Statics

“ And what can assure us that it is not so, except removal of one or other force, and consequent tilting of the lever? The other fundamental axiom of statics, that the pressure on the point of support is the sum of the weights ... is merely a scientific transformation and more refined mode of stating a coarse and obvious result of universal experience, viz. that the weight of a rigid body is the same, handle it or suspend it in what position or by what point we will, and that whatever sustains it sustains its total weight. ”

“ Yet the laws of motion pertain to dynamics, the more special of the divisions. Further on he points out that after Archimedes, who discovered the law of equilibrium of the lever, statics made no progress until the establishment of dynamics enabled us to seek "the conditions of equilibrium through the laws of the composition of forces." And he adds—"At this day this is the method universally employed. At the first glance it does not appear the most rational—dynamics being more complicated than statics, and precedence being natural to the simpler. ”

“ Compare, let us say, the contrast between "statics and dynamics" with that between "historical and cross-section" study. Concrete, realistic history is not dynamic theory. A realistic description of society viewed at a given short period of time is not static theory. Both [Pg 554] statics and dynamics are abstract. Laws are not the same thing as description and narration. The assertions of both statics and dynamics are commonly made on the assumption, "cæteris paribus." A new bank will stimulate business in a western town if bank-robberies do not come into fashion! ”

“ This disposition to identify the elementary laws of equilibrium and of motion, led men to think too slightingly of the ancient solid and sufficient foundation of Statics, the doctrine of the lever. When the progress of thought had opened men’s minds to a more general view of the subject, it was considered as a blemish in the science to found it on the properties of one particular machine. ”

“ We have seen that forces have two ways of acting: that of compelling rest and that of producing motion. In statics forces act so as to prevent any change of motion, or disturb the body’s original position. In kinetics, on the contrary, the power is recognised as acting so as to produce or change a body’s motion. Now, in polemical science we have these two ways of considering the action of [97] forces. There is the statical or conservative force, which compels rest, which seeks security, stability, and peace, and is not ardently devoted to change. It reduces the system to equilibrium. ”

“ Statics and Dynamics.—We must first turn our attention to a technical distinction of Mechanics into two portions, according as the forces about which we reason produce rest, or motion; the former portion is termed Statics, the latter Dynamics. If a stone fall, or a weight put a machine in motion, the problem belongs to Dynamics; but if the stone rest upon the ground, or a weight be merely supported by a machine, without being raised higher, the question is one of Statics.
3. Equilibrium.—In Statics, forces balance each other, or keep each other in equilibrium. ”

“ Recently many scientists have taken exception to the traditional division of mechanics into statics, or the science of equilibrium, and dynamics, or the science of motion, because it does not correspond to the essence of the thing, equilibrium being only the limit-case of motion. ”

“ The study of the origins of Statics has conducted us thus to a conclusion; in proportion as we have pushed our historical researches earlier and in directions more varied, this conclusion has imposed itself to our spirit with an increasing force; also we dared to formulate it in its full generality: the mechanical and physical science of which we are well within our rights proud in modern times flows, by an uninterrupted series of scarcely sensible improvements, from the doctrines professed in the heart of the schools of the Middle Ages ”

“ Social phaenomena, like all others, present two aspects, the statical, and the dynamical; the phaenomena of equilibrium, and those of motion. The statical aspect is that of the laws of social existence, considered abstractedly from progress, and confined to what is common to the progressive and the stationary state. The dynamical aspect is that of social progress. The statics of society is the study of the conditions of existence and permanence of the social state. The dynamics studies the laws of its evolution. The first is the theory of the consensus, or interdependence of social phaenomena. ”

“ The Science of Statics depends upon the Axiom, that Action and Reaction are equal, which in Statics assumes this form:—When two equal weights are supported on the middle point between them, the pressure on the fulcrum is equal to the sum of the weights. ”

“ A statical or dynamical theorem, however simple, has always for its subject-matter something that is conceived as extended, and as displaying force or forces—as being a seat of resistance, or of tension, or of both, and as capable of possessing more or less of vis viva. If we examine the simplest proposition of Statics, we see that the conception of Force must be joined with the conception of Space, before the proposition can be framed in thought; and if we similarly examine the simplest proposition in Dynamics, we see that Force, Space, and Time, are its essential elements. ”

“ In so far they have been essays in social statics, and inestimably valuable. As samples of statical explanations of the given society in its totality however they have fallen as far short of satisfying the demands of sociological method as a carpenter's account of the structure of a house would fail to fill out the concepts of physics, or as a sailor's account of Defender's last trial would be lacking as an exposition of the science of navigation. ”

“ Another circumstance of discomfort to the mathematician is, that in the historical form in which mechanics at present exists, dynamics is founded on statics, whereas it is desirable that in a science which pretends to deductive completeness the more special statical theorems should be deducible from the more general dynamical principles. ”

“ Stevinns (1548-1603) showed that a force can be completely represented by a straight line. Upon this simple fact a branch of mathematics called graphical statics has been recently founded, and has furnished many elegant geometrical solutions of engineering problems. For an unusually interesting history of statics see Mach's Science of Mechanics. ”

“ It was thus stated, “The motion impressed on each particle of any system by the forces which act upon it, may be resolved into two, the effective motion, and the motion gained or lost: the effective motions will be the real motions of the parts, and the motions gained and lost will be such as would keep the system at rest.” The distinction of statics, the doctrine of equilibrium, and dynamics, the doctrine of motion, was, as we have seen, fundamental; and the difference of difficulty and complexity in the two subjects was well understood, and generally recognized by mathematicians. ”

“ Now from the laws of statics it is known that, in order that a system of forces applied to a system of connected points may be in equilibrium, it is necessary that the sum formed by putting together the products of the forces by the respective distances through which their points of application are capable of moving simultaneously, each along the direction of the force applied to it, shall be zero,—products being considered positive or negative according as the direction of the forces and the possible motions of their points of application are the same or opposite. ”

“ But, from the time of Leonardo and of Cardan down to Descartes and Torricelli, we had been able to follow the development of Statics without the passage of this development having seemed to us essentially different from those that one would attribute commonly to it. ”

“ We no sooner get one element of the social combination, say the industrial, pretty well explained, so that we think we are ready to study its adjustments with the other elements, then we find that we have hardly studied these other elements at all, and our first observations under this latest impulse raise questions that demand more observation of the industrial element. We have done a lot of more or less brilliant guessing about statics and dynamics, but the work which gives the most promise of being permanent is, from the sociologist's point of view, practically all descriptive. ”

“ There is not only qualitative but quantitative prevision.
And this is the unexpressed difference which leads us to consider certain orders of knowledge as especially scientific when contrasted with knowledge in general. Are the phenomena measurable? is the test which we unconsciously employ. Space is measurable: hence Geometry. Force and space are measureable: hence Statics. Time, force, and space are measureable: hence Dynamics. The invention of the barometer enabled men to extend the principles of mechanics to the atmosphere ”

“ The laws of motion of visible and tangible, or molar, matter had been worked out to a great degree of refinement and embodied in the branches of science known as Mechanics, Hydrostatics, and Pneumatics. These laws had been shown to hold good, so far as they could be checked by observation and experiment, throughout the universe, on the assumption that all such masses of matter possessed inertia and were susceptible of acquiring motion, in two ways, firstly by impact, or impulse from without; ”

“ My contention is that if we should make such advances in statical interpretation that we could accurately formulate the equilibrium of the societies which have transmitted civilization in every epoch from the beginning to the present, we should, in consequence, be in possession of means, first for generalizations of statical laws ”

“ In other words, the distinction between static and dynamic phenomena upon which Professor Ward insists is one which I consider no less important than he, but I think he is wrong in assuming that social or other phenomena must always be represented in consciousness either as static or as dynamic.
Representing a fact as part of a static condition, or of a dynamic process is a procedure much more complex than mere perception of the fact; it is interpretation of the fact in relation to other facts. ”

“ The statical definition of Life will express the connexus of the properties of organized substance, all those conditions, of matter, form, and texture, and of relation to external forces, on which the organism depends. These various conditions, condensed into a single symbol, constitute Vitality or Vital Force, and are hence taken as the Cause of vital phenomena. The dynamical definition will express the connexus of Functions and Faculties of the organism, which are the statical properties of organized substance in action, under definite relations. ”

“ For division (which is all that a mill, or pestle, or any other body, does upon another, in reducing it to insensible parts) can never take away either solidity, extension, figure, or mobility from any body, but only makes two or more distinct separate masses of matter, of that which was but one before ; all which distinct masses, reckoned as so many distinct bodies, after division, make a certain number. These I call original or primary qualities of body, which I think we may observe to produce simple ideas in us, viz. solidity, extension, figure, motion or rest, and number. ”

“ The small oscillations of a conservative system about a configuration of equilibrium, and the criterion of stability, are discussed in Mechanics, § 23. The question of the stability of given types of motion is more difficult, owing to the want of a sufficiently general, and at the same time precise, definition of what we mean by “stability.” ”

“ What he could truthfully claim, and what the world could safely admit, was that he had static theory in his favor. Static theory deals with a world which is free, not only from friction and disturbance, but also from those elements of change and progress which are the marked features of actual life. ”

“ The most complex frame-work on which weights are supported, as the roof of a building, or the cordage of a machine, are still examples of equilibrium. In such cases we may have many forces all combining to balance each other; and the equilibrium will depend on various conditions of direction and magnitude among the forces. And in order to understand what are these conditions, we must ask, in the first place, what 214 we understand by the magnitude of such forces;—what is the measure of statical forces. ”

“ The choices of a state-space also constitutes a choice of dynamics: for a system with a high degree of dynamical complexity, there are a large number of state spaces which evince not only interesting static detail, but interesting dynamical detail as well. ”

“ But as we become better used to the large rôle which these phenomena play,—not that the phenomena are new, but that their present importance is new, and hence our serious study of them is new—we are increasingly able to see that other elements of static theory also apply. Static [Pg 565] theory applies increasingly as understanding increases! The vaguely discerned, the novel, the imperfectly analyzed, can be stated only in qualitative terms. As things are better understood, the mind seeks system, taxonomy, quantitative measurement. ”

“ Beside the real system of which the stability is in question, it will be convenient to conceive of another system, to which we shall attribute in its initial state the same homogeneous masses and surfaces of discontinuity which belong to the real system. ”

“ There are, of course, two kinds of equilibrium—stable and unstable—according as the social and political system is in a healthy or unhealthy state. If a body is in stable equilibrium, and any slight motion takes place, the body will return immediately to its former position ”