Untergang der antiken Welt", 2 volumes, Berlin, 1895, 1901.)
The operation of these principles cannot be denied. Man is still an animal, subject to zoological as well as mechanical laws. The dark influence of heredity continues to be effective; and psychical development had begun in lower organic forms,--perhaps with life itself.
The organic and the social struggles for existence are manifestations of the same principle. Environment and climatic influence must be called in to explain not only the differentiation of the great racial sections of humanity, but also the varieties within these sub-species and, it may be, the a.s.similation of distinct varieties. Ritter"s "Anthropogeography"
has opened a useful line of research. But on the other hand, it is urged that, in explaining the course of history, these principles do not take us very far, and that it is chiefly for the primitive ultra-prehistoric period that they can account for human development. It may be said that, so far as concerns the actions and movements of men which are the subject of recorded history, physical environment has ceased to act mechanically, and in order to affect their actions must affect their wills first; and that this psychical character of the causal relations substantially alters the problem. The development of human societies, it may be argued, derives a completely new character from the dominance of the conscious psychical element, creating as it does new conditions (inventions, social inst.i.tutions, etc.) which limit and counteract the operation of natural selection, and control and modify the influence of physical environment. Most thinkers agree now that the chief clews to the growth of civilisation must be sought in the psychological sphere. Imitation, for instance, is a principle which is probably more significant for the explanation of human development than natural selection. Darwin himself was conscious that his principles had only a very restricted application in this sphere, as is evident from his cautious and tentative remarks in the 5th chapter of his "Descent of Man". He applied natural selection to the growth of the intellectual faculties and of the fundamental social instincts, and also to the differentiation of the great races or "sub-species" (Caucasian, African, etc.) which differ in anthropological character. (Darwinian formulae may be suggestive by way of a.n.a.logy. For instance, it is characteristic of social advance that a mult.i.tude of inventions, schemes and plans are framed which are never carried out, similar to, or designed for the same end as, an invention or plan which is actually adopted because it has chanced to suit better the particular conditions of the hour (just as the works accomplished by an individual statesman, artist or savant are usually only a residue of the numerous projects conceived by his brain).
This process in which so much abortive production occurs is a.n.a.logous to elimination by natural selection.)
16. But if it is admitted that the governing factors which concern the student of social development are of the psychical order, the preliminary success of natural science in explaining organic evolution by general principles encouraged sociologists to hope that social evolution could be explained on general principles also. The idea of Condorcet, Buckle, and others, that history could be a.s.similated to the natural sciences was powerfully reinforced, and the notion that the actual historical process, and every social movement involved in it, can be accounted for by sociological generalisations, so-called "laws," is still entertained by many, in one form or another. Dissentients from this view do not deny that the generalisations at which the sociologist arrives by the comparative method, by the a.n.a.lysis of social factors, and by psychological deduction may be an aid to the historian; but they deny that such uniformities are laws or contain an explanation of the phenomena. They can point to the element of chance coincidence. This element must have played a part in the events of organic evolution, but it has probably in a larger measure helped to determine events in social evolution. The collision of two unconnected sequences may be fraught with great results. The sudden death of a leader or a marriage without issue, to take simple cases, has again and again led to permanent political consequences. More emphasis is laid on the decisive actions of individuals, which cannot be reduced under generalisations and which deflect the course of events. If the significance of the individual will had been exaggerated to the neglect of the collective activity of the social aggregate before Condorcet, his doctrine tended to eliminate as unimportant the roles of prominent men, and by means of this elimination it was possible to found sociology. But it may be urged that it is patent on the face of history that its course has constantly been shaped and modified by the wills of individuals (We can ignore here the metaphysical question of freewill and determinism. For the character of the individual"s brain depends in any case on ante-natal accidents and coincidences, and so it may be said that the role of individuals ultimately depends on chance,--the accidental coincidence of independent sequences.), which are by no means always the expression of the collective will; and that the appearance of such personalities at the given moments is not a necessary outcome of the conditions and cannot be deduced. Nor is there any proof that, if such and such an individual had not been born, some one else would have arisen to do what he did. In some cases there is no reason to think that what happened need ever have come to pa.s.s. In other cases, it seems evident that the actual change was inevitable, but in default of the man who initiated and guided it, it might have been postponed, and, postponed or not, might have borne a different cachet. I may ill.u.s.trate by an instance which has just come under my notice. Modern painting was founded by Giotto, and the Italian expedition of Charles VIII, near the close of the sixteenth century, introduced into France the fashion of imitating Italian painters.
But for Giotto and Charles VIII, French painting might have been very different. It may be said that "if Giotto had not appeared, some other great initiator would have played a role a.n.a.logous to his, and that without Charles VIII there would have been the commerce with Italy, which in the long run would have sufficed to place France in relation with Italian artists. But the equivalent of Giotto might have been deferred for a century and probably would have been different; and commercial relations would have required ages to produce the rayonnement imitatif of Italian art in France, which the expedition of the royal adventurer provoked in a few years." (I have taken this example from G.
Tarde"s "La logique sociale" 2 (page 403), Paris, 1904, where it is used for quite a different purpose.) Instances furnished by political history are simply endless. Can we conjecture how events would have moved if the son of Philip of Macedon had been an incompetent? The aggressive action of Prussia which astonished Europe in 1740 determined the subsequent history of Germany; but that action was anything but inevitable; it depended entirely on the personality of Frederick the Great.
Hence it may be argued that the action of individual wills is a determining and disturbing factor, too significant and effective to allow history to be grasped by sociological formulae. The types and general forms of development which the sociologist attempts to disengage can only a.s.sist the historian in understanding the actual course of events. It is in the special domains of economic history and Culturgeschichte which have come to the front in modern times that generalisation is most fruitful, but even in these it may be contended that it furnishes only partial explanations.
17. The truth is that Darwinism itself offers the best ill.u.s.tration of the insufficiency of general laws to account for historical development. The part played by coincidence, and the part played by individuals--limited by, and related to, general social conditions--render it impossible to deduce the course of the past history of man or to predict the future. But it is just the same with organic development. Darwin (or any other zoologist) could not deduce the actual course of evolution from general principles. Given an organism and its environment, he could not show that it must evolve into a more complex organism of a definite pre-determined type; knowing what it has evolved into, he could attempt to discover and a.s.sign the determining causes. General principles do not account for a particular sequence; they embody necessary conditions; but there is a chapter of accidents too. It is the same in the case of history.
18. Among the evolutional attempts to subsume the course of history under general syntheses, perhaps the most important is that of Lamprecht, whose "kulturhistorische Methode," which he has deduced from and applied to German history, exhibits the (indirect) influence of the Comtist school. It is based upon psychology, which, in his view, holds among the sciences of mind (Geisteswissenschaften) the same place (that of a Grundwissenschaft) which mechanics holds among the sciences of nature. History, by the same comparison, corresponds to biology, and, according to him, it can only become scientific if it is reduced to general concepts (Begriffe). Historical movements and events are of a psychical character, and Lamprecht conceives a given phase of civilisation as "a collective psychical condition (seelischer Gesamtzustand)" controlling the period, "a diapason which penetrates all psychical phenomena and thereby all historical events of the time."
("Die kulturhistorische Methode", Berlin, 1900, page 26.) He has worked out a series of such phases, "ages of changing psychical diapason," in his "Deutsche Geschichte" with the aim of showing that all the feelings and actions of each age can be explained by the diapason; and has attempted to prove that these diapasons are exhibited in other social developments, and are consequently not singular but typical. He maintains further that these ages succeed each other in a definite order; the principle being that the collective psychical development begins with the h.o.m.ogeneity of all the individual members of a society and, through heightened psychical activity, advances in the form of a continually increasing differentiation of the individuals (this is akin to the Spencerian formula). This process, evolving psychical freedom from psychical constraint, exhibits a series of psychical phenomena which define successive periods of civilisation. The process depends on two simple principles, that no idea can disappear without leaving behind it an effect or influence, and that all psychical life, whether in a person or a society, means change, the acquisition of new mental contents. It follows that the new have to come to terms with the old, and this leads to a synthesis which determines the character of a new age. Hence the ages of civilisation are defined as the "highest concepts for subsuming without exception all psychical phenomena of the development of human societies, that is, of all historical events."
(Ibid. pages 28, 29.) Lamprecht deduces the idea of a special historical science, which might be called "historical ethnology," dealing with the ages of civilisation, and bearing the same relation to (descriptive or narrative) history as ethnology to ethnography. Such a science obviously corresponds to Comte"s social dynamics, and the comparative method, on which Comte laid so much emphasis, is the princ.i.p.al instrument of Lamprecht.
19. I have dwelt on the fundamental ideas of Lamprecht, because they are not yet widely known in England, and because his system is the ablest product of the sociological school of historians. It carries the more weight as its author himself is a historical specialist, and his historical syntheses deserve the most careful consideration. But there is much in the process of development which on such a.s.sumptions is not explained, especially the initiative of individuals. Historical development does not proceed in a right line, without the choice of diverging. Again and again, several roads are open to it, of which it chooses one--why? On Lamprecht"s method, we may be able to a.s.sign the conditions which limit the psychical activity of men at a particular stage of evolution, but within those limits the individual has so many options, such a wide room for moving, that the definition of those conditions, the "psychical diapasons," is only part of the explanation of the particular development. The heel of Achilles in all historical speculations of this cla.s.s has been the role of the individual.
The increasing prominence of economic history has tended to encourage the view that history can be explained in terms of general concepts or types. Marx and his school based their theory of human development on the conditions of production, by which, according to them, all social movements and historical changes are entirely controlled. The leading part which economic factors play in Lamprecht"s system is significant, ill.u.s.trating the fact that economic changes admit most readily this kind of treatment, because they have been less subject to direction or interference by individual pioneers.
Perhaps it may be thought that the conception of SOCIAL ENVIRONMENT (essentially psychical), on which Lamprecht"s "psychical diapasons"
depend, is the most valuable and fertile conception that the historian owes to the suggestion of the science of biology--the conception of all particular historical actions and movements as (1) related to and conditioned by the social environment, and (2) gradually bringing about a transformation of that environment. But no given transformation can be proved to be necessary (pre-determined). And types of development do not represent laws; their meaning and value lie in the help they may give to the historian, in investigating a certain period of civilisation, to enable him to discover the interrelations among the diverse features which it presents. They are, as some one has said, an instrument of heuretic method.
20. The men engaged in special historical researches--which have been pursued unremittingly for a century past, according to scientific methods of investigating evidence (initiated by Wolf, Niebuhr, Ranke)--have for the most part worked on the a.s.sumptions of genetic history or at least followed in the footsteps of those who fully grasped the genetic point of view. But their aim has been to collect and sift evidence, and determine particular facts; comparatively few have given serious thought to the lines of research and the speculations which have been considered in this paper. They have been reasonably shy of compromising their work by applying theories which are still much debated and immature. But historiography cannot permanently evade the questions raised by these theories. One may venture to say that no historical change or transformation will be fully understood until it is explained how social environment acted on the individual components of the society (both immediately and by heredity), and how the individuals reacted upon their environment. The problem is psychical, but it is a.n.a.logous to the main problem of the biologist.
XXVIII. THE GENESIS OF DOUBLE STARS. By Sir George Darwin, K.C.B., F.R.S.
Plumian Professor of Astronomy and Experimental Philosophy in the University of Cambridge.
In ordinary speech a system of any sort is said to be stable when it cannot be upset easily, but the meaning attached to the word is usually somewhat vague. It is hardly surprising that this should be the case, when it is only within the last thirty years, and princ.i.p.ally through the investigations of M. Poincare, that the conception of stability has, even for physicists, a.s.sumed a definiteness and clearness in which it was previously lacking. The laws which govern stability hold good in regions of the greatest diversity; they apply to the motion of planets round the sun, to the internal arrangement of those minute corpuscles of which each chemical atom is constructed, and to the forms of celestial bodies. In the present essay I shall attempt to consider the laws of stability as relating to the last case, and shall discuss the succession of shapes which may be a.s.sumed by celestial bodies in the course of their evolution. I believe further that h.o.m.ologous conceptions are applicable in the consideration of the trans.m.u.tations of the various forms of animal and of vegetable life and in other regions of thought.
Even if some of my readers should think that what I shall say on this head is fanciful, yet at least the exposition will serve to ill.u.s.trate the meaning to be attached to the laws of stability in the physical universe.
I propose, therefore, to begin this essay by a sketch of the principles of stability as they are now formulated by physicists.
I.
If a slight impulse be imparted to a system in equilibrium one of two consequences must ensue; either small oscillations of the system will be started, or the disturbance will increase without limit and the arrangement of the system will be completely changed. Thus a stick may be in equilibrium either when it hangs from a peg or when it is balanced on its point. If in the first case the stick is touched it will swing to and fro, but in the second case it will topple over. The first position is a stable one, the second is unstable. But this case is too simple to ill.u.s.trate all that is implied by stability, and we must consider cases of stable and of unstable motion. Imagine a satellite and its planet, and consider each of them to be of indefinitely small size, in fact particles; then the satellite revolves round its planet in an ellipse. A small disturbance imparted to the satellite will only change the ellipse to a small amount, and so the motion is said to be stable. If, on the other hand, the disturbance were to make the satellite depart from its initial elliptic orbit in ever widening circuits, the motion would be unstable. This case affords an example of stable motion, but I have adduced it princ.i.p.ally with the object of ill.u.s.trating another point not immediately connected with stability, but important to a proper comprehension of the theory of stability.
The motion of a satellite about its planet is one of revolution or rotation. When the satellite moves in an ellipse of any given degree of eccentricity, there is a certain amount of rotation in the system, technically called rotational momentum, and it is always the same at every part of the orbit. (Moment of momentum or rotational momentum is measured by the momentum of the satellite multiplied by the perpendicular from the planet on to the direction of the path of the satellite at any instant.)
Now if we consider all the possible elliptic orbits of a satellite about its planet which have the same amount of "rotational momentum," we find that the major axis of the ellipse described will be different according to the amount of flattening (or the eccentricity) of the ellipse described. A figure t.i.tled "A "family" of elliptic orbits with constant rotational momentum" (Fig. 1) ill.u.s.trates for a given planet and satellite all such orbits with constant rotational momentum, and with all the major axes in the same direction. It will be observed that there is a continuous transformation from one orbit to the next, and that the whole forms a consecutive group, called by mathematicians "a family"
of orbits. In this case the rotational momentum is constant and the position of any orbit in the family is determined by the length of the major axis of the ellipse; the cla.s.sification is according to the major axis, but it might have been made according to anything else which would cause the orbit to be exactly determinate.
I shall come later to the cla.s.sification of all possible forms of ideal liquid stars, which have the same amount of rotational momentum, and the cla.s.sification will then be made according to their densities, but the idea of orderly arrangement in a "family" is just the same.
We thus arrive at the conception of a definite type of motion, with a constant amount of rotational momentum, and a cla.s.sification of all members of the family, formed by all possible motions of that type, according to the value of some measurable quant.i.ty (this will hereafter be density) which determines the motion exactly. In the particular case of the elliptic motion used for ill.u.s.tration the motion was stable, but other cases of motion might be adduced in which the motion would be unstable, and it would be found that cla.s.sification in a family and specification by some measurable quant.i.ty would be equally applicable.
A complex mechanical system may be capable of motion in several distinct modes or types, and the motions corresponding to each such type may be arranged as before in families. For the sake of simplicity I will suppose that only two types are possible, so that there will only be two families; and the rotational momentum is to be constant. The two types of motion will have certain features in common which we denote in a sort of shorthand by the letter A. Similarly the two types may be described as A + a and A + b, so that a and b denote the specific differences which discriminate the families from one another. Now following in imagination the family of the type A + a, let us begin with the case where the specific difference a is well marked. As we cast our eyes along the series forming the family, we find the difference a becoming less conspicuous. It gradually dwindles until it disappears; beyond this point it either becomes reversed, or else the type has ceased to be a possible one. In our shorthand we have started with A + a, and have watched the characteristic a dwindling to zero. When it vanishes we have reached a type which may be specified as A; beyond this point the type would be A - a or would be impossible.
Following the A + b type in the same way, b is at first well marked, it dwindles to zero, and finally may become negative. Hence in shorthand this second family may be described as A + b,... A,... A - b.
In each family there is one single member which is indistinguishable from a member of the other family; it is called by Poincare a form of bifurcation. It is this conception of a form of bifurcation which forms the important consideration in problems dealing with the forms of liquid or gaseous bodies in rotation.
But to return to the general question,--thus far the stability of these families has not been considered, and it is the stability which renders this way of looking at the matter so valuable. It may be proved that if before the point of bifurcation the type A + a was stable, then A + b must have been unstable. Further as a and b each diminish A + a becomes less p.r.o.nouncedly stable, and A + b less unstable. On reaching the point of bifurcation A + a has just ceased to be stable, or what amounts to the same thing is just becoming unstable, and the converse is true of the A + b family. After pa.s.sing the point of bifurcation A + a has become definitely unstable and A + b has become stable. Hence the point of bifurcation is also a point of "exchange of stabilities between the two types." (In order not to complicate unnecessarily this explanation of a general principle I have not stated fully all the cases that may occur. Thus: firstly, after bifurcation A + a may be an impossible type and A + a will then stop at this point; or secondly, A + b may have been an impossible type before bifurcation, and will only begin to be a real one after it; or thirdly, both A + a and A + b may be impossible after the point of bifurcation, in which case they coalesce and disappear.
This last case shows that types arise and disappear in pairs, and that on appearance or before disappearance one must be stable and the other unstable.)
In nature it is of course only the stable types of motion which can persist for more than a short time. Thus the task of the physical evolutionist is to determine the forms of bifurcation, at which he must, as it were, change carriages in the evolutionary journey so as always to follow the stable route. He must besides be able to indicate some natural process which shall correspond in effect to the ideal arrangement of the several types of motion in families with gradually changing specific differences. Although, as we shall see hereafter, it may frequently or even generally be impossible to specify with exactness the forms of bifurcation in the process of evolution, yet the conception is one of fundamental importance.
The ideas involved in this sketch are no doubt somewhat recondite, but I hope to render them clearer to the non-mathematical reader by h.o.m.ologous considerations in other fields of thought (I considered this subject in my Presidential address to the British a.s.sociation in 1905, "Report of the 75th Meeting of the British a.s.soc." (S. Africa, 1905), London, 1906, page 3. Some reviewers treated my speculations as fanciful, but as I believe that this was due generally to misapprehension, and as I hold that h.o.m.ologous considerations as to stability and instability are really applicable to evolution of all sorts, I have thought it well to return to the subject in the present paper.), and I shall pa.s.s on thence to ill.u.s.trations which will teach us something of the evolution of stellar systems.
States or governments are organised schemes of action amongst groups of men, and they belong to various types to which generic names, such as autocracy, aristocracy or democracy, are somewhat loosely applied. A definite type of government corresponds to one of our types of motion, and while retaining its type it undergoes a slow change as the civilisation and character of the people change, and as the relationship of the nation to other nations changes. In the language used before, the government belongs to a family, and as time advances we proceed through the successive members of the family. A government possesses a certain degree of stability--hardly measurable in numbers however--to resist disintegrating influences such as may arise from wars, famines, and internal dissensions. This stability gradually rises to a maximum and gradually declines. The degree of stability at any epoch will depend on the fitness of some leading feature of the government to suit the slowly altering circ.u.mstances, and that feature corresponds to the characteristic denoted by a in the physical problem. A time at length arrives when the stability vanishes, and the slightest shock will overturn the government. At this stage we have reached the crisis of a point of bifurcation, and there will then be some circ.u.mstance, apparently quite insignificant and almost unnoticed, which is such as to prevent the occurrence of anarchy. This circ.u.mstance or condition is what we typified as b. Insignificant although it may seem, it has started the government on a new career of stability by imparting to it a new type. It grows in importance, the form of government becomes obviously different, and its stability increases. Then in its turn this newly acquired stability declines, and we pa.s.s on to a new crisis or revolution. There is thus a series of "points of bifurcation" in history at which the continuity of political history is maintained by means of changes in the type of government. These ideas seem, to me at least, to give a true account of the history of states, and I contend that it is no mere fanciful a.n.a.logy but a true h.o.m.ology, when in both realms of thought--the physical and the political--we perceive the existence of forms of bifurcation and of exchanges of stability.
Further than this, I would ask whether the same train of ideas does not also apply to the evolution of animals? A species is well adapted to its environment when the individual can withstand the shocks of famine or the attacks and compet.i.tion of other animals; it then possesses a high degree of stability. Most of the casual variations of individuals are indifferent, for they do not tell much either for or against success in life; they are small oscillations which leave the type unchanged. As circ.u.mstances change, the stability of the species may gradually dwindle through the insufficiency of some definite quality, on which in earlier times no such insistent demands were made. The individual animals will then tend to fail in the struggle for life, the numbers will dwindle and extinction may ensue. But it may be that some new variation, at first of insignificant importance, may just serve to turn the scale. A new type may be formed in which the variation in question is preserved and augmented; its stability may increase and in time a new species may be produced.
At the risk of condemnation as a wanderer beyond my province into the region of biological evolution, I would say that this view accords with what I understand to be the views of some naturalists, who recognise the existence of critical periods in biological history at which extinction occurs or which form the starting-point for the formation of new species. Ought we not then to expect that long periods will elapse during which a type of animal will remain almost constant, followed by other periods, enormously long no doubt as measured in the life of man, of acute struggle for existence when the type will change more rapidly?