We have seen how Rumford showed that heat was motion, and how he approximately determined its mechanical equivalent. Seguin, a nephew of Montgolfier, endeavoured to show that, when a steam-engine was working, less heat entered the condenser than when the same amount of steam was blown idly through the engine. This Hirn succeeded in showing, thus proving that heat was actually used up in doing work.

Mayer, of Heilbronn, measured the work done in compressing air, and the heat generated by the compression, and a.s.sumed that the whole of the work done in the compression, and no more, was converted into the heat developed, which was the same thing as a.s.suming that no work was done in altering the positions of the particles of gas. From these measurements he deduced a value of the mechanical equivalent of heat.

The a.s.sumption which Mayer made was shown experimentally by Joule to be nearly correct. Joule proved that, when air expands from a high pressure into a vacuum, no heat is generated or absorbed on the whole.

This he did by compressing air in an iron bottle, which was connected with another bottle from which the air had been exhausted, the connecting tube being closed by a stop-c.o.c.k. The whole apparatus was immersed in a bath of water, and on allowing the air to rush from one vessel into the other, and then stirring the water, the temperature was found to be the same as before. When the iron bottles were in separate baths of water, that from which the air rushed was cooled, and that into which it rushed was heated to the same extent. Joule and Thomson afterwards showed that a very small amount of heat is absorbed in this experiment. Joule also showed that the heat generated in a battery circuit is proportional to the product of the electro-motive force and the current, or to the product of the resistance and the square of the current, which, in virtue of Ohm's law, is the same thing. This relation is often known as Joule's law. He also proved that, for the same amount of chemical action in the battery, the heat generated was the same, whether it were all generated within the battery or part in the battery and part in an external wire; and that in the latter case, if the wire became so hot as to emit light, the heat measured was less than before, on account of the energy radiated as light. With a magneto-electric machine he employed mechanical power to produce a current, and the energy of the current he converted into heat. In all cases he found that, _whatever transformations the energy might undergo in its course, a definite amount of mechanical energy, if entirely converted into heat, always produced the same amount of heat_; and he thereby proved, not only that heat is essentially _motion_, but that it corresponds precisely with that particular dynamical quant.i.ty which is called _energy_; and thus justified the attempt to find a relation between heat and energy, or to express the mechanical equivalent of heat as so many foot-pounds.

Joule then set to work to determine, in the most accurate manner possible, the number of foot-pounds of work which, if entirely converted into heat, would raise one pound of water through 1 Fahr.

The best known of his experiments is that in which he caused a paddle to revolve by means of a falling weight, and thereby to churn a quant.i.ty of water contained in a cylindrical vessel, the rotation of the water being prevented by fixed vanes. In these experiments he allowed for the work done outside the vessel of water or calorimeter, for the buoyancy of the air on the descending weight, and for the energy still retained by the weight when it struck the floor. From the results obtained he deduced 772 foot-pounds as the mechanical equivalent of heat. Expressed in terms of the Centigrade scale, Joule's equivalent, that is, the number of foot-pounds of work in the lat.i.tude of Manchester, which, if entirely converted into heat, will raise one pound of water 1 C., is 1390.

Joule's experiments show that the same amount of energy always corresponds to, and can be converted into, the same amount of heat, and that no transformations, electrical or other, can ever increase or diminish this quant.i.ty. Maxwell expressed this principle as follows:--

_The energy of a system is a quant.i.ty which can neither be increased nor diminished by any actions taking place between the parts of the system, though it may be transformed into any of the forms of which energy is susceptible._

This is the great principle of the conservation of energy which is applicable equally to all branches of science.

Another principle, almost equally general in its applicability, is that of the dissipation of energy, for which we are indebted in the first instance to Sir William Thomson. All forms of energy may be converted into heat, and heat tends so to diffuse itself throughout all bodies as to bring them to one uniform temperature. This is its ultimate state of degradation, and from that state no methods with which we are acquainted can transform any portion of it. When energy is possessed by a system in consequence of the relative positions or motions of bodies which we can handle, and whose movements we may control, the whole of the energy may be employed in doing any work we please; in fact, it is all _available_ for our purpose, or its _availability_ may be said to be perfect. Energy in any other form is limited in its availability by the conditions under which we can place it. For example, the energy of chemical action in a battery may be used to produce a current, and this to drive a motor by which mechanical work is effected, but some of the energy must inevitably be degraded into the form of heat by the resistance of the battery and of the conductor, and this portion will be greater as the rate of doing work is increased. The ratio of the quant.i.ty of energy which can be employed for mechanical purposes with the means at our disposal, to the whole amount present, is called the _availability_ of the energy.

All forms of energy may be wholly converted into heat, but only a fraction of any quant.i.ty of heat can be transformed into higher forms of energy, and this depends on the temperature of the source of heat and of the coldest body which can be employed as a condenser, being greater the greater the difference between the temperatures of the source and condenser, and the lower the temperature of the latter. In every operation which takes place in nature there is a degradation of energy, and though some portion of the energy may be raised in availability, another portion is lowered, so that on the whole the availability is diminished. Thus, in the case of the heat-engine, work can be obtained from heat only by allowing another portion of the heat to fall in temperature; and, as originally stated by Sir William Thomson, "it is impossible, by means of inanimate material agency, to obtain mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects," and to leave the working substance in the same condition in which it was at the commencement of the operations. Accepting this principle, Professor James Thomson showed that increase of pressure must lower the freezing point of water, for otherwise it would be possible to construct an engine which, working by the expansion of water in freezing, would continue to do work by cooling a body below the temperature of any other body available, and he calculated the amount of pressure necessary to lower the freezing point through one degree.

The conclusion was afterwards experimentally verified by Sir William Thomson, and served to explain all the phenomena of regelation. Thus, like the principle of the conservation of energy, the principle of the dissipation of energy serves as a guide in the search after truth. But there is this difference between the two principles--no one can conceive of any method by which to circ.u.mvent the conservation of energy; but Clerk Maxwell showed that the principle of dissipation of energy might be overridden by the exercise of intelligence on the part of any creature whose faculties were sufficiently delicate to deal with individual molecules. In the case of gases, the temperature depends on the average energy of motion of the individual particles, and heat consists simply of this motion; but in any ma.s.s of gas, whatever the average energy may be, some of the particles will be moving with very great, and some with very small, velocities. By imagining two portions of gas, originally at the same temperature, separated by a part.i.tion containing trap-doors which could be opened or closed without expenditure of energy, and supposing a "demon"

placed in charge of each door, who would open the door whenever a particle was approaching very rapidly from one side, or very slowly from the other, but keep it shut under other circ.u.mstances, he showed that it would be possible to sort the particles, so that those in the one compartment should have a great velocity, and those in the other a small one. Hence, out of a ma.s.s of gas at uniform temperature, two portions might be obtained, one at a high temperature and the other at a low, and, by means of a heat-engine, work could be obtained until the two portions were again at equal temperatures, when the services of the "demons" might be again taken advantage of, and the operations repeated until all the heat was used up.

Any theory which is brought forward to explain a phenomenon, or any process which is proposed to effect any operation, must in the first instance submit to the test of the application of these two principles of conservation and dissipation of energy; and any proposal which fails to bear these tests may be at once rejected. The essential feature of the science of to-day is its quant.i.tative character. We must, for instance, not only know that radiant energy comes to us from the sun, but we must learn how much energy is annually received by the earth in this way; and, in the next place, how much energy is radiated by the sun in all directions in the same time. When we have learned this, we want to know what is the source of this energy; and no theory of the sun which does not enable us to explain how this constant expenditure of energy is maintained can be accepted. Last century it was possible to believe, with Sir William Herschel, that the greater part of the sun's ma.s.s is comparatively cool, and that it is surrounded by only a thin sheet of flame. To-day such a theory would be rejected at once, simply because the thin sh.e.l.l of flame could not provide energy for the solar radiation for any considerable time. The contact theory of the galvanic cell, as originally enunciated, fell to the ground for a similar reason. The simple contact of dissimilar metals could afford no continuous supply of energy to sustain the current. Applied to the steam-engine, the doctrine of energy teaches us, not only that, corresponding to the combustion of a pound of coal, there is a definite quant.i.ty of work which is the mechanical equivalent of the heat generated, and is such that no engine of which we can conceive is capable of deriving from the combustion of the pound of coal a greater amount of work, but it teaches us that there is a further limitation fixed to the amount of work obtainable. This limitation depends upon the range of temperature at our command; and, when the range is known, we can express the amount of energy realizable by a perfect engine working through that range as a definite fraction of the whole energy corresponding to the heat of combustion of the fuel. Thus, if we find that a particular engine realizes only 15 per cent. of the energy of its fuel in work done, we must not suppose that mechanical improvements in the engine would enable us to realize any considerable portion of the other 85 per cent.; for it may be that a theoretically perfect engine, working with its boiler and condenser at the same temperatures as those of the engine considered, could only realize 25 per cent. of the energy of the fuel, reducing the margin for improvement from 85 to 10 per cent., as long as the range of temperature is unaltered. To improve the efficiency beyond this limit, the range of temperature must be increased, that is, generally, hotter steam must be used.

The principles of energy are thus guides, not only to the scientific theorist, but to the practical engineer, and they have been established only through careful measurement. The simple observation of phenomena, and of the conditions under which they occur, could never have led to the establishment of such principles; and, though the carrying out of experiments which do not involve measurements is of great value, it is the careful measurement, however simple, which affords the highest training to the mind and hand, and without which any course of instruction in experimental physics is of little value.

The Hindoos used to regard the earth as a vast dome carried on the backs of elephants. The elephants themselves, however, required support, and were represented as standing on the back of a gigantic tortoise. It does not, however, appear that any support was provided for the tortoise. In some respects this figure represents the apparently perpetual condition of scientific knowledge. Phenomena are investigated, and are shown to depend upon other actions which appear simpler or more fundamental than the phenomena at first observed.

These, again, are found to obey laws which are of much wider application, or appear to be still more fundamental; but it may be that we are as far off as ever from discovering the great secret of the universe, the ultimate nature of all things.