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affecting all branches of science. To Helmholtz himself it appeared that he had erred, if at all, by labouring selfevident arguments and planting batteries against breached walls ; he found, with surprise, that he had incurred the opposite reproach of unmeasured wildness in speculation. Dissent from his views was almost unanimously expressed, Jacobi, the mathematician, alone adopting them; and Poggendorff refused them the countenance of publication in bis celebrated ‘Annalen. The paper was, however, read, July 23, 1847, before the Berlin Physical Society, the radical tendencies of which secured it a welcome. It created an European sensation. Yet the dynamical theory of heat was not, strictly speaking, a novelty. It had been propounded by Mayer of Heilbronn, by Colding of Copenhagen, and by Joule of Manchester. The great principle of the indestructibility of energy was virtually acquired to science before Helmholtz started independent inquiries on the subject. Its rapid and brilliant triumph was, however, due to him. His
weighty statements,' Clerk Maxwell wrote,* acted on other minds like an irresistible driving power.' He showed a light which it was impossible not to follow.
What did it mean, this new principle? Mass, or quantity of matter, was shown by Lavoisier to be unalterable. Accounts kept with the aid of the balance proved rigidly exact. The same weight of substance persisted throughout the most diversified series of experiments. Gaseous, liquid, or solid, fused or frozen, it remained constant in amount. It could be changed qualitatively, not quantitatively. The law demonstrated by Helmholtz was correlative to the law demonstrated by Lavoisier. Mass without energy is as unreal to experience as energy apart from mass. of a body is its capacity for doing work, and augments with its motion. But motion may be either molar or molecular. It may affect matter in the lump, or interstitially. And the two kinds are reciprocally related. Motion arrested externally proceeds with rigorous equivalence internally. Every savage recognises the fact that heat is educed by friction; what savages do not recognise is that a definite amount of heat results from the employment of a certain quantity of effort in friction. Fundamentally, this was what Mayer, Joule, and Helmholtz demonstrated. They fixed the ' mechanical equivalent of heat.' Many developements ensued. It was ascertained further that the total energy
of any body, or system of bodies, is a quantity which can ' neither be increased nor diminished by any mutual action • of these bodies, though it may be transformed into any of • the forms of which energy is susceptible.' These forms are very various. Impeded motion
motion can reassert itself, not only as heat, but as electricity, magnetism, chemical action, light, or sound. And always by calculable measure. In other words, energy can be transformed, not destroyed. This is not a necessary truth. It has been learned by experience, and therefore belongs to the empirical order. We can only say that every known fact harmonises with it. The severest tests have failed to impair its validity. Its importance, as Clerk Maxwell remarked, consists in its fertility. It may be relied upon as an unerring guide in devising experiments, in colligating facts, in constructing new methods. A very divining-rod for the springs of knowledge, it teaches how to locate investigation with the best chance of success. Its practical infallibility then assures us that it corresponds to the primary verities of things. Exceptions to the rule would be looked for in vain.
An application of this principle, memorable in the history of astronomical physics, was made by Helmholtz in 1854.1 The maintenance of the sun's heat was at that time an unsolved problem. The prodigious thermal output, by a minute fraction of which our globe is vivified, has been in progress, geological evidence assures us, during some millions of years. There must be a compensatory source of supply; where is it to be found ? Various unsatisfactory answers had been given; Helmholtz, in a lecture before a popular audience at Königsberg, provided one that carried thorough and general conviction. He enunciated what is familiarly known as the 'shrinkage-theory' of solar heat. The sun necessarily contracts as it radiates. The wasting of heat secures a gradual victory for gravitation. Heat tends to diffusion, gravity to concentration; with the loss of heat, then, the central force must more and more effectually prevail. But by the very process of shrinkage heat is restored. A definite quantity is evolved by the fall, from a higher to a lower level, of each constituent particle. In other words, a certain proportion of its ' potential' energy is made available as actual energy. Moreover, the
* Clerk Maxwell, Theory of Heat,' tenth edition, p. 92.
attendant reduction in the sun's dimensions would be for ages imperceptible to observation. It is computed that the drain of energy due to his copious emissions into space would be amply met by an annual shortening of his diameter to the extent of 250 feet—an amount bearing so insignificant a proportion to the whole that the effects, after ten thousand years, would be scarcely, if at all, discernible with our finest instruments. This, accordingly, is the sun's vital secret; it consists in the transformation into heat of motion persistently imparted by gravity. Here is the recuperative principle, apart from which his 'surpassing glory' would indeed be short-lived.
Recuperation, nevertheless, has limits. The sun's resources are enormous ; they are not inexhaustible. The materials of the solar globe, in condensing from an indefinite degree of tenuity, have engendered, by Helmholtz's calculation, heat enough to support radiation at its present intensity during twenty-two million years; and it may last, through a continuation of the same process, without serious diminution, for about seventeen million future years. A total life-span of nearly forty million years was thus assigned, on purely mechanical grounds, to the ruler of our system. In forty millions years from the moment of primitive kindling, he will have passed from a nebulous to a nearly planetary condition—from gaseity to partial solidification from dim, all-pervading luminosity through the brilliant photospheric stage of concentrated superficial lustre to a dulled glow preluding final extinction.
These conclusions, although substantially unassailable, are naturally subject to qualifications in detail. Celestial chronologies are but loose estimates, based upon information likely to be defective in a thousand particulars. Their authority is on a par with that which might be claimed for dates in English history (for instance) deduced solely from the observed rate of some physical change. Thus the Norman Conquest might be fixed with reference to the submergence of the Goodwin Sands; the usurpation of Bolingbroke by the depth of salt water above the site of Ravenspur; and the reign of Elizabeth by noting the inroads of the sea on the south coast, and computing the number of years that must have elapsed since the old fishing village of Brighthelmstone was buried in the shingle. The limits of error would indeed be wide. And so, for analogous reasons,
* Popular Lectures on Scientific Subjects, series ii. p. 182.
are those within which the occurrence of cosmical events can be timed.
The views enunciated by Helmholtz were, however, independent of chronological accuracy. Their importance was due to the breadth of the novel prospects they embraced. The study of world-developement was by their introduction raised to a truly scientific status. A positive element was imported into discussions previously of a highly speculative character. The nebular hypothesis took rank as a definite and serviceable theory : not necessarily the nebular hypothesis under the form given to it by Laplace, but some modification of it. We may be said to know that the sun is growing smaller year by year; nor merely since yesterday. The fact is antique; the operation ceaselessly progressive. Travelling backward in thought, we find then his globe continually more distended; so that the time must have been when it filled the orbits of all the planets with inconceivably rare matter. Out of this primitive nebula-as it may fairly be designated—the solar system was somehow fashioned. The precise mode of its fashioning we are not here concerned to expound. The subject indeed bristles with difficulties, and no longer admits of the off-hand treatment which passed muster a century ago. What we seek to emphasise is that a nebular hypothesis of some kind makes part of the shrinkage-theory of solar heat. The two are so intimately related as to be inseparable. The earth and its sister-planets are warmed and illuminated to-day through the prolongation of the same series of developemental changes to which they owed their birth. And this conclusion applies universally. The principle of the conservation of energy governs all sidereal transformations. It affords a clue to stellar and nebular affinities. It guides speculation as to the relative ages of the stars.'
There is another aspect under which it may be viewed. It prescribes, as we have ju
we have just seen, the sun's possible duration. He can no more keep on shining indefinitely than a steamer can run for evermore' without replenishing its bunkers. And every star within the circuit of the Milky Way is similarly circumstanced. Each has its allotted term of vitality which cannot be exceeded. What becomes, it may be asked, of their spent power ? Energy cannot be annihilated. If one body parts with it, must not some other receive it, and so the beneficent play of cosmic interaction be maintained interminably? This is not assured to us. The energy of the universe, although constant in quantity,
may vary indefinitely in effectiveness. This depends upon the manner of its distribution. Now the developement of the heavenly bodies is conditioned by changes in the distribution of energy. Those more richly stored send their extra supplies abroad into space, until their superiority comes to an end. As we know by familiar experience, hot bodies cool down of themselves to the temperature of their surroundings. Thus, inequalities are perpetually in course of getting effaced; the universe, through the progress of what is known as the dissipation of energy, tends to establish itself on a dead level. The attainment of such a state would, however, involve complete stagnation. Action of every kind would cease; the physical forces would lie paralysed; energy would not have been destroyed, but it would have been rendered useless for purposes of work. The universe would consist of a multitude of inert orbs, ruled inexorably by their mutual gravity. Such, according to Lord Kelvin's cheerless forecast, is the destiny in reserve for the great scheme of things. That it is justified by the facts of science, rigidly interpreted, cannot be denied; yet we suspect that something undreamt of in our philosophy will intervene to prevent the dismal consummation. The Maker of the machine can be trusted, it seems to us, to provide means for winding it up before it hopelessly runs down.
From the date of his essay on the Conservation of Energy ' the name of Helmholtz became widely celebrated. As we have said, others were in the field before him, although he entered it by a way of his own. All found the gold; he minted it into current coin. Notwithstanding his disclaimers of priority, it went into circulation stamped with the impress of his genius. His appointment to the Chair of Physiology in the University of Königsberg ensued in 1849, and he was transferred thence, in a similar capacity, to Bonn in 1856, and to Heidelberg in 1859. Heidelberg was just then a sort of hub of the universe' in science, and the centre of the hub was a tall mansion at the west end of the Hauptstrasse, popularly known as “ Der Riese. In its top story was the laboratory of Bunsen and Kirchhoff, where spectrum analysis took its effective origin, and the chemistry of the sun originated. Under its roof, Helmholtz analysed vowel-sounds, and his assistant, Wilhelm Wundt, gave demonstrations in the graphical registration of muscular contractions. On the ground-floor was the pupil's workroom, and Dr. Hugo Kronecker, who was one of them, describes the strained attention
attention given by them to