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^[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 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.

And now, let us see: –Our usual notions of irradiation –in fact 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 reaction – that is, gravitation –as existing now –since, while an act is continued, no reaction, of course, can take place. My assumption, then, or rather my inevitable deduction from just premises –was that of a determinate irradiation –one finally dis continued.

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 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, Reaction, as far as we know any thing of it, is Action conversed. The general principle of Gravity being, in the first place, understood as the reaction 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 a 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, a 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] 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.