Georges-Louis Le Sage

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ In order to extricate themselves from this difficulty the atomists would necessarily have rejoined 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, and that these other atoms were in motion exactly like those encountered by the earth. ”

“ Practically, if one omits from the theory of central forces those curious propositions and generalizations which can only be regarded as its luxuries, as well as the delicate evaluations which are required only for the perfecting of astronomical tables, all the rest may be demonstrated sufficiently for the uses of the physicist by the aid of lemmas less exact and universal than those of the calculus. ”

“ Upon this the Epicureans would not have been slow to reply that since the distance from the [144] 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. ”

“ 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. ”

“ That the law of areas proportional to times is a necessary consequence of gravitation, always directed toward a single point, is demonstrated by elementary geometry in the first proposition of Newton's Principia. ”

“ 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. ”

“ For example, several hundred times greater relative to the velocity of the earth than the gravitation of the earth toward the sun multiplied by the number of times the firmament would contain the disc of the sun is greater than the greatest resistance which the secular differences in the length of the year permit us to suppose the earth experiences from celestial matter. ”

“ But the atomists would have encountered one very serious objection, to which they were necessarily exposed in common with all physicists who undertake an explanation of gravitation. For by having thickness a roof receives not a whit more of hail, or a shield of arrows; whereas, remaining otherwise unchanged, the weight of all bodies is augmented in direct proportion of their thickness. ”

“ Already some impartial philosophers are agreed that such conjectures if lucid and capable of evaluation might be useful to the most rigorous physicists, were it only in suggesting to them definite points of view from which to direct experiment, in the place of that indecision in which the mere vague wish for new investigation has often left them. ”

“ The gravitational atoms are directed not only toward the centers of the greater bodies, but toward each of their particles as well, since they move indiscriminately in all directions in space. The atoms, moreover, act effectively in those directions in which their antagonists are intercepted; that is to say, in all directions in which there are particles of matter. Therefore they tend to move the heavy masses which they encounter not toward the heavenly bodies in gross, but toward each of their particles in detail. ”

“ 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. ”

“ Inasmuch as one body is pushed toward another by the atoms which the second body has deprived of direct antagonists, while the latter body is pushed toward the former by these same antagonists, the two bodies are necessarily pushed toward each other with equal force, whatever be the inequality of their masses or the differences in their forms. ”

“ On the whole, then, the tenor of modern thought goes in the direction in which we are led by this theory, if by that we understand it, not in its first crude enunciations, but with the modifications which can now be legitimately associated with it, and which tend to make it both more suggestive and to maintain a continued interest in it-an interest which seems to justify the present publication of a paper with which so few are familiar at first hand. ”

“ 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. ”

“ Such a supposed character for these philosophers is by no means forced, since the physical and speculative dogmas of Epicurus did not necessarily entail his moral precepts and practices.↑ To assign to these corpuscles the velocity of sound even would be sufficient. For the velocity of sound is more than thirty-four times as rapid as that of a body which has fallen one second, or more than seventeen times as great as that of one that has fallen two seconds, etc. ”

“ But it has never been found by merchants and artisans, who are continually in the habit of weighing, that bodies appear heavier in open air than when under cover, and gold-beaters have never perceived that the weight of the metal augments in proportion to the increase of its surface. ”

“ They are so thinly scattered-that is to say, their diameters are so small relative to their mutual mean distance-that there are no more than a few hundreds which encounter one another in the course of a thousand years. ”

“ 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. ”

“ According to the report of Diogenes, Laertius, and of Porphyry, Democritus had attended the teaching of the Pythagoreans; and besides, the Eleatic sect (if one may credit Strabo) was nothing bnt an offshoot of the Italic. Finally, the atomists, following Democritus, would have had opportunity to be even better instructed than he in regard to the earth's motion. For this doctrine was supported by a multitude of philosophers of all countries, among whom the principal names, in addition to those already cited, are Archimedes and Nicetas, of Syracnse ”

“ 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. ”

“ 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. ”

“ Such things, for example, as the famous Kepler's laws - discovered scarcely two centuries ago, and founded in part upon gratuitous conjectures and in part upon tedious gropings - would have been nothing but special inevitable corollaries of the general knowledge which the ancient philosophers could easily draw from nature's own mechanism. ”

“ Parallel to each of these directions there moves a stream or torrent of corpuscles. Now, in order to give it no more than the necessary size, the transverse section of this current has the same contour as [159] the orthogonal projection of the visible universe upon the plane of this section.
Sixth. The different parts of a single current are sensibly of equal density, either where contemporary portions of sensible magnitude or successive portions occupying sensible times in traversing a given surface are compared. The densities of different currents are also equal. ”

“ Thales and Zeno had taught it, and all the astronomers believed it. (See the Timams of Plato, the close of the second book of Aristotle upon the Heavens, the Hour-Glass of Archimedes, and the tenth chapter of the third book of Plutarch upon the Opinions of the Philosophers.) ↑ Neither Epicurus nor Lucretius discovered the figure of the earth. But it seems probable that they conformed to the opinions of Democritus upon all questions where they did not expressly oppose him. ”