The Epicurean System
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The disciples of Epicurus were convinced that the Earth was flat.
- This would make the movement of their atomic theory in parallel and perpendicular ways on a plane surface.
The following objection would of course have been raised by some to this view: Part of these atoms must necessarily encounter the moon before reaching the earth, and by their pelting would push her toward us; and on the other hand the force exerted upon those terrestrial objects which she shields would be less because of her interposition.
Consequently we should see the moon descending and a part of the waters of the ocean rising to meet her, as if rendered lighter by the interception of the atoms, and consequently yielding their place to the adjacent waters.
In view of these objections the Epicureans would have had to see if some phenomenon of this nature did not really exist.
They would have answered their opponents that the moon did not recede from us on a tangent, but really did approach the earth at each instant, and that the alternating motions of the ocean, so accordant with those of the moon, exhibited this very effect in question, due to the inequality introduced in the stream of atoms by the interposition of this great body.
The example of a pebble projected horizontally, which circulates for a few moments about the earth before falling, and longer in proportion as the motion is more rapid, would have made it clear that the moon, which occupies but a month in such a great journey, might’ not of necessity actually approach the earth except in the sense of being nearer than if she had gone off on a tangent.
A persistent antagonist, fortified by some theorems of centrifugal force similar to those of Huygens (which are easily demonstrated by elementary geometry for polygonal orbits such as would result from intermittent collisions) might further have objected that the motion of the moon was still 60 times too slow to prevent her actual approach to us, taking into consideration the very considerable force of gravitation found at the surface of the earth. Upon this the Epicureans would not have been slow to reply that since the distance from the  moon to the center of our globe is 60 times as great as our distance from this same center, the spherical surface having the radius of the moon’s orbit is 3,600 times as great as that of the earth. So that if the outer surface were traversed by the same number of atoms as the inner, their distribution would be 3,600 times rarer, and they would in consequence cause a gravitation 3,600 times less. This would be exactly that required by the theorems, for this gravitating force would suffice to sustain at a distance 60 times as great a moving body whose absolute velocity was 60 times less than that required by a body revolving at the surface of the earth.
The parallelism of path which Epicurus had introduced in the atomic theory of Leucippus and Democritus was not exact, since had it been so these atoms, all moving with equal velocity, could never have come in collision. But Epicurus required that they should collide in order that he might explain the formation of compound bodies without assuming the intervention of a superior cause.
Hence he supposed the paths of the atoms to be slightly inclined to each other, and it is well known that the introduction of the correction subjected him to many pleasantries and objections from philosophers of other sects.
If, however, Epicurus had embraced the doctrine of the convergence of the atoms toward a center, undoubtedly his opponents would have attacked this hypothesis quite as vigorously. The Epicureans in replying would have been able to explain this convergence by returning to the system of Leucippus and Democritus as follows: Imagine the atoms to move fortuitously in every direction, and let us trace the result in  the case of a body near the earth. All the atoms coming toward the body from the direction of the earth would be cut off by it, while from all other directions the body would be subjected to uninterrupted bombardment. Consequently there would be a resultant motion of the earth, that is in the line of diminished resistance, and this resultant motion would be exactly the same as if the bombarding atoms all converged toward the earth’s center instead of moving fortuitously.
The Epicureans would have even seized with avidity upon this occasion to give an air of disorder to the primitive movements of the universe. For this would accord the better with their system of the origin of things (otherwise sufficiently absurd and impious) that there was no appearance of parallelism, perfect or imperfect, whereas all tendency to parallelism would appear to be the result of some particular design, and consequently to indicate the operation of some intelligent being.
I speak of disorder in connection with primitive movements only. The resultant motion of bodies having inertia would be directed toward the center of our globe with great exactness, in consequence of the combination of a vast number of impulses in different directions. For it is a well-known result of the doctrine of chances that minor irregularities, when in great number, mutually compensate each other exactly, so that each several inequality becomes imperceptible in its effect upon the resultant.
Still another consideration would have led the atomists to make this same modification of the direction of motion of the gravitational atoms. All will agree with me that they were certain to have met with one or other of these two objections or to have themselves raised them. As the earth revolves without cessation about the sun, the hypothesis that  all the atoms are directed toward the center of the earth would have required that each new shower of atoms must seek it in a different direction from that followed by the shower next preceding, a condition not in accord with the predilection of the sect of the Epicureans for the operations of chance, nor with their antipathy for occult qualities.
In order to extricate themselves from this difficulty, the atomists said that there was no place in the heavens, equal in dimension to the earth, toward which there did not advance in a given time quite as many atoms as our planet encounters in the same portion of time.
These other atoms were in motion exactly like those encountered by the earth.
Not that there was any particular relation between places and the streams setting toward them, but, since it was essentially a confused movement, equal areas must naturally intercept, one equally as much as another, the paths of the atoms which blindly traverse space; and in consequence they must be equally exposed to their visits.