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]
Примечания
1
"Murders in the Rue Morgue."
2
Succinctly –The surfaces of spheres are as the squares of their radii.
3
See previous paragraph, "I reply that they do; as will be distinctly…"