Equilibrium

“ If equilibrium be disturbed at one point, it is reestablished only by propagating its own disturbance to all the internal equilibria; and, in order that it may itself endure, it must not be disturbed by a perturbation of reaction from within; the internal equilibria must be restored at the expense of the forces developed by the nutrition, and must be fixed by modifications of structure. ”

“ They are regarded as satisfying a certain well-defined class of conditions of equilibrium, but as not satisfying at all certain other conditions which would be necessary for complete equilibrium, in consequence of which they are subject to gradual changes, which ultimately determine their rupture. ”

“ The equilibrium which is due to such passive properties is thus widely distinguished from that caused by the balance of the active tendencies of the system, where an external influence, or a change in the initial state, infinitesimal in amount, is sufficient to produce change either in the positive or negative direction. ”

“ If there is just as much of the wood or ice above the water as is equal to the bulk of the man, then the man, in stepping upon it, will sink it just to the water's edge."
"But perhaps one man would be heavier than another man," said Marco.
"Yes," replied Forester; "but then he would be larger, and so, according to the principle, he would make more wood sink before the equilibrium was reached."
"What is equilibrium?" asked Marco.
"Equilibrium is an equality between two forces," replied Forester. ”

“ Stated in the abstract, the problem is how to explain the origin of purpose in a moving equilibrium—commencing from the solar system and proceeding to a self-feeding engine and pursuing our investigation to the abstract moving equilibrium of forces in which external inimical or favourable forces generate internal forces as a counterbalance, either of opposition or harmony of adjustment. ”

“ Let us consider once more the concept of equilibrium. Inhibition of action through antagonistic impulses, or action returning upon itself, we have defined it; and the line cannot be drawn sharply between these types. The visual analogue for equilibrium may be either symmetrical figure or circle; the excursion from the centre may be either the swing of the pendulum or the sweep of the planet. The RETURN is the essential. Now it is a commonplace of criticism--though the significance of the dictum has never been sufficiently seen--that the great drama, novel, or symphony does return upon itself. ”

“ LXII. THE EQUILIBRIUM BETWEEN HEAVEN AND HELL. For any thing to have existence there must be an equilibrium of all things. Without equilibrium is no action and reaction; for equilibrium is between two forces, one acting and the other reacting, and the state of rest resulting from like action and reaction is called equilibrium. ”

“ It is a corollary that when the environment is changed, the equilibrium of functions is disturbed, and there must follow one of two results—either the equilibrium is overthrown or it is re-adjusted: there is a re-equilibration. ”

“ Pushing it to or fro as may be necessary, I finally discover that equilibrium results from a reciprocal proportion between the amount of weight and the length of the levers. Thus my little student of physics can rectify balances without having ever seen them.
When we thus learn by ourselves instead of learning from others, our ideas are far more definite and clear. Besides, if our reason is not accustomed to slavish submission to authority, this discovering relations, linking one idea to another, and inventing apparatus, renders us much more ingenious. ”

“ But, the question may be asked, Granting all this, may not the activity at some time come to an end? May not an equilibrium be finally reached—a state in which, activity having played its part, becoming passes into being, a changeless goal of all preceding change? ”

“ 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 ”

“ By virtue of what does friction disappear? What is it that makes our abstract picture of economic life, as a fluid equilibrium, with its nice marginal adjustments, its timeless logical relations, correspond as closely as it does to reality? ”

“ Cases in which equilibrium does not subsist were formally excluded by my subject, and indeed could not be satisfactorily treated without the introduction of new ideas quite foreign to those necessary for the treatment of equilibrium. ”

“ Symbols of all the various processes society passes through in its growth and extension can be found in every other department of the universe; or, to assert the same fact differently, everywhere in the universe there is a constant effort to attain an equilibrium—a continuous working to supply wants, an unceasing process of demand and supply, which are universal exemplifications of the law that motion is always in the direction of the least resistance or the greatest traction, or the resultant of the two operating conjointly. ”

“ And in the absence of this hypothesis there remains only one other. The alternative possibility is, that the balance of the preservative and destructive forces is self-sustaining—is of the kind distinguished as a stable equilibrium: an equilibrium such that any excess of one of the forces at work, itself generates, by the deviation it produces, certain counter-forces which eventually out-balance it, and initiate an opposite deviation. ”

“ The equations which express the condition of equilibrium, as also its statement in words, are to be interpreted in accordance with the general usage in respect to differential equations, that is, infinitesimals of higher orders than the first relatively to those which express the amount of change of the system are to be neglected. But to distinguish the different kinds of equilibrium in respect to stability, we must have regard to the absolute values of the variations. ”

“ We shall get a truer idea of the way in which karma works if we think of it as a necessary readjustment of equilibrium disturbed by our action — as a kind of illustration of the law that action and reaction are always equal. ”

“ If the system is not unstable, the equilibrium is either neutral or stable. Of course we can determine which of these is the case by reference to the imaginary system, since the determination depends upon states of equilibrium, in regard to which the real and imaginary systems do not differ. ”

“ The various industrial actions and re-actions thus continually alternating, constitute a dependent moving equilibrium like that which is maintained among the functions of an individual organism. And this dependent moving equilibrium parallels those already contemplated, in its tendency to become more complete. During early stages of social evolution, while yet the resources of the locality inhabited are unexplored, and the arts of production undeveloped, there is never anything more than a temporary and partial balancing of such actions, under the form of acceleration or retardation of growth. ”

“ And the fact which we have here particularly to observe, is, that as a corollary from the general law of equilibration above set forth, the evolution of every aggregate must go on until this equilibrium mobile is established; since, as we have seen, an excess of force which the aggregate possesses in any direction, must eventually be expended in overcoming resistances to change in that 448direction: leaving behind only those movements which compensate each other, and so form a moving equilibrium. ”

“ As there is one earth drawing toward its center each billiard ball of the dozen in equilibrium in a bowl, so there is behind the budget of the individual one complex personal conception of a way of life that fixes more or less certainly and clearly the kinds and intensities of his wants and assigns to each its share of purchasing power. That the units or elements in equilibrium hold their positions with reference to each other for reasons capable of separate statement for each unit seems a supposition no less impossible in the one case than in the other. ”

“ A kind of equilibrium establishes itself between the value of all the productions of the land, the consumption of the different kinds of commodities, the different sorts of works, the number of men employed at them, and the price of their wages.
Wages can be fixed and remain constantly at a definite point only in virtue of this equilibrium, and of the influence which all the parts of the society, all the branches of production and commerce, exercise upon one another. ”

“ I. For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy, the variation of its entropy shall either vanish or be negative. ”

“ Let us first examine the case in which is positive and the equilibrium is stable. As does not vanish at the point in question, there is a definite isopiestic passing through that point, on one side of which the pressures are greater, and on the other less, than on the line itself. ”

“ But that all that we call "being" is motion: and that all motion is the expression, not of equilibrium, but of equilibrating, or of equilibrium unattained: that life-motions are expressions of equilibrium unattained: that all thought relates to the unattained: that to have what is called being in our quasi-state, is not to be in the positive sense, or is to be intermediate to Equilibrium and Inequilibrium. ”

“ Tendency to equilibrium of force and to permanency of form then, are the characters of that portion of the universe which does not live—the domain of the chemist and physicist.
Tendency to disturb existing equilibrium,—to take on forms which succeed one another in definite cycles, is the character of the living world. ”

“ But equilibrium and stability are never perfect. Permanent social equilibrium would be social stagnation and decay. Therefore, we must study society also in its onward movement—the equilibrium ever disturbed, only to be readjusted on a higher plane with more and more complexly inter-related parts. This is dynamics—social progress. It is evolution. ”

“ Thus a constant equilibrium is maintained in the atmosphere; and thus, by a system of perpetual rotation or everlasting merry-go-round, the same substances serve, indefinitely, to support life of every opposite description. ”

“ Suppose, then, that the horse is being maintained in equilibrium between ten degrees of impulsion and ten degrees of opposition. If, now, the impulsion is increased from ten degrees to fifteen, the opposition still remaining at ten, the horse must move forward, with the condition of equilibrium still maintained. ”

“ Of course we are: but there is a universal balance throughout nature, and everything finds its level. There is order, when there appears disorder—and no stream runs in one direction, without a counter stream, to restore the equilibrium. ”

“ If we see two boys pull at two ends of a rope so that neither of them in the smallest degree prevails over the other, we have a case in which two forces are in equilibrium. The two forces are evidently equal, and are a statical exemplification of action and reaction, such as are spoken of in the third axiom concerning causes. Now the same exemplification occurs in every case of equilibrium. No point or body can be kept at rest except in virtue of opposing forces acting upon it; and these forces must always be equal in their opposite effect. ”

“ But if a subjective factor is admitted into the problem, then it is necessary to understand in what way it becomes part of, and in what way it affects, a process of equilibration on the part of a moving equilibrium in which it is a factor. The peculiar nature of a biological moving equilibrium, and the respect in which it differs from a physical or mechanical moving equilibrium, consists in the fact that it works towards, if indeed it does not purposely aim at self-continuance by assimilation of force and self-continuance by means of self-protection from adverse forces in the environment. ”

“ Every change is towards a balance of forces; and of necessity can never cease until a balance of forces is reached. When treating of equilibration under its general aspects (First Principles, Part II., Chap. xxii.) , we saw that every aggregate having compound movements tends continually towards a moving equilibrium; since any unequilibrated force to which such an aggregate is subject, if not of a kind to overthrow it altogether, must continue modifying its state until an equilibrium is brought about. ”

“ Do the advantages more than compensate for the disadvantages, or vice versa? You perceive? Sometimes there seems to be a complete balance of forces—an equilibrium—the scale will not incline either way. ”

“ While thus ruling the oscillations of value, they themselves obey a superior force, which makes value gravitate towards Cost of Production, and which would settle it and keep it there, if fresh disturbing influences were not continually arising to make it again deviate. To pursue the same strain of metaphor, demand and supply always rush to an equilibrium, but the condition of stable equilibrium is when things exchange for each other according to their cost of production, or, in the expression we have used, when things are at their Natural Value. ”

“ As the equations of condition, of which we have made use, are such as always apply to matter enclosed in a rigid, impermeable, and non-conducting envelop, the particular conditions of equilibrium which we have found will always be sufficient for equilibrium. ”

“ The condition of equilibrium is that this expression (which we may for the sake of distinctness call the potential energy) shall be a minimum. This condition when worked out gives not only the equation of the free surface in the form already established by Laplace, but the conditions of the angle of contact of this surface with the surface of a solid. ”

“ If both the masses are infinitely large, or if one which contains all the components of the system is infinitely large, and will be constant, and the condition reduces to
The equilibrium will therefore be stable or unstable according as the surface of tension is less or greater than a hemisphere. ”