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 elsewhere1 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.
1 »Murders in the Rue Morgue.«