Mr. Spencer proposes to deduce the phenomena of evolution (celestial, organic, social, etc.) from the conservation of energy. The obvious insufficiency of this principle taken alone. Mr. Spencer's conception of it contrasted with that of Helmholtz.
How Mr. Spencer connects this ‘persistence of force,’ as he prefers to call it, with his doctrine of the Absolute. The vagueness of his terms.
The three principles in Mr. Spencer's interpretation: 1. Instability of the homogeneous. But is the homogeneous necessarily unstable? Quite the contrary. Moreover, Mr. Spencer cannot by analysis get at such a beginning as he supposes. How much can evolution possibly account for, and how little need it presuppose? No clear advance to be made from Mr. Spencer's standpoint. Some illustrative instances of Mr. Spencer's procedure: (a) self-rotating nebulæ: in a single homogeneous object no ground of change; (b) instability of circular orbits: looseness of Mr. Spencer's terminology; (c) chemical differentiation, instability of the heterogeneous: two-edged arguments.
2. Multiplication of effects. An instance of what Mr. Spencer understands by one cause and many effects. Illusory deduction of this principle from the fundamental one of persistence of force.
3. Segregation. This ‘the key to the advance from vague chaotic heterogeneity to orderly heterogeneity.’ The process described: it turns out to require only ‘forces acting indiscriminately.’ Relation of this principle to the other two. Difficulties for Mr. Spencer in connection with the distribution of the chemical elements. Also in the characteristics of organisms and the products of human industry. But Mr. Spencer's terminology is happily ‘plastic.’
AS we shall have to refer frequently to Mr. Spencer's formula of evolution in its final form, I will begin by quoting it at length: “Evolution is an integration of matter and concomitant dissipation of motion [so much answers to ‘simple evolution’ and has been quoted already; what follows includes ‘compound evolution’] during which the matter passes from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity; and during which the retained motion undergoes a parallel transformation.”1
“The task before us,” says Mr. Spencer, the law of evolution being ascertained, “is that of exhibiting the phenomena of Evolution in synthetic order. Setting out from an established ultimate principle, it has to be shown that the course of transformation among all kinds of existences cannot but be that which we have seen it to be. It has to be shown that the redistribution of matter and motion must everywhere take place in those ways and produce those traits, which celestial bodies, organisms, societies, alike display. And it has to be shown [here is the point] that this universality of process results from the same necessity which determines each simplest movement around us, down to the accelerated fall of a stone or the recurrent beat of a harp-string. In other words, the phenomena of Evolution have to be deduced from the Persistence of Force. As before said—‘to this an ultimate analysis brings us down; and on this a rational synthesis must build up.’”2
By Force Mr. Spencer means, among other things, Energy. Now I think it is quite clear that, so far from accounting for all the phenomena of evolution, the doctrine of the persistence of energy alone will not account for a single one. The celestial, organic, social, and other phenomena which make up what Mr. Spencer calls cosmic evolution are so many series of qualitative changes. But the conservation of energy is not a law of change, still less a law of qualities. It does not initiate events, and furnishes absolutely no clue to qualitative diversity. It is entirely a quantitative law. When energy is transformed, there is precise equivalence between the new form and the old; but of the circumstances determining transformation and of the possible kinds of transformation the principle tells us nothing. If energy is transferred, then the system doing work loses precisely what some other part of the universe gains; but again the principle tells us nothing of the conditions of such transferences.
As I tried to shew briefly in the sixth of these lectures, this principle may be regarded as primarily and fundamentally a priori. Somewhere or other we postulate persistence or conservation, and finding so far as experience goes that mass and energy are conserved, we apply to them this a priori postulate. It might turn out that we were wrong in this application, but the postulate in its abstract generality we should still not question. In some sense it must be true to say Causa quat effectum, and meanwhile there is a vast body of evidence to shew that it is true of the transferences and transformations of energy. But now the fact that the principle of energy involves in this wise both an a priori and an empirical factor is continually ignored by Mr. Spencer. He lays all the stress on the a priori factor, i.e. on his own extraordinary version of it; and does not see that this by itself is ludicrously insufficient. Hence such language as this, with which his chapter on the Persistence of Force concludes: “Deeper than demonstration–deeper even than definite cognition–deep as the very nature of mind, is the postulate at which we have arrived. Its authority transcends all other whatever; for not only is it given in the constitution of our own consciousness, but it is impossible to imagine a consciousness so constituted as not to give it.”3 And now let me quote for comparison with this a sentence or two from the conclusion of Helmholtz's famous essay on the same subject: “I believe that what has been here advanced has shewn this law to be contradicted by no facts at present known to science, but to be strikingly confirmed by a very large number. I have striven to exhibit as completely as possible such consequences as follow from it in combination with the laws of natural phenomena so far ascertained, consequences which must still await experimental verification. It has been my aim to lay before physicists with all possible completeness the theoretical, practical, and heuristic importance of this law, the complete establishment of which may well be regarded as one of the chief undertakings of the immediate future.”4 Such language as this would be not only sheer nonsense, but a sheer impossibility if Mr. Spencer's philosophy were right. Clearly Helmholtz does not regard the persistence of force as a datum of consciousness. But now Mr. Spencer, in a very solemn passage, declares that “if it can be shewn that the persistence of force is not a datum of consciousness; or if, etc.,” why, “then, indeed,” he adds, “it will be shewn that the theory of Evolution has not the high warrant here claimed for it.”5 The burden of proof, however, plainly lies with him. Here is a principle, of which physicists fifty years ago were unaware, a principle which has had to fight its way to recognition, a principle the range of which is still a question–the notion of dynamically non-conservative systems being therefore not absurd; if this principle lies so wondrous deep, “deeper than demonstration, deeper even than definite cognition,” then let Mr. Spencer explain Newton's ignorance of it and the general scepticism that greeted its enunciation by Mayer, Joule, and Helmholtz. Perhaps the terrible depth from which they must have brought it is the explanation!
Taking this principle, then, as physicists understand it, and not as it is misunderstood by Mr. Spencer, I repeat that it will not carry us one step towards his evolutionary formula. You could not deduce from it even those “simplest movements,” “the accelerated fall of a stone or the recurrent beat of a harp-string,” which he assumes to be necessarily determined by it. Yet still more hopeless, if possible, would it be to find for “the theory of evolution the high warrant claimed for it” if we took Mr. Spencer's own version of the persistence of force instead of the accepted doctrine.
To examine this version must appear, I fear, some what of a digression. But let me remind you how often this recognised champion of naturalistic evolution reiterates his confidence that nothing short of a refutation of this ultimate position can shake his general conclusions: “to this,” he has said, “an ultimate analysis brings us down and on this a rational synthesis must build up.” “But now what is the force of which we predicate persistence?” asks Mr. Spencer; and he answers: “It is not the force we are immediately conscious of in our own muscular efforts…the force of which we assert persistence is that Absolute Force, of which we are indefinitely conscious.… By the persistence of Force [capital F], we really mean the persistence of some Power [capital P] which transcends our knowledge and conception. The manifestations, as recurring either in ourselves or outside of us, do not persist; but that which persists is the Unknown Cause [capitals again] of these manifestations.”6 7 In this statement it is important to note two things. First, that between the manifestations or phenomenal forces, according to the usual phrase, and this ‘Absolute Force’ or Power, there stretches all that gulf, which Mr. Spencer has elsewhere magnified, separating the known and comprehensible from the unknown and incomprehensible. Secondly, that by persistence as applied to phenomenal forces he means the quantitative constancy of these in their totality; while by persistence as applied to Absolute Force he means, as he says, to assert “an Unconditioned Reality, without beginning or end.” Now, if Mr. Spencer's cosmic philosophy does not fall between these two supports or lose itself in that ‘ugly, broad ditch’ Schelling spoke of, between Nature and the Absolute, it will be luckier than most eclectic attempts. If it had started from the Absolute and Unconditioned Reality, of which we are said to be indefinitely conscious, it would obviously have been gratuitous—nay, self-contradictory and nonsensical—to assume that the manifestations of this Unknowable to finite intelligences must remain always quantitatively the same. If “rational synthesis” of things is what we seek, it is surely more reasonable to say with Lotze: “What lies beneath all is not a quantity which is bound eternally to the same limits and compelled through many diverse arrangements, continuously varied, to manifest always the very same total. On the contrary, should the self-realisation of the Idea require it, there is nothing to hinder the working elements of the world being at one period more numerous and yet more intense; at another period less intense as well as fewer. Then would the course of Nature be like a melody, not flowing in monotonous uniformity, but with crescendos and diminuendos as each in turn is required to express the meaning of the whole.”8
If now, on the other hand, Mr. Spencer had started from the phenomenal, then, allowing as he does, that of the conservation of energy neither inductive proof nor demonstration is possible, he ought to have regarded that law as, like the still wider law of causation, a postulate or regulative principle connecting together the various branches of physics. But a basis so tentative and restricted would not suffice for a theory which essays to exhibit all the changes of celestial bodies, organisms, and societies as necessary results of the same universal principle. “The recognition of a persistent Force, ever changing its manifestations but unchanged in quantity throughout all past time and all future time, is,” he declares, “that which alone makes possible each concrete interpretation and at last unifies all concrete interpretations.”9 So he is led to perpetrate two or three astounding feats of philosophical jugglery. The apparatus of the first of these we have now before us. Persistence in the sense of permanence is secured first of all by reference to the Unconditioned Reality; the non-existence of which is unthinkable, although any knowledge of it is impossible—since to know is to condition. Next persistence, but in the sense of quantitative constancy, is transferred from this Unconditioned Reality to its phenomenal manifestations, but only by first affirming of it precisely that statement which we are not empirically warranted to affirm absolutely of them. Let me present this apparatus anew in Mr. Spencer's own words. Item No. 1. “Getting rid of all complications and contemplating pure Force, we are irresistibly compelled by the relativity of our thought, to vaguely conceive some unknown force as the correlative of the known force.”10 Item No. 2. “Every antecedent mode of the Unknowable must have an invariable connexion, quantitative and qualitative, with that mode of the Unknowable which we call its consequent. For to say otherwise is to deny the persistence of force.”11 Item No. 3. “For persistence is nothing more than continued existence, and existence cannot be thought of as other than continued.”12 In the first we get the absolute existence of Force, with a capital F, at the price of absolute ignorance concerning it; in the second, we get the absolute constancy of force, with a little f, at the price of making precise and definite statements concerning that Unknowable. The intellectual somersault thus rapidly performed is covered by taking continued existence to involve invariable quantity. How quantity of Unconditioned and Unknowable Reality is to be measured we are not told, nor yet what the unit of measure is to be. Does not this step deserve the name of intellectual jugglery: on two items of ignorance to establish an ultimate principle determining what the course of transformation among all kinds of existences must be? We do not know what the Absolute is and we cannot prove that the quantity of force remains always the same. But since no consciousness can think being as not being, the persistence of the persistent is the fundamental cognition from which all others are derived; hence the Unknowable in persisting must make the knowable that does not persist a constant quantity.
By such fetches of ingenuity to resolve the Absolute into a fixed quantity would, after all, not be worth the pains, unless, as I have said, force is to have a much wider meaning and the conservation of energy a much wider range than science at present allows to them. Otherwise it would be impossible to bring organisms and societies and all thereto pertaining—life, mind, character, language, literature, and institutions of every kind—under the cover of a single formula. We are therefore not surprised to find Mr. Spencer treating of the transformation of physical forces into mental forces and insisting on a quantitative equivalence between the two, just as he treats of the transformation of mechanical work into heat and the value in foot-pounds of a calorie. The poetry of Milton and the British Constitution, nay, the human mind and the Christian religion, are all according to him, equally with the tidal bore on the Severn or gales at the equinoxes, so many secondary results of the nebular hypothesis, cases of integration of matter and dissipation of motion in obedience to the persistence of force. It is to encompass all these within one formula that he is tempted to stretch a great physical generalisation beyond all meaning, and to justify his venture by questionable metaphysics concerning Absolute Being. But it will be time enough to deal with the hopeless vagueness of Mr. Spencer's conceptions of “knowable force” as they arise. Meanwhile, having seen how little he succeeds in obtaining for his theory of evolution the high warrant he claims for it, let us turn to some of the details of the theory itself.
At once we make a great descent. We leave behind the Ultimate Cause, Inscrutable Power, Unconditioned Reality, supposed to be indispensable to Mr. Spencer's “rational synthesis.” We now find ourselves confronted, as the complete theory requires, by the whole universe in “a diffused imperceptible state.” “On setting out,” says our guide, “the proposition which comes first in logical order, is that some rearrangement must result: and this proposition may best be dealt with under the more specific shape that the condition of homogeneity is a condition of unstable equilibrium.” Or more precisely: “The absolutely homogeneous must lose its equilibrium, and the relatively homogeneous must lapse into the relatively less homogeneous.”13 14 But this is going too fast. Il n'y a que le premier pas qui coûte: so we must be wary here. That homogeneity implies instability is anything but self-evident. For one thing, if such were the case, it would be difficult to see how, on Mr. Spencer's theory, such homogeneity could ever arise. Any given era of evolution we are free to regard, according to his principles, as preceded by an era of dissolution, the persistence of force being supreme throughout. We seem required to picture the whole universe, as soon as evolution is complete, beginning to decompose and continuing so to do in such a manner that the state of homogeneity shall be simultaneously reached by every part of it. Otherwise, owing to the instability of the homogeneous, the counter-process of redintegration would begin in one part before the others were ready. There seems, however, but one way in which such a simultaneous dissolution is possible, viz.: by the precise and instantaneous reversal of every movement throughout the whole, as stated, e.g., in the passage from Helmholtz quoted in the last lecture. The universe would then be like a reversible musical box which could play its tunes backwards; and, assuming it to have started from a homogeneous state, it would in this way return to it. But this is not what Mr. Spencer understands by dissolution. In truth, however, homogeneity is not necessarily instability. Quite otherwise. If the homogeneity were absolute,—that of Lord Kelvin's primordial medium, say,—then the stability would be absolute too. In other words, if “the indefinite, incoherent homogeneity,” in which, according to Mr. Spencer, some rearrangement must result, were a state devoid of all qualitative diversity and predicable of the universe, then, as we saw 15in discussing mechanical ideals, any “rearrangement ” could result only from external interference; it could not begin from within. All physicists are agreed, as Messrs. Tait and Stewart put it, that “in the production of the atom from a perfect fluid, we are driven at once to the unconditioned—to the Great First Cause; it is, in fine, an act of creation and not of development.”16 Thus, the very first step in Mr. Spencer's evolution seems to necessitate a breach of continuity. This fatal defect is not apparent in his exposition; but only because, as remarked in the last lecture, the whole vast problem of molecular development is lost in the haziness of the nebular theory; and, further, as we now see, is slurred over by the vagueness of such terms as “indefinite, incoherent homogeneity.” Mr. Spencer's attempt to evolve the chemical elements from prime atoms by means of the nebular hypothesis has, I believe, impressed nobody—unless it be with his failure to realise the endless complications with which such a problem is beset. But suppose this stage of evolution satisfactorily explained, still what of the prime atom? Are we to call that indefinite, incoherent, homogeneous? How can an atom be indefinite or incoherent? How, then, if we are to begin with the indefinite and incoherent, can we begin with an atom of any sort? And if we go beyond atoms to some cosmic protyle such as that of Sir William Crookes, must we not assume, too, as he suggests, that this “elementary protyle contains within itself the potentiality of every possible combining proportion or atomic weight,”17 and then how can it be homogeneous? There is, however, no end to such questions. At any rate our reflections on the kinetic ideal of matter brought us, it may be remembered, to this conclusion.
That conclusion suggests two or three further remarks on Mr. Spencer's “interpretation of evolution.” In the first place, the synthetic philosophy cannot begin at the beginning of evolution because physical analysis can never place it there. Such conceptions as prime atoms, primordial media, prima materia, and the like, are obviously ideal limits and not possibly presentable realities. In the next place, such limiting conceptions, taken alone and treated as realities, lead straightway to absurdities. We cannot begin operating with zeros and infinities, though we recognise quantities that approximate to them asymptotically. So, in like manner, qualitative diversity may be replaced by quantitative formulæ and the range of mathematical description extended without assignable limit. But such procedure is plainly one of abstraction, and—if carried to the uttermost—leaves us, as we saw, with absolutely no real content to which our numbers and diagrams apply. A real world is sublimated into “non-matter in motion.” To such epistemological reflections our synthetic philosopher seems altogether a stranger, or he could never have perpetrated the transparent absurdity, doubly an absurdity in his case, of representing any heterogeneity as arising simply—provided only there is quantitative equivalence—out of absolute homogeneity. Such homogeneity is essentially stable; and thus the first step in his scheme of evolution becomes impossible, because, in his zeal to be thorough, our author has eliminated all ground of difference. Or if he has not, he has failed to make good his undertaking, and begins not at the beginning, but with atoms having indefinitely many potentialities and distributed according to some specific configuration; in other words, begins with the manufactured articles of Herschel and Maxwell, and the collocations of Chalmers and Mill. In point of fact he begins, as said, with the ‘nebular hypothesis,’ all that goes before it being adroitly covered by the utterly unscientific and unphilosophical phrase ‘indefinite incoherent homogeneity.’
One further remark before we proceed; the proposal to start with complete homogeneity leads us to ask: How much can evolution possibly account for, and how little need it presuppose? According to Mr. Spencer's drift, it would seem that evolution, expounded in thorough, philosophical fashion, will account for all form, provided only a fixed quantity of matter and energy is given. As Professor Riehl humorously puts it: “Listen to Herbert Spencer and you must believe that literally everything there is has evolved, including forsooth even evolution itself.”18 But so long as we look at things from a purely mechanical standpoint, as Mr. Spencer does, it is difficult to see what ground there is for asserting any increase of complexity at all. Given a certain aggregate of mass-points regarded as a conservative system, then there will be a certain number of possible configurations through which it can pass; but on what grounds, I would ask, is one to be called more homogeneous or more heterogeneous than another? “The portions of which the whole is made up may be severally regarded as minor wholes,”19 says Mr. Spencer. No doubt they may be, but all such individualisation is, from a strictly mechanical standpoint, purely arbitrary. There may be teleological reasons in plenty, or what we may call methodological reasons, or reasons of practical interest; but all such grounds as these transcend the level of Mr. Spencer's primordial truth and its corollaries. Keeping strictly to that, there is only one true homogeneity, the homogeneity of an undifferentiated plenum such as Descartes or Lord Kelvin supposes. Between such a plenum and an aggregate of elements in motion there is no continuity; to secure the differentiation that an aggregate implies, a catastrophe is indispensable. But once such a system is secured, it is meaningless to call it indefinite or incoherent. A configuration cannot be indefinite; and as the forces between every pair of elements depend solely on their masses and positions, such a system is never incoherent, that is to say, is never disconnected. To the Laplacean calculator, i.e. according to what Thomson and Tait call ‘accurate mathematical investigation’ by ‘the only perfect method,’ a chunk of granite or even a whirl of dust may be just as definite, just as connected, just as heterogeneous as a chronometer or a balance, just as much a pure mechanism conforming to the laws of energy.20 Summing up on this head, then, we may say: (1) That this opposition of homogeneity and heterogeneity is essentially out of place in a rigorously mechanical theory. (2) That on such a theory it is impossible to interpret Mr. Spencer strictly when he says, “The absolutely homogeneous must lose its equilibrium and the relatively homogeneous must lapse into the relatively less homogeneous”;21 for instability is incompatible with absolute, and independent of relative, homogeneity. (3) That mere indefiniteness and incoherence entitle him to assert nothing either concerning homogeneity, or stability, or anything else.
Any one at the trouble to read at all critically the long chapter devoted to this so-called Instability of the Homogeneous, cannot fail to discover instances in plenty of what I say. Mr. Spencer's main example I may perhaps be allowed to mention, though it has been already exposed;22 for in this he flatly contradicts the very mechanical principles he has declared to be so unfathomably fundamental. Having by a series of gratuitous and sometimes erroneous suppositions got from pristine homogeneity as far as “irregular masses of slightly aggregated nebular matter” all in motion, he continues thus: “Established mechanical principles… justify the conclusions that the motions of these irregular masses…towards their common centre of gravity must be severally rendered curvilinear, by the resistance of the medium from which they were precipitated; and that in consequence of the irregularities of distribution already set up, such conflicting curvilinear motions must, by composition of forces, end in a rotation of the incipient sidereal system.”23 Now this is a gigantic and palpable blunder, one that even the least mathematically-minded might have avoided by reflecting that matter being essentially inert can hardly be conceived to set itself spinning merely because there is plenty of it. This felicitous plan for securing the rotation that Laplace was content to assume conflicts with what is technically called the Conservation of Angular Momentum; and this, it is well known, is directly deducible from Newton's third law. Now the odd thing is that Mr. Spencer—very inaccurately, to be sure—identifies the said law, that action and reaction are equal and opposite, with the law of the conservation of energy. Thus an important scene in his evolutionary drama is out of keeping with its main motive.
Of course Mr. Spencer has had no difficulty in finding instances in plenty of comparatively homogeneous states lapsing into more heterogeneous ones; and had he so minded he could have found just as many instances of ‘heterogeneous’ states lapsing into more ‘homogeneous’ ones—as he does indeed when he wishes to illustrate dissolution.24 And all such instances alike are conformable to the principle of the conservation of energy; thereby shewing, as we have already seen, that that principle is a sufficient basis for none. Whether an egg is transformed into a chicken, into an omelette, or into rottenness, one change is as much, or as little, as the other deducible from that persistence of force which Mr. Spencer always mentions with such mystic awe. Moreover, all such instances require that besides the homogeneous and unstable object or the heterogeneous and unstable object, as the case may be, there should be external forces affecting it. An egg alone in the void would neither hatch nor cook nor smell: it is on the object+external causes that the result—be it more, be it less complexity —essentially depends. Now the universe, regarded as a single object and homogeneous, has no environment, is not amenable to extraneous forces —a peculiarity that makes Mr. Spencer's instances rather refute than corroborate his main thesis, but confirms on the other hand the antithesis we have opposed to it.
Perhaps the most striking thing about Mr. Spencer's multitudinous illustrations of the transitoriness of all things homogeneous and their inevitable lapses into heterogeneity, is the looseness with which these terms are used. Thus he chooses to regard a circular orbit as homogeneous and elliptic orbits as heterogeneous, and then remarks: “All orbits, whether of planets or satellites, are more or less excentric…and were they perfect circles they would soon become ellipses. Mutual perturbations would inevitably generate excentricities. That is to say, the homogeneous relations would lapse into heterogeneous ones.”25 Now in the first place let an orbit be what it may, the relations determining it are invariable, involve no more factors at one time than at another. But even if an orbit could with propriety be called a relation, it is especially absurd in Mr. Spencer to contrast a circle which is a single figure with ellipses of which there may be an indefinite multitude. Compare an elliptic orbit of definite eccentricity with a circular orbit, which is itself an elliptic orbit of definite, i.e. zero, eccentricity, and both appear equally homogeneous and equally stable. Apropos of this a mathematical critic of Mr. Spencer, after comparing him to a man “who thought that Nature had a spite against the figure 3, because he had noticed that it was much more usual to find that a number did not end with 3 than that it did,” proceeds to remark: “Of course, if you put all elliptical orbits in one class and leave the circle to form another class by itself, it is likely that the orbit will tend to belong to the first-named class; for it can change through all possible ellipses without altering the appellation of its orbit, while the slightest variation from a circle is reflected in a change of name.”26 A blunder of this kind, though it shows how flimsy Mr. Spencer's constructions are, would scarcely be worth mention if it were isolated. Unhappily the fallacy underlying it is general and vitiates an indefinite number of ‘the great evolutionist's’ arguments; for the homogeneous is ever one and the heterogeneous always many.
Yet another instance may be mentioned in view of its subsequent importance. Mr. Spencer devotes one section of his long chapter on the Instability of the Homogeneous to what he calls “chemical differentiations.” In the course of it he illustrates the well known, but for his argument somewhat anomalous, fact that in general “simple combinations can exist at a higher temperature than complex ones,” in other words that “chemical stability decreases as chemical complexity increases,” so that for example what we ordinarily regard as chemical elements at one extreme cannot be decomposed by any heat that we can artificially produce, whereas organic compounds at the other extreme, which are extremely complex, are readily decomposed at quite moderate temperatures. Now as all ponderable matter is in some chemical state or other, and as the half of our evolutionary formula relates to redistribution of matter, this fact—that the chemically more homogeneous matter is the more stable—surely cuts a monstrous cantle out of the best of Mr. Spencer's realm.27 I say the best, for here, at any rate, the terms homogeneous and heterogeneous are strictly applicable. The strange thing, however, is that when, in a subsequent volume of his philosophy, Mr. Spencer comes to treat of the evolution of organic life, this instability of the heterogeneous becomes the mainstay of his argument.28
But why, you may wonder, does he bring it forward in a general chapter that has to prove the instability of the homogeneous, where it seems so irrelevant and inopportune? It is the earth's crust which is here the direct object of Mr. Spencer's exposition: his purpose, he says, is “to show how, in place of that comparative homogeneity of the earth's crust, chemically considered, which must have existed when its temperature was high, there has arisen during its cooling, an increasing chemical heterogeneity, each element or compound, being unable to maintain its homogeneity in presence of various surrounding affinities, having fallen into heterogeneous combinations.”29 Let us examine this argument for a moment. If the comparatively homogeneous as such is unstable, then a fortiori the altogether homogeneous should be unstable, if the argument is to be worth anything. Let us then, as we surely may, imagine the incandescent globe to have been wholly of oxygen or of silicon, ought we not then to expect that heterogeneous combinations would appear sooner and more conspicuously? Again if the instability is due to homogeneity simply, why is it essential to reduce the temperature and to insure “the presence of various surrounding affinities” before the lapse into heterogeneity can begin? Further, if the homogeneity involves instability, how comes it that once combination has begun “the stability decreases as the complexity increases?” Lastly, what warrant has Mr. Spencer for saying that “each element or compound falls into combination, being unable to maintain its homogeneity”? Does he mean that, when oxygen and hydrogen form water, or acid and base form a salt, both components disappear? How then can the combination be called heterogeneous; we should surely have a new homogeneous, presumably as unstable as before! On the whole I think we may say that while Mr. Spencer's main argument here is an instance of the “indefinite incoherent” confounding of things in themselves distinct, it incidentally opens a whole floodgate to facts very damaging to the homogeneity of his theory.
With other instances of the instability of the homogeneous supposed to be deducible from the persistence of energy, such as the development of intelligence and the desynonymisation of words, it is impossible to deal here. Mr. Spencer is considerate enough to anticipate his readers' misgivings so far as to assure them that “any difficulty felt in understanding” these and like instances “will disappear on contemplating acts of mind as nervous functions.” All such parts of Mr. Spencer's doctrine, then, may for the present stand over. There remain still two steps in what our cosmic philosopher calls the rationale of evolution, its deduction, that is to say, from the persistence of force. At each of these we must glance briefly.
To secure his first step, Mr. Spencer, as we have seen, was led to maintain that the homogeneous is essentially unstable; his second step consists in maintaining that “the effect is universally more complex than the cause.”30 “This secondary cause of change from homogeneity to heterogeneity,” he remarks, “obviously becomes more potent in proportion as the heterogeneity increases,”—in fact, “the multiplication of effects,” as he entitles his second step, must, he contends, “proceed in geometrical progression. Each stage of evolution must initiate a higher stage.” All these conclusions, of course, he proceeds as before to shew, “are not only to be established inductively, but are to be deduced from the deepest of all truths.”31 And again I can only contend that strictly interpreted this second position is as devoid of foundation as the first, and is only made to look plausible by a very loose use of leading terms and a superabundance of specious analogies.
Let us see, for instance, what Mr. Spencer means by one cause and by many effects. Here is an example. He gives a detailed description of the leading physical features of the earth,—its mountain ranges, irregular coast line, its continents, and its oceans; and then concludes by saying: “Thus endless is the accumulation of geological and geographical results slowly brought about by this one cause—the escape of the earth's primitive heat.”32 The effects, no doubt, are multitudinous enough, but on what ground is the cause accounted one? Suppose the earth to be a single gas cooling under constant pressure, or to consist entirely of one pure metal—the escape of the primitive heat could take place as before, but how many of the endless effects of this one cause would there be left? If such loose and popular language is to pass as scientific induction, it would be every whit as easy to shew that a single effect is due to a multiplicity of causes.33 The historian, for example, may in all seriousness so regard the Reformation or the French Revolution, and the more patient and pertinacious he is the more multitudinous the causes he will find for that one result.
But when causes and effects are to be deduced from a quantitative law and expressed in terms of matter and motion, we have a right to expect more precision. Mr. Spencer begins by using the language of the exact sciences, talks much of incident forces, of action and reaction being equal and opposite, and so forth, but in the end he is as careless as one quite ignorant of mechanical principles. Thus, for instance, he first describes the fracture of a stone by a hammer as a case in which a single force is changed by ‘conflict with matter’ partly into forces differing in their directions and partly into forces differing in their kinds. He then proceeds further to describe the former of these as a change of a homogeneous momentum into a group of momenta, heterogeneous in both amounts and directions. Lastly he mentions as instances of the second the sound produced, the heat disengaged, and the sparks struck off, etc. In the course of half a page force is used in three different senses—as mechanical energy, as momentum, as a physical sense-impression—and all wrong. But, above all, what is to be understood by “a conflict of force with matter?” To the physicist proper, Professor Tait say, for whom matter is essentially passive and inert, such language is nonsense; it can hardly have more meaning for a writer who, like Mr. Spencer, maintains that matter is force and nothing else. How, we wonder, by the way, did the homogeneous lapse into this kind of heterogeneity?
From the inductions, of which these are specimens, Mr. Spencer next passes to the deduction of this second step from “the deepest of all truths,” and in so doing he becomes suddenly very perfunctory. After the parallel deduction in the case of his first step, a like argument, he thinks, “seems here scarcely required,” and he is content “for symmetry's sake briefly to point out how the multiplication of effects, like the instability of the homogeneous, is a corollary from the persistence of force.” In less than two pages the thing is done, or rather not done, not even attempted—a result which in view of the flimsiness of the inductive argument is only to be regretted. What Mr. Spencer has to prove can be stated simply enough. It is that if “the quantity of Force remains always the same,” there must be, and unless the quantity of Force remains always the same, there cannot be, what he calls the multiplication of effects in geometrical progression. What he actually does, however, is merely to draw out with needless parade a proposition, which, as he is frank enough to allow “is in essence a truism,” viz., that unlike causes, or, as he prefers to say, ‘unlike forces’ will have unlike effects. To this he merely appends the remark that each different modification “must produce its equivalent reaction; and must so affect the total reaction. To say otherwise is to say this differential force will produce no effect, which is to say that force is not persistent.”34 In a word, instead of shewing that, given the persistence of energy, there must be this geometrical increase in the diversity of effects, what Mr. Spencer does is to assert that given this diversity, every effect is the equivalent transformation of its cause—which is not to deduce anything as a consequence of the law of conservation; it is only a needless reiteration of the law itself.
We come at length to the final step in the rationale of evolution. Mr. Spencer devotes to it the last chapter of his exposition of this subject, and his opening sentences ought to surprise us: “The general interpretation of Evolution,” he begins, “is far from being completed in the preceding chapters.…Thus far no reason has been assigned why there should not ordinarily arise a vague chaotic heterogeneity in place of that orderly heterogeneity displayed in Evolution.” “We have found…that the homogeneous must lapse into the heterogeneous and that the heterogeneous must become more heterogeneous.” “But,” says our author, “the laws already set forth furnish no key to this arrangement in so far as it is an advance from the indefinite to the definite.” As to the advance from the incoherent to the coherent the key to this, we must suppose, is furnished by that ‘simplest and most general aspect’ of evolution to which Mr. Spencer ascribes the mere integration or aggregation of matter. But there is, it seems, a further “local integration” or segregation of like from unlike in the heterogeneous mixture. Now it is by this process that orderly heterogeneity arises out of the vague and chaotic. Surprised as we naturally are to find ourselves thus near to the close of the great interpretation, and yet not out of the range of chaos, we await with some anxiety the rationale of this final step by which at the last moment a cosmos is secured. “The rationale,” says Mr. Spencer, “will be conveniently introduced by a few instances in which we may watch this segregative process taking place.”35
Let us be content with one and that the briefest of these instances: “In every river we see how the mixed materials, carried down, are separately deposited—how in rapids the bottom gives rest to nothing but boulders and pebbles; how when the current is not so strong, sand is let fall; and how, in still places, there is a sediment of mud.”36 After this and other introductory instances and an assurance that there are countless similar ones, we have the following generalisation: “In each case we see in action a force which may be regarded as simple or uniform —fluid motion in a certain direction at a certain velocity.… In each case we have an aggregate made up of unlike units—unlike in their specific gravities, shapes, or other attributes.… And in each case these unlike units or groups of units, of which the aggregate consists, are, under the influence of some resultant force, acting indiscriminately on them all, separated from each other—segregated into minor aggregates, each consisting of units that are severally like each other and unlike those of the other minor aggregates.”37 Thus we see that even the transition from the indefinite to the definite, from the vague and chaotic to the cosmical and orderly, is assigned to “force acting indiscriminately.” Mens agitat molem is a maxim for which the mechanical theory of evolution has nowhere a place. It is at any rate satisfactory to come to the end and be clear on this point. But I must defer general reflections till the next lecture. For the present let us be content with briefly considering how this indiscriminate sifting process will work in conjunction with the other two.
A good deal will depend on their respective intensities, how they are matched against each other; for it is obvious that in several respects the process of segregation will counterwork the two other causes of evolution. Thus, in producing local integrations of like units, it must act counter to the instability of the homogeneous, according to which the like lapses into the unlike. In so doing, again, it will frustrate the multiplication of effects within the limits of such local integration, for this is efficient ‘in proportion as the parts are unlike.”38 Imagine segregation to have been in full play while the existing chemical elements of the solar system, though present in the nebula, were still uncombined, and that in consequence these elements were separated into minor aggregates severally like each other and unlike the rest—those of high specific gravity or strong physical likeness near together and the unlike far apart. Thus the conceit of the alchemists that the seven metals correspond to the seven planets might have been realised; and as to the gases, oxygen, hydrogen, nitrogen, indispensable constituents of living things—they might have been sifted off into space before planetary consolidation began. We know of course that this has not happened or we should not be here. But if Mr. Spencer's principle of segregation is really the potent factor in evolution that he takes it to be, it is at least remarkable to find that with a whole nebula as a field for its activity and untold ages in which to work, it has nevertheless left no trace of itself. Let me quote an excellent authority. “We do not find them [i.e. the chemical elements],” said Sir William Crookes in his British Association Address, “evenly distributed throughout the globe. Nor are they associated in accordance with their specific gravities, the lighter elements placed on or near the surface and the heavier ones following serially deeper. Neither can we trace any distinct relation between local climate and mineral distribution. And by no means can we say that elements are always or chiefly associated in nature in the order of their so-called chemical affinities: those which have a strong tendency to form with each other definite chemical combinations being found together, while those which have little or no such tendency exist apart.” Then definitely raising the question,—but without any reference to Mr. Spencer, let me say,—“Is there any power which regularly and systematically sorts out the different kinds of matter from promiscuous heaps, conveying like to like and separating unlike from unlike?” this distinguished chemist answers: “I must confess that I fail to trace any such distributive agency, nor indeed, do I feel able to form any distinct conception of its nature.”39 Surely Mr. Spencer should have had something to say to this, but though his new edition has an admirable index, there is no mention of Sir W. Crookes.
One other point as to the relation of the two chaotic or differentiating processes to this cosmic, selectively integrating, principle. At first blush the situation reminds us of that intellectual guidance referred to in the last lecture, when we were distinguishing teleological from mechanical evolution. When human ingenuity constructs a machine or a house, or when Maxwell's sorting demon separates molecules moving with more than average velocity from those moving with less, the processes are what Mr. Spencer might call processes of segregation and local integration. But they differ from Mr. Spencer's process in several respects. First, the result is secured, not by a force acting indiscriminately, but by intelligence counterworking the downhill trend of energy towards dissipation. Also in the case of the products of human skill the result is rather that unlike things are brought together than that unlike things are separated. Nowhere do we find so little segregation, in the sense of Mr. Spencer's sifting and winnowing processes, as in living organisms and the products of human industry. Lastly, organisms and machines are not aggregates of aggregates, but individuals consisting of members. Spite of these essential differences, Mr. Spencer, no doubt, thinks mechanical segregation will cover both, and it must be confessed that by sufficient license in the use of the term ‘force’ and the free substitution of unit for fragment, individual for aggregate, and the like, the task is feasible,—and the result quite worthless. When sparks rise and dust falls we say each moves along the line of least resistance, their densities and gravitation being the segregating forces; and when the virtuous man ‘rises’ and the vicious ‘falls’ we may, if we like, say again that each follows the line of least resistance, and may call their desires and public opinion the segregating forces. This is what Mr. Spencer does like to do; it is what he calls synthetic philosophy.
First Principles, § 145, stereo. ed., p. 396; rev. ed., p. 367, altered.
First Principles, § 147, stereo. ed., p. 398; rev. ed., p. 369.
First Principles, § 62, stereo. ed., p. 192; omitted in rev. ed.
Erhaltung der Kraft. Ostwald's edition, p. 53.
First Principles, § 192, stereo. ed., p. 553; rev. ed., p. 508.
First Principles, § 60, stereo. ed., p. 189; rev. ed., § 62, p. 175, very much altered.
Note iv.—Mr. Spencer (Fortnightly, p. 899) sees nothing but a comment on his mode of writing in this reference to the distinction between Force and force. “Supposing even,” he says, “that capitals were in such cases inappropriate … only one with a strong animus would have gone out of his way to notice it.” But obviously my point is that Mr. Spencer's usually correct mode of writing serves to indicate the essential difference between Force as Absolute, which does not, and force as phenomenal, which does, admit of measurement.
The confusions and the inconsistencies of Mr. Spencer's exposition of his fundamental principle are incredible. I have dealt with them at some length in my Reply to him (Fortnightly, 465-467); I will quote here only the last paragraph:—
“Now I have contended that it is meaningless to apply quantitative notions to an Absolute Force, alias Ultimate Cause, alias Unconditional Reality, especially meaningless when it is only an Unknowable that ‘we are irresistibly compelled by the relativity of our thought to vaguely conceive,’ etc. (F. P. p. 170). Moreover, returning to the chapter on Relativity, to which chapter Mr. Spencer himself seems to direct us (cf. F. P. p. 91), we find that he, too, allows that it is ‘impossible to give to this consciousness [of the Non-Relative or Absolute] any qualitative or quantitative expression whatever.’ If now we agree with Mr. Spencer that ‘definite conclusions can be reached only by the use of well-defined terms,’ may we not reasonably ask how ‘the phenomena of evolution’ can be as he says they ‘have to be, deduced from the Persistence of Force,’ when this Force turns out to be the Non-Relative or Absolute? (cf. F. P. p. 398). For ‘this non-relative spoken of as a necessary complement to the Relative is not spoken of,’ Mr. Spencer reminds us, ‘as a conception but as a consciousness; and I have,’ he continues, “in sundry passages distinguished between those modes of consciousness which, having limits, and constituting thought proper, are subject to the laws of thought, and the mode of consciousness which persists when the removal of limits is carried to the uttermost, and when distinct thought consequently ceases’ (Replies to Criticisms, p. 252). What have we got here more than the bare notion of pure being? How are we going to deduce the ‘Instability of the Homogeneous,” or ‘Equilibration’ from this ‘indefinite consciousness of the unformed and unlimited’? How, indeed, save as everything that is, let it be what it may, is implied in an Ultimate Cause and included under the category of Existence? The force of a blow and the force of an argument, nay, any two things whatever, will have their equivalents in this ‘pure Force.’ But what ‘transcends experience’ can never be ‘the basis of any scientific organisation of experience’ (cf. F. P. p. 192). Between Force = Ultimate Cause and force = energy Mr. Spencer's cosmic philosophy is, I have contended, bound to fall. But he has not deigned to notice my argument, yet in replying to Mr. Moulton he advances one of these meanings, and in replying to me he advances the other.”
Metaphysik, 1879, § 209.
First Principles, § 191, stereo. ed., p. 552; rev. ed., p. 507.
First Principles, § 50, stereo. ed., p. 170; rev. ed., omitted.
First Principles, § 63, stereo. ed., p. 193; rev. ed., p. 177.
First Principles, § 65, stereo. ed., p. 195; rev. ed., omitted.
First Principles, §§ 149, 155, stereo. ed., pp. 400, 429; rev. ed., pp. 372, 397, altered.
Note v.—In the earlier editions of his First Principles Mr. Spencer's philosophy, as a complete unification of the knowable, professes to set before us the evolution of the universe from beginning to end, i.e. from the imperceptible to the imperceptible. “ Philosophy has to formulate this passage,” for “wherever we now find Being so conditioned as to act on our senses, there arise the questions—how came it to be thus conditioned? and how will it cease to be thus conditioned?… Hence our Theory of Things, considered individually and in their totality, is confessedly incomplete, so long as any past or future portions of their sensible existences are unaccounted for.” The start accordingly is made with the absolutely homogeneous, since no other state would necessarily be imperceptible, and any heterogeneity would have to ‘be accounted for.’ But “some rearrangement [of the absolutely homogeneous] must result,” Mr. Spencer has said. Certainly there would be no evolution otherwise: so we reach the proposition that “the absolutely homogeneous must lose its equilibrium.”
But in the revised edition Mr. Spencer, as we have already seen, drops the universe and omits alike the beginning and the end of the evolutionary process. And now we find that he also parts with the absolutely homogeneous. He makes all these renunciations, however, in a very vacillating fashion, like one unwilling to abandon an ancient domain. Thus “only at the last moment, when…all the rest of the volume is standing in type,” he perceives that his, “definition of Evolution needs qualifying by the introduction of the word ‘relatively’ before, each of its antithetical clauses,” and in an appendix he gives his reasons for the change (see the Note, rev. ed. p. 367). In the said appendix (App. A) he tells us that “the transformation we call Evolution must be regarded as falling between two ideal limits, neither of which is reached”! (rev. ed. p. 514). Nevertheless he still maintains that “the absolutely homogeneous (supposing it to exist) must lose its equilibrium” (rev. ed. p. 397italics mine). ‘Now, since even Mr. Spencer's revised theory of evolution begins with relative homogeneity—and instability, and ends with relative heterogeneity—and equilibration, one might suppose that the instability of the absolutely homogeneous—or the ideal initial limit—was still inferred from his empirical formula. If, proceeding forwards, “the relatively homogeneous must lapse into the relatively less homogeneous”—and this is still maintained—then surely, regressing backwards, the relatively less homogeneous must arise from the relatively more homogeneous, and so the absolutely homogeneous, absolutely unstable, might still be regarded at least ideally as the beginning of evolution. How else are we to interpret the two extremes between which all evolution lies—indefinite, incoherent homogeneity, with potential energy a maximum, and definite, coherent heterogeneity with all the energy dissipated? But such an interpretation Mr. Spencer, it seems, never intended, and now emphatically disavows. “No special instability,” he now maintains, “characterizes the homogeneous.” By way of emphasising this still further he has even amended the title of the chapter in which he expounds this principle; it is now headed, The Instability of the Homogeneous, exemplifying Instability at large, and the principle itself is reduced to “a corollary from the truth that change is universal and unceasing”(App. A, p. 515). But we are now at a loss to know why “the more homogeneous must tend ever to become less homogeneous,” and the ‘lapse’ in the opposite direction be an impossibility. We are well aware, of course, that there are instances in plenty of changes in both directions, when only parts of the universe are regarded—even what to us are very large parts; but Mr. Spencer's philosophy still implies that for the universe as a whole in its evolutionary phase the change is only in one direction. He still speaks of the instability of the homogeneous as “one end of the series of metamorphoses,” and because of “the universality of this perpetual increase of structure” finds it “requisite to begin with the structureless ” (App. A, p. 516). On the whole Mr. Spencer now leaves us more puzzled than ever to find any necessary connexion between “those traits which celestial bodies, organisms, societies, alike display” and “instability at large.” It is a long step from such instability, or “the truth that change is universal and unceasing,” to “the one increasing purpose” which evolution implies. The most effectual refutation of Mr. Spencer is surely here supplied by himself!
Cf. pp. 133 f. above.
Unseen Universe, 2nd ed., p. 117.
Address at Brit. Assn., 1886, Nature, vol. xxxiv, p. 428
Der philosophische Kriticismus, Bd. ii, 2te Th. p. 75.
First Principles, § 155, stereo. ed., p. 428; rev. ed., p. 396.
Note vi.—Mr. Spencer, of course, cannot accept what he is pleased to call my “dictum respecting the utterly unscientific and unphilosophical phrase ‘indefinite incoherent homogeneity.’” But the only reply he makes to my reasons for this ‘dictum’ is to ask whether it is not proper to describe an egg as more homogeneous than the chicken which evolves from it. The egg is a great stand-by of Mr. Spencer's: he has hurled it against opponents more than once before. But here it altogether misses the mark: so far as his attack is relevant, I will try to rebut it presently. The immediate question, however, is the meaning of indefinite, incoherent homogeneity. I maintain it to be meaningless, and it is for Mr. Spencer, if he can, to point out a case in which it is not. An egg, even if regarded as homogeneous, is not, from the standpoint of the synthetic philosophy, such a case; and what is more important, a nebula also is not. In terms of matter and motion, both are perfectly definite in configuration and dynamically coherent—no part can move independently of the rest. And coming now to Mr. Spencer's question, I reply that from the standpoint of his theory it is not proper to describe an egg as more homogeneous than the chicken which is hatched from it. Both are but different arrangements of the same elements as truly as Bceeeehnprrrst and Herbert Spencer are but different arrangements of the same letters. It may be easier to halve the egg than to halve the chicken, but to dissipate the egg into the imperceptibility of matter primeval would be as hard as dissipating the chicken: both in that respect are equally far removed from the structureless.
Spite of this Mr. Spencer, in an earlier foot-note, cuts away the ground from under his own feet by bargaining that “the terms here used must be understood in a relative sense.” Cf. § 116, stereo. ed., p. 330; rev. ed., p. 302.
Cf. British Quarterly Review, 1873, vol. 58.
First Principles, § 150, stereo. ed., p. 407; rev. ed., p. 377, altered.
Note vii.—Dr. Venn (Empirical Logic, p. 109) had, I find, already called attention to the weakness of Mr. Spencer's argument here.
First Principles, § 150, stereo. ed., p. 410; rev. ed., omitted.
British Quarterly Review, article above referred to.
- 27. Our author elsewhere (§ 101) accounts for this greater stability of what is chemically homogeneous by asserting the comparative absence from it of “contained motion.” But even this surrenders the point that the homogeneous, merely as homogeneous, is unstable. It suggests, indeed, the precisely opposite conclusion.
- 28. Note viii.—In his revised edition Mr. Spencer devotes two closely printed pages to this paragraph. Some of his points in this defence have been already incidentally dealt with in the preceding notes. But there are one or two that perhaps call for some reply. “I might urge,” he begins, “that since the law of evolution, as everywhere represented by me, is a law of the re-distribution of matter and motion within sensible aggregates, and not as a law of re-distribution within their insensible molecules, it might suffice for its establishment were it proved applicable to the first without taking any note of the last” (rev. ed., App. C, p. 535). He then objects that I have “ignored entirely the distinction between simple and compound evolution,” and explains that the latter is only possible when the process of evolution is slow, and when “there continues a partial mobility among the concentrating units.” “Ignoring this fundamental distinction, Professor Ward,” he says, “has assumed that chemical units are aggregates, which can present this secondary re-distribution; whereas, as he knows, they are aggregates suddenly formed, and, if considered as evolved, can exhibit only that simple evolution seen in the integration of matter and dissipation of motion: the contrast between homogeneity and heterogeneity cannot arise” (rev. ed., p. 535—italics mine). For my part, I must disclaim this ‘knowledge’ with which Mr. Spencer credits me: I fancy every school-boy knows better. Has Mr. Spencer, we wonder, forgotten the difference between old wine and new, or Nature's slow elaboration of the juices of fruits and the scents of flowers? Have starch, sugar, albumen, no history? In particular, if molecules never retain ‘a partial mobility among their concentrating units’ what becomes of Mrs. Spencer's ingenious theory concerning ‘certain specific molecules’ which he has called ‘physiological units’: and if they exemplify simple evolution merely, what was to fill the two missing volumes devoted to pre-organic evolution? Nay, if it be a question whether chemical units are to be ‘considered as evolved,’ and if evolution, as everywhere expounded by Mr. Spencer, is a law applicable only to sensible aggregates and not to their insensible molecules, is there anything missing in the Synthetic Philosophy after all? But then how came Mr. Spencer to say: “The evolution of the elements, if not systematically dealt with within the limits of the Synthetic Philosophy, has not been ignored. In an essay on ‘The Nebular Hypothesis’ five groups of traits are enumerated which support the belief that they originated by a process of evolution like that everywhere going on” (Fortnightly Review, l.c. p. 900)?
First Principles, § 151, stereo. ed., p. 411; rev, ed., p. 380, all after ‘heterogeneity’ omitted.
First Principles, § 156, stereo. ed., p. 433.
First Principles, § 162, stereo. ed., p. 458.
First Principles, § 158, stereo. ed., p. 438.
Note ix.—In this criticism, again, it has been pointed out to me, that I have been anticipated. Cf. Mr. F. H. Bradley's Principles of Logic, p. 496.
First Principles, § 162, stereo. ed., p. 457; rev. ed., p. 422.
First Principles, § 163, stereo. ed., p. 459; rev. ed., p. 423.
First Principles, § 163, stereo. ed., p. 460; rev. ed., p. 424.
First Principles, § 163, stereo. ed., p. 461; rev. ed., p. 425. Italics mine.
First Principles, § 162, stereo. ed., p. 458; rev. ed., p. 422.
Nature, 1886, vol. xxxiv, pp. 425 f.