Execration

“ Would it not be simpler to consider the law of acceleration as a definition in all cases, and to regard the experiments in question, not as verifications of this law, but as verifications of the principle of reaction, or as demonstrating that the deformations of an elastic body depend only on the forces to which this body is subjected? ”

“ For determining the state of a given mass when in equilibrium and having a given volume and given energy or entropy, the condition of equilibrium affords an additional equation corresponding to each of the independent relations between the n component substances. But the equations which express our knowledge of the matter in the given mass will be correspondingly diminished, being in number, like the equations of condition relating to the quantities of the component substances, which may be derived from the former by differentiation. ”

“ V. A top supported above its centre of gravity, or a body which would be in stable equilibrium if not spinning, precesses in the opposite direction to that of its spinning.
VI. The last two statements come to this:—When the forces acting on a spinning body tend to make the angle of precession greater, the precession is in the same direction as the spinning, and vice versâ.
Having by observation obtained a rule, every natural philosopher tries to make his rule a rational one; tries to explain it. I hope you know what we mean when we say that we explain a phenomenon ”

“ Hence different effects may proceed from one and the same cause, and equal effects from different causes, acting under different conditions.
IV. The exertion of power is called action, and its intensity, in the material world, depends on the distance of the agent from the patient.
V. The amount of the exertion, or the quantity of the action, is measured by its true effect, which is the only true exponent or representative of the degree of the exertion; for, all matter being equally indifferent to receive motion, the amount of its passion must always agree with the amount of the action received ”

“ When the stretch is of a certain amount, there is equilibrium—the action of the spring just balances the weight,—and if the spring be stretched further there will be a balance of pull developed tending to bring the system back towards the equilibrium position. ”

“ Excluding water and one or two other substances, the fact of such expansion might be said to be invariable, and, as regards bodies whose gaseous condition is known, the law of expansion can be stated in a form no less simple and definite than the law of gravitation. ”

“ What we term inertia, or the passiveness of matter, is but the equilibrium of opposing forces; and when this equilibrium is destroyed, as for example in chemical changes, motion and activity become visible, and continue until the equilibrium be restored. ”

“ The cure, which nature has provided for the increased exertion of any part of the system, consists in the consequent expenditure of the sensorial power. But as a greater torpor follows this exhaustion of sensorial power, as explained in the next paragraph, and a greater exertion succeeds this torpor, the constitution frequently sinks under these increasing librations between exertion and quiescence; till at length complete quiescence, that is, death, closes the scene. ”

“ So, too, when the body is in motion as it now is I cannot stop it without the exertion of force. See how the spring is stretched and how strong a pull has thus been exerted to deprive the body of motion. Notice also that while a small force applied sufficiently long will always restore the body to rest, yet that to produce rest quickly a large force will be required. ”

“ I am rejoiced to see that you have acquired that power of exertion, which is so useful both to young and old—and that you have the will, as well as the power, to conquer little habits that are disagreeable to your friends. ”

“ Two forces, F and F′, which I suppose, for simplicity, to be acting vertically upwards, are respectively applied to two bodies, C and C′. I attach a body weighing P first to C and then to C′; if there is equilibrium in both cases I conclude that the two forces F and F′ are equal, for they are both equal to the weight of the body P. But am I certain that the body P has kept its weight when I transferred it from the first body to the second? ”

“ These little heaps, which are raised by degrees, give way to permit the eruptive matter to escape, and afterwards fall in, when the tertiary formations are exhausted, in a space of time of greater or less duration. ”

“ To satisfy the condition of equilibrium, as thus understood, it is necessary and sufficient that throughout the solid mass that throughout the surfaces where the solid meets the fluid and that throughout the internal surfaces of discontinuity where the suffixed numerals distinguish the expressions relating to the masses on opposite sides of a surface of discontinuity. ”

“ But all these calculations leave out the elementary mechanical law: "What is gained in power is lost in time." The elevation of a ton to a given height represents an expenditure of an equal amount of force, whether the labor is performed by flea, man, or horse. ”

“ We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such another body, if it were applied to it. ”

“ Let us now seek the complete value of the variation of the energy of a system of heterogeneous fluid masses, in which the influence of gravity and of the surfaces of discontinuity shall be included, and deduce from it the conditions of internal equilibrium for such a system. ”

“ When there are two components, neither of which is confined to the surface of discontinuity, the reëstablishment of equilibrium after the extension of the surface does not necessitate any processes reaching into the interior of the masses except the transmission of heat between the surface of discontinuity and the interior of the masses. ”

“ IV. The continuous extension, or geometric quantity, usually predicated of bodies, is the extension of the place comprised within the extreme limits of each body. It is, in other terms, the extension of the volume, not of the matter. Nevertheless, such an extension may be called “material,” not only because the terms of its dimensions are material, but also because in most bodies the elements and the molecules are so close that their action on our senses produces the appearance of material continuity. ”

“ It is true, of course, that avulsive action ordinarily calls to mind something somewhat sudden or, at least, of short duration, whereas accretion has as its essence the gradual deposit of material over a period by action of water flow. ”

“ Their modifications are new directions, amplitudes of new vibrations, which place them in equilibrium with the forces which the ensemble of the aggregate, as modified by the environment, brings to bear upon them. These modifications endure as long as equilibrium endures, and are ever transmitted to the new units which spring from the former ones, until, on the equilibrium being disturbed, a new breaking-up of the existing relations necessitates others. ”

“ 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. ”

“ If the expansion is not fast enough, a more or less insignificant amount of the sun's material explodes, thus enlarging by force the radiant surface to whatever extent is necessary to restore equilibrium. ”

“ It is required to determine the conditions of stability for a system in equilibrium, consisting of two different homogeneous masses meeting at a surface of discontinuity, the perimeter of which is invariable, as well as the exterior of the whole system, which is also impermeable to heat. ”

“ To judge of the true intensity of the actual exertion, it is necessary to exclude from the calculation the whole of the past or future actions, and to take into account the only action which corresponds to the infinitesimal present. ”

“ He throws a stone: if it is light, little exertion propels it a considerable distance; if very heavy, great exertion only a short distance. So, also, if he jumps, a slight effort raises him to a short height, a greater effort to a greater height. ”

“ There is nothing extraordinary in this, nor any exertion of strength necessarily greater than human, in proportion to the size of the body. For it is evident that if the size and strength of any creature be expanded or diminished in proportion to each other, the distance through which it can leap, the time it can maintain exertion, or any other third term resultant, remains constant ”

“ For if, while we are applying this force, wind or water or any other agent supplies an additional force just exceeding two tons, the body will be raised; thus proving that the force we applied exerted its full effect, by neutralizing an equivalent portion of the weight which it was insufficient altogether to overcome. ”

“ Then, having seen how Land and Human Exertion produced in the days of our grandfathers a heap of this special size, we must proceed to inquire why three generations later the same land and the exertions of a similar number of men produce a heap which is nearly three times as large. For the difference of result cannot be due to nothing. ”

“ What race would not be indolent and insouciant when things are so arranged, that they derive no advantage from forethought or exertion? If such are the arrangements in the midst of which they live and work, what wonder if the listlessness and indifference so engendered are not shaken off the first moment an opportunity offers when exertion would really be of use? ”

“ Inertia.—But this principle of the equality of action and reaction appears also in another way. Not only when we exert force upon bodies at rest, but when, by our exertions, we put them in motion, they react. If we set a large stone in motion, the stone 210 resists; for the operation requires an effort. By increasing the effort, we can increase the effect, that is, the motion produced ”

“ Conditions of equilibrium relating to irreversible changes.—The conditions of equilibrium relating to the absorption, by any part of the system, of substances which are not actual components of that part have been given on page 282. Those relating to the formation of new masses and surfaces are included in the conditions of stability relating to such changes, and are not always distinguishable from them. They are evidently independent of the action of gravity. ”

“ Suppose a weight is lying on the floor and a stool is standing beside it: if a man raise the weight and place it upon the stool, the exertion that he expends is energy in the sense in which the word is used in mechanics. The amount of exertion necessary to place the weight upon the stool depends upon two things, the magnitude of the weight and the height of the stool. ”

“ The doctrine of the English cases is that accretion is an addition to land conterminous with the water, which is formed so slowly that its progress cannot be perceived, and does not admit of the view that, in order to be accretion, the formation must be one not discernible by comparison at two distinct points of time. ”

“ Now that we have thus become acquainted with the physical cause of that movement of the earth's axis which gives rise to what is called the precession of the equinoxes, we have next to enter with somewhat greater detail into some of the results of the movement. ”

“ The incessant tendency of material forces is toward final equilibrium; and if the quantity of this tendency be finite, a time of repose must come at last. If one portion of the universe be hotter than another, a flux instantly sets in to equalise the temperatures; while winds blow and rivers roll in search of a stable equilibrium. ”

“ The external work of expansion per degree is equal to R, being the product of the pressure and the expansion, and represents the difference of the specific heats S—s, at constant pressure and volume, assuming as above that the internal work of expansion is negligible. ”

“ This fact is that if the actual changes of motion which the different particles of bodies experience are each resolved in its appropriate way, each component acceleration is precisely such as is prescribed by a certain law of Nature, according to which bodies in the relative positions which the bodies in question actually have at the moment, [32] always receive certain accelerations, which, being compounded by geometrical addition, give the acceleration which the body actually experiences. ”

“ Our exertional action is ab initio mingled in and forms really an integral part of the dynamic system in which our life is involved. The ever operative forces of Gravity, Cohesion, Chemical Affinity, and so forth are the phenomenal expression of the laws of energetic transmutation in which we partake and of which we are organically a part, [65] however apparently separate and disparate our bodies may seem to be. ”