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For this he appears to have been well qualified. He says of himself, that the structure of his mind was such, as had fitted him for understanding the mathematicks well, but not extensively. “ Propre à bien savoir les mathematiques, mais non a en savoir beaucoup.” The first part of this assertion, we imagine, may be understood more literally than the last ; though it is probably true that he was not quite master of all the modern improvements of the calculus. Some of his remarks on the state of the mathematical sciences in France are worth attending to. In a letter to the duke de Rochefoucault, whom he had had the honour to instruct in the mathematicks, dated in 1778, he has this observation.
In their elementary treatises of mathematicks and physicks, the French writers take so little trouble about the foundations of those calculations which they accumulate without end, that it seems as if they wanted to make all their pupils mere clerks in a banking house, or assistants in an observatory. They treat geometry the least geometrically possible, under the pretence that algebraick demonstrations are the shortest: as if the only object were to get to the end, and as if the road leading to it were of no importance. They are in haste to give a few notions, rather grammatical than intellectual, of the sublimer parts, before they have sufficiently developed the elements. They seem desirous of reducing astronomy, the science of motion, and chymistry, to be nothing but the humble attendants on navigation, gunnery, and the arts; as if all the world was destined for inspectors of the marine, of artillery, or manufactures; and as if the cultivation of reason was nothing in comparison with the art of getting wealth This was not the proceeding of Descartes or Newton. p. 272.
This character of the French elementary writers, though, in certain respects, just, evidently has something of the air of satire, and must not be received as perfectly correct. Of too little regard to the methods of pure geometry, and too much haste to reach the more profound parts of the calculus, they may certainly be accused. But a general preference of the methods of algebra and analysis, cannot be regarded as an errour, is the foundations of those methods are carefully and accurately explained. Analytical reasonings are so much preferable to synthetical, and the art of investigation is so much more easily learned in the school of algebra than in any other, that, in a system of mathematical instruction, this latter science is undoubtedly of the first consideration. It is true, on the other hand, that the methods of analysis are not confined to algebra. Geometry has its analytical reasonings, not so extensive, nor so general, as those of algebra, but possessing a degree of simplicity and beauty that is not excelled, or rather, we think, not equalled in any other branch of science. It is a stronger proof of the neglect of geometry, among the French mathematicians, than any thing that Le Sage has alleged, that in the Encyclopedie, intended to exhibit a complete picture of the knowledge of the eighteenth century, the article geometrical analysis is not to be found.
The love of accurate and precise knowledge, which Le Sage possessed eminently, probably qualified him well for a teacher of the mathematical sciences. He had several illustrious pupils, and none, certainly, who does him more credit than the present professor of mathematicks in the university of Geneva M. S. L'Huilier was his relation, and was instructed by him in the science which he now professes with so much credit both to his master and himself. He is one of the few mathematicians equally versed in the simple and elegant methods of the ancient geometry, and in the profound resear. ches of the modern analysis.
Le Sage, through his whole life, had to struggle with a feeble constitution, as well as the mental defects which have been already mentioned. He was particularly afflicted with sleeplessness, which, at times, used greatly to affect his intellectual powers, and reduce them to a state of extreme debility. Notwithstanding this, by employing every moment, when his mind was
clear and active, preserving such order and regularity as supplied the want of memory, committing every thing to writing, and having his papers in a state of the most complete arrangement, he was able to accomplish a great deal, and to devote much time to philosophical pursuits.
His studies, however, were rendered less useful than they might have been with the originality of his turn of thinking, the precision of his knowledge, and the extent of his views, by the number of objects to which he directed his attention, and by his frequent changes from one pursuit to another. Though he came back easily to the same object, yet this did not entirely make up for the want of the continued application necessary in all great undertakings.
Accordingly, though few men wrote so much, and so accurately, he published nothing in his lifetime but mere opuscula, and has left few, if any, of his numerous manuscripts completely ready for the press.
One of the principal pieces which appeared in his lifetime, shared the prize proposed by the academy of Dijon, in 1758, on the cause of chymical affinities. He entitled it, Essai de Chimie Mechaniyue, and endeavoured to explain the whole of chymical action on the principle of impulse. He supposed the impelling fluid to be composed of particles of two kinds; the one greater, and the other less : and he demonstrated, in virtue of that single supposition, that homogeneous bodies must attract one another more than heterogeneous. This, however, it must be confessed, comprehends but a small part of the phenomena of chymistry. It was connected with the work on gravity, which was the great business, and the favourite occupation of his life.
An essay, “ Sur les Forces Mortes," which he sent to the academy of sciences at Paris, was never published.
In the bistory of the same academy for 1756, a remark is inserted from Le Sage, containing the detection of an errour committed by Euclid, in the eleventh book of his Elements, on the subject of solid angles. It is remarkable, that nearly about the same time, Dr. Simpson, of Glasgow, made a similar detection, with respect to the manner in which equal solids are treated by the Greek geometer.
The tract, entitled “ Lucrece Nutonien," was published in the Berlin Memoirs for 1782.
Besides these, he published a few other occasional pieces, and seems to have kept up a pretty extensive correspondence with several of the first philosophers of the age. His manuscripts are, a large treatise “ Sur les Corpusculus Ultramondains;" subordinate to which is “ Histoire Critique de la Pesanteur." This contains much learning, and treats of all the notions that have been entertained on the subject of gravity, and all the theories contrived for explaining it. A treatise on cohesion, intended to show that it cannot be explained by the Newtonian attraction, is recommended by M. Prevost as a work of great inerit, written during the full activity and vigour of the author's mind.
To these must be added the following: on elastick fluids ; on gene. ral physicks; on logick; on moral philosophy; and on final causes : also, Melanges Dystactiques, &c. Among the latter was an Essay on Punctuation, concerning which he had a system of his own. To this system he adhered rigidly; and it is said to be very philosophical; but, perhaps, for that very reason, it has never come into use.
It may be thought extraordinary, that so much should have been done, and yet so little completed. The habit of continually amassing materials, without reducing them into form, had grown on Le Sage to an excessive
degree; and he used to apologize for it by saying, “ that as long as he could find any thing new to put on paper, he grudged the time that must be employed in polishing old materials, or casting them over again."
The ingenuity of his mind, and the original turn of his thoughts, added to a character of great probity and worth, procured him esteem and respect wherever he was known. M. Pervost has given extracts from a number of very interesting letters, which passed between him and several of the most distinguished persons of the age. Among these are Madame Necker, the Dutchess d’Enville, earl Stanhope, the Duke de Rochefoucault, M. M. d'Alembert Euler, Turgot, Boscovich, Lambert, &c.
Though his constitution was originally weak, and his health always infirm, he reached the age of eighty, and died in 1803. His biographer has given a sketch of his intellectual character, from which we shall extract a few passages.
It is impossible not to recognise, in the works of Le Sage, and his manner of thinking, a strong character of originality ; and, if a cautious and regulated invention be characteristick of genius, this philosopher must be numbered with those whom nature has particularly distinguished. All who knew him were at the same time sensible of his peculiarities, which he himself did not, indeed, attempt to conceal, but endeavoured to explain. He acknowledged that two of his faculties were weak-attention and memory. He was unable to fix the former on one, object for any considerable length of time; and, as he could not attend, without great difficulty, to more than one thing at the same moment, he was very easily interrupted. “I supply,” said he, “the want of extent in my attention by great order and regularity; and its want of continuance, by frequently returning to the same subject.”. From this methodical proceeding it arose, that few men were ever more persevering than Le Sage in directing their researches to the same objects.
His memory was unmanageable and capricious in a high degree. He had no power over it; and, in order to direct it, was obliged to have recourse to all sorts of artifices. He siezed, with avidity, the moments when his ideas were clearest, and his faculties most active. “I have,” says he, “ extreme difficulty in connecting my thoughts, so as to make an assemblage at all supportable; and ain like a painter who would work in the night, without any other illumination than what was derived from sudden and unexpected flashes of lightning:
His method and order, in some respects, supplied so well the weakness of his memory, that, in conversation, no defect of that faculty was at all discernible. It was, accordingly, one of his constant sources of complaint, that he could not convince his friends of the badness of his memory. They who conversed with him, heard liim perpetually relate, with precision, the dates, and even the most minute circumstances, of very inconsiderable events. They believed his memory to be tenacious; whereas the truth was, that he kept notes of every thing, and was every now and then consulting his repertories. Such being the
weakness of his intellectual organization, he often asked himself, how he had ever been able to do any thing at all. To this question, his own manuscripts afford many answers; one of the best of which is in a note, entitled “ Clef de Mon Tour d'Esprit.” I have been born with four dispositions well adapted for making progress in science, but with two great defects in the faculties necessary for that purpose. !. An ardent desire to know the truth. 2. Great activity of mind. 3. An uncommon (justesee] soundness of understanding. 4. A strong desire for precision and distinctness of ideas. 5. An excessive weakness of meinory. 6. A great incapacity of continued attention.
By using the resources which nature had bestowed, and compensating, by much skill and labour, the want of the qualities she withheld, he was able to make no small progress even as an inventer in science. He used to apply to himself the saying of Bacon-Claudum in via cursorem extra viam antevertere.
One of the principal causes that retarded the publication of his works, was the difficulty of making his favourite system be relished in the scientifick world. The conviction which he himself had of its truth, and the com
plete persuasion that it must ultimately prevail, could not prevent him from perceiving, that though all acknowledged the ingenuity, yet few were prepared to admit the truth of his theory. He was perfectly aware, that his own way of thinking on this, as well as many other subjects, was peculiar, and not readily adopted by other men.
This is strongly marked by the title of one of his parcels of notes ; “ On the immiscibility of my thoughts with those of others." He has investigated, in his usual way, the causes of this immiscibility, and has divided his readers into different classes, according to their greater or less fitness to judge of the principles of his philosophy. He has applied to himself a line of Ovid, with much truth
Non ego cessavi, nec fecit inertia serum. Without entering on this discussion, we shall endeavour to give the best idea we can of the system so often mentioned, as far as we have been able to collect it from his letters, and from the very ingenious tract, Lucrece Neutonien, which M. Prevost has introduced into his Appendix.
The object of this system was to explain the law of gravity both as it prevails on the earth and in the heavens, by the principle of impulse. The causes of all the motions we perceive in the material world, may be reduced to three-Impulse, Attraction, and Repulsion. Impulse acts by contact; one moving body communicates motion to another body; and the rule by which this change is produced, is, that the motion communicated in any given direction, and that which is lost in the same direction, are precisely equal. The motions that we ourselves impress on the bodies around us, are of this nature.
Again ; when a stone falls to the ground, or when iron approaches a magnet, motion is produced without contact. Both the bodies acquire motions which are equal, but in opposite directions. The motions ascribed to repulsion are of the same kind with these last, inasmuch as there is no contact, and as the motions acquired in opposite directions are equal. The only difference is, that the bodies, instead of approaching, recede from one another. Whether attraction and repulsion may not be regarded as one and the same law, acting under different circumstances, we do not at present inquire. The object of Le Sage was to reduce them both to impulse ; and, could this be done, it would, no doubt, be a great advance in science; and we might seem, in one quarter at least, to have pushed our researches to their legitimate and proper termination. Our idea of the communication of motion by impulse, is not without difficulty; but it is clearer and more familiar to us than any other, and is that with which the inind is most disposed to remain satisfied.
The chrystalline spheres of the ancients may be regarded as the first attempt to explain the motion of the heavenly bodies by impulse. The vortices of Descartes is the next. The ether of Newton is the third. The first is known to be without foundation. The second is a vague and gratuitous supposition. And the third is, at best, far from being satisfactory.
Le Sage has certainly been more fortunate than any of his predecessors; and his hypothesis has this undoubted superiority above all the others that have been proposed for explaining gravitation, that it assigns a satisfactory reason why that force varies inversely as the square of the distance.
Suppose that, through any one point of space, innumerable straight lines are drawn in all different directions, each making a very small angle with those that are nearest it; and let a torrent of particles, or indivisible stoms. move continually in a direction parallel to each of these lines, the section of each torrent, in a transverse direction to its motion, being equal
to the section of the sensible world in the same direction. Thus, there will be an indefinite number of torrents of atoms intersecting one another, in every possible direction, much like the streams of light which issue from all the points of the surface of a luminous body. The analogy between the emanation of light and the motion of those corpuscles, is so close, that an imagination which is familiar with the one, will not experience much difficulty in becoming familiar with the other. Like light, also, the atoms, of which these torrents are composed, must be supposed to move with inconceivable rapidity, and to be of such extreme minuteness, that, though flowing continually in all directions, they do not obstruct or interfere with the motions of one another.
If, now, it be supposed that these atoms are unable to penetrate the solid and indivisible particles of bodies, and, when they enter bodies, can only pass through the intervals or vacuities between their particles, it is evident that they must strike against those particles, and must, therefore, communicate a certain degree of motion to them, or to the bodies of which they are composed.
If, then, there were but a single body in the universe, with whatever force the torrents of atoms struck against its particles, the body would remain at rest, the impulses in opposite directions being perfectly equal. But if there be two bodies, then, since each of them, by intercepting a part of the atoms of the torrents, will shelter the other from the action of so much force, it is evident that the bodies will be both impelled toward one another, and that each of them will receive fewer shocks on the side where the other body is, than on the opposite. Further, if we suppose the bodies spherical, the intensity of this force, cateris paribus, will be proportional to the angular space included within a cone, which has for either base the transverse section of the bodies. Now, it is easy to prove that this angular space is proportional to the square of the distance of the bodies inversely. Therefore, the force with which the bodies will be urged toward one another, will be inversely as the square of the distance, which is the law followed by gravity.
This will be true if the bodies are equal in quantity of matter, so as to intercept equal quantities of the atoms. But if their quantities of matter are unequal, then, at an average of all the chances, each will intercept a number of particles proportional to its quantity of matter, and so the forces with which the bodies are impelled toward one another, will be as the quantity of matter directly, and the square of the distance inversely. This is precisely the law of gravitation; and the particles by which this effect is brought about, are called by Le Sage the gravifick, or the ultramundane atoms.
This hypothesis, as already observed, must be confessed to have done what no other attempt to account for gravity can boast of; that is, to have assigned a reason why that force is inversely as the square of the distance, and directly as the quantity of matter. It has, then, the precision which belongs to truth, and which, though it does not amount to a proof of a hypothesis where it is found, is an abundant reason for rejecting one, where it is wanting.
The vortices of Descartes, and the ether of Newton, do neither of them give any reason why gravity should be supposed to obey one law more than another; why it should be inversely as the squares, any more than the cubes, or any other power, nay, any other function, of the distances. The extreme vagueness of such hypotheses is an unsurmountable objection to them, and, even were they true, it renders them of no use whatsoever.