Intermolecular force

“ The possibility of thus eliminating the size of the particle and with it the resistance of the medium to its motion can be seen at once from the simple consideration that so long as we are dealing with one and the same particle the ratio between the force acting and the velocity produced by it must be the same, whether the acting force is due to gravity or an electrical held, as in the oil-drop experiments, or to molecular impacts as in Brownian-movement work. ”

“ The average kinetic energy of translation, therefore, tends to become the same for each kind of gas, and as before, it is this average energy of translation which measures the temperature.
A molecule in the theory is a portion of a gas which moves about as a single body. It may be a mere point, a centre of force having inertia, capable of doing work while losing velocity. There may be also in each molecule systems of several such centres of force bound together by their mutual actions. Again, a molecule may be a small solid body of determinate form ”

“ All molecular masses of metal represent in their interstitial molecular spaces incalculable amounts of latent force, which, if awakened and brought into intense vibratory action by the medium of sympathetic liberation, would result in thousands of billions more power in foot-pounds than that necessary to awaken it. The resultant development of any and all forces is only accomplished by conditions that awaken the latent energy they have carried with them during molecular aggregation. ”

“ The electrolyte is supposed homogeneous in planes parallel to the ends, which are formed by the electrodes.
Of course we should have equilibrium if proper forces could be applied to prevent the migration of the ions and also of the part of the solutum which is not dissociated. What would these forces be? For the molecules (12) which are not dissociated, the force per unit of mass would be (The problem is practically the same as that discussed in E.H.S. [this volume] , pp. 144 ff.) ”

“ The molecule is a material system, the parts of which are connected in some definite way, and from the fact that the bright lines of the emitted light have always the same wave-lengths, we learn that the vibrations corresponding to these lines are always executed in the same periodic time, and therefore the force tending to restore any part of the molecule to its position of equilibrium in the molecule must be proportional to its displacement relative to that position. ”

“ A hydrogen atom—its electron far from the proton falls in, and from it there goes a flash of radiation, and the electron is nearer to the proton, in a new orbit. Another flash—it is nearer. Always falling nearer, and only constant force will keep it from falling to that one state—then, for some reason no more does it drop. ”

“ It reveals to us that while they are held together by one force, they are kept asunder by another, their position at any moment depending on the equilibrium of attraction and repulsion. The atoms behave as if connected by elastic springs, which oppose at the same time their approach and their retreat, but which tolerate the vibration called heat. The molecular vibration once set up is instantly shared with the aether, and diffused by it throughout space. ”

“ Now, these examples are sufficient to show that molecular attraction or cohesion, as this is called, is a force which acts very powerfully through a certain small distance, but which vanishes altogether when this distance becomes perceptible. Cohesion is strongest in solids, while in liquids it is much diminished, and in gases it may be said to vanish altogether. ”

“ Surface tension is due to molecular force, to force that is to say arising from the action of one molecule upon another, and it is accordingly exerted throughout a small thickness of material, comparable to the range of the molecular forces. We imagine that within the interior of the liquid mass such molecular interactions negative one another: but that at and near the free surface, within a layer or film ap­prox­i­mate­ly equal to the range of the molecular force, there must be a lack of such equi­lib­rium and consequently a manifestation of force. ”

“ In its approach to B there will come a moment when A's motion will slacken. Then astronomical phenomena will end and the phenomena special to physics will begin. At last the molecule A will stop; it has become inert, and can not advance further toward B. It is bound by cohesion. If, now, we suppose a pressure to be imposed on A, to bring it down to B, physical phenomena will cease, the resistance of A will diminish with the distance, and finally the molecule will ally itself with B without touching it; then we have chemical phenomena. The force that unites A and B is affinity. ”

“ Besides this the atom is endowed with potential force, that is to say, that any two atoms attract or repel each other with a force depending on their distance apart. The law of this force, for all distances greater than say the thousandth of an inch, is an attraction varying as the inverse square of the distance. ”

“ Molecular energies, on the other hand, act with vastly greater force, but at very small distances, and appear sometimes as attractive and sometimes as repulsive forces. Thus solid bodies are held together by a force of cohesion which is very powerful, but acts only at very small distances, as we may see if we break a piece of glass and try to mend it by pressing the broken edges together. We cannot bring them near enough to bring the molecular attraction again into play and make the broken glass solid. ”

“ The particles must be conceived to roll without sliding between the vortices which they separate, and not to touch each other, so that, as long as they remain within the same complete molecule, there is no loss of energy by resistance. When, however, there is a general transference of particles in one direction, they must pass from one molecule to another, and in doing so, may experience resistance, so as to waste electrical energy and generate heat. ”

“ As the resistance opposed by bodies to compression increases indefinitely with the reduction of their volume, though their molecules have not come into contact with each other, it shows that the force which they exercise is repulsive at the least distances. At a distance greater than these, but still imperceptible, it must vary with great rapidity, and become attractive, in order that a steady equilibrium of the molecules may be possible ”

“ The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. The first step, therefore, in reducing these phenomena into scientific form, is to ascertain the magnitude and direction of the force acting between the bodies, and when it is found that this force depends in a certain way upon the relative position of the bodies and on their electric or magnetic condition, it seems at first sight natural to explain the facts by assuming the existence of something either at rest or in motion in each body, constituting its electric or magnetic state, and capable of acting at a distance according to mathematical laws. ”

“ Finally, as heat increases, and more and more work is done, against the centripetal force of cohesion, most substances, and doubtless all if we could get heat enough, are converted from solids into fluids, and ultimately into gases, in which latter state the molecules have got altogether beyond the sphere of their mutual attraction, and tend to dart off indefinitely in the direction of their own proper centrifugal motions, unless confined, in which case they dart about, collide, rebound, and exercise pressure on the containing surface. ”

“ An observer who is sitting eccentrically on the disc is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference-body . But the observer on the disc may regard his disc as a reference-body which is "at rest"; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field. ”

“ Newton’s Law of Motion is a law of maya: “To every action there is always an equal and contrary reaction; the mutual actions of any two bodies are always equal and oppositely directed.” Action and reaction are thus exactly equal. “To have a single force is impossible. There must be, and always is, a pair of forces equal and opposite.” ”

“ What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It is, replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration?
These difficulties are inextricable.
When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. ”

“ He who has sailed in a modern steamship through an ocean storm has seen the mighty vessel cleave the billows and scarcely slacken her speed in the teeth of the hurricane. Down in the depths of the ship men are piling coal on the furnaces and releasing a force—the imprisoned sun-power of uncounted ages—that baffles the waves and defies the whirlwind. ”

“ What boots a life which in such haste forsakes thee?
Thou'rt wondrous frolic, being to die so soon,
And passing proud a little colour makes thee.
If thee thy brittle beauty so deceives,
Know then the thing that swells thee is thy bane;
For the same beauty doth, in bloody leaves,
The sentence of thy early death contain.
Some clown's coarse lungs will poison thy sweet flower,
If by the careless plough thou shalt be torn;
And many Herods lie in wait each hour
To murder thee as soon as thou art born—
Nay, force thy bud to blow—their tyrant breath
Anticipating life, to hasten death! ”

“ The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or of moving uniformly forward in a right line. ”

“ It is to Gauss, to the Magnetic Union, and to magnetic observers in general, that we owe our deliverance from that absurd method of estimating forces by a variable standard which prevailed so long even among men of science. It was Gauss who first based the practical measurement of magnetic force (and therefore of every other force) ”

“ "Yes, but water decomposed into its primitive elements," replied Cyrus Harding, "and decomposed, doubtless; by electricity, which will then have become a powerful and manageable force, for all great discoveries, by some inexplicable law, appear to agree and become complete at the same time. Yes, my friends, I believe that water will one day be employed as fuel, that hydrogen and oxygen which constitute it, used singly or together, will furnish an inexhaustible source of heat and light, of an intensity of which coal is not capable. ”

“ If one now reflects that a molecule commonly contains, so far as we know, quite a large number of different freely moving constituents, certainly, that a normal molecule of a monatomic gas, e. g., mercury, possesses numerous freely moving electrons, then, in accordance with the law of uniform energy distribution, the intra-molecular energy must constitute a much larger fraction of the whole specific heat of the gas, and therefore must turn out much smaller, than is consistent with the measured values. ”

“ A number of molecules moving in obedience to dynamical laws will pass through a series of configurations which can be, theoretically determined as soon as the structure of each molecule and the initial position and velocity of every part of it are known. The determination of the series of configurations developing out of given initial conditions is not, however, the problem of the kinetic theory: the object of this theory is to explain the general properties of all gases in terms only of their molecular structure. ”

“ Since much smaller values are found for more complex molecules, we may suppose that, in these cases, the energy of rotation of a polyatomic molecule may be greater than its energy of translation, or else that heat is expended in splitting up molecular aggregates, and increasing energy of vibration. ”

“ This establishes the result stated, that the kinetic energy of the moving molecule is made up of an internal energy, the same up to the first order of the ratio of its velocity to that of radiation as if it were at rest, and the energy of translation of its electrons. The coefficient of half the square of the velocity of translation in the latter part is therefore, up to that order, the measure of the inertia, or mass, of the molecule thus constituted. ”

“ Thus when n=0, the whole energy must be translational: there can be no energy of rotation or of internal motion. The molecules of gases for which n=0 must accordingly be spherical in shape and in internal structure, or at least must behave at collisions as though they were spherical, for they would otherwise be set into rotation by the forces experienced at collisions. In the light of these results it is of extreme significance that the four gases for which n=0 are all believed to be monatomic: the molecules of these gases consist of single atoms. ”