Works of grant allen, p.784
Works of Grant Allen, page 784
This relation is quantitative — that is to say, a definite amount of Potential Energy passes always into a definite amount of Kinetic, and vice versa, while a definite quantity of each species is equivalent to a definite quantity of each other species, in either Mode. The law of conservation may therefore be subsumed under the following formula, where A stands for Potential and B for Kinetic Energy; 1, 2, 3, and 4 for the Molar, Molecular, Atomic, and Electrical species, and 5 for the Kinetic Energy of the ether (of which more hereafter):
A1 + A2 + A3 + A4 + B1 + B2 + B3 + B4 + B5 = a constant quantity.
But while the total of Energy, like the total of Force, is thus constant, the total of each mode and species varies from moment to moment. Whereas the total of each Species of Force is as constant as the sum of their totals.
Again, while each unit of Force is rigidly bound up with each atom of matter (with which it is perhaps identical), each unit of Energy may pass from one mass, molecule, atom, or electrical unit to another. It may also pass from matter to the ethereal medium, and vice versa. This can only happen, however, to Energy in the Kinetic Mode.
A mass in motion parts always with portions of its motion to all other bodies with which it comes in contact. It does so either by imparting to them a portion of its motion in the molar form (as when one billiard ball strikes another), or in the molecular form (as when heat is generated by friction). Hence every moving mass tends to part with all its Kinetic Energy more or less quickly, according as it is more or less impeded in its motion by more or less cohesion and gravitation. Thus a cannon ball parts with all its Molar Kinetic Energy at once when it strikes an iron target, and very quickly when it is fired in the air; a billiard ball parts with it more slowly, as it hits the other balls and the cushions; a quoit on ice more slowly still, as it meets the resistance of the air and the gentle friction of the ice; while a pendulum under an air pump hardly parts with it perceptibly by friction on its knife-edge, and a planet only by infinitesimal decrements to the ethereal medium. A molecule in motion parts similarly with a portion of its motion to every other molecule with which it comes in contact. When the two molecules, however, possess equal motions, or, as we oftener say, are at the same temperature, the amounts of gain and loss neutralise one another. But when the motions of the Molecules differ, the more energetic parts with a disproportionate amount of its motion to the less energetic, until the Energies of both are equal. Hence it happens that whenever the molecules of any mass have a higher Kinetic Energy than that of surrounding bodies, the motion of its molecules is imparted to the surrounding bodies till a state of equality is reached. As to Atomic and Electrical motions, we know too little of their nature to speak with any confidence, but we see at least that they also tend to pass away from the bodies with which they were associated, and to assume the forms of light and heat. In short, without fully anticipating the chapter on the Dissipation of Energy, we may say that whenever masses, molecules, atoms, or electrical units are free to act in accordance with their aggregative tendencies, without interference of antagonistic Forces or restraining power of continuous Kinetic Energies, they immediately unite, and impart their former Potential Energy in the Kinetic Mode directly to surrounding bodies, and ultimately to the ethereal medium.
We may thus summarise the contents of the present chapter: the sum total of all Energies in the Universe is a constant quantity; and whenever one mode or species of Energy disappears it is replaced by an equivalent quantity of another mode or species.
CHAPTER X.
THE INDESTRUCTIBILITY OF POWER.
The two generalisations briefly stated in the two preceding chapters under the titles of ‘The Persistence of Force’ and ‘The Conservation of Energy’ may be summed up under a still wider generalisation to which we shall apply the title of ‘The Indestructibility of Power.’ It may be formulated as follows.
The total amount of Power, aggregative or separative, in the Universe, is a constant quantity, and no Power can ever disappear or be destroyed.
This short chapter cannot be enlarged by the addition of any further remarks. Like our first chapter on Power generally it does not admit of amplification.
CHAPTER XI.
THE MUTUAL INTERFERENCE OF FORCES.
As the various portions of matter, molar, molecular, and atomic, all possess Forces of their own, it must necessarily happen that many bodies or particles are attracted in different directions with varying intensities by surrounding bodies or particles. Hence arises a certain cross-attraction or Mutual Interference of Forces. We shall consider in regular order the various modes in which each species of Force is opposed by interfering Forces.
Molar Force may be opposed to another Molar Force when two neighbouring masses each tend to attract a third mass. If all three masses be in every respect free — that is to say, if there be no other restraining Force, and no continuous Energy of relative motion — the three masses will aggregate simply. But in the large planetary bodies exposed to our observation the orbital Energy counteracts all the Forces; and we consequently see the sun, the earth, and the moon retaining their relative positions in spite of gravitation. There are certain instances, however, where the interference of Forces is seen, even in the case of Molar Forces. Thus, a large body like a table does not perceptibly attract even very small bodies on the floor, owing to the superior Power of the earth’s attraction as a whole. Yet in the neighbourhood of much larger masses, such as mountains, a slight deflection of the plummet has been observed, because the attraction of the mountain has proved strong enough to counteract in part the attraction of the earth as a whole.
Molar Force is more commonly interfered with by Molecular Force or cohesion. A weight placed on a table or a ball suspended by a cord cannot aggregate with the earth generally, because the Force of gravitation is overpowered by that of cohesion. At a certain point, however, the Power of gravitation outweighs that of cohesion, and the table or the rope gives way.
We can scarcely say with any certainty that Molar Force is interfered with by Atomic and Electrical Forces: but there seems no reason to doubt that chemical attraction may act in opposition to gravitation by causing an atom to aggregate with another atom so as to raise it slightly above its previous level: while the position of a lump of iron suspended from a magnet (permanent or electro-magnetic) probably represents the interference of electrical with molar Force. Our acquaintance with these phenomena, however, is so very superficial that it would be premature to do more than hint at possible analogies.
Molecular Force may be opposed by Molar Force in the above-cited instances of a mass laid on a table or hung by a cord. If the Molar Force overpowers the Molecular, the table or cord breaks, and the mass falls to the ground. One Molecular Force is opposed by another Molecular Force in the curious case of what is called Molecular Tension. In such an instance, certain molecules on either side of a particular set of molecules tend to draw it towards them, and the stronger attraction finally succeeds in doing so, leaving a disrupted portion on one side of the line. Molecular Force is probably opposed by Atomic and Electrical Forces, though here again no very obvious instance can be cited.
Atomic Force is possibly opposed by Molar Force as noted above. It is also possibly opposed by Molecular Force; and this seems not improbable when we recollect that many bodies will not combine chemically unless at a high temperature — in other words, unless their Molecular Force has been counteracted by an antagonistic energy. One Atomic Force is certainly opposed by another Atomic Force when two different atoms, each having affinity for a third atom, are brought into close conjunction with it. This occurs in all ordinary reactions; and, as we see, the stronger affinity overpowers the weaker one. What may be the relations of Atomic to Electrical Force it would be premature even to guess.
Electrical Force as a whole is too little understood to permit of definite treatment. We may conjecture, however, that it is similarly affected with other Forces. In one case, at least, we can feel sure of an analogy. One Electrical Force can be opposed to another by placing two balls, pretty equally charged with Positive Electricity, opposite to one another, and at equal distances from a ball charged with Negative Electricity. In this case we set up a state of cross-tension like that of the interfering masses, the molecular tension, or the rival chemical affinities: and any slight difference in the two attractions will cause the one to outweigh the other. It would also seem as though, in the case of a Leyden jar, the molecular Force of the glass opposed the Electrical Force which tends to aggregate the opposite electricities: for when the Electrical Force reaches a very high pitch, the electricities escape from some point on the metal surface, and leave a hole pierced through the glass. The analogy of this case to that of the broken rope or table is obvious. On the whole, however, the subject is still too ill-correlated with other departments of physics to allow of positive statements.
In all the cases where the interference of Forces produces an actual separation between masses or particles previously in (relative) contact, it might at first sight seem as though there were really an exhibition of Energy and not of Force. As in the case of aggregative Energies, however, a little consideration will correct this idea. For the bodies always follow the stronger Force; and the result is, a total of closer and more intimate aggregation than that which before subsisted. If the cord can resist the power of gravitation, then the union between its molecules is a more intimate one than that which would result from the aggregation of the ball and the earth. If, on the other hand, the cord cannot resist it, then the total of aggregation is increased by the fall of the ball. So, too, if a body in chemical combination with another body can resist the affinity of a third body brought near it, the existing union is shown to be a closer one than that proposed for it. If, on the other hand, it cannot resist it, then the new union proves itself thereby to be closer and more intimate than the previous one. When we come to consider the material universe as an aggregating total, whose separative Energy is being imparted to the ethereal universe, this point will become much clearer.
CHAPTER XII.
THE SUPPRESSION OF ENERGIES.
When a set of particles possessing Kinetic Energy is entirely surrounded by other particles, bound together by Force, it is possible up to a certain limit to suppress the Energy of the contained particles by limiting their mutual movements; whereupon the Energy appears to exist in a dormant state. But when a certain point of suppression is reached, the Energy of the contained particles overpowers the Force of the containing particles, and a disruption takes place. Such a disruption is commonly known as an Explosion. Or again, at a point short of disruption, such an active separative impulse exists amongst the contained particles, that if any aperture be made in the containing wall, the contained particles rush out with Explosive Energy.
The abstract statement of this principle must be enforced by a few concrete examples.
The boiler of a steam-engine is a wall or partition of molecules, rigidly bound together by cohesion. Within it, is a mass of water and steam, which is being raised to a high pitch of molecular motion by the fire underneath. Up to a certain point, it is possible to suppress or restrain the separative Energy of the steam by opposing to it the cohesive Force of the iron wall. But when a certain point of suppression is reached, the Energy outbalances the Force, and an Explosion takes place. At a point short of the Explosion, it is possible to open a valve and ‘blow off steam’: the energetic particles then rush forth with Explosive Energy. Similarly when a gas is reduced by pressure to the liquid state. Up to a certain point the Energy of the gas is suppressed; but when that point is passed, the Energy outbalances the Force, and an Explosion takes place. Short of the Explosion, it is possible to open the vessel, whereupon the gas rushes forth with Explosive Energy.
It is possible that certain (so-called) chemical combinations are really of this nature. Thus, certain compounds of nitrogen are very apt to explode, and it would seem not unreasonable to suppose that in their case the Energy of the free gas may be in some way confined by the combining atoms: while a match or other detonating agent may be the analogue of the valve or the stopcock in the above cited cases. This possibility will be more fully discussed in the succeeding chapter.
It is important to notice that one Energy may be opposed to another in producing a suppression. Thus Energy is expended in compressing a gas or bending a bow (a case which will be fully considered hereafter). So that just as Forces interfere with Forces, Energies sometimes oppose Energies. A suppressed Energy is regarded in the ordinary text-books as Potential. It is clear, however, that it cannot be so regarded from our present standpoint. It is essentially Kinetic, though its Kinesis is masked by surrounding bodies.
CHAPTER XIII.
LIBERATING ENERGIES.
When any body or particle possessing Potential Energy is prevented from aggregating with any other body or particle which attracts it, by the interference of an antagonistic Force, its Energy can only assume the Kinetic Mode through the intervention of some external Energy. Such external Energy is itself necessarily in the Kinetic Mode. It is known as a Liberating Energy.
Put in more concrete language, this principle may be otherwise stated thus. A body can only be disengaged from the attraction of one Force and brought under the direct influence of another, by some movement affecting it. A moment’s consideration will make it clear that this is a corollary from previously stated laws.
As we saw that the stronger Force necessarily outweighs the weaker, and as Forces cannot increase or decrease in intensity, the only manner in which any body or particle can be released from the Force which actually governs it and brought under the influence of another Force, is by some movement which either severs it from the sphere of the existing Forces, or brings it within the sphere of a stronger one. In the latter case, it is immaterial whether the movement brings the body into proximity with other bodies, or brings other bodies into proximity with it.
Molar Liberating Energies are those which release masses from the interference of a Force antagonistic to gravitation. The commonest instance of such a Liberating Energy is seen when we remove some obstacle which by its cohesion prevented the aggregation of gravitating masses. Thus a ball suspended by a thread is released by the separative Energy of a knife or scissors. A clock weight wound up but checked by a catch, is released through the Energy which removes the catch. A stone perched on a ledge is released by the puff of wind or the blow from a hand which causes it to topple over. A head of water confined by a sluice is released by the Energy which raises the sluice. A mass of ice on a mountain top is released by the Energy of heat, which breaks down the cohesion of its particles and allows it to trickle down the sides. Even in those cases where the intervention of the Energy is less apparent, we can see in an ultimate analysis that such Energy is really the moving Power at work. Thus, when the string decays instead of being cut, it might seem at first sight that the cohesion melted away imperceptibly; but a closer consideration will show us that the dropping of water, the action of heat and light, the approach of chemical solvents in minute quantities, and the incidence of other unobserved Energies is really the cause of the decay. So, too, if the water makes a way through the sluice, or cuts a path for itself through the bank, it can only do so by the slow action of incident Energies, which wear away the cohering substance that retains it. And the stone can never topple over from its ledge unless some animal pushes it, or some slow water action wears away its supporting mass. Molar Liberating Energies may also be seen in a few cases where a chemical body undergoes a separation which precipitates the heavier among its constituents.
Molecular Liberating Energies are those which release molecules from the interference of a Force antagonistic to cohesion. Two planed pieces of iron cannot cohere if laid side by side on a table: they are restrained in their places by gravitation. But the energy which apposes them to one another acts in this case as a liberator. In other instances, heat performs the same function, by loosening cohering molecules from their existing arrangement, and bringing them within the sphere of their mutual attractions, as when we weld two pieces of iron by heating them, or by hammering them together. The contained energy of water fulfils a like office in gumming or glueing, and in mixing plastic clay or dough. In these cases, one cohesion has interfered with another, and the Liberating Energy, by causing a partial disengagement, finally permits the complete saturation of both affinities.
Atomic Liberating Energies are those which release atoms from the interference of a Force antagonistic to Chemical Affinity. Occasionally it is the mere Force of gravitation or cohesion which opposes this affinity, and in that case, the Energy employed in bringing the substances together is the liberating agent; as when we expose phosphorus to Chlorine. In other instances, however, the mere apposition of the elements is not sufficient, as when we expose carbon to oxygen; heat is then needed as a liberating agent; and we may conjecture that it acts by setting up such a molecular vibration in the carbon as takes each atom out of its existing stable arrangement with other like atoms, into a compound carbon molecule, and brings it within the sphere of the stronger affinity exerted by oxygen. This case leads on to those where the interference is between rival Chemical Affinities. The Energy which brings together two substances and permits the stronger affinity to overcome the weaker acts as a liberating agent. In this instance, too, heat is sometimes necessary as an additional factor, probably for the same reason as before. In the case of Cl and H light acts as the liberating energy. Other less obvious cases resemble those of a match, where friction performs the same function.
