# The Conservation of Energy/Chapter 4

CHAPTER IV.

TRANSMUTATIONS OF ENERGY.

Energy of Visible Motion.

121 Let us begin our list of transmutations with the energy of visible motion. This is changed into energy of position when a stone is projected upwards above the earth, or, to take a case precisely similar, when a planet or a comet goes from perihelion, or its position nearest the sun, to aphelion, or its position furthest from the sun. We thus see why a heavenly body should move fastest at perihelion, and slowest at aphelion. If, however, a planet were to move round the sun in an orbit exactly circular, its velocity would be the same at all the various points of this orbit, because there would be no change in its distance from the centre of attraction, and therefore no transmutation of energy.

122. We have already (Arts. 108, 109) said that the energy in an oscillating or vibrating body is alternately that of actual motion, and that of position. In this respect, therefore, a pendulum is similar to a comet or heavenly body with an elliptical orbit. Nevertheless the change of energy is generally more complete in a pendulum or vibrating body than it is in a heavenly body; for in a pendulum, when at its lowest point, the energy is entirely that of actual motion, while at its upper point it is entirely that of position. Now, in a heavenly body we have only a lessening, but not an entire destruction, of the velocity, as the body passes from perihelion to aphelion—that is to say, we have only a partial conversion of the one kind of energy into the other.

123. Let us next consider the change of actual visible energy into absorbed heat This takes place in all cases of friction, percussion, and resistance. In friction, for instance, we have the conversion of work or energy into heat, which is here produced through the rubbing of surfaces against each other; and Davy has shown that two pieces of ice, both colder than the freezing point, may be melted by friction. In percussion, again, we have the energy of the blow converted into heat; while, in the case of a meteor or cannon ball passing through the air with great velocity, we have the loss of energy of the meteor or cannon ball through its contact with the air, and at the same time the production of heat on account of this resistance.

The resistance need not be atmospheric, for we may yet the cannon ball to pierce through wooden planks or through sand, and there will equally be a production of heat on account of the resistance offered by the wooden planks or by the sand to the motion of the ball. We may even generalize still further, and assert that whenever the visible momentum of a body is transferred to a larger mass, there is at the same time the conversion of visible energy into heat.

124. A little explanation will be required to make this point clear.

The third law of motion tells us that action and reaction are equal and opposite, so that when two bodies come into collision the forces at work generate equal and opposite quantities of momentum. We shall best see the meaning of this law by a numerical example, bearing in mind that momentum means the product of mass into velocity.

For instance, let us suppose that an inelastic body of mass 10 and velocity 20 strikes directly another inelastic body of mass 15 and velocity 15, the direction of both motions being the same.

Now, it is well known that the united mass will, after impact, be moving with the velocity 17. What, then, has been the influence of the forces developed by collision? The body of greater velocity had before impact a momentum ${\displaystyle 10\times 20=200}$, while its momentum after impact is only ${\displaystyle 10\times 17=170}$; it has therefore suffered a loss of 30 units as regards momentum, or we may consider that a momentum of 30 units has been impressed upon it in an opposite direction to its previous motion.

On the other hand, the body of smaller velocity had before impact a momentum ${\displaystyle 15\times 15=225}$, while after impact it has ${\displaystyle 15\times 17=255}$ units, so that its momentum has been increased by 30 units in its previous direction.

The force of impact has therefore generated 30 units of momentum in two opposite directions, so that, taking account of direction, the momentum of the system is the same before and after impact; for before impact we had a momentum of ${\displaystyle 10\times 20+15\times 15=425}$, while after it we have the united mass 25 moving with the velocity 17, giving the momentum 425 as before.

125. But while the momentum is the same before and after impact, the visible energy of the moving mass is undoubtedly less after impact than before it. To see this we have only to turn to the expression of Art. 28, from which we find that the energy before impact was as follows:—Energy in kilogrammetres ${\displaystyle ={\frac {mv^{2}}{19.6}}={\frac {10\times 20^{2}+15\times 15^{2}}{19.6}}=376}$ nearly; while that after impact ${\displaystyle ={\frac {25\times 17^{2}}{19.6}}=368}$ nearly.

120. The loss of energy will be still more manifest if we suppose an inelastic body in motion to strike against a similar body at rest. Thus if we have a body of mass 20 and velocity 20 striking against one of equal mass, but at rest, the velocity of the double mass after impact will obviously be only 10; but, as regards energy, that before impact will be ${\displaystyle {\frac {20\times 20^{2}}{19.6}}={\frac {8000}{19.6}}}$ while that after impact will be ${\displaystyle {\frac {40\times 10^{2}}{19.6}}={\frac {4000}{19.6}}}$ or only half the former.

127. Thus, there is in all such cases an apparent loss of visible energy while at the same time there is the production of heat on account of the blow which takes place. If, however, the substances that come together be perfectly elastic (which no substance is), the visible energy after impact will be the same as that before, and in this case there will be no conversion into heat. This, however, is an extreme supposition, and inasmuch as no substance is perfectly elastic, we have in all cases of collision a greater or less conversion of visible motion into heat.

128. We have spoken (Art. 122) about the change of energy in an oscillating or vibrating body, as if it were entirely one of actual energy into energy of position, and the reverse.

But even here, in each oscillation or vibration, there is a greater or less conversion of visible energy into heat. Let us, for instance, take a pendulum, and, in order to make the circumstances as favourable as possible, let it swing on a knife edge, and in vacuo; in this case there will be a slight but constant friction of the knife edge against the plane on which it rests, and though the pendulum may continue to swing for hours, yet it will ultimately come to rest.

And, again, it is impossible to make a vacuum so perfect that there is absolutely no air surrounding the pendulum, so that part of the motion of the pendulum will always be carried off by the residual air of the vacuum in which it swings.

129. Now, something similar happens in that vibratory motion which constitutes sound. Thus, when a bell is in vibration, part of the energy of the vibration is carried off by the surrounding air, and it is in virtue of this that we hear the sound of the bell; but, even if there were no air, the bell would not go on vibrating for ever. For there is in all bodies a greater or less amount of internal viscosity, a property which prevents perfect freedom of vibration, and which ultimately converts vibrations into heat.

A vibrating bell is thus very much in the same position as an oscillating pendulum, for in both part of the energy is given off to the air, and in both there is unavoidable friction—in the one taking the shape of internal viscosity, and in the other that of friction of the knife edge against the plane on which it rests.

130. In both these cases, too, that portion of the energy which goes into the air takes ultimately the shape of heat. The oscillating pendulum communicates a motion to the air, and this motion ultimately heats the air. The vibrating bell, or musical instrument, in like manner communicates part of its energy to the air. This communicated energy first of all moves through the air with the well-known velocity of sound, but during its progress it, too, no doubt becomes partly converted into heat. Ultimately, it is transmitted by the air to other bodies, and by means of their internal viscosity is sooner or later converted into heat. Thus we see that heat is the form of energy, into which all visible terrestrial motion, whether it be rectilinear, or oscillatory, or vibratory, is ultimately changed.

131. In the case of a body in visible rectilinear motion on the earth's surface, this change takes place very soon—if the motion be rotatory, such as that of a heavy revolving top, it may, perhaps, continue longer before it is ultimately stopped, by means of the surrounding air, and by friction of the pivot; if it be oscillatory, as in the pendulum, or vibratory, as in a musical instrument, we have seen that the air and internal friction are at work, in one shape or another, to carry it off, and will ultimately succeed in converting it into heat.

132. But, it may be said, why consider a body moving on the earth's surface? why not consider the motion of the earth itself? Will this also ultimately take the shape of heat?

No doubt it is more difficult to trace the conversion in such a case, inasmuch as it is not proceeding at a sensible rate before our eyes. In other words, the very conditions that make the earth habitable, and a fit abode for intelligent beings like ourselves, are those which unfit us to perceive this conversion of energy in the case of the earth. Yet we are not without indications that it is actually taking place. For the purpose of exhibiting these, we may divide the earth's motion into two—a motion of rotation, and one of revolution.

133. Now, with regard to the earth's rotation, the conversion of the visible energy of this motion into heat is already well recognized. To understand this we have only to study the nature of the moon's action upon the fluid portions of our globe. In the following diagram (Fig. 11) we have an exaggerated representation of this, by which we see that the spherical earth is converted

Fig. 11.

into an elongated oval, of which one extremity always points to the moon. The solid body of the earth itself revolves as usual, but, nevertheless, this fluid protuberance remains always pointing towards the moon, as we see in the figure, and hence the earth rubs against the protuberance as it revolves. The friction produced by this action tends evidently to lessen the rotatory energy of the earth—in other words, it acts like a break—and we have, just as by a break-wheel, the conversion of visible energy into heat. This was first recognized by Mayer and J. Thomson.

134. But while there can be no doubt about the fact of such a conversion going on, the only question is regarding its rate of progress, and the time required before it can cause a perceptible impression upon the rotative energy of the earth.

Now, it is believed by astronomers that they have detected evidence of such a change, for our knowledge of the motions of the sun and moon has become so exact, that not only can we carry forward our calculations so as to predict an eclipse, but also carry them backwards, and thus fix the dates and even the very details of the ancient historical eclipses.

If, however, between those times and the present, the earth has lost a little rotative energy on account of this peculiar action of the moon, then it is evident that the calculated circumstances of the ancient total eclipse will not quite agree with those actually recorded; and by a comparison of this nature it is believed that we have detected a very slight falling off in the rotative energy of our earth. If we carry out the argument, we shall be driven to the conclusion that the rotative energy of our globe will, on account of the moon's action, always get less and less, until things are brought into such a state that the rotation comes to be performed in the same time as the revolution of the moon, so that then the same portion of the terrestrial surface being always presented to the moon, it is evident that there will be no effort made by the solid substance of the earth, to glide from under the fluid protuberance, and there will in consequence be no friction, and no further loss of energy.

135. If the fate of the earth be ultimately to turn the same face always to the moon, we have abundant evidence that this very fate has long since overtaken the moon herself Indeed, the much stronger effect of our earth upon the moon has produced this result, probably, even in those remote periods when the moon was chiefly fluid; and it is a fact well known, not merely to astronomers, but to all of us, that the moon nowadays turns always the same face to the earth.[1] No doubt this fate has long since overtaken the satellites of Jupiter, Saturn, and the other large planets; and there are independent indications that, at least in the case of Jupiter, the satellites turn always the same face to their primary.

136. To come now to the energy of revolution of the earth, in her orbit round the sun, we cannot help believing that there is a material medium of some kind between the sun and the earth; indeed, the undulatory theory of light requires this belief But if we believe in such a medium, it is difficult to imagine that its presence will not ultimately diminish the motion of revolution of the earth in her orbit; indeed, there is a strong scientific probability, if not an absolute certainty, that such will be the case. There is even some reason to think that the energy of a comet of small period, called Encke's comet, is gradually being stopped from this cause; in fine, there can be hardly any doubt that the cause is really in operation, and will ultimately affect the motions of the planets and other heavenly bodies, even although its rate of action may be so slow that we are not able to detect it.

We may perhaps generalize by saying, that wherever in the universe there is a differential motion, that is to say, a motion of one part of it towards or from another, then, in virtue of the subtle medium, or cement, that binds the various parts of the universe together, this motion is not unattended by something like friction, in virtue of which the differential motion will ultimately disappear, while the loss of energy caused by its disappearance will assume the form of heat.

137. There are, indeed, obscure intimations that a conversion of this kind is not improbably taking place in the solar system; for, in the sun himself, we have the matter near the equator, by virtue of the rotation of our luminary, carried alternately towards and from the various planets. Now, it would seem that the sun-spots, or atmospheric disturbances of the sun, affect particularly his equatorial regions, and have likewise a tendency to attain their maximum size in that position, which is as far away as possible from the influential planets, such as Mercury or Venus;[2] so that if Venus, for instance, were between the earth and the sun, there would be few sun-spots in the middle of the sun's disc, because that would be the part of the sun nearest Venus.

But if the planets influence sun-spots, the action is no doubt reciprocal, and we have much reason to believe that sun-spots influence, not only the magnetism, but also the meteorology of our earth, so that there are most displays of the Aurora Borealis, as well as most cyclones, in those years when there are most sun-spots.[3] Is it not then possible that, in these strange, mysterious phenomena, we see traces of the machinery by means of which the differential motion of the solar system is gradually being changed into heat?

138. We have thus seen that visible energy of actual motion is not unfrequently changed into visible energy of position, and that it is also very often transformed into absorbed heat. We have now to state that it may likewise be transformed into electrical separation. Thus, when an ordinary electrical machine is in action, considerable labour is spent in turning the handle; it is, in truth, harder to turn than if no electricity were being produced—in other words, part of the energy which is spent upon the machine goes to the production of electrical separation. There are other ways of generating electricity besides the frictional method. If, for instance, we bring an insulated conducting plate near the prime conductor of the electrical machine, yet not near enough to cause a spark to pass, and if we then touch the insulated plate, we shall find it, after contact, to be charged with an electricity the opposite of that in the machine; we may then remove it and make use of this electricity.

It requires a little thought to see what labour we have spent in this process. We must bear in mind that, by touching the plate, we have carried off the electricity of the same name as that of the machine, so that, after touching the insulated plate it is more strongly attracted to the conductor than it was before. When we begin to remove it, therefore, it will cost us an effort to do so, and the mechanical energy which we spend in removing it will account for the energy of electrical separation which we then obtain.

139. We may thus make use of a small nucleus of electricity, to assist us in procuring an unlimited supply, for in the above process the electricity of the prime conductor remains unaltered, and Ave may repeat the operation as often as we like, and gather together a very large quantity of electricity, without finally altering the electricity of the prime conductor, but not, however, without the expenditure of an equivalent amount of energy, in the shape of actual work.

140. While, as we have seen, there is a tendency in all motion to be changed into heat, there is one instance where it is, in the first place at least, changed into a current of electricity. We allude to the case where a conducting substance moves in the presence of an electric current, or of a magnet.

In Art. 104 we found that if one coil connected with a battery were quickly moved into the presence of another coil connected with a galvanometer, an induced current would be venerated in the latter coil, and would affect the galvanometer, its direction being the reverse of that passing in the other. Now, an electric current implies energy, and we may therefore conclude that some other form of energy must be spent, or disappear, in order to produce the current which is generated in the coil attached to the galvanometer.

Again, we learn from Art. 100 that two currents going in opposite directions repel one another. The current generated in the coil attached to the galvanometer or secondary current will, therefore, repel the primary current, which is moving towards it; this repulsion will either cause a stoppage of motion, or render necessary the expenditure of energy, in order to keep up the motion of this moving coil. We thus find that two phenomena occur simultaneously. In the first place, there is the production of energy in the secondary coil, in the shape of a current opposite in direction to that of the primary coil; in the next case, owing to the repulsion between this induced current and the primary current, there is a stoppage or disappearance of the energy of actual motion of the moving coil. We have, in fact, the creation of one species of energy, and at the same time the disappearance of another, and thus we see that the law of conservation is by no means broken.

141. We see also the necessary connection between the two electrical laws described in Arts. 100 and l04. Indeed, had these laws been other than what they are, the principle of conservation of energy would have been broken.

For instance, had the induced current in the case now mentioned been in the same direction as that of the primary, the two currents would have attracted each other, and thus there would have been the creation of a secondary current, implying energy, in the coil attached to the galvanometer, along with an increase of the visible energy of motion of the primary current—that is to say, instead of the creation of one kind of energy, accompanied with the disappearance of another, we should have had the simultaneous creation of both; and thus the law of conservation of energy would have been broken.

We thus see that the principle of conservation enables us to deduce the one electrical law from the other, and this is one of the many instances which strengthen our belief in the truth of the groat principle for which we are contending.

142. Let us next consider what will take place if we cause the primary current to move from the secondary coil instead of towards it.

In this case we know, from Art. 104, that the induced current will be in the same direction as the primary, while we are told by Art. 100 that the two currents will now attract each other. The tendency of this attraction will be to stop the motion of the primary current from the secondary one, or, in other words, there will be a disappearance of the energy of visible motion, while at the same time there is the production of a current. In both cases, therefore, one form of energy disappears while another takes its place, and in both there will be a very perceptible resistance experienced in moving the primary coil, whether towards the secondary or from it. Work will, in fact, have to be spent in both operations, and the outcome of this work or energy will be the production of a current in the first place, and of heat in the second; for we learn from Art. 98 that when a current passes along a wire its energy is generally spent in heating the wire.

We have thus two phenomena occurring together. In the first place, in moving a current of electricity to and from a coil of wire, or any other conductor, or (which is the same thing, since action and reaction are equal and opposite) in moving a coil of wire or any other conductor to and from a current of electricity, a sense of resistance will be experienced, and energy will have to be spent upon the process; in the second place, an electrical current will be generated in the conductor, and the conductor will be heated in consequence.

143. The result will be rendered very prominent if we cause a metallic top, in rapid rotation, to spin near two iron poles, which, by means of the battery, we can suddenly convert into the poles of a powerful electro-magnet. When this change is made, and the poles become magnetic, the motion of the top is very speedily brought to rest, just as if it had to encounter a species of invisible friction. This curious result can easily be explained. We have seen from Art. 101 that a magnet resembles an assemblage of electric currents, and in the metallic top we have a conductor alternately approaching these currents and receding from them; and hence, according to what has been said, we shall have a series of secondary currents produced in the conducting top which will stop its motion, and which will ultimately take the shape of heat. In other words, the visible energy of the top will be changed into heat just as truly as if it were stopped by ordinary friction.

144. The electricity induced in a metallic conductor, moved in the presence of a powerful magnet, has received the name of Magneto-Electricity; and Dr. Joule has made use of it as a convenient means of enabling him to determine the mechanical equivalent of heat, for it is into heat that the energy of motion of the conductor is ultimately transformed. But, besides all this, these currents form, perhaps, the very best means of obtaining electricity; and recently very powerful machines have been constructed by Wild and others with this view.

145. These machines, when large, are worked by a steam-engine, and their mode of operation is as follows:—The nucleus of the machine is a system of powerful permanent steel magnets, and a conducting coil is made to revolve rapidly in presence of these magnets. The current produced by this moving coil is then used in order to produce an extremely powerful electro-magnet, and finally a coil is made to move with great rapidity in presence of this powerful electro-magnet, thus causing induced currents of vast strength. So powerful are these currents, that when used to produce the electric light, small print may be read on a dark night at the distance of two miles from the scene of operation!

It thus appears that in this machine a double use is made of magneto-electricity. Starting with a nucleus of permanent magnetism, the magneto-electric currents are used, in the first instance, to form a powerful electro-magnet much stronger than the first, and this powerful electro-magnet is again made use of in the same way as the first, in order to give, by means of magneto-electricity, an induced current of very great strength.

146. There is, moreover, a very great likeness between a magneto-electric machine like that of Wild's for generating electric currents, and the one which generates statical electricity by means of the method already described Art. 139. In both cases advantage is taken of a nucleus, for in the magneto-electric machine we have the molecular currents of a set of permanent magnets, which are made the means of generating enormous electric currents without any permanent alteration to themselves, yet not without the expenditure of work.

Again, in an induction machine for generating statical electricity, we have an electric nucleus, such as we have supposed to reside in the prime conductor of a machine; and advantage may be taken, as we have seen, of this nucleus in order to generate a vast quantity of statical electricity, without any permanent alteration of the nucleus, but not without the expenditure of work.

147. We have now seen under what conditions the visible energy of actual motion may be changed—1stly, into energy of position; 2ndly, into the two energies which embrace absorbed heat; 3rdly, into electrical separation; and finally into electricity in motion. As far as we know, visible energy cannot directly be transformed into chemical separation, or into radiant energy.

Visible Energy of Position.

148. Having thus exhausted the transmutations of the energy of visible motion, we next turn to that of position, and find that it is transmuted into motion, but not immediately into any other form of energy; we may, therefore, dismiss this variety at once from our consideration.

Absorbed Heat.

149. Coming now to these two forms of energy which embrace absorbed heat, we find that this may be converted into (A) or actual visible energy in the case of the steam-engine, the air-engine, and all varieties of heat engines. In the steam-engine, for instance, part of the heat which passes through it disappears as heat, utterly and absolutely, to reappear as mechanical effect. There is, however, one condition which must be rigidly fulfilled, whenever heat is changed into mechanical effect—there must be a difference of temperature, and heat will only be changed into work, while it passes from a body of high temperature to one of low.

Carnot, the celebrated French physicist, has ingeniously likened the mechanical power of heat to that of water; for just as you can get no work out of heat unless there be a flow of heat from a higher temperature level to a lower, so neither can you get work out of water unless it be falling from a higher level to a lower.

150. If we reflect that heat is essentially distributive in its nature, we shall soon perceive the reason for this peculiar law; for, in virtue of its nature, heat is always rushing from a body of high temperature to one of low, and if left to itself it would distribute itself equally amongst all bodies, so that they would ultimately become of the same temperature. Now, if we are to coax work out of heat, we must humour its nature, for it may be compared to a pack of schoolboys, who are always ready to run with sufficient violence out of the schoolroom into the open fields, but who have frequently to be dragged back with a very considerable expenditure of energy. So heat will not allow itself to be confined, but will resist any attempt to accumulate it into a limited space. Work cannot, therefore, be gained by such an operation, but must, on the contrary, be spent upon the process.

151. Let us now for a moment consider the case of an enclosure in which everything is of the same temperature. Here we have a dull dead level of heat, out of which it will be impossible to obtain the faintest semblance of work. The temperature may even be high, and there may be immense stores of heat energy in the enclosure, but not a trace of this is available in the shape of work. Taking up Carnot's comparison, the water has already fallen to the same level, and lies there without any power of doing useful work—dead, in a sense, as far as visible energy is concerned.

152. We thus perceive that, firstly, we can get work out of heat when it passes from a higher to a lower temperature, but that, secondly, we must spend work upon it in order to make it pass from a lower temperature to a higher one; and that, thirdly and finally, nothing in the shape of work can be got out of heat which is all at the same temperature level.

What we have now said enables us to realize the conditions under which all heat engines work. The essential point about such engines is, not the possession of a cylinder, or piston, or fly wheels, or valves, but the possession of two chambers, one of high and the other of low temperature, while it performs work in the process of carrying heat from the chamber of high to that of low temperature.

Let us take, for example, the low-pressure engine. Here we have the boiler or chamber of high, and the condenser or chamber of low, temperature, and the engine works while heat is being carried from the boiler to the condenser—never while it is being carried from the condenser to the boiler.

In like manner in the locomotive we have the steam generated at a high temperature and pressure, and cooled by injection into the atmosphere.

153. But, leaving formal engines, let us take an ordinary fire, which plays in truth the part of an engine, as far as energy is concerned. We have here the cold air streaming in over the floor of the room, and rushing into the fire, to be there united with carbon, while the rarefied product is carried up the chimney. Dismissing from our thoughts at present the process of combustion, except as a means of supplying heat, we see that there is a continual in-draught of cold air, which is heated by the tire, and then sent to mingle with the air above. Heat is, in fact, distributed by this means, or carried from a body of high temperature, i.e. the fire, to a body of low temperature, i.e. the outer air, and in this process of distribution mechanical effect is obtained in the up-rush of air through the chimney with considerable velocity.

154. Our own earth is another instance of such an engine, having the equatorial regions as its boiler, and the polar regions as its condensers; for, at the equator, the air is heated by the direct rays of the sun, and we have there an ascending current of air, up a chimney as it were, the place of which is supplied by an in-draught of colder air along the ground or floor of the world, from the poles on both sides. Thus the heated air makes its way from the equator to the poles in the upper regions of the atmosphere, while the cold air makes its way from the poles to the equator along the lower regions. Very often, too, aqueous vapour as well as air is carried up by means of the sun's heat to the upper and colder atmospheric regions, and there deposited in the shape of rain, or hail, or snow, which ultimately, finds its way back again to the earth, often displaying in its passage immense mechanical energy. Indeed, the mariner who hoists his sail, and the miller who grinds his corn (whether he use the force of the wind or that of running water), are both dependent upon this great earth-engine, which is constantly at work producing mechanical effect, but always in the act of carrying heat from its hotter to its colder regions.

155. Now, if it be essential to an engine to have two chambers, one hot and one cold, it is equally important that there should be a considerable temperature difference between the two.

If Nature insists upon a difference before she will give us work, we shall not be able to pacify her, or to meet her requirements by making this difference as small as possible. And hence, cœteris paribus, we shall obtain a greater proportion of work out of a certain amount of heat passing through our engine when the temperature difference between its boiler and condenser is as great as possible. In a steam-engine this difference cannot be very great, because if the water of the boiler were at a very high temperature the pressure of its steam would become dangerous; but in an air-engine, or engine that heats and cools air, the temperature difference may be much larger. There are, however, practical inconveniences in engines for which the temperature of the boiler is very high, and it is possible that these may prove so formidable as to turn the scale against such engines, although in theory they ought to be very economical.

156. The principles now stated have been employed by Professor J. Thomson, in his suggestion that the application of pressure would be found to lower the freezing point of water; and the truth of this suggestion was afterwards proved by Professor Sir W. Thomson. The following was the reasoning employed by the former:—

Suppose that we have a chamber kept constantly at the temperature 0° C, or the melting point of ice, and that we have a cylinder, of which the sectional area is one square metre, filled one metre in height with water, that is to say, containing one cubic metre of water. Suppose, next, that a well-fitting piston is placed above the surface of the water in this cylinder, and that a considerable weight is placed upon the piston. Let us now take the cylinder, water and all, and carry it into another room, of which the temperature is just a trifle lower, In course of time the water will freeze, and, as it expands in freezing, it will push up the piston and weight about ${\displaystyle {\frac {9}{100}}}$ths of a metre; and we may suppose that the piston is kept fastened in this position by means of a peg. Now carry back the machine into the first room, and in the course of time the ice will be melted, and we shall have water once more in the cylinder, but there will now be a void space of ${\displaystyle {\frac {9}{100}}}$ths of a metre between the piston and the surface. We have thus acquired a certain amount of energy of position, and we have only to pull out the peg, and allow the piston with its weight to fall down through the vacant space, in order to utilize this energy, after which the arrangement is ready to start afresh. Again, if the weight be very great, the energy thus gained will be very great; in fact, the energy will vary with the weight. In fine, the arrangement now described is a veritable heat engine, of which the chamber at 0° C. corresponds to the boiler, and the other chamber a trifle lower in temperature to the condenser, while the amount of work we get out of the engine—or, in other words, its efficiency—will depend upon the weight which is raised through the space of ${\displaystyle {\frac {9}{100}}}$ths of a metre, so that, by increasing this weight without limit, we may increase the efficiency of our engine without limit. It would thus at first sight appear that by this device of having two chambers, one at 0° C, and the other a trifle lower, we can get any amount of work out of our water engine; and that, consequently, we have managed to overcome Nature. But here Thomson's law comes into operation, showing that we cannot overcome Nature by any such device, but that if we have a large weight upon our piston, we must have a proportionally large difference of temperature between our two chambers—that is to say, the freezing point of water, under great pressure, will be lower in temperature than its freezing point, if the pressure upon it be only small.

Before leaving this subject we must call upon our readers to realize what takes place in all heat engines. It is not merely that heat produces mechanical effect, but that a given quantity of heat absolutely passes out of existence as heat in producing its equivalent of work. If, therefore, we could measure the mere heat produced in an engine by the burning of a ton of coals, we should find it to be less when the engine was doing work than when it was at rest.

In like manner, when a gas expands suddenly its temperature falls, because a certain amount of its heat passes out of existence in the act of producing mechanical effect.

157. We have thus endeavoured to show under what conditions absorbed heat may be converted into mechanical effect. This absorbed heat embraces (Art. 110) two varieties of energy, one of these being molecular motion, and the other molecular energy of position.

Let us now, therefore, endeavour to ascertain under what circumstances the one of these varieties may be changed into the other. It is well known that it takes a good deal of heat to convert a kilogramme of ice into water, and that when the ice is melted the temperature of the water is not perceptibly higher than that of the ice. It is equally well known that it takes a great deal of heat to convert a kilogramme of boiling water into steam, and that when the transformation is accomplished, the steam produced is not perceptibly hotter than the boiling water. In such cases the heat is said to become latent.

Now, in both these cases, but more obviously in the last, we may suppose that the heat has not had its usual office to perform, but that, instead of increasing the motion of the molecules of water, it has spent its energy in tearing them asunder from each other, against the force of cohesion which binds them together.

Indeed, we know as a matter of fact that the force of cohesion which is perceptible in boiling water is apparently absent from steam, or the vapour of water, because its molecules are too remote from one another to allow of this force being appreciable. We may, therefore, suppose that a large part, at least, of the heat necessary to convert boiling water into steam is spent in doing work against molecular forces.

When the steam is once more condensed into hot water the heat thus spent reassumes the form of molecular motion, and the consequence is that we require to take away somehow all the latent heat of a kilogramme of steam before we can convert it into boiling water. In fact, if it is difficult and tedious to convert water into steam, it is difficult and tedious to convert steam into water.

158. Besides the case now mentioned, there are other instances in which, no doubt, molecular separation becomes gradually changed into heat motion. Thus, when a piece of glass has been suddenly cooled, its particles have not had time to acquire their proper position, and the consequence is that the whole structure is thrown into a state of constraint. In the course of time such bodies tend to assume a more stable state, and their particles gradually come closer together.

It is owing to this cause that the bulb of a thermometer recently blown gradually contracts, and it is no doubt owing to the same cause that a Prince Rupert's drop, formed by dropping melted glass into water, when broken, falls into powder with a kind of explosion. It seems probable that an all such cases these changes are attended with heat, and that they denote the conversion of the energy of molecular separation into that of molecular motion.

159. Having thus examined the transmutations of (C) into (D), and of (D) back again into (C), let us now proceed with our list, and see under what circumstances absorbed heat is changed into chemical separation.

It is well known that when certain bodies are heated, they are decomposed; for instance, if limestone or carbonate of lime be heated, it is decomposed, the carbonic acid being given out in the shape of gas, while quicklime remains behind. Now, heat is consumed in this process, that is to say, a certain amount of heat energy absolutely passes out of existence as heat and is changed into the energy of chemical separation. Again, if the lime so obtained be exposed, under certain circumstances, to an atmosphere of carbonic acid, it will gradually become changed into carbonate of lime; and in this change (which is a gradual one) we may feel assured that the energy of chemical separation is once more converted into the energy of heat, although we may not perceive any increment of temperature, on account of the blow nature of the process.

At very high temperatures it is possible that most compounds are decomposed, and the temperature at which this takes place, for any compound, has been termed its temperature of disassociation.

160. Heat energy is changed into electrical separation when tourmalines and certain other crystals are heated.

Let us take, for instance, a crystal of tourmaline and raise its temperature, and we shall find one end positively, and the other negatively, electrified. Again, let us take the same crystal, and suddenly cool it, and we shall find an electrification of the opposite kind to the former, so that the end of the axis, which was then positive, will now be negative. Now, this separation of the electricities denotes energy; and we have, therefore, in such crystals a case where the energy of heat has been changed into that of electrical separation. In other words, a certain amount of heat has passed out of existence as heat, while in its place a certain amount of electrical separation has been obtained.

161. Let us next see under what circumstances heat is changed into electricity in motion. This transmutation takes place in thermo-electricity.

Fig. 12.
Suppose, for instance, that we have a bar of copper or antimony, say copper, soldered to a bar of bismuth, as in Fig. 12. Let us now heat one of the junctions, while the other remains cool. It will be found that a current of positive electricity circulates round the bar, in the direction of the arrow-head, going from the bismuth to the copper across the heated junction, the existence of which may be detected by means of a compass needle, as we see in the figure.

Here, then, we have a case in which heat energy goes out of existence, and is converted into that of an electric current, and we may even arrange matters so as to make, on this principle, an instrument which shall be an extremely delicate test of the existence of heat.

By having a number of junctions of bismuth and antimony, as in Fig. 13, and heating the upper set, while
Fig. 13.
the lower remain cool, we get a strong current going from the bismuth to the antimony across the heated junctions, and we may pass the current so produced round the wire of a galvanometer, and thus, by increasing the number of our junctions, and also by using a very delicate galvanometer, we may get a very perceptible effect for the smallest heating of the upper junctions. This arrangement is called the thermopile, and, in conjunction with the reflecting galvanometer, it affords the most delicate means known for detecting small quantities of heat.

162. The last transmutation on our list with respect to absorbed heat is that in which this species of energy is transformed into radiant light and heat. This takes place whenever a hot body cools in an open space—the sun, for instance, parts with a large quantity of his heat in this way; and it is due, in part at least, to this process that a hot body cools in air, and wholly to it that such a body cools in vacuo. It is, moreover, due to the penetration of our eye by radiant energy that we are able to see hot bodies, and thus the very fact that we see them implies that they are parting with their heat.

Radiant energy moves through space with the enormous velocity of 188,000 miles in one second. It takes about eight minutes to come from the sun to our earthy so that if our luminary were to be suddenly extinguished, we should have eight minutes, respite before the catastrophe overtook us. Besides the rays that affect the eye, there are others which we cannot see, and which may therefore be termed dark rays. A body, for instance, may not be hot enough to be self-luminous, and yet it may be rapidly cooling and changing its heat into radiant energy, which is given off by the body, even although neither the eye nor the touch may be competent to detect it. It may nevertheless be detected by the thermopile, which was described in Art. 161. We thus see how strong is the likeness between a heated body and a sounding one. For just as a sounding body gives out part of its sound energy to the atmosphere around it, so does a heated body give out part of its heat energy to the ethereal medium around it. When, however, we consider the rates of motion of these energies through their respective media, there is a mighty difference between the two, sound travelling through the air with the velocity of 1100 feet a second, while radiant energy moves over no less a space than 188,000 miles in the same portion of time.

Chemical Separation.

163. We now come to the energy denoted by chemical separation, such as we possess when we have coal or carbon in one place, and oxygen in another. Very independently this form of energy of position is transmuted into heat when we burn the coal, or cause it to combine with the oxygen of the air; and generally, whenever chemical combination takes place, we have the production of heat even although other circumstances may interfere to prevent its recognition.

Now, in accordance with the principle of conservation, it may be expected that, if a definite quantity of carbon or of hydrogen be burned under given circumstances, there will be a definite production of heat; that is to say, a ton of coals or of coke, when burned, will give us so many heat units, and neither more or less. We may, no doubt, burn our ton in such a way as to economize more or less of the heat produced; but, as far as the mere production of heat is concerned, if the quantity and quality of the material burned and the circumstances of combustion be the same, we expect the same amount of heat.

164. The following table, derived from the researches of Andrews, and those of Favre and Silbermann, shows us how many units of heat we may get by burning a kilogramme of various substances.

 Units of Heat developed by Combustion in Oxygen. Substance⁠Burned. Kilogrammes of Water raised 1° C.by the combustion of one kilogrammeof each substance. Hydrogen .mw-parser-output .nowrap,.mw-parser-output .nowrap a:before,.mw-parser-output .nowrap .selflink:before{white-space:nowrap}. . . . . . . . . . . . . 34,135 Carbon . . . . . . . . . . . . . . . 07,991 Sulphur . . . . . . . . . . . . . . 02,263 ​ Phosphorus . . . . . . . . . . . . 05,748 Zinc . . . . . . . . . . . . . . . . . . 01,302 Iron . . . . . . . . . . . . . . . . . . 01,577 Tin . . . . . . . . . . . . . . . . . . 01,234 Olefiant Gas . . . . . . . . . . 11,901 Alcohol . . . . . . . . . . . . . . 07,017

165. There are other methods, besides combustion, by which chemical combination takes place.

When, for instance, we plunge a piece of metallic iron into a solution of copper, we find that when we take it out, its surface is covered with copper. Part of the iron has been dissolved, taking the place of the copper, which has therefore been thrown, in its metallic state, upon the surface of the iron. Now, in this operation heat is given out—we have in fact burned, or oxidized, the iron, and we are thus furnished with a means of arranging the metals, beginning with that which gives out most heat, when used to displace the metal at the other extremity of the series.

166. The following list has been formed, on this principle, by Dr. Andrews:—

 1. Zinc2. Iron3. Lead4. Copper 5. Mercury6. Silver7. Platinum
—that is to say, the metal platinum can be displaced by any other metal of the series, but we shall get most heat if we use zinc to displace it.

We may therefore assume that if we displace a definite quantity of platinum by a definite quantity of zinc, we shall get a definite amount of heat. Suppose, however, that instead of performing the operation in one step, we make two of it. Let us, for instance, first of all displace copper by means of zinc, and then platinum by means of copper. Is it not possible that the one of these processes may be more fruitful in heat giving than the other? Now, Andrews has shown us that we cannot gain an advantage over Nature in this way, and that if we use our zinc first of all to displace iron, or copper, or lead, and then use this metal to displace platinum, we shall obtain just the very same amount of heat as if we had used the zinc to displace the platinum at once.

167. It ought here to be mentioned that, very generally, chemical action is accompanied with a change of molecular condition.

A solid, for instance, may be changed into a liquid, or a gas into a liquid. Sometimes the one change counteracts the other, as far as apparent heat is concerned; but sometimes, too, they co-operate together to increase the result. Thus, when a gas is absorbed by water, much heat is evolved, and we may suppose the result to be due in part to chemical combination, and in part to the condensation of the gas into a liquid, by which means its latent heat is rendered sensible. On the other hand, when a liquid unites with a solid, or when two solids unite with one another, and the product is a liquid, we have very often the absorption of heat, the heat rendered latent by the dissolution of the solid being more than that generated by combination. Freezing mixtures owe their cooling properties to this cause; thus, if snow and salt be mixed together, they liquefy each other, and the result is brine of a temperature much lower than that of either the ingredients.

168. When heterogeneous metals, such as zinc and copper, are soldered together, we have apparently a conversion of the energy of chemical separation into that of electrical separation. This was first suggested by Volta as the origin of the electrical separation which we see in the voltaic current, and recently its existence has been distinctly proved by Sir W. Thomson.

To render manifest this conversion of energy, let us solder a piece of zinc and copper together—if we now test the bar by means of a delicate electrometer we shall find that the zinc is positively, while the copper is negatively, electrified. We have here, therefore, an instance of the transmutation of one form of energy of position into another; so much energy of chemical separation disappearing in order to produce so much electrical separation. This explains the fact recorded in Art. 93, where we saw that if a battery be insulated and its poles kept apart, the one will be charged with positive, and the other with negative, electricity.

169. But further, when such a voltaic battery is in action, we have a transmutation of chemical separation into electricity in motion. To see this, let us consider what takes place in such a battery.

Here no doubt the sources of electrical excitement are the points of contact of the zinc and platinum, where, as we see by our last article, we have electrical separation produced. But this of itself would not produce a current, for an electrical current implies very considerable energy, and must be fed by something. Now, in the voltaic battery we have two things which accompany each other, and which are manifestly connected together. In the first place we have the combustion, or at least the oxidation and dissolution, of the zinc; and we have, secondly, the production of a powerful current. Now, evidently, the first of these is that which feeds the second, or, in other words, the energy of chemical separation of the metallic zinc is transmuted into that of an electrical current, the zinc being virtually burned in the process of transmutation.

170. Finally, as far as we are aware, the energy of chemical separation is not directly transmuted into radiant light and heat.

Electrical Separation.

171. In the first place the energy of electrical separation is obviously transmuted into that of visible motion, when two oppositely electrified bodies approach each other.

172. Again, it is transmuted into a current of electricity, and ultimately into heat, when a spark passes between two oppositely electrified bodies.

It ought, therefore, to be borne in mind that when the flash is seen there is no longer electricity, what we see being merely air, or some other material, intensely heated by the discharge. Thus a man might be rendered insensible by a flash of lightning without his seeing the flash—for the effect of the discharge upon the man, and its effect in heating the air, might be phenomena so nearly simultaneous that the man might become insensible before he could perceive the flash.

Electricity in Motion.

173. This energy is transmuted into that of visible motion when two wires conveying electrical currents in the same direction attract each other. When, for instance, two circular currents float on water, both going in the direction of the hands of a watch, we have seen from Art. 100 that they will move towards each other. Now, here there is, in truth, a lessening of the intensity of each current when the motion is taking place, for we know (Art. l04) that when a circuit is moved into the presence of another circuit conveying a current, there is produced by induction a current in the opposite direction; and hence we perceive that, when two similar currents approach each other, each is diminished by means of this inductive influence—in fact, a certain amount of current energy disappears from existence in order that an equivalent amount of the energy of visible motion may be produced.

174 Electricity in motion is transmuted into heat during the passage of a current along a thin wire, or any badly conducting substance—the wire is heated in consequence, and may even become white hot. Most frequently the energy of an electric current is spent in heating the wires and other materials that form the circuit. Now, the energy of such a current is fed by the burning or oxidation of the metal (generally zinc) which is used in the circuit, so that the ultimate effect of this combustion is the heating of the various wires and other materials through which the current passes.

175. We may, in truth, burn or oxidize zinc in two ways—we may oxidize it, as we have just seen, in the voltaic battery, and we shall find that by the combustion of a kilogramme of zinc a definite amount of heat is produced. Or we may oxidize our zinc by dissolving it in acid in a single vessel, when, without going through the intermediate process of a current, we shall get just as much heat out of a kilogramme of zinc as we did in the former case. In fact, whether we oxidize our zinc by the battery, or in the ordinary way, the quantity of heat produced will always bear the same relation to the quantity of zinc consumed; the only difference being that, in the ordinary way of oxidizing zinc, the heat is generated in the vessel containing the zinc and acid, while in the battery it may make its appearance a thousand miles away, if we have a sufficiently long wire to convey our current.

176. This is, perhaps, the right place for alluding to a discovery of Peltier, that a current of positive electricity passing across a junction of bismuth and antimony in the direction from the bismuth to the antimony appears to produce cold.

Fig. 14.
To understand the significance of this fact we must consider it in connection with the thermo-electric current, which we have seen, from Art. 161, is established in a circuit of bismuth and antimony, of which one junction is hotter than the other. Suppose we have a circuit of this kind with both its junctions at the temperature of 100° C. to begin with. Suppose, next, that while we protect one junction, we expose the other to the open air—it will, of course, lose heat, so that the protected junction will now be hotter than the other. The consequence will be (Art. 161) that a current of positive electricity will pass along the protected junction from the bismuth to the antimony.

Now, here we have an apparent anomaly, for the circuit is cooling—that is to say, it is losing energy—but at the very same time it is manifesting energy in another shape, namely, in that of an electric current, which is circulating round it. Clearly, then, some of the heat of this circuit must be spent in generating this current; in fact, we should expect the circuit to act as a heat engine, only producing current energy instead of mechanical energy, and hence (Art. 152) we should expect to see a conveyance of heat from the hotter to the colder parts of the circuit. Now, this is precisely what the current does, for, passing along the hotter junction, in the direction of the arrow-head, it cools that junction, and heats the colder one at C,—in other words, it carries heat from the hotter to the colder parts of the circuit. We should have been very much surprised had such a current cooled C and heated H, for then we should have had a manifestation of current energy, accompanied with the conveyance of heat from a colder to a hotter substance, which is against the principle of Art. 152.

177. Finally, the energy of electricity in motion is converted into that of chemical separation, when a current of electricity is made to decompose a body. Part of the energy of the current is spent in this process, and we shall get so much less heat from it in consequence. Suppose, for instance, that by oxidizing so much zinc in the battery we get, under ordinary circumstances, 100 units of heat. Let us, however, set the battery to decompose water, and we shall probably find that by oxidizing the same amount of zinc we get now only 80 units of heat. Clearly, then, the deficiency or 20 units have gone to decompose the water. Now, if we explode the mixed gases which are the result of the decomposition, we shall get back these 20 units of heat precisely, and neither more nor less; and thus we see that amid all such changes the quantity of energy remains the same.

178. This form of energy is converted into absorbed heat whenever it falls upon an opaque substance—some of it, however, is generally conveyed away by reflexion, but the remainder is absorbed by the body, and consequently heats it.

It is a curious question to ask what becomes of the radiant light from the sun that is not absorbed either by the planets of our system, or by any of the stars. We can only reply to such a question, that as far as we can judge from our present knowledge, the radiant energy that is not absorbed must be conceived to be traversing space at the rate of 188,000 miles a second.

179. There is only one more transmutation of radiant energy that we know of, and that is when it promotes chemical separation. Thus, certain rays of the sun are known to have the power of decomposing chloride of silver, and other chemical compounds. Now, in all such cases there is a transmutation of radiant energy into that of chemical separation. The sun's rays, too, decompose carbonic acid in the leaves of plants, the carbon going to form the woody fibre of the plant, while the oxygen is set free into the air; and of course a certain proportion of the energy of the solar rays is consumed in promoting this change, and we have so much less heating effect in consequence.

But all the solar rays have not this power—for the property of promoting chemical change is confined to the blue and violet rays, and some others which are not visible to the eye. Now, these rays are entirely absent from the radiation of bodies at a comparatively low temperature, such as an ordinary red heat, so that a photographer would find it impossible to obtain the picture of a red-hot body, whose only light was in itself.

180. The actinic, or chemically active, rays of the sun decompose carbonic acid in the leaves of plants, and they disappear in consequence, or are absorbed; this may, therefore, be the reason why very few such rays are either reflected or transmitted from a sun-lit leaf, in consequence of which the photographer finds it difficult to obtain an image of such a leaf; in other words, the rays which would have produced a chemical change on his photographic plate have all been used up by the leaf for peculiar purposes of its own.

181. And here it is important to bear in mind that while animals in the act of breathing consume the oxygen of the air, turning it into carbonic acid, plants, on the other hand, restore the oxygen to the air; thus the two kingdoms, the animal and the vegetable, work into each other's hands, and the purity of the atmosphere is kept up.

1. This explanation was first given by Professors Thomson and Tait in their Natural Philosophy, and by Dr. Frankland in a lecture at the Royal Institution of London.
2. See De La Hue, Stewart, and Loewy's researches on Solar Physics.
3. See the Magnetic Researches of Sir E. Sabine, also C. Meldrum on the Periodicity of Cyclones.