[We webmasters here at Easylit have divided this work into sections to make it easier for you to read.]
page 2 of 6 . . . .
This will be found the sole absolute assumption of my Discourse. I use the word "assumption" in its ordinary sense; yet I maintain that even this my primary proposition, is very, very far indeed, from being really a mere assumption. Nothing was ever more certainly -- no human conclusion was ever, in fact, more regularly -- more rigorously de duced: -- but, alas! the processes lie out of the human analysis -- at all events are beyond the utterance of the human tongue.
Let us now endeavor to conceive what Matter must be, when, or if, in its absolute extreme of Simplicity. Here the Reason flies at once to Imparticularity -- to a particle -- to one particle -- a particle of one kind -- of one character -- of one nature -- of one size -- of one form -- a particle, therefore, "without form and void" -- a particle positively a particle at all points -- a particle absolutely unique, individual, undivided, and not indivisible only because He who created it, by dint of his Will, can by an infinitely less energetic exercise of the same Will, as a matter of course, divide it.
Oneness, then, is all that I predicate of the originally created Matter; but I propose to show that this Oneness is a principle abundantly sufficient to account for the constitution, the existing phaenomena and the plainly inevitable annihilation of at least the material Universe.
The willing into being the primordial particle, has completed the act, or more properly the Conception, of Creation. We now proceed to the ultimate purpose for which we are to suppose the Particle created -- that is to say, the ultimate purpose so far as our considerations yet enable us to see it -- the constitution of the Universe from it, the Particle.
This constitution has been effected by forcing the originally and therefore normally One into the abnormal condition of Many. An action of this character implies reaction. A diffusion from Unity, under the conditions, involves a tendency to return into Unity -- a tendency ineradicable until satisfied. But on these points I will speak more fully hereafter.
The assumption of absolute Unity in the primordial Particle includes that of infinite divisibility. Let us conceive the Particle, then, to be only not totally exhausted by diffusion into Space. From the one Particle, as a centre, let us suppose to be irradiated spherically -- in all directions -- to immeasurable but still to definite distances in the previously vacant space -- a certain inexpressibly great yet limited number of unimaginably yet not infinitely minute atoms.
Now, of these atoms, thus diffused, or upon diffusion, what conditions are we permitted -- not to assume, but to infer, from consideration as well of their source as of the character of the design apparent in their diffusion? Unity being their source, and difference from Unity the character of the design manifested in their diffusion, we are warranted in supposing this character to be at least generally preserved throughout the design, and to form a portion of the design itself: -- that is to say, we shall be warranted in conceiving continual differences at all points from the uniquity and simplicity of the origin. But, for these reasons, shall we be justified in imagining the atoms heterogeneous, dissimilar, unequal, and inequidistant? More explicitly -- are we to consider no two atoms as, at their diffusion, of the same nature, or of the same form, or of the same size? -- and, after fulfilment of their diffusion into Space, is absolute inequidistance, each from each, to be understood of all of them? In such arrangement, under such conditions, we most easily and immediately comprehend the subsequent most feasible carrying out to completion of any such design as that which I have suggested -- the design of variety out of unity -- diversity out of sameness -- heterogeneity out of homogeneity -- complexity out of simplicity -- in a word, the utmost possible multiplicity of relation out of the emphatically irrelative One. Undoubtedly, therefore, we should be warranted in assuming all that has been mentioned, but for the reflection, first, that supererogation is not presumable of any Divine Act; and, secondly, that the object supposed in view, appears as feasible when some of the conditions in question are dispensed with, in the beginning, as when all are understood immediately to exist. I mean to say that some are involved in the rest, or so instantaneous a consequence of them as to make the distinction inappreciable. Difference of size, for example, will at once be brought about through the tendency of one atom to a second, in preference to a third, on account of particular inequidistance; which is to be comprehended as particular inequidistances between centres of quantity, in neighboring atoms of different form -- a matter not at all interfering with the generally-equable distribution of the atoms. Difference of kind, too, is easily conceived to be merely a result of differences in size and form, taken more or less conjointly: -- in fact, since the Unity of the Particle Proper implies absolute homogeneity, we cannot imagine the atoms, at their diffusion, differing in kind, without imagining, at the same time, a special exercise of the Divine Will, at the emission of each atom, for the purpose of effecting, in each, a change of its essential nature: -- so fantastic an idea is the less to be indulged, as the object proposed is seen to be thoroughly attainable without such minute and elaborate interposition. We perceive, therefore, upon the whole, that it would be supererogatory, and consequently unphilosophical, to predicate of the atoms, in view of their purposes, any thing more than difference of form at their dispersion, with particular inequidistance after it -- all other differences arising at once out of these, in the very first processes of mass-constitution: -- We thus establish the Universe on a purely geometrical basis. Of course, it is by no means necessary to assume absolute difference, even of form, among the atoms irradiated -- any more than absolute particular inequidistance of each from each. We are required to conceive merely that no neighboring atoms are of similar form -- no atoms which can ever approximate, until their inevitable reunition at the end.
Although the immediate and perpetual tendency of the disunited atoms to return into their normal Unity, is implied, as I have said, in their abnormal diffusion; still it is clear that this tendency will be without consequence -- a tendency and no more -- until the diffusive energy, in ceasing to be exerted, shall leave it, the tendency, free to seek its satisfaction. The Divine Act, however, being considered as determinate, and discontinued on fulfilment of the diffusion, we understand, at once, a reaction -- in other words, a satisfiable tendency of the disunited atoms to return into One.
But the diffusive energy being withdrawn, and the reaction having commenced in furtherance of the ultimate design -- that of the utmost possible Relation -- this design is now in danger of being frustrated, in detail, by reason of that very tendency to return which is to effect its accomplishment in general. Multiplicity is the object; but there is nothing to prevent proximate atoms, from lapsing at once, through the now satisfiable tendency -- before the fulfilment of any ends proposed in multiplicity -- into absolute oneness among themselves: -- there is nothing to impede the aggregation of various unique masses, at various points of space: -- in other words, nothing to interfere with the accumulation of various masses, each absolutely One.
For the effectual and thorough completion of the general design, we thus see the necessity for a repulsion of limited capacity -- a separate something which, on withdrawal of the diffusive Volition, shall at the same time allow the approach, and forbid the junction, of the atoms; suffering them infinitely to approximate, while denying them positive contact; in a word, having the power -- up to a certain epoch -- of preventing their Coalition, but no ability to interfere with their Coalescence in any respect or degree. The repulsion, already considered as so peculiarly limited in other regards, must be understood, let me repeat, as having power to prevent absolute coalition, only up to a certain epoch. Unless we are to conceive that the appetite for Unity among the atoms is doomed to be satisfied never; -- unless we are to conceive that what had a beginning is to have no end -- a conception which cannot really be entertained, however much we may talk or dream of entertaining it -- we are forced to conclude that the repulsive influence imagined, will, finally -- under pressure of the Uni-tendency collectively applied, but, never and in no degree until, on fulfilment of the Divine purposes, such collective application shall be naturally made -- yield to a force which, at that ultimate epoch, shall be the superior force precisely to the extent required, and thus permit the universal subsidence into the inevitable, because original and therefore normal, One. -- The conditions here to be reconciled are difficult indeed: -- we cannot even comprehend the possibility of their conciliation; -- nevertheless, the apparent impossibility is brilliantly suggestive.
That the repulsive something actually exists, we see. Man neither employs, nor knows, a force sufficient to bring two atoms into contact. This is but the well-established proposition of the impenetrability of matter. All Experiment proves -- all Philosophy admits it. The design of the repulsion -- the necessity for its existence -- I have endeavored to show; but from all attempt at investigating its nature have religiously abstained; this on account of an intuitive conviction that the principle at issue is strictly spiritual -- lies in a recess impervious to our present understanding -- lies involved in a consideration of what now -- in our human state -- is not to be considered -- in a consideration of Spirit in itself. I feel, in a word, that here the God has interposed, and here only, because here and here only the knot demanded the interposition of the God.
In fact, while the tendency of the diffused atoms to return into Unity, will be recognized, at once, as the principle of the Newtonian Gravity, what I have spoken of as a repulsive influence prescribing limits to the (immediate) satisfaction of the tendency, will be understood as that which we have been in the practice of designating now as heat, now as magnetism, now as electricity; displaying our ignorance of its awful character in the vacillation of the phraseology with which we endeavor to circumscribe it.
Calling it, merely for the moment, electricity, we know that all experimental analysis of electricity has given, as an ultimate result, the principle, or seeming principle, heterogeneity. Only where things differ is electricity apparent; and it is presumable that they never differ where it is not developed at least, if not apparent. Now, this result is in the fullest keeping with that which I have reached unempirically. The design of the repulsive influence I have maintained to be that of preventing immediate Unity among the diffused atoms; and these atoms are represented as different each from each. Difference is their character -- their essentiality -- just as no-difference was the essentiality of their course. When we say, then, that an attempt to bring any two of these atoms together would induce an effort, on the part of the repulsive influence, to prevent the contact we may as well use the strictly convertible sentence that an attempt to bring together any two differences will result in a development of electricity. All existing bodies, of course, are composed of these atoms in proximate contact, and are therefore to be considered as mere assemblages of more or fewer differences; and the resistance made by the repulsive spirit, on bringing together any two such assemblages, would be in the ratio of the two sums of the differences in each: -- an expression which, when reduced, is equivalent to this: -- The amount of electricity developed on the approximation of two bodies, is proportional to the difference between the respective sums of the atoms of which the bodies are composed. That no two bodies are absolutely alike, is a simple corollary from all that has been here said. Electricity, therefore, existing always, is developed whenever any bodies, but manifested only when bodies of appreciable difference, are brought into approximation.
To electricity -- so, for the present, continuing to call it -- we may not be wrong in referring the various physical appearances of light, heat and magnetism; but far less shall we be liable to err in attributing to this strictly spiritual principle the more important phaenomena of vitality, consciousness and Thought. On this topic, however, I need pause here merely to suggest that these phaenomena, whether observed generally or in detail, seem to proceed at least in the ratio of the heterogeneous.
Discarding now the two equivocal terms, "gravitation" and "electricity," let us adopt the more definite expressions, "attraction" and "repulsion." The former is the body; the latter the soul: the one is the material; the other the spiritual, principle of the Universe. No other principles exist. All phaenomena are referable to one, or to the other, or to both combined. So rigorously is this the case -- so thoroughly demonstrable is it that attraction and repulsion are the sole properties through which we perceive the Universe -- in other words, by which Matter is manifested to Mind -- that, for all merely argumentative purposes, we are fully justified in assuming that matter exists only as attraction and repulsion -- that attraction and repulsion are matter: -- there being no conceivable case in which we may not employ the term "matter" and the terms "attraction" and "repulsion," taken together, as equivalent, and therefore convertible, expressions in Logic.
I said, just now, that what I have described as the tendency of the diffused atoms to return into their original unity, would be understood as the principle of the Newtonian law of gravity: and, in fact, there can be but little difficulty in such an understanding, if we look at the Newtonian gravity in a merely general view, as a force impelling matter to seek matter; that is to say, when we pay no attention to the known modus operandi of the Newtonian force. The general coincidence satisfies us; but, upon looking closely, we see, in detail, much that appears in coincident, and much in regard to which no coincidence, at least, is established. For example; the Newtonian gravity, when we think of it in certain moods, does not seem to be a tendency to oneness at all, but rather a tendency of all bodies in all directions -- a phrase apparently expressive of a tendency to diffusion. Here, then, is an in coincidence. Again; when we reflect on the mathematical LA0 governing the Newtonian tendency, we see clearly that no coincidence has been made good, in respect of the modus operandi, at least, between gravitation as known to exist and that seemingly simple and direct tendency which I have assumed.
In fact, I have attained a point at which it will be advisable to strengthen my position by reversing my processes. So far, we have gone on a priori, from an abstract consideration of Simplicity, as that quality most likely to have characterized the original action of God. Let us now see whether the established facts of the Newtonian Gravitation may not afford us, a posteriori, some legitimate inductions.
What does the Newtonian law declare? -- That all bodies attract each other with forces proportional to their quantities of matter and inversely proportional to the squares of their distances. Purposely, I have here given, in the first place, the vulgar version of the law; and I confess that in this, as in most other vulgar versions of great truths, we find little of a suggestive character. Let us now adopt a more philosophical phraseology: -- Every atom, of every body, attracts every other atom, both of its own and of every other body, with a force which varies inversely as the squares of the distances between the attracting and attracted atom. -- Here, indeed, a flood of suggestion bursts upon the mind.
But let us see distinctly what it was that Newton proved -- according to the grossly irrational definitions of proof prescribed by the metaphysical schools. He was forced to content himself with showing how thoroughly the motions of an imaginary Universe, composed of attracting and attracted atoms obedient to the law he announced, coincide with those of the actually existing Universe so far as it comes under our observation. This was the amount of his demonstration -- that is to say, this was the amount of it, according to the conventional cant of the "philosophies." His successes added proof multiplied by proof -- such proof as a sound intellect admits -- but the demonstration of the law itself, persist the metaphysicians, had not been strengthened in any degree. "Ocular, physical proof," however, of attraction, here upon Earth, in accordance with the Newtonian theory, was, at length, much to the satisfaction of some intellectual grovellers, afforded. This proof arose collaterally and incidentally (as nearly all important truths have arisen) out of an attempt to ascertain the mean density of the Earth. In the famous Maskelyne, Cavendish and Bailly experiments for this purpose, the attraction of the mass of a mountain was seen, felt, measured, and found to be mathematically consistent with the immortal theory of the British astronomer.
But in spite of this confirmation of that which needed none -- in spite of the so-called corroboration of the "theory" by the so-called "ocular and physical proof" -- in spite of the character of this corroboration -- the ideas which even really philosophical men cannot help imbibing of gravity -- and, especially, the ideas of it which ordinary men get and contentedly maintain, are seen to have been derived, for the most part, from a consideration of the principle as they find it developed -- merely in the planet upon which they stand.
Now, to what does so partial a consideration tend -- to what species of error does it give rise? On the Earth we see and feel, only that gravity impels all bodies towards the centre of the Earth. No man in the common walks of life could be made to see or feel anything else -- could be made to perceive that anything, anywhere, has a perpetual, gravitating tendency in any other direction than to the centre of the Earth; yet (with an exception hereafter to be specified) it is a fact that every earthly thing (not to speak now of every heavenly thing) has a tendency not only to the Earth's centre but in every conceivable direction besides.
Now, although the philosophic cannot be said to err with the vulgar in this matter, they nevertheless permit themselves to be influenced, without knowing it, by the sentiment of the vulgar idea. "Although the Pagan fables are not believed," says Bryant, in his very erudite "Mythology," "yet we forget ourselves continually and make inferences from them as from existing realities." I mean to assert that the merely sensitive perception of gravity as we experience it on Earth, beguiles mankind into the fancy of Concentralization or especiality respecting it -- has been continually biasing towards this fancy even the mightiest intellects -- perpetually, although imperceptibly, leading them away from the real characteristics of the principle; thus preventing them, up to this date, from ever getting a glimpse of that vital truth which lies in a diametrically opposite direction -- behind the principle's essential characteristics -- those, not of concentralization or especiality -- but of universality and diffusion. This "vital truth" is Unity as the source of the phaenomenon.
Let me now repeat the definition of gravity: -- Every atom, of every body, attracts every other atom, both of its own and of every other body, with a force which varies inversely as the squares of the distances of the attracting and attracted atom.
Here let the reader pause with me, for a moment, in contemplation of the miraculous -- of the ineffable -- of the altogether unimaginable complexity of relation involved in the fact that each atom attracts every other atom -- involved merely in this fact of the attraction, without reference to the law or mode in which the attraction is manifested -- involved merely in the fact that each atom attracts every other atom at all, in a wilderness of atoms so numerous that those which go to the composition of a cannon-ball, exceed, probably, in mere point of number, all the stars which go to the constitution of the Universe.
Had we discovered, simply, that each atom tended to some one favorite point -- to some especially attractive atom -- we should still have fallen upon a discovery which, in itself, would have sufficed to overwhelm the mind: -- but what is it that we are actually called upon to comprehend? That each atom attracts -- sympathizes with the most delicate movements of every other atom, and with each and with all at the same time, and forever, and according to a determinate law of which the complexity, even considered by itself solely, is utterly beyond the grasp of the imagination of man. If I propose to ascertain the influence of one mote in a sunbeam upon its neighboring mote, I cannot accomplish my purpose without first counting and weighing all the atoms in the Universe and defining the precise positions of all at one particular moment. If I venture to displace, by even the billionth part of an inch, the microscopical speck of dust which lies now upon the point of my finger, what is the character of that act upon which I have adventured? I have done a deed which shakes the Moon in her path, which causes the Sun to be no longer the Sun, and which alters forever the destiny of the multitudinous myriads of stars that roll and glow in the majestic presence of their Creator.
These ideas -- conceptions such as these -- unthought-like 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 phaenomena 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, 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 LA0 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 irresistable 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 phaenomena 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 Phaenomena. For my part, I am not 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 phaenomena; -- 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 lumimous 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 (see illustration). 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 un uniform 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 in equability of distribution in respect to the matter irradiated.
Now, I have elsewhere * 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.
* "Murders in the Rue Morgue."
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 a priori and then corroborated by the inspection of phaenomena, 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 recess 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.