already quoted from Newton; and the experimental discoveries of Rumford and Davy, extended and completed by Joule and Colding, allow us to put Newton's second or alternative interpretation of his third law of motion into the modern statement of the conservation of energy.

In any system of bodies whatever, to which no energy is communicated by external bodies, and which parts with no energy to external bodies, the sum of the various potential and kinetic energies remains for ever unaltered.

In other words, while the one form of energy becomes changed into the other,―potential into kinetic and kinetic into potential,-yet each change represents at once a creation of the one kind of energy and a simultaneous and equal annihilation of the other, the total energy present, as we have already said, remaining thus unaltered.

103. Taking as our system the whole physical universe, we now see that, according to the test we have already laid down, energy has as much claim to be regarded as an objective reality as matter itself. But the forms of statement are most markedly different for the two. We before spoke of the quantity of matter without qualification, but we now speak of the sum of the two kinds of energy. Let us think for a moment of this, and we see that whereas (to our present knowledge, at least) matter is always the same, though it may be masked in various combinations, energy is constantly changing the form in which it presents itself. The one is like the eternal, unchangeable Fate or Necessitas of the ancients; the other is Proteus himself in the variety and rapidity of its transformations.

104. And again, energy is of use to us solely because it is constantly being transformed. When the sluice is shut, or the fire put out, the machinery stops; when a man cannot

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digest his food, he breaks down altogether. Coal in itself, except on account of an occasional fossil it may contain, or its still somewhat uncertain mode of formation, or (to take a lower point of view) as a material for ornament, is a very useless thing indeed: its grand value consists in its chemical affinity, in virtue of which it possesses great potential energy as regards the oxygen of the air, which can very easily be transformed into its equivalent in heat. "Keep your powder dry" is merely one way of saying" preserve the ready transformability of your energy." In fact, if we think for a moment over what has just been said, to the effect that the only real things in the physical universe are matter and energy, and that of these matter is simply passive, it is obvious that all the physical changes which take place, including those which are inseparably associated with the thoughts as well as the actions of living beings, are merely transformations of energy. Thus it is an inquiry of the very utmost importance as regards the present universe: Are all forms of energy equally susceptible of transformation? To see the importance of this question, the reader has only to reflect that if there be any one form of energy less readily or less completely transformable than the others, and if transformations constantly go on, more and more of the whole energy of the universe will inevitably sink into this lower grade as time advances. Hence the whole possibility of transformation must steadily grow less and less; in scientific language, though the quantity of energy remains for ever unchanged, its availability steadily decreases.

105. Now, every one knows a case in which there may be an unlimited amount of energy present, no part of which is available for transformation. It is the simple one of heat in a number of bodies, when all are at the same

temperature. To obtain work from heat we must have hotter and colder bodies, to correspond, as it were, with the boiler and condenser of a heat engine; and just as we get no work from still water if it be all at the same level, i.e. if no part of it can fall, so in like manner we can get no work from heat unless part of it can fall from a higher to a lower temperature.

106. The first step in the investigation of the transformation of heat into work was taken by Sadi Carnot in 1824: a step of inestimable value in every branch of modern physical science. He devised a method of startling originality for the purpose of attacking this special question of the production of work from heat. His inferences from its application were not all correct; this was due however to no fault of the method, but to the fact that he unfortunately assumed (though with caution, and under a protest almost amounting to an assertion of the opposite) the materiality of heat. His method embraces two perfectly new ideas :

(1.) That, at least with our present knowledge, no inference is possible as to the relation between heat and work, until the heated or working substance is brought back, after a complete Cycle of operations, to its initial physical state.

Obvious as this statement, once made, is, it was altogether ignored (twenty years after Carnot) by Séguin and Mayer, whom some authors still persist in setting forth as the founders of the dynamical theory of heat. Their speculations were entirely vitiated by their violation of this principle.

(2.) That an engine whose cycle of operations is reversible is a perfect engine, that is to say, gives the greatest possible amount of work from a given quantity of heat with any assigned temperatures of boiler and condenser.

The term reversible is not here used in the popular sense in which a mere reversal of the direction of motion of each part is contemplated, i.e. what would be more properly termed "backing," it is used in the higher sense of taking an engine which converts a certain quantity of the heat spent on it into work, while it lets the rest down from the boiler to the condenser, and then changing or converting it into an engine upon which the same amount of work is spent with the result of taking back the heat from the condenser, adding to it the heat-equivalent of the work so spent, and thus restoring the whole of its original loss in heat to the boiler; simply in fact reversing all the results of the direct action.

107. Sir W. Thomson, in 1848, was the first to recall attention to the work of Carnot, after Colding and Joule had published their discoveries; and he pointed out that the action of the reversible engine gave what had been up to that time vainly sought, an absolute definition of temperature—a definition, that is, altogether independent of the properties of any particular species of matter. In fact it is obvious that as reversibility in the sense we have just explained is the stamp of perfection in a heat engine, all reversible engines, whatever be the working substance, will, under the same circumstances, that is to say, with the same temperatures of boiler and condenser, convert the same fraction of the heat spent on them into work. This, of course, still leaves wide scope for a definition of temperature, but that finally determined on by Thomson was chosen (in consequence of a hint from some experimental results of Joule) so as to make the absolute measurement agree nearly with that of the long-known air-thermometer. It therefore stands as follows:

The heat taken in by a perfect engine is to the heat given out by it in the same proportion as the absolute temperature of the boiler to that of the condenser.

Of course it is hardly necessary to state that it is only the difference between the heat taken in and that given out by any engine that can have been converted into available work. This follows at once from the conservation of energy.

Experiments carried on by Joule and Thomson' together have shown that the absolute zero of temperature is nearly 274° below zero of the centigrade scale; so that on the absolute scale the temperature of melting ice is 274° while that of water boiling under the standard pressure is 374°.

108. In 1849 James Thomson made a very remarkable application of Carnot's reasoning, the first of a series of such applications which have since done immense service in the extension of almost every branch of physics. He showed in fact that, because water expands in the act of freezing, the melting point of ice must be lowered by pressure. Sir W. Thomson in the same year verified this deduction, to its numerical details, by direct experiment. Trifling as the predicted and measured effect appears (one degree centigrade for each 2000 lbs. additional pressure per square inch), there can now be no doubt that it goes at least very far to explain the varied effects of the extraordinary plasticity of glacier-ice so beautifully made out by the direct measurements of Forbes.

109. We have said that Carnot unfortunately based his reasoning on the assumed materiality (and therefore inde

one

1 They showed that in a perfect steam-engine with pressure equal to " atmosphere" in its boiler, and with its condenser at the temperature of melting ice, the ratio of the heat taken in to the heat given out is 1.365 to 1. Hence if the difference between the numbers is to be 100, these must be 374, 274.-Phil. Trans., 1854.