Eureka & The Unparalleled Adventure of One Hans Pfaall. Эдгар Аллан По
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