Eureka: A Prose Poem

And now, let us see: – Our usual notions of irradiation – in fact all our distinct notions of it – are caught merely from the process as we see it exemplified in Light. Here there is a continuous outpouring of ray-streams, and with a force which we have at least no right to suppose varies at all. Now, in any such irradiation as this– continuous and of unvarying force – the regions nearer the centre must inevitably be always more crowded with the irradiated matter than the regions more remote. But I have assumed no such irradiation as this. I assumed no continuous irradiation; and for the simple reason that such an assumption would have involved, first, the necessity of entertaining a conception which I have shown no man can entertain, and which (as I will more fully explain hereafter) all observation of the firmament refutes – the conception of the absolute infinity of the Universe of stars – and would have involved, secondly, the impossibility of understanding a rëaction – that is, gravitation – as existing now – since, while an act is continued, no rëaction, of course, can take place. My assumption, then, or rather my inevitable deduction from just premises – was that of a determinate irradiation – one finally discontinued.

Let me now describe the sole possible mode in which it is conceivable that matter could have been diffused through space, so as to fulfil the conditions at once of irradiation and of generally equable distribution.

For convenience of illustration, let us imagine, in the first place, a hollow sphere of glass, or of anything else, occupying the space throughout which the universal matter is to be thus equally diffused, by means of irradiation, from the absolute, irrelative, unconditional particle, placed in the centre of the sphere.

Now, a certain exertion of the diffusive power (presumed to be the Divine Volition) – in other words, a certain force– whose measure is the quantity of matter – that is to say, the number of atoms – emitted; emits, by irradiation, this certain number of atoms; forcing them in all directions outwardly from the centre – their proximity to each other diminishing as they proceed – until, finally, they are distributed, loosely, over the interior surface of the sphere.

When these atoms have attained this position, or while proceeding to attain it, a second and inferior exercise of the same force – or a second and inferior force of the same character – emits, in the same manner – that is to say, by irradiation as before – a second stratum of atoms which proceeds to deposit itself upon the first; the number of atoms, in this case as in the former, being of course the measure of the force which emitted them; in other words the force being precisely adapted to the purpose it effects – the force and the number of atoms sent out by the force, being directly proportional.

When this second stratum has reached its destined position – or while approaching it – a third still inferior exertion of the force, or a third inferior force of a similar character – the number of atoms emitted being in all cases the measure of the force – proceeds to deposit a third stratum upon the second: – and so on, until these concentric strata, growing gradually less and less, come down at length to the central point; and the diffusive matter, simultaneously with the diffusive force, is exhausted.

We have now the sphere filled, through means of irradiation, with atoms equably diffused. The two necessary conditions – those of irradiation and of equable diffusion – are satisfied; and by the sole process in which the possibility of their simultaneous satisfaction is conceivable. For this reason, I confidently expect to find, lurking in the present condition of the atoms as distributed throughout the sphere, the secret of which I am in search – the all-important principle of the modus operandi of the Newtonian law. Let us examine, then, the actual condition of the atoms.

They lie in a series of concentric strata. They are equably diffused throughout the sphere. They have been irradiated into these states.

The atoms being equably distributed, the greater the superficial extent of any of these concentric strata, or spheres, the more atoms will lie upon it. In other words, the number of atoms lying upon the surface of any one of the concentric spheres, is directly proportional with the extent of that surface.

But, in any series of concentric spheres, the surfaces are directly proportional with the squares of the distances from the centre.[2 - Succinctly – The surfaces of spheres are as the squares of their radii.]

Therefore the number of atoms in any stratum is directly proportional with the square of that stratum’s distance from the centre.

But the number of atoms in any stratum is the measure of the force which emitted that stratum – that is to say, is directly proportional with the force.

Therefore the force which irradiated any stratum is directly proportional with the square of that stratum’s distance from the centre: – or, generally,

The force of the irradiation has been directly proportional with the squares of the distances.

Now, Rëaction, as far as we know anything of it, is Action conversed. The general principle of Gravity being, in the first place, understood as the rëaction of an act – as the expression of a desire on the part of Matter, while existing in a state of diffusion, to return into the Unity whence it was diffused; and, in the second place, the mind being called upon to determine the character of the desire – the manner in which it would, naturally, be manifested; in other words, being called upon to conceive a probable law, or modus operandi, for the return; could not well help arriving at the conclusion that this law of return would be precisely the converse of the law of departure. That such would be the case, any one, at least, would be abundantly justified in taking for granted, until such time as some person should suggest something like a plausible reason why it should not be the case – until such period as a law of return shall be imagined which the intellect can consider as preferable.

Matter, then, irradiated into space with a force varying as the squares of the distances, might, à priori, be supposed to return towards its centre of irradiation with a force varying inversely as the squares of the distances: and I have already shown[3 - Page 44. (#x_1_i111)] that any principle which will explain why the atoms should tend, according to any law, to the general centre, must be admitted as satisfactorily explaining, at the same time, why, according to the same law, they should tend each to each. For, in fact, the tendency to the general centre is not to a centre as such, but because of its being a point in tending towards which each atom tends most directly to its real and essential centre, Unity– the absolute and final Union of all.

The consideration here involved presents to my own mind no embarrassment whatever – but this fact does not blind me to the possibility of its being obscure to those who may have been less in the habit of dealing with abstractions: – and, upon the whole, it may be as well to look at the matter from one or two other points of view.

The absolute, irrelative particle primarily created by the Volition of God, must have been in a condition of positive normality, or rightfulness – for wrongfulness implies relation. Right is positive; wrong is negative – is merely the negation of right; as cold is the negation of heat – darkness of light. That a thing may be wrong, it is necessary that there be some other thing in relation to which it is wrong – some condition which it fails to satisfy; some law which it violates; some being whom it aggrieves. If there be no such being, law, or condition, in respect to which the thing is wrong – and, still more especially, if no beings, laws, or conditions exist at all – then the thing cannot be wrong and consequently must be right. Any deviation from normality involves a tendency to return into it. A difference from the normal – from the right – from the just – can be understood as effected only by the overcoming a difficulty; and if the force which overcomes the difficulty be not infinitely continued, the ineradicable tendency to return will at length be permitted to act for its own satisfaction. Upon withdrawal of the force, the tendency acts. This is the principle of rëaction as the inevitable consequence of finite action. Employing a phraseology of which the seeming affectation will be pardoned for its expressiveness, we may say that Rëaction is the return from the condition of as it is and ought not to be into the condition of as it was, originally, and therefore ought to be: – and let me add here that the absolute force of Rëaction would no doubt be always found in direct proportion with the reality – the truth – the absoluteness – of the originality– if ever it were possible to measure this latter: – and, consequently, the greatest of all conceivable reactions must be that produced by the tendency which we now discuss – the tendency to return into the absolutely original– into the supremely primitive. Gravity, then, must be the strongest of forces– an idea reached à priori and abundantly confirmed by induction. What use I make of the idea, will be seen in the sequel.

The atoms, now, having been diffused from their normal condition of Unity, seek to return to – what? Not to any particular point, certainly; for it is clear that if, upon the diffusion, the whole Universe of matter had been projected, collectively, to a distance from the point of irradiation, the atomic tendency to the general centre of the sphere would not have been disturbed in the least: – the atoms would not have sought the point in absolute space from which they were originally impelled. It is merely the condition, and not the point or locality at which this condition took its rise, that these atoms seek to re-establish; – it is merely that condition which is their normality, that they desire. “But they seek a centre,” it will be said, “and a centre is a point.” True; but they seek this point not in its character of point – (for, were the whole sphere moved from its position, they would seek, equally, the centre; and the centre then would be a new point) – but because it so happens, on account of the form in which they collectively exist – (that of the sphere) – that only through the point in question – the sphere’s centre – they can attain their true object, Unity. In the direction of the centre each atom perceives more atoms than in any other direction. Each atom is impelled towards the centre because along the straight line joining it and the centre and passing on to the circumference beyond, there lie a greater number of atoms than along any other straight line – a greater number of objects that seek it, the individual atom – a greater number of tendencies to Unity – a greater number of satisfactions for its own tendency to Unity – in a word, because in the direction of the centre lies the utmost possibility of satisfaction, generally, for its own individual appetite. To be brief, the condition, Unity, is all that is really sought; and if the atoms seem to seek the centre of the sphere, it is only impliedly, through implication – because such centre happens to imply, to include, or to involve, the only essential centre, Unity. But on account of this implication or involution, there is no possibility of practically separating the tendency to Unity in the abstract, from the tendency to the concrete centre. Thus the tendency of the atoms to the general centre is, to all practical intents and for all logical purposes, the tendency each to each; and the tendency each to each is the tendency to the centre; and the one tendency may be assumed as the other; whatever will apply to the one must be thoroughly applicable to the other; and, in conclusion, whatever principle will satisfactorily explain the one, cannot be questioned as an explanation of the other.

In looking carefully around me for rational objection to what I have advanced, I am able to discover nothing; – but of that class of objections usually urged by the doubters for Doubt’s sake, I very readily perceive three; and proceed to dispose of them in order.

It may be said, first: “The proof that the force of irradiation (in the case described) is directly proportional to the squares of the distances, depends upon an unwarranted assumption – that of the number of atoms in each stratum being the measure of the force with which they are emitted.”

I reply, not only that I am warranted in such assumption, but that I should be utterly unwarranted in any other. What I assume is, simply, that an effect is the measure of its cause – that every exercise of the Divine Will will be proportional to that which demands the exertion – that the means of Omnipotence, or of Omniscience, will be exactly adapted to its purposes. Neither can a deficiency nor an excess of cause bring to pass any effect. Had the force which irradiated any stratum to its position, been either more or less than was needed for the purpose – that is to say, not directly proportional to the purpose – then to its position that stratum could not have been irradiated. Had the force which, with a view to general equability of distribution, emitted the proper number of atoms for each stratum, been not directly proportional to the number, then the number would not have been the number demanded for the equable distribution.

The second supposable objection is somewhat better entitled to an answer.

It is an admitted principle in Dynamics that every body, on receiving an impulse, or disposition to move, will move onward in a straight line, in the direction imparted by the impelling force, until deflected, or stopped, by some other force. How then, it may be asked, is my first or external stratum of atoms to be understood as discontinuing their movement at the circumference of the imaginary glass sphere, when no second force, of more than an imaginary character, appears, to account for the discontinuance?

I reply that the objection, in this case, actually does arise out of “an unwarranted assumption” – on the part of the objector – the assumption of a principle, in Dynamics, at an epoch when no “principles,” in anything, exist: – I use the word “principle,” of course, in the objector’s understanding of the word.

“In the beginning” we can admit – indeed we can comprehend – but one First Cause– the truly ultimate Principle– the Volition of God. The primary act– that of Irradiation from Unity – must have been independent of all that which the world now calls “principle” – because all that we so designate is but a consequence of the rëaction of that primary act: – I say “primary” act; for the creation of the absolute material particle is more properly to be regarded as a conception than as an “act” in the ordinary meaning of the term. Thus, we must regard the primary act as an act for the establishment of what we now call “principles.” But this primary act itself is to be considered as continuous Volition. The Thought of God is to be understood as originating the Diffusion – as proceeding with it – as regulating it – and, finally, as being withdrawn from it upon its completion. Then commences Rëaction, and through Rëaction, “Principle,” as we employ the word. It will be advisable, however, to limit the application of this word to the two immediate results of the discontinuance of the Divine Volition – that is, to the two agents, Attraction and Repulsion. Every other Natural agent depends, either more or less immediately, upon these two, and therefore would be more conveniently designated as sub-principle.

It may be objected, thirdly, that, in general, the peculiar mode of distribution which I have suggested for the atoms, is “an hypothesis and nothing more.”

Now, I am aware that the word hypothesis is a ponderous sledge-hammer, grasped immediately, if not lifted, by all very diminutive thinkers, upon the first appearance of any proposition wearing, in any particular, the garb of a theory. But “hypothesis” cannot be wielded here to any good purpose, even by those who succeed in lifting it – little men or great.

I maintain, first, that only in the mode described is it conceivable that Matter could have been diffused so as to fulfil at once the conditions of irradiation and of generally equable distribution. I maintain, secondly, that these conditions themselves have been imposed upon me, as necessities, in a train of ratiocination as rigorously logical as that which establishes any demonstration in Euclid; and I maintain, thirdly, that even if the charge of “hypothesis” were as fully sustained as it is, in fact, unsustained and untenable, still the validity and indisputability of my result would not, even in the slightest particular, be disturbed.

To explain: – The Newtonian Gravity – a law of Nature – a law whose existence as such no one out of Bedlam questions – a law whose admission as such enables us to account for nine-tenths of the Universal phænomena – a law which, merely because it does so enable us to account for these phænomena, we are perfectly willing, without reference to any other considerations, to admit, and cannot help admitting, as a law – a law, nevertheless, of which neither the principle nor the modus operandi of the principle, has ever yet been traced by the human analysis – a law, in short, which, neither in its detail nor in its generality, has been found susceptible of explanation at all– is at length seen to be at every point thoroughly explicable, provided only we yield our assent to – what? To an hypothesis? Why if an hypothesis – if the merest hypothesis – if an hypothesis for whose assumption – as in the case of that pure hypothesis the Newtonian law itself – no shadow of à priori reason could be assigned – if an hypothesis, even so absolute as all this implies, would enable us to perceive a principle for the Newtonian law – would enable us to understand as satisfied, conditions so miraculously – so ineffably complex and seemingly irreconcileable as those involved in the relations of which Gravity tells us, – what rational being could so expose his fatuity as to call even this absolute hypothesis an hypothesis any longer – unless, indeed, he were to persist in so calling it, with the understanding that he did so, simply for the sake of consistency in words?

But what is the true state of our present case? What is the fact? Not only that it is not an hypothesis which we are required to adopt, in order to admit the principle at issue explained, but that it is a logical conclusion which we are requested not to adopt if we can avoid it – which we are simply invited to deny if we can: – a conclusion of so accurate a logicality that to dispute it would be the effort – to doubt its validity beyond our power: – a conclusion from which we see no mode of escape, turn as we will; a result which confronts us either at the end of an inductive journey from the phænomena of the very Law discussed, or at the close of a deductive career from the most rigorously simple of all conceivable assumptions —the assumption, in a word, of Simplicity itself.

And if here, for the mere sake of cavilling, it be urged, that although my starting-point is, as I assert, the assumption of absolute Simplicity, yet Simplicity, considered merely in itself, is no axiom; and that only deductions from axioms are indisputable – it is thus that I reply: —

Every other science than Logic is the science of certain concrete relations. Arithmetic, for example, is the science of the relations of number – Geometry, of the relations of form – Mathematics in general, of the relations of quantity in general – of whatever can be increased or diminished. Logic, however, is the science of Relation in the abstract – of absolute Relation – of Relation considered solely in itself. An axiom in any particular science other than Logic is, thus, merely a proposition announcing certain concrete relations which seem to be too obvious for dispute – as when we say, for instance, that the whole is greater than its part: – and, thus again, the principle of the Logical axiom – in other words, of an axiom in the abstract – is, simply, obviousness of relation. Now, it is clear, not only that what is obvious to one mind may not be obvious to another, but that what is obvious to one mind at one epoch, may be anything but obvious, at another epoch, to the same mind. It is clear, moreover, that what, to-day, is obvious even to the majority of mankind, or to the majority of the best intellects of mankind, may to-morrow be, to either majority, more or less obvious, or in no respect obvious at all. It is seen, then, that the axiomatic principle itself is susceptible of variation, and of course that axioms are susceptible of similar change. Being mutable, the “truths” which grow out of them are necessarily mutable too; or, in other words, are never to be positively depended upon as truths at all – since Truth and Immutability are one.

It will now be readily understood that no axiomatic idea – no idea founded in the fluctuating principle, obviousness of relation – can possibly be so secure – so reliable a basis for any structure erected by the Reason, as that idea – (whatever it is, wherever we can find it, or if it be practicable to find it anywhere) – which is irrelative altogether – which not only presents to the understanding no obviousness of relation, either greater or less, to be considered, but subjects the intellect, not in the slightest degree, to the necessity of even looking at any relation at all. If such an idea be not what we too heedlessly term “an axiom,” it is at least preferable, as a Logical basis, to any axiom ever propounded, or to all imaginable axioms combined: – and such, precisely, is the idea with which my deductive process, so thoroughly corroborated by induction, commences. My particle proper is but absolute Irrelation. To sum up what has been here advanced: – As a starting point I have taken it for granted, simply, that the Beginning had nothing behind it or before it – that it was a Beginning in fact – that it was a beginning and nothing different from a beginning – in short that this Beginning was —that which it was. If this be a “mere assumption” then a “mere assumption” let it be.

To conclude this branch of the subject: – I am fully warranted in announcing that the Law which we have been in the habit of calling Gravity exists on account of Matter’s having been irradiated, at its origin, atomically, into a limited[4 - Limited sphere – A sphere is necessarily limited. I prefer tautology to a chance of misconception.] sphere of Space, from one, individual, unconditional, irrelative, and absolute Particle Proper, by the sole process in which it was possible to satisfy, at the same time, the two conditions, irradiation, and generally-equable distribution throughout the sphere – that is to say, by a force varying in direct proportion with the squares of the distances between the irradiated atoms, respectively, and the Particular centre of Irradiation.

I have already given my reasons for presuming Matter to have been diffused by a determinate rather than by a continuous or infinitely continued force. Supposing a continuous force, we should be unable, in the first place, to comprehend a rëaction at all; and we should be required, in the second place, to entertain the impossible conception of an infinite extension of Matter. Not to dwell upon the impossibility of the conception, the infinite extension of Matter is an idea which, if not positively disproved, is at least not in any respect warranted by telescopic observation of the stars – a point to be explained more fully hereafter; and this empirical reason for believing in the original finity of Matter is unempirically confirmed. For example: – Admitting, for the moment, the possibility of understanding Space filled with the irradiated atoms – that is to say, admitting, as well as we can, for argument’s sake, that the succession of the irradiated atoms had absolutely no end– then it is abundantly clear that, even when the Volition of God had been withdrawn from them, and thus the tendency to return into Unity permitted (abstractly) to be satisfied, this permission would have been nugatory and invalid – practically valueless and of no effect whatever. No Rëaction could have taken place; no movement toward Unity could have been made; no Law of Gravity could have obtained.

To explain: – Grant the abstract tendency of any one atom to any one other as the inevitable result of diffusion from the normal Unity: – or, what is the same thing, admit any given atom as proposing to move in any given direction – it is clear that, since there is an infinity of atoms on all sides of the atom proposing to move, it never can actually move toward the satisfaction of its tendency in the direction given, on account of a precisely equal and counterbalancing tendency in the direction diametrically opposite. In other words, exactly as many tendencies to Unity are behind the hesitating atom as before it; for it is a mere sotticism to say that one infinite line is longer or shorter than another infinite line, or that one infinite number is greater or less than another number that is infinite. Thus the atom in question must remain stationary forever. Under the impossible circumstances which we have been merely endeavoring to conceive for argument’s sake, there could have been no aggregation of Matter – no stars – no worlds – nothing but a perpetually atomic and inconsequential Universe. In fact, view it as we will, the whole idea of unlimited Matter is not only untenable, but impossible and preposterous.

With the understanding of a sphere of atoms, however, we perceive, at once, a satisfiable tendency to union. The general result of the tendency each to each, being a tendency of all to the centre, the general process of condensation, or approximation, commences immediately, by a common and simultaneous movement, on withdrawal of the Divine Volition; the individual approximations, or coalescences —not cöalitions – of atom with atom, being subject to almost infinite variations of time, degree, and condition, on account of the excessive multiplicity of relation, arising from the differences of form assumed as characterizing the atoms at the moment of their quitting the Particle Proper; as well as from the subsequent particular inequidistance, each from each.

What I wish to impress upon the reader is the certainty of there arising, at once, (on withdrawal of the diffusive force, or Divine Volition,) out of the condition of the atoms as described, at innumerable points throughout the Universal sphere, innumerable agglomerations, characterized by innumerable specific differences of form, size, essential nature, and distance each from each. The development of Repulsion (Electricity) must have commenced, of course, with the very earliest particular efforts at Unity, and must have proceeded constantly in the ratio of Coalescence – that is to say, in that of Condensation, or, again, of Heterogeneity.

Thus the two Principles Proper, Attraction and Repulsion– the Material and the Spiritual – accompany each other, in the strictest fellowship, forever. Thus The Body and The Soul walk hand in hand.

If now, in fancy, we select any one of the agglomerations considered as in their primary stages throughout the Universal sphere, and suppose this incipient agglomeration to be taking place at that point where the centre of our Sun exists – or rather where it did exist originally; for the Sun is perpetually shifting his position – we shall find ourselves met, and borne onward for a time at least, by the most magnificent of theories – by the Nebular Cosmogony of Laplace: – although “Cosmogony” is far too comprehensive a term for what he really discusses – which is the constitution of our solar system alone – of one among the myriad of similar systems which make up the Universe Proper – that Universal sphere – that all-inclusive and absolute Kosmos which forms the subject of my present Discourse.

Confining himself to an obviously limited region – that of our solar system with its comparatively immediate vicinity – and merely assuming – that is to say, assuming without any basis whatever, either deductive or inductive —much of what I have been just endeavoring to place upon a more stable basis than assumption; assuming, for example, matter as diffused (without pretending to account for the diffusion) throughout, and somewhat beyond, the space occupied by our system – diffused in a state of heterogeneous nebulosity and obedient to that omniprevalent law of Gravity at whose principle he ventured to make no guess; – assuming all this (which is quite true, although he had no logical right to its assumption) Laplace has shown, dynamically and mathematically, that the results in such case necessarily ensuing, are those and those alone which we find manifested in the actually existing condition of the system itself.

To explain: – Let us conceive that particular agglomeration of which we have just spoken – the one at the point designated by our Sun’s centre – to have so far proceeded that a vast quantity of nebulous matter has here assumed a roughly globular form; its centre being, of course, coincident with what is now, or rather was originally, the centre of our Sun; and its periphery extending out beyond the orbit of Neptune, the most remote of our planets: – in other words, let us suppose the diameter of this rough sphere to be some 6000 millions of miles. For ages, this mass of matter has been undergoing condensation, until at length it has become reduced into the bulk we imagine; having proceeded gradually, of course, from its atomic and imperceptible state, into what we understand of visible, palpable, or otherwise appreciable nebulosity.

Now, the condition of this mass implies a rotation about an imaginary axis – a rotation which, commencing with the absolute incipiency of the aggregation, has been ever since acquiring velocity. The very first two atoms which met, approaching each other from points not diametrically opposite, would, in rushing partially past each other, form a nucleus for the rotary movement described. How this would increase in velocity, is readily seen. The two atoms are joined by others: – an aggregation is formed. The mass continues to rotate while condensing. But any atom at the circumference has, of course, a more rapid motion than one nearer the centre. The outer atom, however, with its superior velocity, approaches the centre; carrying this superior velocity with it as it goes. Thus every atom, proceeding inwardly, and finally attaching itself to the condensed centre, adds something to the original velocity of that centre – that is to say, increases the rotary movement of the mass.

Let us now suppose this mass so far condensed that it occupies precisely the space circumscribed by the orbit of Neptune, and that the velocity with which the surface of the mass moves, in the general rotation, is precisely that velocity with which Neptune now revolves about the Sun. At this epoch, then, we are to understand that the constantly increasing centrifugal force, having gotten the better of the non-increasing centripetal, loosened and separated the exterior and least condensed stratum, or a few of the exterior and least condensed strata, at the equator of the sphere, where the tangential velocity predominated; so that these strata formed about the main body an independent ring encircling the equatorial regions: – just as the exterior portion thrown off, by excessive velocity of rotation, from a grindstone, would form a ring about the grindstone, but for the solidity of the superficial material: were this caoutchouc, or anything similar in consistency, precisely the phænomenon I describe would be presented.

The ring thus whirled from the nebulous mass, revolved, of course, as a separate ring, with just that velocity with which, while the surface of the mass, it rotated. In the meantime, condensation still proceeding, the interval between the discharged ring and the main body continued to increase, until the former was left at a vast distance from the latter.

Now, admitting the ring to have possessed, by some seemingly accidental arrangement of its heterogeneous materials, a constitution nearly uniform, then this ring, as such, would never have ceased revolving about its primary; but, as might have been anticipated, there appears to have been enough irregularity in the disposition of the materials, to make them cluster about centres of superior solidity; and thus the annular form was destroyed.[5 - Laplace assumed his nebulosity heterogeneous, merely that he might be thus enabled to account for the breaking up of the rings; for had the nebulosity been homogeneous, they would not have broken. I reach the same result – heterogeneity of the secondary masses immediately resulting from the atoms – purely from an à priori consideration of their general design —Relation.] No doubt, the band was soon broken up into several portions, and one of these portions, predominating in mass, absorbed the others into itself; the whole settling, spherically, into a planet. That this latter, as a planet, continued the revolutionary movement which characterized it while a ring, is sufficiently clear; and that it took upon itself also, an additional movement in its new condition of sphere, is readily explained. The ring being understood as yet unbroken, we see that its exterior, while the whole revolves about the parent body, moves more rapidly than its interior. When the rupture occurred, then, some portion in each fragment must have been moving with greater velocity than the others. The superior movement prevailing, must have whirled each fragment round – that is to say, have caused it to rotate; and the direction of the rotation must, of course, have been the direction of the revolution whence it arose. All the fragments having become subject to the rotation described, must, in coalescing, have imparted it to the one planet constituted by their coalescence. – This planet was Neptune. Its material continuing to undergo condensation, and the centrifugal force generated in its rotation getting, at length, the better of the centripetal, as before in the case of the parent orb, a ring was whirled also from the equatorial surface of this planet: this ring, having been ununiform in its constitution, was broken up, and its several fragments, being absorbed by the most massive, were collectively spherified into a moon. Subsequently, the operation was repeated, and a second moon was the result. We thus account for the planet Neptune, with the two satellites which accompany him.

In throwing off a ring from its equator, the Sun re-established that equilibrium between its centripetal and centrifugal forces which had been disturbed in the process of condensation; but, as this condensation still proceeded, the equilibrium was again immediately disturbed, through the increase of rotation. By the time the mass had so far shrunk that it occupied a spherical space just that circumscribed by the orbit of Uranus, we are to understand that the centrifugal force had so far obtained the ascendency that new relief was needed: a second equatorial band was, consequently, thrown off, which, proving ununiform, was broken up, as before in the case of Neptune; the fragments settling into the planet Uranus; the velocity of whose actual revolution about the Sun indicates, of course, the rotary speed of that Sun’s equatorial surface at the moment of the separation. Uranus, adopting a rotation from the collective rotations of the fragments composing it, as previously explained, now threw off ring after ring; each of which, becoming broken up, settled into a moon: – three moons, at different epochs, having been formed, in this manner, by the rupture and general spherification of as many distinct ununiform rings.

By the time the Sun had shrunk until it occupied a space just that circumscribed by the orbit of Saturn, the balance, we are to suppose, between its centripetal and centrifugal forces had again become so far disturbed, through increase of rotary velocity, the result of condensation, that a third effort at equilibrium became necessary; and an annular band was therefore whirled off as twice before; which, on rupture through ununiformity, became consolidated into the planet Saturn. This latter threw off, in the first place, seven uniform bands, which, on rupture, were spherified respectively into as many moons; but, subsequently, it appears to have discharged, at three distinct but not very distant epochs, three rings whose equability of constitution was, by apparent accident, so considerable as to present no occasion for their rupture; thus they continue to revolve as rings. I use the phrase “apparent accident;” for of accident in the ordinary sense there was, of course, nothing: – the term is properly applied only to the result of indistinguishable or not immediately traceable law.

Shrinking still farther, until it occupied just the space circumscribed by the orbit of Jupiter, the Sun now found need of farther effort to restore the counterbalance of its two forces, continually disarranged in the still continued increase of rotation. Jupiter, accordingly, was now thrown off; passing from the annular to the planetary condition; and, on attaining this latter, threw off in its turn, at four different epochs, four rings, which finally resolved themselves into so many moons.