Should patch a wall to expel the winter’s flaw!
Now the greatest discovery of our age is that force, like matter, is indestructible, and that it can no more be created than can matter. The reader may perhaps think the statement that we cannot create force is in contradiction to experience. He will be disposed to ask, What is the steam engine for but to create force? Do we not gain force by the pulley, the lever, the hydraulic press? And are not tremendous forces produced when we explode gunpowder or nitro-glycerine? When the principle with which we are here concerned has been developed and stated in accurate terms, it is hoped the reader will see the real nature of these contrivances. We are, however, aware that it is quite impossible within the limits of a short article to do much more than indicate a region of discovery abounding with results which may be yet unfamiliar to some. Into this, if so minded, they should seek for further guidance, which they will pleasantly find in the pages of Dr. Tyndall’s “Heat considered as a Mode of Motion,” and in a little work by Professor Balfour Stewart, entitled “The Conservation of Energy,” and quite fascinating from the clearness and simplicity of its style. We may continue our humble task of merely illustrating the general nature of this, in reality the most important, subject which we have had occasion to bring under the reader’s notice.
Perhaps the first step should be to point out the fact of the various forces of nature—mechanical action, heat, light, electricity, magnetism, chemical action—being so related that any one can be made to produce all the rest directly or indirectly. Some examples of the conversion of one form of force into another occur in the foregoing pages. Thus, on page [485] an experiment is described in which electricity produces a mechanical action; electricity is also shown, on page [496], to produce heat; on page [491] chemical action; on page [501] magnetism. Then, as instances of the inverse actions, there is on page [488], in the first paragraph on “Electric Induction,” an account of the mode in which mechanical movements may give rise to electricity; and in the experiments in pages [508], 509, and particularly in the account of the Gramme machine, page [511], it is shown how mechanical movements can, through magnetism, produce electricity. The voltaic element, page [491], and the galvanic batteries, are instances of chemical action supplying electricity. On page [518] a striking instance is mentioned of changes in the forms of force. Every lighted candle is a case of chemical action giving rise to light; and interesting examples of the inverse relation are referred to on page [608]. On page [168] is represented the conversion of arrested motion into heat and light. We have, indeed, sufficient examples to arrange a series of these conversions of forces in a circle. Thus, chemical action (oxidation in the animal system) supplies muscular power, this sets in motion a Gramme machine, the motion is converted into electricity, the electricity produces the electric light, and light causes chemical action, and with this the cycle is complete. In the steam engine heat is converted into mechanical force, and many cases will present themselves to the reader’s mind in which mechanical actions give rise to heat. The doctrine of a mutual dependence and convertibility among all the forms of force was first definitively taught in England by Mr. (now Justice) Grove, in 1842; and almost simultaneously Dr. Meyer promulgated similar views in Germany. Mr. Grove subsequently embodied his doctrine in a treatise, called “The Correlation of the Physical Forces,” which has seen several editions.
But this teaching included much more than a mere connection between the various forces, for it extended to quantitative relations. It declared that a given amount of one force always produced a definite amount of another, that a certain quantity of heat, for example, would give rise to a certain amount of mechanical action, and that this amount of mechanical action was the equivalent of the heat which produced it, and would in its turn reproduce all that heat. These last doctrines, however, rested on a speculative basis, until Mr. James Prescott Joule, of Manchester, carried out a most patient, laborious, and elaborate experimental investigation of the subject. His labours placed the truth of the numerical equivalence of forces on a foundation which cannot be shaken; and he accomplished for the principle of the indestructibility of force what Lavoisier did for that of the indestructibility of matter—he established it on the incontrovertible basis of accurate and conclusive experiment. His determination of the value of the mechanical equivalent of heat especially is a model of experimental research; and subsequent investigators have, by diversified methods, confirmed the accuracy of his results. A great part of his work consisted in finding what quantity of heat would be produced by a given quantity of work.
Before we proceed to give an indication of one of Dr. Joule’s methods of making this determination, we may point out that if a weight be raised a certain height, the work which is done in raising it will be given out by the weight in its descent. If you carry a 1 lb. weight to the top of the London Monument, which is 200 ft. high, you perform 200 units of work. When the weight is at the top, the work is not lost; for let the weight be attached to a cord passing over a pulley, and it will, as it descends, draw up to the top another 1 lb. weight.[[21]] If you drop the weight so that it falls freely, it descends with a continually increasing velocity, strikes the pavement, and comes to rest. Still your work is not lost. The collision of the weight and the pavement develops heat, just as in the case of the experiment depicted on page [168], but to a less degree—the increase of temperature might not be sensible to the touch, but could be recognized by delicate instruments. Your work, then, has now changed into the form of heat—the weight and the pavement are hotter than before. This heat is carried off by contiguous substances. But still your work is not lost, for it has made the earth warmer. The heat, however, soon flows away by radiation from the earth, and is diffused into space. The final result of your work is, then, that a certain measurable quantity of heat has been sent off into space. Is your work now finally lost? Not so: in reality, it is only diffused throughout the universe in the form of radiant heat of low intensity. Yet it is lost for ever for useful purposes; for from this final form of diffused heat there is no known or conceivable process by which heat can be gathered up again.
[21]. See Note B, at the end.
Dr. Joule arranged paddles of brass or iron, so that they could turn freely in a circular box containing water or quicksilver. From the sides of the box partitions projected inwards, which contained openings that permitted the divided arms of the paddle to pass, and preventing the liquid from moving en masse, thus caused a churning action when the paddle was turned. Now, every one who has worked a rotatory churn knows that a considerable resistance is offered to this action; but every one does not know that under these circumstances the liquid becomes warmer. It was Dr. Joule’s object to discover how much the temperature of his liquid was raised by a measured quantity of work. He used very delicate thermometers, and had to take a number of precautions which need not here be described; and he obtained the definite quantity of work by the descent of a known weight through a known distance, a cord attached to the weight being wound on a drum, which communicated motion to the paddle. The experiments were conducted with varying circumstances, to avoid chances of error, and were repeated very many times until uniform and consistent indications were always obtained. The result of the experiments showed that 772 units of work (foot-pounds) furnished heat which would raise the temperature of 1 lb. of water from 32° to 33° F., which is the unit of heat. This number, 772, is a constant of the greatest importance in scientific and practical calculations, and is called “the mechanical equivalent of heat.” The amount of work it represents is sometimes called a “Joule,” and is always represented in algebraical formulæ by “J.” Mr. Joule’s first paper appeared in 1843, and soon afterwards various branches of the subject of “The Equivalence and Persistence of Forces” were taken up by a number of able men, who have advanced its principles along various lines of inquiry. Among the most noted contributors to this question we find the names of Sir William Thomson, Helmholtz, James Thomson, Rankin, Clausius, Tait, Andrews, and Maxwell.
In the steam engine the case is the inverse of that presented by the above-named experiment of Dr. Joule’s. Here we have heat producing work. Now, the quantity of steam which enters the cylinder of a steam engine may be found, and the temperature of the steam can be determined, and from these the amount of heat which passes into the cylinder per minute, say, can be calculated. A large portion of this heat is, in an ordinary engine, yielded up to the condensing water, and another part is lost by conduction and radiation from the cylinder, condenser, pipes, &c. But both these quantities can be estimated. When the amount is compared with that entering the cylinder in the steam, a difference is always found, which leaves a quantity of heat unaccounted for. When this quantity is compared with the work done by the engine in the same interval (which work can be measured as described on page [10]), it is always found that for every 772 units of work a unit of heat has disappeared from the cylinder. The numerical relation between work and heat which is established in these two cases has been tested in many quite different ways; and, within the limits of experimental errors, always with the same numerical result. But equally definite quantitative relations are known to exist among all the other forms of force; and the manner in which these are convertible into each other has already been indicated, although want of space prevents full illustration of this part of the subject. It may, however, be seen that each form of force can be mediately or immediately converted into mechanical effect, hence each is expressible in terms of work. That is to say, we can assign to a unit of electricity, for example, a number expressing the work which it would do if entirely converted into work; and the same number also expresses the work which would be required to produce the unit of electricity. An ounce of hydrogen in combining with 8 oz. of oxygen produces a certain measurable quantity of heat. If that heat, say = H, were all converted into work, we now know that the work would = HJ. Hence we can express a definite chemical action in terms of work. The same is generally true of all physical forces, though in some cases, such as light, vital action, &c., the quantitative relations have not yet been definitely determined.
Since, then, all the forces with which we are acquainted are expressible (though the exact relations of some have yet to be discovered) in terms of work, it is found of great advantage to consider the power of doing work as the common measure of doing all these. Thus, if we define energy as that which does, or that which is capable of doing, work, we have a term extremely convenient in the description of some aspects of our subject. Thus we can now speak of the energies of nature, instead of the forces. And all forces, active or passive, may be summed up in one word—energy. And, further, the great discovery of the conservation of forces under definite equivalents, may be summed up very briefly in this statement—THE AMOUNT OF ENERGY IN THE UNIVERSE IS CONSTANT. To make this statement clear requires that a distinction between two forms of every kind of energy be pointed out. To recur to the example before imagined: if you carry the 1 lb. weight up the Monument, and deposit it on the ledge at the top, it might lie there for a thousand years before it was made to give back the work you had performed upon it. That work has been, in a manner, stored up by the position you have given to your weight. Now, in taking up the weight, you expended energy—you really performed work: that is an instance of energy in operation, and may be termed “actual energy.” In what form does the energy exist during the thousand years we may suppose your weight to lie at the top of the Monument? It is ready to yield up your work again at any moment it is permitted to descend, and it possesses therefore during the whole period a potential energy equal in amount to the actual energy you bestowed upon it. A similar distinction between actual and potential energy exists with regard to every form of force. If by any means you separate an atom of carbon from an atom of oxygen, you exert actual energy. The process is analogous to carrying up the weight. The atoms when separated possess potential energy,—they can rush together again, like the weight to the earth, and in doing so will give out the work which was expended on their separation. A parallel illustration might be drawn from electrical force.
A typical example of the storing up of energy is furnished by a crossbow. The moment a man begins to bend the bow he is doing work, because he pulls the string in opposition to the bow’s resistance to a change in its form; and it is plain that the amount of energy thus expended is measurable. Suppose, now, the bow has been bent and the string caught in the notch, from which it is released by drawing the trigger when the discharge of the bow is desired. The bow may be retained for an indefinite period in the bent condition, and in this state it possesses, in the form of potential energy, all the work which has been expended in bending it, and which it will, in fact, give out, in some way or other, whenever the trigger is drawn. To fix our ideas, let us suppose that to draw the string over the notch required a pull of 50 lbs. over a space of 6 in.; that is equivalent to 50 × ½ = 25 units of work. Now let the bow be used to shoot an arrow weighing ¼ lb. vertically upwards. The height in feet to which the arrow will rise multiplied into its weight in pounds will be the work done upon it by the bow. Now, we say that experiment proves that in the case supposed the arrow would rise just 100 ft., so that the work done by the bow (¼ × 100 = 25) would be precisely that done upon it. For the sake of simplicity, we keep this illustration free from the mention of interfering causes, which have to be considered and allowed for when the matter is put to the real test of quantitative experiment. The instance of the crossbow brings into notice a highly instructive circumstance, which is this: the bow, which it may have taken the strength of a Hercules to bend, will shoot its bolt by the mere touch of a child on the trigger. In the same way, when a man fires a gun, he merely permits the potential energy contained in the charge to convert itself into actual, or kinetic, energy. The real source of the energy, in the case of the child discharging the crossbow, is the muscular power of the man who drew it; the real source of the energy in exploding gunpowder is the separation of carbon atoms from oxygen atoms, and that has been done by the sun’s rays, as truly as the string was pulled away from the bow by muscular power. If we turn our attention to nitro-glycerine or to nitro-cellulose, we can, by following the chemical actions giving rise to these substances, in like manner trace their energies to our great luminary. The unstable union by which oxygen and nitrogen atoms are locked up in the solid and liquid forms of nitro-cellulose and nitro-glycerine is also the work of the sun; for nitrogen acids, or rather nitrates, are produced naturally under certain electrical and other conditions of the atmosphere, which are due, directly or indirectly, to the sun’s action; and they cannot be formed artificially, except by imitating the natural conditions, as by passing electric sparks through air, &c.