These ideas – conceptions such as these—unthoughtlike thoughts – soul-reveries rather than conclusions or even considerations of the intellect – ideas, I repeat, such as these, are such as we can alone hope profitably to entertain in any effort at grasping the great principle, Attraction.
But now, – with such ideas – with such a vision of the marvellous complexity of Attraction fairly in his mind – let any person competent of thought on such topics as these, set himself to the task of imagining a principle for the phænomena observed – a condition from which they sprang.
Does not so evident a brotherhood among the atoms point to a common parentage? Does not a sympathy so omniprevalent, so ineradicable, and so thoroughly irrespective, suggest a common paternity as its source? Does not one extreme impel the reason to the other? Does not the infinitude of division refer to the utterness of individuality? Does not the entireness of the complex hint at the perfection of the simple? It is not that the atoms, as we see them, are divided or that they are complex in their relations – but that they are inconceivably divided and unutterably complex – it is the extremeness of the conditions to which I now allude, rather than to the conditions themselves. In a word, is it not because the atoms were, at some remote epoch of time, even more than together—is it not because originally, and therefore normally, they were One—that now, in all circumstances – at all points – in all directions – by all modes of approach – in all relations and through all conditions – they struggle back to this absolutely, this irrelatively, this unconditionally one?
Some person may here demand – "Why – since it is to the One that the atoms struggle back – do we not find and define Attraction 'a merely general tendency to a centre?'—why, in especial, do not your atoms – the atoms which you describe as having been irradiated from a centre – proceed at once, rectilinearly, back to the central point of their origin?"
I reply that they do; as will be distinctly shown; but that the cause of their so doing is quite irrespective of the centre as such. They all tend rectilinearly towards a centre, because of the sphereicity with which they have been irradiated into space. Each atom, forming one of a generally uniform globe of atoms, finds more atoms in the direction of the centre, of course, than in any other, and in that direction, therefore, is impelled – but is not thus impelled because the centre is the point of its origin. It is not to any point that the atoms are allied. It is not any locality, either in the concrete or in the abstract, to which I suppose them bound. Nothing like location was conceived as their origin. Their source lies in the principle, Unity. This is their lost parent. This they seek always – immediately – in all directions – wherever it is even partially to be found; thus appeasing, in some measure, the ineradicable tendency, while on the way to its absolute satisfaction in the end. It follows from all this, that any principle which shall be adequate to account for the law, or modus operandi, of the attractive force in general, will account for this law in particular – that is to say, any principle which will show why the atoms should tend to their general centre of irradiation with forces inversely proportional to the squares of the distances, will be admitted as satisfactorily accounting, at the same time, for the tendency, according to the same law, of these atoms each to each – for the tendency to the centre is merely the tendency each to each, and not any tendency to a centre as such. – Thus it will be seen, also, that the establishment of my propositions would involve no necessity of modification in the terms of the Newtonian definition of Gravity, which declares that each atom attracts each other atom and so forth, and declares this merely; but (always under the supposition that what I propose be, in the end, admitted) it seems clear that some error might occasionally be avoided, in the future processes of Science, were a more ample phraseology adopted – for instance – "Each atom tends to every other atom &c. with a force &c.: the general result being a tendency of all, with a similar force, to a general centre."
The reversal of our processes has thus brought us to an identical result; but, while in the one process intuition was the starting-point, in the other it was the goal. In commencing the former journey I could only say that, with an irresistible intuition, I felt Simplicity to have been the characteristic of the original action of God – in ending the latter I can only declare that, with an irresistible intuition, I perceive Unity to have been the source of the observed phænomena of the Newtonian gravitation. Thus, according to the schools, I prove nothing. So be it – I design but to suggest – and to convince through the suggestion. I am proudly aware that there exist many of the most profound and cautiously discriminative human intellects which cannot help being abundantly content with my – suggestions. To these intellects – as to my own – there is no mathematical demonstration which could bring the least additional true proof of the great Truth which I have advanced—the truth of Original Unity as the source – as the principle of the Universal Phænomena. For my part, I am not so sure that I speak and see – I am not so sure that my heart beats and that my soul lives – of the rising of to-morrow's sun – a probability that as yet lies in the Future – I do not pretend to be one thousandth part as sure – as I am of the irretrievably by-gone Fact that All Things and All Thoughts of Things, with all their ineffable Multiplicity of Relation, sprang at once into being from the primordial and irrelative One.
Referring to the Newtonian Gravity, Dr. Nichol, the eloquent author of "The Architecture of the Heavens," says – "In truth we have no reason to suppose this great Law, as now revealed, to be the ultimate or simplest, and therefore the universal and all-comprehensive, form of a great Ordinance. The mode in which its intensity diminishes with the element of distance, has not the aspect of an ultimate principle; which always assumes the simplicity and self-evidence of those axioms which constitute the basis of Geometry."
Now, it is quite true that "ultimate principles," in the common understanding of the words, always assume the simplicity of geometrical axioms – (as for "self-evidence," there is no such thing) – but these principles are clearly not "ultimate;" in other terms what we are in the habit of calling principles are no principles, properly speaking – since there can be but one principle, the Volition of God. We have no right to assume, then, from what we observe in rules that we choose foolishly to name "principles," anything at all in respect to the characteristics of a principle proper. The "ultimate principles" of which Dr. Nichol speaks as having geometrical simplicity, may and do have this geometrical turn, as being part and parcel of a vast geometrical system, and thus a system of simplicity itself – in which, nevertheless, the truly ultimate principle is, as we know, the consummation of the complex – that is to say, of the unintelligible – for is it not the Spiritual Capacity of God?
I quoted Dr. Nichol's remark, however, not so much to question its philosophy, as by way of calling attention to the fact that, while all men have admitted some principle as existing behind the Law of Gravity, no attempt has been yet made to point out what this principle in particular is – if we except, perhaps, occasional fantastic efforts at referring it to Magnetism, or Mesmerism, or Swedenborgianism, or Transcendentalism, or some other equally delicious ism of the same species, and invariably patronized by one and the same species of people. The great mind of Newton, while boldly grasping the Law itself, shrank from the principle of the Law. The more fluent and comprehensive at least, if not the more patient and profound, sagacity of Laplace, had not the courage to attack it. But hesitation on the part of these two astronomers it is, perhaps, not so very difficult to understand. They, as well as all the first class of mathematicians, were mathematicians solely – their intellect, at least, had a firmly-pronounced mathematico-physical tone. What lay not distinctly within the domain of Physics, or of Mathematics, seemed to them either Non-Entity or Shadow. Nevertheless, we may well wonder that Leibnitz, who was a marked exception to the general rule in these respects, and whose mental temperament was a singular admixture of the mathematical with the physico-metaphysical, did not at once investigate and establish the point at issue. Either Newton or Laplace, seeking a principle and discovering none physical, would have rested contentedly in the conclusion that there was absolutely none; but it is almost impossible to fancy, of Leibnitz, that, having exhausted in his search the physical dominions, he would not have stepped at once, boldly and hopefully, amid his old familiar haunts in the kingdom of Metaphysics. Here, indeed, it is clear that he must have adventured in search of the treasure – that he did not find it after all, was, perhaps, because his fairy guide, Imagination, was not sufficiently well-grown, or well-educated, to direct him aright.
I observed, just now, that, in fact, there had been certain vague attempts at referring Gravity to some very uncertain isms. These attempts, however, although considered bold and justly so considered, looked no farther than to the generality – the merest generality – of the Newtonian Law. Its modus operandi has never, to my knowledge, been approached in the way of an effort at explanation. It is, therefore, with no unwarranted fear of being taken for a madman at the outset, and before I can bring my propositions fairly to the eye of those who alone are competent to decide upon them, that I here declare the modus operandi of the Law of Gravity to be an exceedingly simple and perfectly explicable thing – that is to say, when we make our advances towards it in just gradations and in the true direction – when we regard it from the proper point of view.
Whether we reach the idea of absolute Unity as the source of All Things, from a consideration of Simplicity as the most probable characteristic of the original action of God;—whether we arrive at it from an inspection of the universality of relation in the gravitating phænomena;—or whether we attain it as a result of the mutual corroboration afforded by both processes;—still, the idea itself, if entertained at all, is entertained in inseparable connection with another idea – that of the condition of the Universe of stars as we now perceive it – that is to say, a condition of immeasurable diffusion through space. Now a connection between these two ideas – unity and diffusion – cannot be established unless through the entertainment of a third idea – that of irradiation. Absolute Unity being taken as a centre, then the existing Universe of stars is the result of irradiation from that centre.
Now, the laws of irradiation are known. They are part and parcel of the sphere. They belong to the class of indisputable geometrical properties. We say of them, "they are true – they are evident." To demand why they are true, would be to demand why the axioms are true upon which their demonstration is based. Nothing is demonstrable, strictly speaking; but if anything be, then the properties – the laws in question are demonstrated.
But these laws – what do they declare? Irradiation – how – by what steps does it proceed outwardly from a centre?
From a luminous centre, Light issues by irradiation; and the quantities of light received upon any given plane, supposed to be shifting its position so as to be now nearer the centre and now farther from it, will be diminished in the same proportion as the squares of the distances of the plane from the luminous body, are increased; and will be increased in the same proportion as these squares are diminished.
The expression of the law may be thus generalized – the number of light-particles (or, if the phrase be preferred, the number of light-impressions) received upon the shifting plane, will be inversely proportional with the squares of the distances of the plane. Generalizing yet again, we may say that the diffusion – the scattering – the irradiation, in a word – is directly proportional with the squares of the distances.
For example: at the distance B, from the luminous centre A, a certain number of particles are so diffused as to occupy the surface B. Then at double the distance – that is to say at C – they will be so much farther diffused as to occupy four such surfaces – at treble the distance, or at D, they will be so much farther separated as to occupy nine such surfaces – while, at quadruple the distance, or at E, they will have become so scattered as to spread themselves over sixteen such surfaces – and so on forever.
In saying, generally, that the irradiation proceeds in direct proportion with the squares of the distances, we use the term irradiation to express the degree of the diffusion as we proceed outwardly from the centre. Conversing the idea, and employing the word "concentralization" to express the degree of the drawing together as we come back toward the centre from an outward position, we may say that concentralization proceeds inversely as the squares of the distances. In other words, we have reached the conclusion that, on the hypothesis that matter was originally irradiated from a centre and is now returning to it, the concentralization, in the return, proceeds exactly as we know the force of gravitation to proceed.
Now here, if we could be permitted to assume that concentralization exactly represented the force of the tendency to the centre—that the one was exactly proportional to the other, and that the two proceeded together – we should have shown all that is required. The sole difficulty existing, then, is to establish a direct proportion between "concentralization" and the force of concentralization; and this is done, of course, if we establish such proportion between "irradiation" and the force of irradiation.
A very slight inspection of the Heavens assures us that the stars have a certain general uniformity, equability, or equidistance, of distribution through that region of space in which, collectively, and in a roughly globular form, they are situated – this species of very general, rather than absolute, equability, being in full keeping with my deduction of inequidistance, within certain limits, among the originally diffused atoms, as a corollary from the evident design of infinite complexity of relation out of irrelation. I started, it will be remembered, with the idea of a generally uniform but particularly ununiform distribution of the atoms;—an idea, I repeat, which an inspection of the stars, as they exist, confirms.
But even in the merely general equability of distribution, as regards the atoms, there appears a difficulty which, no doubt, has already suggested itself to those among my readers who have borne in mind that I suppose this equability of distribution effected through irradiation from a centre. The very first glance at the idea, irradiation, forces us to the entertainment of the hitherto unseparated and seemingly inseparable idea of agglomeration about a centre, with dispersion as we recede from it – the idea, in a word, of inequability of distribution in respect to the matter irradiated.
Now, I have elsewhere[1] observed that it is by just such difficulties as the one now in question – such roughnesses – such peculiarities – such protuberances above the plane of the ordinary – that Reason feels her way, if at all, in her search for the True. By the difficulty – the "peculiarity" – now presented, I leap at once to the secret – a secret which I might never have attained but for the peculiarity and the inferences which, in its mere character of peculiarity, it affords me.
The process of thought, at this point, may be thus roughly sketched – I say to myself—"Unity, as I have explained it, is a truth – I feel it. Diffusion is a truth – I see it. Irradiation, by which alone these two truths are reconciled, is a consequent truth – I perceive it. Equability of diffusion, first deduced à priori and then corroborated by the inspection of phænomena, is also a truth – I fully admit it. So far all is clear around me – there are no clouds behind which the secret – the great secret of the gravitating modus operandi—can possibly lie hidden;—but this secret lies hereabouts, most assuredly; and were there but a cloud in view, I should be driven to suspicion of that cloud." And now, just as I say this, there actually comes a cloud into view. This cloud is the seeming impossibility of reconciling my truth, irradiation, with my truth, equability of diffusion. I say now – "Behind this seeming impossibility is to be found what I desire." I do not say "real impossibility;" for invincible faith in my truths assures me that it is a mere difficulty after all – but I go on to say, with unflinching confidence, that, when this difficulty shall be solved, we shall find, wrapped up in the process of solution, the key to the secret at which we aim. Moreover – I feel that we shall discover but one possible solution of the difficulty; this for the reason that, were there two, one would be supererogatory – would be fruitless – would be empty – would contain no key – since no duplicate key can be needed to any secret of Nature.
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]
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 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."