(A.) Visible energy of actual motion—in the planets, in meteors, in the cannon ball, in the storm, in the running stream, and in other instances of bodies in actual visible motion, too numerous to be mentioned.
Visible Energy of Position.
(B.) We have also visible energy of position—in a stone on the top of a cliff, in a head of water, in a rain cloud, in a cross-bow bent, in a clock or watch wound up, and in various other instances.
108. Then we have, besides, several cases in which there is an alternation between (A) and (B).
A pendulum, for instance, when at its lowest point, has only the energy (A), or that of actual motion, in virtue of which it ascends a certain distance against the force of gravity. When, however, it has completed its ascent, its energy is then of the variety (B), being due to position, and not to actual motion; and so on it continues to oscillate, alternately changing the nature of its energy from (A) to (B), and from (B) back again to (A).
109. A vibrating body is another instance of this alternation. Each particle of such a body may be compared to an exceedingly small pendulum oscillating backwards and forwards, only very much quicker than an ordinary pendulum; and just as the ordinary pendulum in passing its point of rest has its energy all of one kind, while in passing its upper point it has it all of another, so when a vibrating particle is passing its point of rest, its energy is all of the variety (A), and when it has reached its extreme displacement, it is all of the variety (B).
Heat Motion.
110. (C.) Coming now to molecular or invisible energy, we have, in the first place, that motion of the molecules of bodies which we term heat. A better term would be absorbed heat, to distinguish it from radiant heat, which is a very different thing. That peculiar motion which is imparted by heat when absorbed into a body is, therefore, one variety of molecular energy.
Molecular Separation.
(D.) Analogous to this is that effect of heat which represents position rather than actual motion. For part of the energy of absorbed heat is spent in pulling asunder the molecules of the body under the attractive force which binds them together (Art. 73), and thus a store of energy of position is laid up, which disappears again after the body is cooled.
Atomic or Chemical Separation.
111. (E.) The two previous varieties of energy may be viewed as associated with molecules rather than with atoms, and with the force of cohesion rather than with that of chemical affinity. Proceeding now to atomic force, we have a species of energy of position due to the separation of different atoms under the strong chemical attraction they have for one another. Thus, when we possess coal or carbon and also oxygen in a state of separation from one another, we are in possession of a source of energy which may be called that of chemical separation.
Electrical Separation.
112 (F.) The attraction which heterogeneous atoms possess for one another, sometimes, however, gives rise to a species of energy which manifests itself in a very peculiar form, and appears as electrical separation, which is thus another form of energy of position.
Electricity in Motion.
113 (G.) But we have another species of energy connected with electricity, for we have that due to electricity in motion, or in other words, an electric current which probably represents some form of actual motion.
Radiant Energy.
114 (H.) It is well known that there is no ordinary matter, or at least hardly any, between the sun and the earth, and yet we have a kind of energy which we may call radiant energy, which proceeds to us from the sun, and proceeds also with a definite, though very great velocity, taking about eight minutes to perform its journey. Now, this radiant energy is known to consist of the vibrations of an elastic medium pervading all space, which is called ether, or the ethereal medium. Inasmuch, therefore, as it consists of vibrations, it partakes of the character of pendulum motion, that is to say, the energy of any ethereal particle is alternately that of position and that of actual motion.
Law of Conservation.
115. Having thus endeavoured, provisionally at least, to catalogue our various energies, we are in a position to state more definitely what is meant by the conservation of energy. For this purpose, let us take the universe as a whole, or, if this be too large, let us conceive, if possible, a small portion of it to be isolated from the rest, as far as force or energy is concerned, forming a sort of microcosm, to which we may conveniently direct our attention.
This portion, then, neither parts with any of its energy to the universe beyond, nor receives any from it. Such an isolation is, of course, unnatural and impossible, but it is conceivable, and will, at least, tend to concentrate our thoughts. Now, whether we regard the great universe, or this small microcosm, the principle of the conservation of energy asserts that the sum of all the various energies is a constant quantity, that is to say, adopting the language of Algebra—
(A) + (B) + (C) + (D) + (E) + (F) + (G) + (H) = a constant quantity.
116. This does not mean, of course, that (A) is constant in itself, or any other of the left-hand members of this equation, for, in truth, they are always changing about into each other—now, some visible energy being changed into heat or electricity; and, anon, some heat or electricity being changed back again into visible energy—but it only means that the sum of all the energies taken together is constant. We have, in fact, in the left hand, eight variable quantities, and we only assert that their sum is constant, not by any means that they are constant themselves.
117. Now, what evidence have we for this assertion? It may be replied that we have the strongest possible evidence which the nature of the case admits of. The assertion is, in truth, a peculiar one—peculiar in its magnitude, in its universality, in the subtle nature of the agents with which it deals. If true, its truth certainly cannot be proved after the manner in which we prove a proposition in Euclid. Nor does it even admit of a proof so rigid as that of the somewhat analogous principle of the conservation of matter, for in chemistry we may confine the products of our chemical combination so completely as to prove, beyond a doubt, that no heavy matter passes out of existence that—when coal, for instance, burns in oxygen gas—what we have is merely a change of condition. But we cannot so easily prove that no energy is destroyed in this combination, and that the only result is a change from the energy of chemical separation into that of absorbed heat, for during the process it is impossible to isolate the energy—do what we may, some of it will escape into the room in which we perform the experiment; some of it will, no doubt, escape through the window, while a little will leave the earth altogether, and go out into space. All that we can do in such a case is to estimate, as completely as possible, how much energy has gone away, since we cannot possibly prevent its going. But this is an operation involving great acquaintance with the laws of energy, and very great exactness of observation: in fine, our readers will at once perceive that it is much more difficult to prove the truth of the conservation of energy than that of the conservation of matter.
118. But if it be difficult to prove our principle in the most rigorous manner, we are yet able to give the strongest possible indirect evidence of its truth.
Our readers are no doubt familiar with a method which Euclid frequently adopts in proving his propositions. Starting with the supposition that they are not true, and reasoning upon this hypothesis, he comes to an absurd conclusion—hence he concludes that they are true. Now, we may adopt a method somewhat similar with regard to our principle, only instead of supposing it untrue, let us suppose it true. It may then be shown that, if it be true, under certain test conditions we ought to obtain certain results—for instance, if we increase the pressure, we ought to lower the freezing point of water. Well, we make the experiment, and find that, in point of fact, the freezing point of water is lowered by increasing the pressure, and we have thus derived an argument in favour of the conservation of energy.
119. Or again, if the laws of energy are true, it may be shown that, whenever a substance contracts when heated, it will become colder instead of hotter by compression. Now, we know that ice-cold water, or water just a little above its freezing point, contracts instead of expanding up to 4° C.; and Sir William Thomson has found, by experiment, that water at this temperature is cooled instead of heated by sudden compression. India-rubber is another instance of this relation between these two properties, for if we stretch a string of india-rubber it gets hotter instead of colder, that is to say, its temperature rises by extension, and gets lower by contraction; and again, if we heat the string, we find that it contracts in length instead of expanding like other substances as its temperature increases.
120. Numberless instances occur in which we are enabled to predict what will happen by assuming the truth of the laws of energy; in other words, these laws are proved to be true in all cases where we can put them to the test of rigorous experiment, and probably we can have no better proof than this of the truth of such a principle. We shall therefore proceed upon the assumption that the conservation of energy holds true in all cases, and give our readers a list of the various transmutations of this subtle agent as it goes backwards and forwards from one abode to another, making, meanwhile, sundry remarks that may tend, we trust, to convince our readers of the truth of our assumption.