The Epicurean System

Section 21

A second difficulty which would have embarrassed the more scrupulous atomists, is that the mutual collision of the atoms would retard their motions repeatedly, and diminish, consequently, the gravitational action.

Any such effect, nevertheless, has hitherto been imperceptible. Now, it would be useless to offer in explanation that the sum of the motions would remain the same, since this is only true when the word sum is used in the sense of geometers, who comprehend by it the difference of contraries.

Such a definition is readily seen to offer no assistance to the atomist in the case of equality of contrary movements. For the algebraic sum of the motions of the atoms is zero before as after the collision; but before the collision they were capable of effects of which they are incapable afterwards.

Section 22

Such mutual encounters would be the more rare the smaller the atoms were supposed to be compared with the intervals between them. These intervals can not, however, be assumed very great since gravitation manifests no sensible interruption even in places and times the most adjacent; so that the only conceivable recourse to render the encounter of the gravitational atoms sufficiently rare is to suppose them extremely small.

Happily this device is completely sufficient.

Let us assume 2 balls whose centers trace given courses in different planes.

In order that they may never meet it suffices to diminish the sum of their semi-diameters till it becomes less than the least distance between their paths.

But since, with diminishing size, the atoms would be less efficient to produce gravitation, the intensity of which is fixed by phenomena,[19] it is necessary to see if their effectiveness may be maintained by some other properties.

I see no recourse of this nature except in the increase of individual density or of velocity. These two recourses appear very natural, and are at the same time the more satisfactory because they were (very probably) in accord with the spirit of the atomists of whom I speak, and would probably have sufficed to close the mouths of their adversaries.

Section 23

Third difficulty: Each celestial body perpetually finds atoms in its path which it necessarily displaces in passing onward.

This can not occur without the atoms communicating to the body a part of their motion, and in consequence causing its retardation. Exclusive of all other elements except the mass displaced, this retardation is proportional [154] to the density of the medium made up of these atoms and their interstices.

Now, the gravitation of the body (exclusive of all other elements than this atomic mass) is proportional to this same mean density. How, then, can it be that the retardation is imperceptible while the gravitation is so sensible?

The objection is rendered the more forcible when we consider that the retardation of a revolving body is brought about by all the atoms which it meets in its orbit, while its gravitation is produced only by those which at any one position in its orbit are directed toward the central body.

Section 24

Reply: Other things being equal, the force of gravitation, being produced by the single stream of atoms deprived of antagonists, is proportional to the square of the velocity of the atoms (by a proposition demonstrated generally), while the retardation above spoken of, being caused by the stream opposing the planet in its motion, is proportional to the product of this velocity of the atoms by that of the revolving body (as we shall prove directly).

Consequently (things being equal) the gravitation is to the retardation as the velocity of the atoms is to that of the revolving body.

We can believe that the velocity of the atoms is greater than that of the revolving body. All that we have heretofore said would lead to the presumption that it is incomparably greater.

Hence, the system of thin-sown atoms moving in every direction agrees very well with a condition of gravitation incomparably greater than the retardation, and it agrees still, despite the consideration which fortifies the difficulty which we are considering, since a velocity has always been assigned to the atoms greater than would have been necessary to obviate this latter difficulty alone.

Remark: I have said that the retardation of a great body caused by the opposing, stream of atoms moving much more rapidly than the body itself would be proportional to the product of the velocity of the atoms by that of the great body. I shall first demonstrate this proposition with respect to the couple of opposed streams parallel to the direction of the great body, and in so doing I shall have proved it for the case of opposing streams oblique to this direction, since their motions may be decomposed in two directions, the one parallel and the other perpendicular to the direction of the body, of which the first is nearly always much greater than the motion of the body, and of which the second produces no effect.

Demonstration: The total retardation of the body is the excess of the simple retardation it experiences from the stream which it encounters over the simple acceleration which it experiences on the part of the stream which pursues it. Now, these simple factors are proportional to the squares of velocities, which are respectively the sum and difference of the absolute velocity of the atoms and the absolute velocity [155] of the body. Consequently, the resultant retardation is proportional to the excess of the square of the sum over the square of the difference, which (by the eighth proposition of the second book of the Elements of Euclid) is four times the product of the absolute velocities in question.

Section 25

To the three difficulties above mentioned may be reduced all those which are plausible, since there can be no other changes in the motions of a heavy body, or in the motions of the gravitational fluid, or in their constitution, except those which proceed from some opposition or interposition, either on the part of the particles of the heavy body, which hinder the atoms composing the fluid from reaching their destination, or from particles of the fluid itself, the one opposing the other, or, finally, from the effect of the latter on the path of the heavy body. The solutions of all these difficulties depend either on the permeability of the heavy body or the subtlety and rapidity of the gravitational atoms - properties to none of which we are obliged to assign two opposing limits. This last expression signifies that while several considerations may unite to augment the intensity of such or such property, yet no consideration requires a diminution in the intensity of the same property, and that reciprocally no considerations tend to limit the diminutiveness of properties of which certain other considerations limit more and more the magnitude. There are no conditions which give opposing indications, and which therefore obstruct the choice of remedies. This assertion would be tedious to establish, but very few readers will contest its correctness.

XXVI.

While we speak of alterations and remedies it is for me to conform to the irregularity of our ordinary progress in research. Truth never permits us to discover her at first seeking, with all her following train of verities, but we proceed gradually in discovery by tedious gropings and corrections. To this procedure a writer ought also in some measure to conform, in the exposition of truths which he has finally discovered, when the greatness or smallness of the objects discussed transcends that of the majority of those objects with which we are familiar, and when he believes that his reader will not at first be disposed to countenance suppositions so excessive, but only in a measure as he shall have shown him their necessity. For the reader will have had no perspective to apply to this immensity or that diminutiveness if it has been assumed at the start in sufficient measure to satisfy all phenomena. The author might with equal justice assume at the start a magnitude or diminutiveness sufficient for the purpose, since in explaining the phenomena the physicist takes the place (so far as he may) of the Creator - a being who, having determined precisely in advance all the [156] consequences of the different intensities which might be given to such or such properties, has chosen in each case that intensity most proper to attain the desired result and has precisely determined the consequences without any preliminary trial.

XXVII.

All other conceivable objections are founded on certain regularities or irregularities of detail which have not been minutely set forth, but gratuitously assumed, and which, in consequence, ought not seriously to be taken into account. Or, in the second place, such objections may be founded on the tenets of some metaphysical sect. Before responding to such objections I pray these metaphysicists to first agree among themselves. Or, finally, they address themselves to the imagination rather than to the understanding. Thus some may be shocked at what in this system is extreme, strange, or extraordinary-as if it was after our gross and limited measures that the subtlety and grandeur of Nature must be evaluated! As if a confused repugnance sufficed to condemn a theory which depends neither on taste nor sentiment! Or as if one ought to follow servilely the beaten track, even in researches where no success has ever come to those who have followed it!

XXVIII.

If one is satisfied with the exact agreement of this system with physical astronomy and with terrestrial phenomena, he ought not to distrust it, as if this apparent conformity were the effect of the artfulness with which I have adjusted matters or as if other systems also might be rectified so as to agree throughout with the phenomena should a hand more skilful take the same pains to accommodate them to each other. I have not added to the atoms sung by Lucretius any feature directed solely toward the explanation of the great laws discovered by the Moderns. But, on the contrary, I have merely divested the motion of these atoms of an arbitrary feature (the nearly perfect parallelism) by which Epicurus had disfigured the unrestricted motion assumed by Democritus. That was a motion so simple that it would appear as if its inventor had proposed it with no other end but the most absolute simplicity, unconcerned that it might in no way explain real phenomena, but rather, perhaps, contradict them; so that it is impossible that any system can equal this in simplicity. I would even have had no need to advise myself of this correction, in reading the poem of Lucretius, if I had been instructed beforehand in the system of Leucippus and Democritus as I was long after this reading. Finally, the explanations which I have offered ought not to be regarded as in any respect modifications of this system of atoms, for it would be impossible not to fall upon these explanations in seeking to follow out the necessary consequences of this system.[157]

XXIX.

I did not take undue credit to myself when as a child I rectified the system taught by Lucretius and drew from it immediately its most important consequences, for this was extremely easy or rather entirely natural. Besides, I knew but little more the value and solidity of my little views than the child ordinarily knows the wit or sense which we find in its repartees and sallies. Indeed, the extremely simple idea of trying to explain the principal natural phenomena by the aid of a subtle fluid vigorously agitated in every direction has come to many writers who have before presented it in a vague and ill-assured fashion, not to mention that there has been without doubt a still greater number who have not even deigned to communicate at all. I am well convinced that since the law governing the intensity of universal gravitation is similar to that for light, the thought will have occurred to many physicists that an ethereal substance moving in rectilinear paths may be the cause of gravitation, and that they may have applied to it whatever of skill in the mathematics they have possessed.

XXX.

But we may say, How is it that none of these physicists have pushed these consequences to their conclusion and communicated the research? Doubtless because the most of them having no clear view of this chaos (of which the first glance is, I admit, frightful) they have not known how to disentangle it and subject it to their calculations. Or not having firmly grasped the principles of the theory, they have allowed themselves to be seduced by specious sophisms, by which men have pretended to refute in advance all imaginable explanations of gravitation. Or they will have had the foible of bowing to the authority of great names, when it is alleged (whether justly or falsely) that they have pronounced upon the impossibility of this or upon the uselessness of that branch of knowledge. Or they have lacked sufficient love of truth or courage of their convictions to abandon easy pleasures and exterior advantages in order to devote themselves simply to researches at the time difficult and little welcome. Or, finally, they have failed to become impressed with the strength and fecundity of this beautiful system so distinctly as to lead them, in their enthusiasm, to sacrifice to it their other views and projects.