Distinction of mass and molecule. The molecule not a ‘minute body.’

The advance from abstract mechanics to molecular physics: Mechanics historically a usurper.

Molecular mechanics is (a) indirect and (b) ideal.

(a i.) The evidence for molecules examined. Clerk Maxwell's theory of ‘manufactured articles.’ Clifford's criticisms. Further criticisms. Maxwell's theistic bias. The status of the molecule hypothetical. Statistical physics commented upon.

(a ii.) Evolution applied to the molecule. The mechanical theory bound, if possible, to resolve it into something simpler: the prime-atom.

(a iii.) The ether—one or more. Lord Kelvin sure of it, but chiefly because the mechanical theory cannot get on otherwise. New ethers invented to meet new mechanical problems. Signs of a reaction. Professors Drude and K. Pearson quoted. Hypothetical mechanisms and illustrative mechanisms distinct, but apt to get confused. Masterful analogies dangerous: is nothing intelligible but what is mechanical?

THERE is no obvious similarity between the swinging of a pendulum or the motion of colliding billiard balls; and the light and warmth of a glowing coal or of the sun. Still, as we have seen, Newton entertained the hope that both kinds of process might be described by means of the same mechanical principles. This hope we find has become an axiom for modern science; and the special conceptions involved and the peculiar methods employed in thus applying mechanical principles to molecular physics are what we must endeavour to examine to-day.

The distinction of mole and molecule, of large mass and small mass, is clearly not in itself a distinction of kind. It is due in the first instance to a psychological fact entirely external and irrelevant to the pure science of mechanics, to the fact, I mean, that we cannot perceive bodies of less than a certain size, changes of position of less than a certain extent, intervals of time of less than a certain duration, and so on. Still, however irrelevant to the mathematician, the fact of such minima sensibilia necessarily entails important differences of method upon the physicist, when he essays to apply mechanical principles to systems whose parts and motions are no longer directly discernible. The use of artificial means of magnification convinces us of what was already a priori probable, viz.: that the limits imposed by our senses are merely accidental limits without any objective significance. Consider in this connexion two statements that we often hear: the one that a given mole or molecule is divisible without limit into ever smaller particles; the other that such given mass or molecule consists of a finite number of absolutely indiscerptible particles called ultimate atoms. It is the latter far more than the former of these propositions that is logically open to suspicion. For the latter is an absolute statement, and since it is an absolute statement that cannot claim to be a necessity of thought, it is one that seems clearly incapable of proof. But to propositions of the former type, propositions, that is to say, asserting or implying the existence of bodies of indefinitely small dimensions and perhaps of indefinitely great complexity, we can have at any rate no a priori objection.

The molecules of modern physics and the so-called chemical atoms, however, are not bodies in this sense, and it is difficult to imagine that much would be gained by the assumption of their existence, if they were. This may sound paradoxical; I will try to explain. There is a passage in Laplace's Exposition du système du monde, one that has excited some discussion recently, which will serve admirably to illustrate what I mean, for it supposes an extreme case. Referring to the law of actions varying inversely as the square of the distance, as the law that holds for all forces and emanations that set out from a centre, he remarks: “Thus this law, answering exactly to all the phenomena, is to be regarded, both on account of its simplicity and its generality, as a rigorous law. One of its remarkable properties is that if the dimensions of all the bodies of the universe, their mutual distances and their velocities, were to increase or diminish proportionally, they would describe curves entirely similar to those they describe now; so that the universe thus continuously reduced down to the smallest space imaginable would present always the same appearances to observers.”1 If then we can have the universe on any scale, we might—if it is finite, as Laplace inclined to think it—have it complete within the head of a pin; and ought therefore to feel no surprise at physicists who, on the one hand, compare ‘a compound atom,’ as Jevons does, to a stellar system, each star a minor system in itself; “or who, on the other; talk of Jupiter and his satellites as a planetary molecule.”2 But if a molecule were a constellation on a vastly smaller scale, then the phenomena of light, heat, magnetism, and the like, to explain which the molecular constitution of bodies has been assumed, would reappear in the molecule, and again in the molecule of the molecule, and so on indefinitely. On such lines then no logical advance could be made. There may be molecules or atoms of many orders, but, effectively to replace physical properties by mechanical processes, the molecule of any order must be divested of whatever property its motions are to explain or describe. Thus the molecules whose motions on the kinetic theory of heat answer to that state of a body which we call its temperature are not themselves credited with heat. Again, magnetism is not explained by resolving the smallest steel particles in a magnet severally into magnets, but by an imponderable fluid circulating round the particle, and so on.

Let us now attempt to characterise in a general way the application of abstract mechanics to molecular physics. We start with bodies of sensible dimensions. The dynamical transactions between such bodies can be directly observed and described, such description requiring no conceptions beyond those of mass, force, space, and time, except of course, number, which measurement involves. In confining itself to these conceptions, molar physics employs methods that are invariably abstract. Those important qualities possessed by every body in its own specific fashion, the differences of which remain for our perception as unique and irresolvable as are the sensations of our several senses,—all these it simply ignores. They receive their proximate scientific handling in the various branches of experimental physics, e.g., chemistry. Here numerous empirical laws are ascertained that do not in general overstep the qualitative barriers just mentioned. These comparatively restricted generalisations, obtained from experiments on light, heat, electricity, chemical composition and decomposition, and the like, are the material to which the theoretical physicist applies his mechanical scheme of molecules, molecular motions, and molecular forces. No doubt by this time the mathematical physicist himself undertakes or initiates experiments for the purpose of verifying or advancing his molecular constructions. But this in no way, affects the fact that molecular physics can never come to close quarters with its molecules as molar physics can with the sensible masses and motions, from which the principles of the mechanical theory were first of all deduced.

To put the case in another way. Molar physics or mechanics was historically but one branch of general physics coördinate with those other experimental branches called Optics, Acoustics, Thermotics, etc. So matters stood in Newton's time, when he completed the main outlines of that mathematical edifice, now known as abstract dynamics, or, as he called it, ‘rational mechanics.’ Molecular physics is then, historically regarded, nothing but the endeavour to include the less perfect branches of physics within the domain of the most perfect—an endeavour that Newton himself, as we have seen, fully approved. The discovery that the stresses between electrified or magnetised bodies also varied inversely as the square of the distance between them, as do the stresses between gravitating masses, led to a wider use of the conception of centres of attraction or repulsion. Thus the mechanism which Newton found exemplified in the case of the heavenly bodies came to be regarded as a sort of type or paradigm. It would apply, as we have seen Laplace pointing out, on any scale, however great or small. So we come by the general hypothesis of molecular physics: that all physical phenomena —however complete, however ultimate, however numerous, their qualitative diversities may be, and remain, for our perception—can still be shewn to correspond to, and to be summed up by, purely dynamical equations, such equations describing the configurations and motions of a system of masses called molecules from their minuteness (according to the Homo Mensura standard). In other words, the hypothesis of molecular physics is that all the qualitative variety of the external world can be resolved into quantitative relations of time, space, and mass, that is of mass and motion.

This general characterisation of molecular physics we may now resume under two heads, each of which it will repay us to discuss somewhat further. First of all, the descriptions of molar physics may be called direct, whereas those of molecular physics are always indirect, the indirectness being often, if I may say so, of many removes from directness. Secondly, the descriptions of molar physics are abstract: one property of bodies, that of massiveness, of which we can have sensible evidence, is taken; the remaining properties are simply left out of account. But the descriptions of molecular physics taken together are not in this sense abstract. They leave no properties out of account; on the contrary, they transform everything qualitative into quantitative equivalents. It was to this point that I referred at the outset of this discussion (in the second lecture) in calling the methods of molecular physics ideal.3 I should be glad of some less ambiguous term, but can only hope that at the end of our discussion its meaning may be clearer.

To begin with the indirectnesses. Nobody has ever seen or felt, and if the physicists are to be trusted, no instruments of magnification are possible by which in the future any one can be helped to see or feel, an individual molecule. This, of course, would be a matter of no importance if the molecule were merely regarded as a mass-element in some homogeneous mass of sensible volume. But the atoms and molecules of modern science, if they have any real existence at all are distinct individuals; at all events, they have more title to be so described than either the earth or the sun, which we commonly regard as individual objects. For the earth or sun are after all but aggregate masses, constantly receiving additions—as in the meteoric showers that feed the sun; and probably—in the case of the earth and many smaller bodies, at least—constantly scattering part of their mass into space, as the moon, for example, is supposed to have diffused away its free gases and vapours. Not so the atoms and molecules of the chemist. The progress of stellar spectroscopy and of chemical physics, we are told, shuts us up to the view that the whole universe apart from the ether or ethers—of which more presently—consists entirely of varying arrangements of incalculable numbers of some seventy different elements, the individuals of each kind being absolutely identical in their properties, and all alike entirely beyond the reach of change or decay. Philosophic speculations of this sort are, of course, no novelty; but when we are asked to accept such statements as scientific truth and verity on evidence that can only be indirect, we may well be pardoned by ‘those who know’ if we look a little critically, even sceptically, at that evidence. But you may wish first of all to have the statement itself in some accredited form. Let me then quote two or three sentences from the Collected Papers of Clerk Maxwell (vol. ii, pp. 361 ff.):— “The same kind of molecule, say that of hydrogen, has the same set of periods of vibration, whether we procure the hydrogen from water, from coal, or from meteoric iron.… Whether in Sirius or in Arcturus [it] executes its vibrations in precisely the same time.” “Though in the course of ages catastrophes have occurred, and may yet occur, in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins; the molecules out of which these systems are built—the foundation stones of the material universe—remain unbroken and unworn.” Elsewhere Maxwell proceeds to make inferences concerning the supernatural from this position. “None of the processes of Nature,” he says, “since the time when Nature began, have produced the slightest difference in the properties of any molecule. We are therefore unable to ascribe either the existence of the molecules or the identity of their properties to the operation of any of the causes which we call natural. On the other hand, the exact equality of each molecule to all others of the same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article, and precludes the idea of its being eternal and self-existent.” This argument would be open to question even if it were certain that the molecules of any given element are exactly alike. To many it would seem more reasonable in such case to side with Democritus and regard what within the whole range of actual or possible experience is absolutely permanent and without the shadow of a change as realising all that we can understand by ‘self-subsistent and eternal.’ Moreover, the disparity between the conception of creation and the conception of manufactured goods is so complete as to make all attempts at analogy futile.

But to return to our immediate question: Of what nature is the evidence, on which molecules of hydrogen, oxygen, or any supposed element are pronounced to be respectively, each to each, exactly alike, the same through all vicissitudes and everlasting as time itself. As to the exact likeness—let me once more remark that it is impossible to deal directly with the individual molecules; and, even if it were, no measurements and no physical comparisons are exact. But the measurements of molecules, besides being indirect, are all made in bulk. What is really measured is the combined effect of millions, or it may be billions, of molecules. So that, even supposing disturbing causes to be entirely excluded, the resulting measurement is true only of the average molecule and leaves the range of the individual deviations at best but partially determined. The most delicate test so far available, that of the spectroscope, seems always to be beset by at least one disturbing factor. On this method the qualitative identity of the molecules of a given element in the gaseous state is inferred from their light-note. But every one who has heard the sound-note of the whistle of a train in motion must have observed that this note sounds higher so long as the train is approaching, and lower as soon as it has passed and begun to recede. To get the light note true, the molecules should be observed free from their translatory motions towards and away from the observer. The variations thus produced can only be set down entirely to the account of the translatory motions after independent proof has been adduced of the absolute likeness of the molecules. Meanwhile it has to be shared between the two. But since Maxwell wrote the passages I have quoted, it has been shewn that the spectra of several elements vary with the temperature and the pressure to which the gas is exposed; and when a gas approaches the liquid condition these changes appear to be greater still. What various degrees of aggregation there may be in the liquid or solid state, and how far the individuality of the molecule disappears in such aggregation—these are problems for which there appears at present no definite solution.4

Graham's familiar method of dialysis, or atom-sifting, is also appealed to by Maxwell to establish the perfect identity of the molecules of the same kind of matter. Graham found, it will be remembered, that light gases pass through a porous septum more rapidly than heavier ones. Maxwell is referring to this method when at the close of his book on Heat he says: “If of the molecules of some substance such as hydrogen, some were of sensibly greater mass than others… in this way we should be able to produce two kinds of hydrogen, one of which would be somewhat denser than the other. As this cannot be done, we must admit that the equality which we assert to exist between the molecules of hydrogen applies to each individual molecule, and not merely to the average of groups of millions of molecules.”5 But there is a world of difference between saying of a million molecules that the mass of no one of them is ‘sensibly greater’ than that of the rest, and saying that the masses of all are absolutely equal.

I cannot help thinking that Clifford reasons far more soundly than Maxwell in dealing with this same method of dialysis. “If we put any single gas into a vessel,” he says, “and we filter it through a septum of black lead into another vessel, we find no difference between the gas on one side of the wall and the gas on the other side. That is to say, if there is any difference, it is too small to be perceived by our present means of observation. It is upon that sort of evidence that the statement rests that the molecules of a given gas are all very nearly of the same weight. Why do I say very nearly? Because evidence of that sort can never prove that they are exactly of the same weight. The means of measurement we have may be exceedingly correct, but a certain limit must always be allowed for deviation; and if the deviations of molecules of oxygen from a certain standard of weight were very small, and restricted within certain limits, it would be quite possible for our experiments to give us the results which they do now. Suppose, for example, the variation in the size of the oxygen atoms were as great as that in the weight of different men, then it would be very difficult indeed to tell by such a process of sifting what that difference was, or, in fact, to establish that it existed at all. But, on the other hand, if we suppose the forces which originally caused all those molecules to be so nearly alike as they are to be constantly acting and setting the thing right as soon as by any sort of experiment we set it wrong, then the small oxygen atoms on one side would be made up to their right size and it would be impossible to test the difference by any experiment which was not quicker than the process by which they were made right again.”6 7 Had Clifford been writing now he might have illustrated this last point by a reference to Mr. Galton's principle of reversion towards the mean, in accordance with which the children of giants, for example, tend to be of less stature, and the children of dwarfs to be of greater stature, than their parents.8

But Maxwell felt himself “debarred from imagining any cause of equalisation on account of the immutability of each individual molecule ”— this being the second article of his molecular creed, as that of exact likeness was the first. There is, I fear, something circular in Maxwell's arguments for these two positions. On the one hand the ingenerability and immutability seem to be used in proof of the qualitative and quantitative identity; although, on the other, this very identity had served as an argument for that everlasting constancy which in turn it now helps to prove. Nay, his argument seems even weaker than that, for he takes for granted that the persistence which he asserts for his normal molecules would belong also to abnormal ones, if any such there were. And so, assuming the exact equality of all the individual molecules of hydrogen, etc., within the range of our experience, he asks where can the eliminated molecules have gone to? He then proceeds: “The time required to eliminate from the whole of the visible universe every molecule whose mass differs from that of some of our so-called elements, by processes similar to Graham's method of dialysis, which is the only method we can conceive of at present, would exceed the utmost limits ever demanded by evolutionists as many times as these exceed the period of vibration of a molecule.” But surely it is quite gratuitous to assume that they could only disappear by being sifted out on some chaotic dust-heap beyond the fixed stars, a sort of limbo for manufactured articles spoilt in the making.

And this remark suggests a more searching question: What, precisely, is it of which this immutable individuality is affirmed? Is it of a form or is it of a substance?9 The biologist can tell us of species that have persisted unchanged from times so long anterior to ours that the hoariest mountain ranges appear by comparison to have sprung up but yesterday. But here it is only the form that endures, the particular individuals being quite transitory. A lake dries up and its tiny inhabitants perish; after a longer or shorter interval the water returns and the old living forms reappear. But the biologist does not follow the analogy of the chemist, and pronounce these to be necessarily the earlier individuals emerging from some quasi-chemical condition in which their characteristic properties have been suspended or masked. Now physical astronomers find that the spectra of certain of the whiter, and presumably hotter, stars yield indications of no element save hydrogen; also that as stars approximate to a red colour, and so have presumably a lower temperature, they furnish more varied and complex spectra, indicating the presence of many other elements besides hydrogen. The simplest supposition we can make—and it is one actually made—is that in the earlier stages of stellar evolution, of which we thus get peeps, the various chemical elements come successively into being, as do various forms of vegetable and animal life in the later stages of the same vast process.10 But what becomes of a the molecule as an article manufactured before natural processes began? The best that can be said is, not that the individual article is a fabric of timeless origin, but only that its form or pattern is thus (relatively) immutable and ingenerable. It is still possible, however, to reinstate some persisting individual by falling back on primal atoms or elements of a higher order. And phenomena daily observed by the chemist at once suggest this step. As ordinary chemical compounds can be decomposed at high temperatures, it is probable that our so-called elements may be ‘split up’ into elements of a new order by temperatures greatly in excess of any that we can command. Those who think fit may regard this higher order of element as furnishing “the foundation stones of the material universe” and remaining—though the firmament be dissolved and renewed again—“in the precise condition in which they first began to exist.” But such an opinion can no longer be entertained of the molecules ‘built up’ of these stones,—molecules that processes now going on seem to make and unmake, as the chemist makes further compounds out of them, which he can afterwards decompose again. Maxwell was evidently prepared for this alternative. In the closing paragraph of his Theory of Heat, he asks, “But if we suppose the molecules to be made at all, or if we suppose them to consist of some thing previously made, why should we expect any irregularity to exist among them?”

But surely it is far from indifferent which of these alternatives we adopt when inquiring what amount of “irregularity” we may expect among the molecules of any given chemical stuff. If the molecules of oxygen, hydrogen, etc., are themselves primeval and immutable individuals, they are like nothing else that we know, and we can have no scientific grounds for expecting anything about them one way or other. But if they are compounds that are put together and again ‘split up’ in the course of nature, then, in the absence of certain knowledge to the contrary, we may expect among their forms any of the regularities or irregularities that we find elsewhere among dissoluble products. In particular we might expect, for example, that certain of these forms, like some of the chemical compounds that we know as such, would prove very unstable, and so disappear almost as soon as they arose; others again, like certain refractory minerals long regarded as elements, might persist indefinitely. The striking analogy between the grouping of chemical elements, when ranged as in the periodic laws of Meyer and Mendelejeff, and the grouping of biological forms, might tempt us to entertain the hypothesis, mutatis mutandis, of some sort of chemical evolution. But absolute qualitative identity, for which Herschel and Maxwell contended, would be almost as incompatible with such an hypothesis as absolute immutability. Both these absolute ideas would be alien to the notion of continuous transmutability or of connecting forms.

Digressing for a moment, let me remark that both these ideas, there can be little doubt, are far more due to theological zeal than to the bare logic of the facts. In the fine conclusion of his text-book on Heat, after asking, “Why should we expect any irregularity to exist among them,”—the molecules, i.e. of the same kind of matter,—Maxwell continues: “Why should we not rather look for some indication of that spirit of order, our scientific confidence in which is never shaken … and of which our moral estimation is shown in all our attempts to think and speak the truth, and to ascertain the exact principles of distributive justice?”11 But why so confidently assume, we might reply, that a rigid and monotonous uniformity is the only, or the highest, indication of the spirit of order, the order of an everliving Spirit above all? How is it then that we depreciate machine-made articles and prefer those in which the artistic impulse or the fitness of the individual case is free to shape and to control what is literally manufactured, hand-made? The work of an engine-fitter is greatly facilitated by the use of Whitworth bolts, tubing of regulation sizes, and the like, but surely it is trivial to frame teleological arguments concerning the universe from the standpoint of a millwright. So, the existence of a limited number of absolute constants in nature might bring the universe within the compass of the Laplacean calculator. But, dangerous as teleological arguments in general may be, we may at least safely say the world was not designed to make science easy. Struggling men and women, like the soldier on the march when his machine-made shoe pinches, might reasonably complain if science should succeed in persuading them that Nature's doles and Nature's dealings from first to last are ruthlessly and rigidly mechanical. To call the verses of a poet, the politics of a statesman, or the awards of a judge mechanical, implies, as Lotze has pointed out, marked disparagement: although it implies, too, precisely those characteristics—exactness and invariability—in which Maxwell would have us see a token of the Divine.

But, returning to our facts and avoiding altogether any question as to why we should expect this or why we should expect that, for such questions lie beyond the legitimate pale of science, let us gather up what we find. Chemical molecules are not presented realities: in other words, a molecule—say of oxygen—is not a small body which is known to exist as an individual of a definite species, distinct, say, from a molecule of nitrogen, an individual of another definite species of small body. Individual chemical molecules are not known, as rubies or palms are known, i.e. as instances of species and distinct from diamonds or cedars, instances of other species. The chemical molecule is a hypothetical conception. Such things may exist or the hypothesis would not be legitimate. Whether they actually exist or not, they, at any rate, serve, like certain legal and commercial fictions, to facilitate the business of scientific description. If they exist, then facts show that the molecules of a given species are very nearly alike; the said facts admitting of interpretation according to statistical methods. As in other cases admitting of statistical treatment, so here the physicist is free to regard all molecules of a class as exactly like his mean or average molecule. But he is not entitled to let this abstract simplification harden into concrete fact. Perhaps it may be thought that such rigorism is pedantic. So far as any particular physical inquiry is concerned it may be, but I am very doubtful even of this. At all events, if such unwarrantable concreting of abstracts is to lead logically to a mechanical theory of the universe, we do well to take note of it.

To make the bearing of this remark clearer, let us turn our attention for a moment to the very parallel case of economic theory and the interpretation of industrial and social statistics. The science of so-called pure or deductive economics has much in common with physics, that is to say, it sets out from definitions and axioms and seeks to describe economic facts by means of mathematical equations. The ‘economic man’ as conceived by Ricardo, a ‘market’ as defined by Cournot, James Mill's ‘doses of capital,’ the ‘margin of cultivation,’ or Jevons's ‘supply and demand curves,’ are not things we expect to meet with in real life. They are abstractions that summarise experience, not concrete realities directly experienced. Englishmen about to marry are not observed to be exclusively interested in women their juniors by 2.05 years, though according to the tables this is the difference of age between the Englishman and his wife. But, again, the Englishman or the Frenchman, or the civilised man or the savage, is a concept, not a reality. Yet a science of anthropology is possible in which different races of men and different stages of human development are compared by the help of mean values obtained by dealing with nations and societies en bloc. And perhaps “in this way,” as Lotze has said, “we may easily imagine how all kinds of formulæ may be arrived at, expressive of the acceleration and breadth and depth and colouring of the current of historical progress, formulæ which, if applied to particulars, would be found to be utterly inexact, but which can yet claim to express the true law of history as freed from disturbing individual influences.” It was precisely this misapplication to particulars that led Buckle to say that in a given state of society a certain number of persons must put an end to their own lives. Now, if, when both the varying particulars and the statistical constants are alike well known, it is possible for a reasonable man to fall into the error of converting the one into an iron necessity which rules over the other, no wonder this should be the prevalent attitude in departments of knowledge where particulars are beyond our ken. I contend then that the most the physicist is entitled to assert is, that, if there are molecules, the mass of the mean oxygen ‘atom’ is sixteen, that of the mean hydrogen ‘atom’ being taken as unity; and so on for the rest of his table of masses. He is not entitled to say that if there are molecules the mass of every oxygen atom is precisely sixteen times the mass of any hydrogen atom. Try to picture to yourselves the sort of science of man and of society that would be formulated by an intelligence whose data were confined to anthropometrical and other statistical results and who treated his data in the customary physical fashion. You will conclude, I think, that his human beings or homunculi would come out surprisingly like Herschel's molecules as ‘manufactured articles,’ and that his theory of society would have more than a superficial resemblance to the kinetic theory of gases.

Finally, as the facts do not justify the assertion of exact likeness among molecules, neither do they afford ground for the assertion that individual molecules are immutable and incorruptible. Once this is clear, then molecules, if there are such things, come within the range of the great conception of evolution and facts pointing in this direction are known already and are steadily accumulating. As Huxley well says: “The idea that atoms are absolutely ingenerable and immutable ‘manufactured articles’ stands on the same sort of foundation as the idea that biological species are ‘manufactured articles’ stood thirty years ago; and the supposed constancy of the elementary atoms, during the enormous lapse of time measured by the existence of our universe, is of no more weight against the possibility of change in them … than the constancy of species in Egypt since the days of Rameses or of Cheops is evidence of their immutability during all past epochs of the earth's history. It seems safe to prophesy that the hypothesis of the evolution of the elements from a primitive matter will, in future, play no less a part in the history of science than the atomic hypothesis, which, to begin with, had no greater, if so great, an empirical foundation.”12 13 We may, I think, go even farther. Somehow or other the qualitative diversity of the chemical elements must admit of description by means of quantitative relations of mass-points, configurations, and movements—if the mechanical theory is to make good its claims. Indeed, the unceasing efforts of chemists and physicists in this direction can be regarded as an emphatic admission that they have laid this charge upon themselves. Moreover, in what is called the New Chemistry or General Chemistry—take Ostwald's well-known Outlines as an example—we see how much they have already accomplished; and also, I will add, how very much more still remains to be done.

But let us turn now to another order of facts. If the molecules concerned in chemical reactions and in the kinetic theory of gases are beyond sensible reach, the forms of matter immediately concerned in the phenomena of radiation, electricity, and magnetism are more remote still. It is in connexion with these that the ether or ethers come upon the scene. I say ethers because it is by no means certain that one will suffice. “It is only when we remember,” says Maxwell, “the extensive and mischievous influence on science which hypotheses about ethers used formerly to exercise, that we can appreciate the horror of ethers which soberminded men had during the eighteenth century, and which, probably as a sort of hereditary prejudice, descended even to the late J. S. Mill.” Time seems to have brought its revenge, for nowadays the ether is regarded as preëminently real. Thus, in a lecture given about ten years ago and recently published, our foremost physicist said to his hearers: “You can imagine particles of something, the thing whose motion constitutes light. This thing we call the luminiferous ether. That is the only substance we are confident of in dynamics. One thing we are sure of, and that is the reality and substantiality of the luminiferous ether.”14 Yet in spite of this confidence of Lord Kelvin's I cannot help thinking that a jury of logicians would side with Mill. But possibly some of you may be disposed to ask, What has the question as to the real or hypothetical nature of the luminiferous ether to do with the mechanical theory of the universe? Simply that unless a material medium for its propagation is either found or assumed, the phenomena of light cannot be mechanically described. And the remark applies equally to other forms of radiation as well as to electricity and magnetism. If not themselves massive, these phenomena must depend on the configuration or motions of something that is massive, or it is obviously impossible to describe them in the mechanical terms at present in vogue. That need entail no detriment to the special physical sciences concerned with their description and measurement by means of a more concrete and qualitative terminology; and, indeed, some able physicists prefer to leave the question of a medium entirely aside.15 But to do this so far puts a stop to the resolution of all physical changes into mechanical processes. We shall all perhaps allow a reasonable presumption in favour of any theory that will unify the variety of physical facts. But then some of us feel that physicists have too hastily assumed that, unless these facts have a common mechanical foundation, they can have no intelligible connexion at all. Even if the mechanical theory turn out to be true in fact, there is no a priori necessity about it. Yet covertly or overtly some such necessity is assumed; and it is mainly on the basis of this postulate that the ether is raised from the subsidiary position of a descriptive hypothesis to the rank of a thing having “reality and substantiality.” Grant, first, that the world must be intelligible; grant, secondly, that to be intelligible it must be mechanical; and then grant that to be mechanical there must be an ether or ethers whose motions constitute light, electromagnetism, etc., grant all this and then—spite of the absence of direct evidence—we might say the existence of ether is indirectly proved. But the first two steps in this argument, it will be observed, are philosophical and the second very disputable philosophy. Science, however, has no right to build on philosophical premisses, and is forward, as we have seen, to disown, with much needless blasphemy, all such a priori methods. Leave aside then any presuppositions of this kind, and the ether remains but a mechanical hypothesis; its perceptual reality, if proved at all, can only be proved by some crucial experiment or by cumulative experimental evidence. No doubt its value as a descriptive hypothesis has been greatly enhanced since Mill's time—notably by the labours of Maxwell and Hertz. But as to the worth of their results I suppose Poincaré's remark upon it is not too cautious: “There still remains much to be done; the identity of light and electricity is from to-day something more than a seducing hypothesis; it is a probable truth, but it is not yet a proved truth.”16

But though the conception of an all-pervading ether has gained in scientific importance since Mill's controversy with Whewell, it has also been repeatedly modified, I might even say transformed. At one time or other it has been regarded as a gas, as an elastic solid of small density but high rigidity, as a ‘quasi-solid’ constituted by turbulent motion in an incompressible inviscid fluid—with two or three sub-varieties of this hydrokinetic type. And when a new ether is invented the problem is to ascertain how many of the special laws of radiation or electricity can be mechanically deduced from it. In no case has this demand been adequately met; hence the attempts, continually renewed, to devise more satisfactory ethers. Surely if the ether were a definite thing, the reality of which was an established fact, it would be impossible to take these liberties with it. On the other hand, is it not certain that if, conceivably, some non-mechanical hypothesis were to afford a simpler and more complete unification of optical and electrical phenomena, there would be an end of luminiferous and electric ethers, just as there was an end of phlogiston in the days of Priestley and Lavoisier, and as there has been an end of caloric and electrical fluids in our own? By a non-mechanical hypothesis, I mean here one in which some or all of the Newtonian laws are denied or modified.17 I should hardly have ventured even to suggest such a thing on my own responsibility. But I observe that several physicists in the present unsettled state of the science are prepared to entertain such heresies. I will quote two. Professor Drude, on succeeding to a new chair at Leipzig, devoted his inaugural lecture to the Theory of Physics. Referring to the characteristic difference between what we call matter and what we call ether, viz.: that the former consists of smallest inhomogeneities, —a finely grained structure, as we say in English,—while the latter is thoroughly homogeneous, he continues: “The physics of matter must then appear the more complicated compared with the physics of the ether. Is not that an indication that no simplification can result if we attempt to describe the physics of the ether formally in the same manner as the physics of matter, that is to say, by means of mechanical equations?”18 Again, Professor Karl Pearson, in his Grammar of Science, referring to the Newtonian laws, asks: “Ought we to assert that these laws hold in their entirety for all the scale from particle to ether-element? Or will it be more advantageous to postulate that mechanism in whole or part flows from the ascending complexity of our structure, that the ether-element is largely the source of mechanism, but is not completely mechanical in the sense of obeying the laws of motion as given in dynamical text-books? ” And in another passage: “The object of science is to describe in the fewest words the widest range of phenomena, and it is quite possible that a conception of the ether may one day be formed in which the mechanism of gross ‘matter’ itself may, to a great extent, be resumed. Indeed, it is on these points of the constitution of the ether, and the structure of the prime atom, that physical theory is at present chiefly at fault. There is plenty of opportunity for careful experiments to define more narrowly the perceptual facts we want to describe scientifically; but there is still more need for a brilliant use of the scientific imagination. There are greater conceptions yet to be formed than the law of gravitation or the evolution of species by natural selection. It is not problems that are wanting, but the inspiration to solve them; and those who shall unravel them will stand the compeers of Newton and Darwin.”19

The remarks and queries just quoted apply to the electric and luminiferous medium or media, though the medium the writers have also in view is doubtless what has been called “the primordial medium”; such, e.g., as the perfect fluid of Lord Kelvin's vortex-atoms, from which ultimate ether the proximate ether of light and electricity is supposed to be formed. At this primordial and absolutely homogeneous fluid the physical theorist is content at last to stop; and for this at present no confident claim is advanced to “reality and substantiality.” Will the physicists of fifty years hence remain as modest—should the hypothesis, as seems likely, hold its ground so long?

So much then must serve to illustrate what I called the indirectness of molecular physics. Under this head we have noted a tendency to treat statistical means and hypothetical mechanism as concrete realities. And here it seems needful to make a distinction or we may be charged with unfairness—a distinction, I mean, between hypothetical mechanisms and illustrative mechanisms employed solely for expository purposes. To the latter class, for example, belong unquestionably the “idle wheels ” of Maxwell's electro-magnetic theory and again Lord Kelvin's gyrostatic cells. On the other hand his quasi-elastic ether, or his quasi-labile ether, seem to be meant as real and not as merely illustrative analogies. But it is to be feared that physicists of the school of Maxwell and Lord Kelvin, who—to use Boltzmann's description of them—“are particularly fond of the variegated garment of mechanical representation,” are apt unconsciously to play fast and loose with the difference between fiction and fact, when elaborating their mechanical models. Analogy, as we know, is a good servant, but a bad master; for, when master, it does more to blind than it may previously have done to illuminate. Most of us, I suppose, have chanced to observe a bee buzzing up and down within the four sides of a window-pane, vainly endeavouring to escape by the only obvious way—the way most light comes; whereas by merely traversing the dark border of the window-frame it might at once reach the open casement. The history of science is full of instances of able men similarly thwarted by a too-prepossessing analogy. In his lectures at the Johns Hopkins University Lord Kelvin is reported to have said, “I never satisfy myself till I can make a mechanical model of a thing. If I can make a mechanical model I can understand it. As long as I cannot make a mechanical model all the way through, I cannot understand, and that is why I cannot get the electro-magnetic theory of light.”20 Now I should like respectfully to ask whether this is not possibly a case of unwarrantable submission to analogies. As before, I ask again: Why must mechanism “all the way through” be the one and only means of intelligibility? When we recollect the comparatively small range of the experiences within which mechanical laws are found to be verifiable abstractions, are we bound to assume that they are the only concrete realities at the very foundations of physical things? This question brings us to the second characteristic of molecular mechanics just now referred to—its ideal of matter. The consideration of this may perhaps give us further light, but must be deferred till the next lecture.

• 1.

  Laplace's Exposition du système du monde, bk. v, chap. v fin., Œuvres complètes, 1893, vol. vi, p. 471.

• 2.

  Cf. Stallo, Concepts of Modern Physics, p. 122.

• 3.

  Cf. above, p. 51.

• 4.

  Cf. Ostwald, Outlines, pp. 189, f.

• 5.

  Heat, p. 339.

• 6.

  Lectures and Essays, vol. i, p. 207.

• 7.

  Note i.—The experiments which have led Professor J. J. Thomson to propound the hypothesis of ‘bodies smaller than atoms’ give additional credibility to this supposition of Clifford's.

• 8.

  It is well known that some chemists agree with Sir William Crookes in thinking that “probably our atomic weights merely represent a mean value around which the actual atomic weights of these atoms vary within certain narrow limits,” reminding us of Newton's ‘old worn particles,’ save that the result is not supposed to be due to wear and tear. Besides referring to Sir William Crookes's researches into the fractionation of yttrium—one more instance, and a splendid one, of the saying that genius is patience—I may mention the experiments on the homogeneity of helium just published by Messrs. Ramsay and Collie. See Nature, 1896, vol. liv, p. 408.

• 9.

  Note ii.—Professor Poynting reminds me that Professor Larmor's hypothesis concerning the nature of material elements, the immutable individuality discussed in this paragraph, is not due to substance—as with Maxwell—but to form. It consists of a ‘strain centre’ that flits from point to point of the ether, different parts of the ether coming into the strain, as that moves about.

• 10.

  Cf. Sir W. Crookes's brilliant Address to the Chemical Section of the British Association, 1886, Nature, vol. xxxiv, pp. 423 ff.

• 11.

  Heat, p. 342.

• 12.

  Collected Essays, vol. i, pp. 79 f.

• 13.

  Note iii.—Since Huxley wrote this passage, Sir Norman Lockyer has published an interesting little book entitled Inorganic Evolution as studied by Spectrum Analysis, 1900.

• 14.

  Lord Kelvin, Popular Lectures and Addresses, vol. i, p. 310.

• 15.

  F. E. Neumann, for example. Cf. Volkmann, Theorie des Lichts, p. 4.

• 16.

  Nature, 1894, vol. l, p. 11.

• 17.

  Perhaps such a restriction is in itself unwarranted, but it serves my purpose here.

• 18.

  Die Theorie in der Physik, 1895, p. 13.

• 19.

  Grammar of Science, 2nd ed., pp. 284, 312.

• 20.

  Nature, vol. xxxi, p. 603.