The possibility of constructing a general, abstract sociology remains a most important problem; it is one of the principal points upon which we shall have to throw light, by the very fact of our new endeavor, although failure of our effort can never be invoked against the possibility of a more happy result in the future. This failure should be attributed only to the incapacity of the author, and in every case partial failure will be inevitable on account of the insufficient elaboration of the particular social sciences, and especially because of the incomplete development of the unitary, world-wide organization, which, by itself, is destined to facilitate the establishment of sociological monism in the collective consciousness. So, nearly all our efforts will bear especially upon the method to follow in order to succeed in the organization of an abstract sociology, rather than upon a more or less complete realization of this organization.

Thus, by a process both natural and logical, concrete and descriptive sociology is transformed into an abstract philosophy whose laws, more and more reduced to unity, will be the co-ordinated expression of relations common to all societies from the smallest and simplest to the largest and most complex, without regard to their variable conditions in the present, the past, and the future, except from the point of view of the constancy and regular order of these variations themselves.

If the conclusions of the different schools which admit only historical laws were well founded, positive philosophy itself would be condemned and decapitated, for this would admit that there does not exist an abstract philosophy of the social sciences, which are, therefore, different in this respect from the other sciences; in a word, there would not be any sociology except that of a discriptive and historical character. It seems to me that this narrow point of view must be abandoned; it was itself a simple, temporary, and relatively necessary reaction against the old absolute and metaphysical conception of so-called natural laws and orders of societies. This justified reaction has served to show that these laws and these orders, far from being complete and immutable, are in constant evolution. It is now necessary to make another step by recognizing that the divers

historical periods (a truth which is admitted especially by Karl Marx) are bound together in such a way that the periods in question, not being closed to each other, necessarily have common relations and laws which permit us to reduce them to a unitary structure and life.

II.

Abstract as well as concrete sociology is either static or dynamic. We prefer in place of this terminology that of general structure and general life of societies. In fact, we conceive of society as superorganic, and sociology has more direct relations with the sciences of life than with mechanics. The terms "static" and "dynamic" may be re-employed some day, provided that social phenomena as well as organic phenomena are reduced to a purely mechanical and mathematical interpretation, from the monistic point of view of general philosophy; until that time the use of these expressions must be rejected, as it implies that the social facts are of less complex nature than the organic, or even the chemical and physical, facts, when, on the contrary, they are both quantitatively and qualitatively superior.

The expression "social statics" was borrowed from mechanical science. The first social theorists who observed that societies are mobile naturally interpreted social phenomena at first by the laws of mechanics. Then, in the case of those with whom the immobile aspect of societies was predominant, a still simpler and more general explanation was demanded from mathematics, the science of magnitudes, either arithmetic or geometric. The first legislators or social organizers were true architects, working according to pre-established plans traced conformably to lines and materials entirely susceptible of being reduced to a unit of measure or of number.

It is thus that, by an application of the law of apparent return to primitive forms, abstract sociology of the future, although under entirely different conditions, will perhaps succeed in expressing sociological laws in mechanical formula which are themselves reducible to a general mathematical theorem or formula. Humanity appears to have traversed a scientific circle,

and it seems that its point of arrival is the same as its point of departure; in reality humanity, like a sound-wave in the ear, will have travesed a spiral, that is to say, a plane curve which continuously departs more and more from the point about which it revolves.

Necessarily, the mathematico-mechanical conception of the social order had to be the primitive conception. In fact, the fundamental scientific idea is that of measurement. Without measurement there is no comparison, no science unless it is qualitative and descriptive; knowledge of phenomena is exact and complete only when the statements of these phenomena express quantitative relations which can be represented by equations. Extension, the basis of geometry, movement, the basis of mechanics, together with the idea of quantity, the bases of the sciences of calculation, constitute the abstract mathematical sciences, and are applicable to all bodies in nature, even the social bodies. Nevertheless, as Poinsot' so well said: "Let us guard carefully against believing that a science is constructed when one has reduced it to analytical formulæ. Nothing can exempt us from studying the things themselves." Thus, not only is one unable to deduce a sociology from mathematics, mechanics, physics, chemistry, or even from biology and psychology, but also the analysis which we have made of societies in the preceding volumes cannot suffice; it must be completed by the study of societies themselves.

Rational mechanics is founded upon principles which spring from the very nature of movement, which is a primary and general idea, like that of matter and form. The mechanical relations of magnitudes of movement may themselves be expressed in algebraic and geometric formulæ, reducible to units of measurement such as space and time, which are functions of each other. It was mainly the mechanical interpretation of societies which led to distinguishing in them the static aspect and the dynamic aspect. It was a natural step in the organization of sociology when later rational astronomy, physics, chemistry, first inorganic and then organic, repeatedly introduced more special points of 1 Théorie nouvelle de la rotation des corps, pp. 30, 31.

view until, in the last of these points of view, the biological factor appeared and then the psychic factor in particular, the last of which completed the series of sciences whose co-ordination, not isolated, but encyclopædic, is at the basis of sociology. Now, it is only after these divers interpretations, at first exclusive, but later more and more combined, that, following the principle of Poinsot, we shall be able in time to begin to study societies in themselves as phenomena in part distinct from antecedent phenomena, although they are but the more complicated continuation of the same.

As in mechanics we call the causes of movement forces, without inquiring into the nature of these causes, in the same way we call the causes of social movement social forces. There are social forces as there were before them vital, physical, chemical, and astronomical forces.

The general problem of rational mechanics is to determine the effect of different forces acting simultaneously upon a given body, the separate effect of each of the forces being known. Mechanics is, then, the science of the combinations of forces. So long as social science was in the domain of empiricism, and so long as statesmen were able to imagine that they were the mechanicians of the societies whose forces they combined in view of certain results, the mechanical conception lent itself admirably to their illusion; besides, it was a first step toward truth. In politics, as in mechanics, it was observed that the meeting of forces may result either in their reciprocal neutralization, the consequence of which is repose, equilibrium, or else in movement. Mechanical science and political art had, therefore, this object in common: the investigation of the conditions. or circumstances of equilibrium and of movement; the only difference was in the nature of the bodies constituting the subject of research.

The definition of forces implies the law of inertia; a body remains in repose so long as no exterior force acts upon it; or, if it is in motion and no new force intervenes, its movement will be uniform and in a straight line. The statesmen applied this law of inertia by isolating their peoples, by protecting them as

far as possible from foreign influences; and, being unable to suppress movement entirely, they at least maintained the unity of its direction, knowing very well, in general, that when a movement is arrested by an obstacle the force manifests itself by a pressure or a traction upon the obstacle.

In reality, up to the eighteenth century political science was based mainly upon mechanics, and through mechanics was united to geometry and arithmetic. In fact, forces may always be expressed in units of weight which in turn are convertible into units of length. The law of Newton was one application of this valuation which was extended to political science: action is equal and opposite to reaction, the body of impact is itself always the object of an equal but contrary pressure exercised by the body of resistance.

In like manner the mechanical law of independence of movements dominated politics; whatever the development of the state might be, the relations of the citizens to each other, the social system, need not thereby be altered. From the simplest point of view, this law expressed the general fact that a uniform, rectilinear movement, exactly common to all the bodies of any system, does not modify the particular movements of those different bodies with respect to each other; these movements continue to take place just as if the whole of the system were immobile. Thus, in the case of a moving ship, whatever may be the swiftness and the direction of its motion, the relative movements of the objects and the persons on board take place as if the ship were immobile, although to outside observers these movements form part of the whole movement. It appeared to be the same in the case of the voyagers upon the ship of state. Moreover, it was an eminently scientific point of view to extend to societies the mechanical principle that forces are always proportional to the accelerations of motion that they produce.

Social statics was, then, a mechanical statics. Like the latter, it treated of the conditions of equilibrium of a system; in it the element of time was not considered. A phenomenon was considered as fixed, the variations which the forces of the sys