(Roger Joseph), one of the most eminent mathematicians and philosophers of the present age, was born, of virtuous and pious parents, on the He studied Latin grammar in the schools which were taught by the Jesuits in his native city. Here it soon appeared that he was endowed with superior talents for the acquisition of learning. He received knowledge with great facility, and retained it with equal firmness. None of his companions more readily perceived the meaning of any precept than he; none more justly applied general rules to the particular cases contained under them. He enounced his thoughts with great perspicuity, and came soon to compose with propriety and elegance. His application was equal to his capacity, and his progress was rapid. At the beginning of the 15th year of his age, he had already gone through the grammar classes with applause, and had studied rhetoric for some months. His moral behaviour had likewise been very good; he was respectful and obedient to his parents and masters, affable and obliging to his equals, and exemplary in all the duties of religion. It was now time for him to determine what course he would steer through life; nor did he hesitate long in coming to a resolution.

The Jesuit fathers, by teaching the sciences to youth, were very useful, and at the same time had a fine opportunity of observing their scholars, and of drawing into their society those boys who seemed fit for their purpose. Such a subject as the young Boscovich could not escape their attention. They showed him particular kindness, to which he was not insensible. He had an ardent thirst for learning; to advance in which he felt himself capable; and he thought he could nowhere have a better opportunity of gratifying this laudable inclination than in their order, in which so many persons had shone in the republic of letters. Accordingly, with the consent of his parents, he petitioned to be received among them; and his petition was immediately granted, because it was desired by those to whom it was made.

It was a maxim with the Jesuits to place their most eminent subjects at Rome, as it was of importance for them to make a good figure on that great theatre. Wherefore, as Roger's masters had formed great expectations of him, they procured his being called to that city; whether he was sent in the year 1725, and entered the noviciate with great alacrity. This noviciate was a space of two years, in which the candidate made a trial of his new state of life; and in the mean time his new superiors observed him, and deliberated whether or not they would admit him into their body. During these two years, the novice was principally employed in exercises of piety, in studying books of Christian morality, and in becoming perfectly acquainted with the rules and constitutions of the order. After these two years were past, the Jesuits were willing to retain Boscovich, and he was no less desirous of remaining with them. He therefore passed to the Boscovich-school of rhetoric; in which, for two other years under the most expert masters of the society, young men perfected themselves in the arts of writing and speaking, which was of so great consequence to persons who were destined to treat so much with their neighbours. Here Boscovich became perfectly well acquainted with all the classical authors, and applied with some predilection to Latin poetry.

After this he removed from the noviciate to the Roman College, in order to study philosophy, which he did for three years. In order to understand the doctrine of physics, it was necessary to premise the knowledge of the elements of geometry, which is also otherwise proper for forming the mind, and for giving to it a true taste for truth. Here it was that our young philosopher came to be in his true element; and it now appeared how extremely fit his genius was for this kind of study. His master, though he was able and expert, instead of leading him on, was scarcely able to keep pace with him, and his disciples were left far behind. He likewise found the application of the mathematics to natural philosophy pleasant and easy. From all this, before the end of the three years, he had made a great advancement in physical and mathematical knowledge, and his great merit was generally acknowledged by his companions, and well known to his superiors. He had already begun to give private lessons on mathematics.

According to the ordinary course followed by the Jesuits, their young men, after studying philosophy, were wont to be employed in teaching Latin and the belles lettres for the space of five years, that so they might become still better acquainted with polite learning, and arrive at the study of theology and the priesthood at a riper age. But as Roger had discovered extraordinary talents for geometrical studies, it was thought by his superiors that it would be a pity to detain him from his favourite pursuits in a drudgery for which so many others were fit enough. He was therefore dispensed with from teaching those schools, and was commanded to commence the study of divinity.

During the four years that he applied to that sublime science, he still found some leisure for geometry and physics; and even before that space was ended, he was named professor of his beloved mathematics.

He was now placed in an office for which he was superlatively fit, and for which he had a particular predilection. Besides having seen all the best modern productions on mathematical subjects, he studied diligently the ancient geometers, and from them learned that exact manner of reasoning which is to be observed in all his works. Although he himself perceived easily the concatenation of mathematical truths, and could follow them into their most abstruse recesses, yet he accommodated himself with a fatherly condescension to the weaker capacities of his scholars, and made every demonstration clearly intelligible to them. When he perceived that any of his disciples were capable of advancing faster than the rest, he himself would propose his giving

(a) For this article we are indebted to a dignified clergyman of the church of Rome, who was one of Boscovich's favourite pupils. Bolcovich, giving them private lessons, that so they might not lose their time; or he would propose to them proper books, with directions how to study them by themselves, being always ready to solve difficulties that might occur to them.

To the end that he might be the more useful to his scholars, he took time from higher pursuits to compose new elements of arithmetic, algebra, plain and solid geometry, and of plain and spheric trigonometry; and although these subjects had been well treated by a great many authors, yet Bolcovich's work will always be esteemed by good judges as a masterly performance, well adapted to the purpose for which it was intended. To this he afterwards added a new exposition of conic sections; in which, from one general definition, he draws, with admirable perspicuity, all the properties of those three most useful curves. He had meditated a complete body of pure and mixed mathematics, in which were to be comprehended treatises on music, and on civil and military architecture; but from accomplishing this he was prevented by other necessary occupations.

According to the custom of schools, every class in the Roman College, towards the end of the scholastic year, gave to the public specimens of their proficiency. With this view Bolcovich published yearly a dissertation on some interesting physico-mathematical subject. The doctrine of this dissertation was defended publicly by some of his scholars, assisted by their master. At these literary dissertations there was always a numerous concourse of the most learned men in Rome. His new opinions in philosophy were here rigorously examined and warmly controverted by persons well versed in physical studies; but he proposed nothing without solid grounds; he had foreseen all their objections, answered them victoriously, and always came off with great applause and increase of reputation. He published likewise dissertations on other occasions; and these works, though small in size, are very valuable both for the matter they contain, and also for the manner in which it is treated. The principal subjects of these dissertations are the following: the spots in the sun; the transit of mercury under the sun; the geometrical construction of spheric trigonometry; the aurora borealis; a new use of the telescope for the determination of celestial objects; the figure of the earth; the arguments made use of by the ancients to prove the rotundity of the same; the circles which are called osculators; the motion of bodies projected in a space void of resistance; the nature of infinites and of infinitely little quantities; the inequality of gravity in different parts of the earth; the annual aberration of the fixed stars; the limits of the certainty to which astronomical observations can arrive; a discussion on the whole of astronomy; the motion of a body attracted by certain forces towards an immovable centre in spaces void of resistance; a mechanical problem on the field of greatest attraction; a new method of using the observation of the phases in the lunar eclipses; the cycloid; the loxodrome and certain other curves; the forces that are called gravity; the comets; the flux and reflux of the seas; light; whirlwinds; a demonstration and illustration of a passage in Newton concerning the rainbow; the demonstration and illustration of a method given by Euler regarding the calculation of fractions; the determination of the orbits of a planet by means of catoptries, certain conditions of its motions being given; Bolcovich the centre of gravity and that of magnitude; the atmosphere of the moon; the law of continuity, and the consequences of it in the elements of matter and their forces; the law of the forces that exist in nature; lenses and dioptrical telescopes; the perturbation which appears to be caused mutually by Jupiter and Saturn, and that chiefly about the time of their conjunction; the divisibility of matter and the elements of bodies; the objective micrometer; besides other subjects of the like nature, of which he has treated in separate pieces, or in communications inserted in the transactions of literary societies or academies, he being a member of those that are most famous in Europe. It was in some of the abovementioned dissertations that Bolcovich made known first to the world his sentiments concerning the nature of body, which he afterwards digested into a regular theory, which is justly become so famous among the learned.

Father Noceti, another Jesuit, had composed two excellent poems on the rainbow and the aurora borealis. These poems were published with learned annotations by Bolcovich; in which, among other things, he with great sagacity discovers errors in optics into which De Dominici, Kepler, and others, had fallen.

His countryman, Benedict Stay, after having published the philosophy of Descartes in Latin verse, attempted the same with regard to the more modern and more true philosophy, and has executed it with wonderful success, to the admiration of all good judges. The two first volumes of this elegant and accurate work were published with annotations and supplements by Bolcovich. These supplements are so many short dissertations on the most important parts of physics and mathematics. Here is to be found a solution of the problem of the centre of oscillation, to which Huygens had come by a wrong method; here he confutes Euler, who had imagined that the vis inertiae was necessary in matter; here he refutes the ingenious efforts of Riccati on the Leibnizian opinion of the forces called living. He likewise shews the falsehood of the mathematical prejudices, according to which the right line is considered as essentially more simple than curves, and makes it appear, that the notion of the said right line is commonly accompanied with many paradoxes. He demonstrates by the doctrine of combinations, some beautiful theorems concerning the space occupied by the small masses of body, with many useful observations on space and time.

Benedict XIV., who was a great encourager of learning, and a benevolent patron of learned men, was not ignorant how valuable a subject Rome possessed in Bolcovich; and this pope gave him many proofs of the esteem he had for him. Two figures which had been perceived in the cupola of the church of St Peter's on the Vatican had occasioned some alarm. The pope desired Bolcovich and some other mathematicians to make their observations and give their opinion on the same. They obeyed, and their opinion was printed. They showed that there was no cause to apprehend danger; but, for greater security, they proposed certain precautions, which were adopted and put in execution.

The high opinion which the pope had formed of his talents, and the favour in which he was with Cardinal Valenti, Boschi Valenti, minister of state, proved hindrances to his going to America, for which a proposal was made to him by the court of Lisbon. Some differences had long subsisted between Spain and Portugal concerning the boundaries of their respective dominions in that great continent; and John V. of Portugal wished that Bofcovich would go over and make a topographical survey of the country in dispute. He was not unwilling to undertake such a task, which was entirely to his taste; and he was resolved at the same time to measure a degree of the meridian in Brazil, which might be compared with that measured at Quito by the French academicians Bouguer and Condorcet, with the Spaniards Ulloa and Doy. But the pope hearing of this proposal, signified to the Portuguese minister at Rome, that his master must needs excuse him for detaining Bofcovich in Italy, where he had occasion for him, and could by no means consent to part with him.

Accordingly a commission was given to Bofcovich by Benedict to correct the maps of the papal estate, and to measure a degree of the meridian, passing through the same. This he performed with great accuracy, assisted by F. Christopher Maire an English Jesuit, and likewise a great mathematician. Their map was engraved at Rome, and is perhaps the most exact piece of the kind that ever was printed, as all the places are laid down from triangular observations made by the ablest hands. Bofcovich also published, in a quarto volume in Latin, an account of the whole expedition, which appeared at Rome in the year 1755, and was afterwards printed at Paris in French in the year 1770. Here he gives a detail of their observations and of the methods they followed, and likewise of the difficulties they encountered, and how they were surmounted. One of these embarrassed them a good deal at the time, but was afterwards matter of diversion to them and others. Some of the inhabitants of the Apennines, seeing them pass from hill to hill with poles and strange machines, imagined that they were magicians come among their mountains in search of hidden treasures, of which they had some traditions; and as tempests of thunder and hail happened about the same time, they supposed that these calamities were caused by the sorceries of their new visitants. They therefore insisted that Bofcovich and Maire should depart; and it was not easy to convince them that their operations were harmless. In this work there is inserted a description of the instruments made use of in determining the extent of the degree of the meridian; and the whole work may be extremely useful to practical geometers and astronomers.

In the year 1737 the republic of Lucca entrusted Bofcovich with the management of an affair which was to them of considerable importance. Between that republic and the regency of Tuscany there had arisen a disagreeable dispute concerning the draining of a lake, and the direction to be given to some waters near the boundaries of the two states. The Lucchese senate chose our philosopher to treat of this business on their part. He repaired to the spot, considered it attentively, and drew up a writing, accompanied with a map, to shew more clearly what appeared to him most equitable and most advantageous for both parties. In order to enforce his reasons the more effectually, it was thought proper that he should go to Vienna, where the emperor Francis I. who was likewise grand duke of Tuscany, resided. He was so successful in this negotiation, that he obtained every thing that Lucca desired, and at the same time acquired great esteem at the imperial court. In proof of this, the empress queen made his opinion be asked concerning the library of the Cæsarian library, and the repairs to be made in it; which he gave in writing, and it was received with thanks, as being very well grounded.

When he had concluded the affair which had brought him to Vienna, he foresaw that, for a month or two, the snows in the Alps would not allow him to return to Italy. He therefore resolved to employ that time in completing his system of natural philosophy, on which he had been meditating for the space of thirteen years. He published his work on that great subject in the beginning of the year 1758, in the abovementioned city. We shall in the end give an account of that celebrated system, and here go on with our narration.

On his return to Lucca, he not only met with the approbation of all he had done for the interest of the republic, but also the senate, in testimony of their gratitude, made him presents, and enrolled him in the number of their nobility, which was the greatest honour they had in their power to confer on him.

He, who was thus useful to foreigners, could not refuse to be serviceable to his own country when an occasion of being so offered itself. The British ministry had been informed, that ships of war, for the French, had been built and fitted out in the sea-ports of Ragusa, and had signified their displeasure on that account. This occasioned uneasiness to the senate of Ragusa, as their subjects are very seafaring, and much employed in the carrying trade; and therefore it would have been inconvenient for them to have caused any difficulty against them in the principal maritime power. Their countryman Bofcovich was desired to go to London, in order to satisfy that court on the abovementioned head; and with this desire he complied cheerfully on many accounts. His success at London was equal to that at Vienna. He pleaded the cause of his countrymen effectually there, and that without giving any offence to the French, with whom Ragusa soon after entered into a treaty of commerce.

Bofcovich came to London the more willingly, as he was desirous of conversing with the learned men of Britain. He was received by the president and principal members of the Royal Society with great respect; and to that great body he dedicated his poem on the eclipses of the sun and moon, which was printed on this occasion at London, in the year 1760. This is one of his works on which he himself put the greatest value, and it has been much esteemed by the learned. An edition of it was published at Venice the year following, and a third at Paris, which is the most correct: a translation of it into French has likewise been published at Paris. In this very elegant Latin poem he gives an exact compend of astronomy, which serves as an introduction to the subject; he then explains all that belongs to the doctrine of eclipses, and their use in geography; he considers the phenomena that are observed in the eclipses of the sun, and likewise of the moon; he proposes a theorem, which is his own, concerning the distribution of light reflected from the atmosphere of the earth by the shadow of the moon, which happens... happens in the lunar eclipses; he explains the phenomenon of the reddish colour which often appears in the moon when she is eclipsed, of which a sufficient explication had not before been given: this the author draws from the fundamental doctrine of Newton's theory concerning light and colours; and hence takes occasion to give a clear idea of the principal consequences of the said theory. All this is clothed with a beautiful poetical dress, and is adorned with pleasant episodes, not to mention the learned annotations which are subjoined. This poem was composed, for the most part, whilst the author was in journeys, or by way of amusement, when he was obliged to wait for the opportunities of making astronomical observations.

The fellows of the Royal Society invited Boscovich to accompany some of their number to America, to observe the transit of Venus, which was to happen in the year 1762; but being otherwise engaged, he could not accept of that invitation. He intended, however, by all means to observe that remarkable phenomenon, and had fixed on Constantinople as a proper place for doing so. He was conducted thither in a Venetian man of war, and much honoured by one of the bays of that republic, who commanded the vessel; but, to his great regret, they arrived too late. He returned, by land, in the company of the English ambassador; and a relation of that journey was published in French and afterwards in Italian.

During these journeys, Boscovich's place in the Roman College was well filled by some of those whom he himself had trained up in mathematical learning. He was now called by the senate of Milan to teach mathematics in the university of Pavia, with the offer of a very considerable salary. He and his superiors thought proper to accede to this proposal, and he was received without being subjected to any previous examination; which was always observed, excepting in such an extraordinary case, by the decrees of the university. Here he taught, with great applause, for the space of six years, having at the same time the care of the observatory of the Royal College of Brera. About the year 1770, the empress queen made him professor of astronomy and optics in the Palatine schools of Milan; requiring of him, however, that he should continue to improve the observatory of Brera; which, under his direction, became one of the most perfect in Europe.

Here he was extremely happy, teaching the sciences, applying to his favourite studies, and conversing and corresponding with men of learning and of polished manners; when an event happened which caused to him the most sensible affliction. In the year 1773, the society to which he belonged, and to which he had been from his youth warmly attached, was, to his great regret and disappointment, abolished. They who had been Jesuits were allowed no longer to teach publicly; nor was there any exception made in favour of Boscovich, neither (such was his humour then) would he have accepted of it, though it had been offered him. Proposals were made to him by several persons of distinction; and, after some deliberation, he chose Paris for his place of abode; to which he was induced by the circumstance of his being intimately acquainted with the prime minister at that court. He had not been many months at Paris when the university of Pisa sent him an invitation to go thither, in order to profess astronomy. But the French minister, understanding this, declared to the minister of Tuscany, that it was the intention of his most Christian majesty to make his dominions agreeable to Boscovich, by giving him liberal appointments. In fact he was soon naturalized, and two large pensions were bestowed on him; the one as an honourable support, to the end that he might prosecute his sublime studies at his ease and in affluence; the other as a salary annexed to a new office, created in his favour, under the name of Director of Optics for the Sea Service, and with the sole obligation of perfecting the lenses which are used in achromatic telescopes.

At Paris he remained ten years, applying principally to optics, and much regarded, not only by the most reasonable men of letters, but likewise by the princes and ministers, both of France and of other nations. But the greatest men are not exempt from being envied. Some of the French were displeased that a foreigner should appear superior to themselves; others of them could not forget that Boscovich had discovered and exposed their mistakes. The irreligion which prevailed too much among those who bore the name of philosophers, was disagreeable to him. These, and other such circumstances, made him wearied of Paris, and he desired to revisit his friends in Italy; for which purpose he obtained leave of absence for two years.

The first place in Italy in which he made any stay was at Bassano, a town in the territories of Venice. Here, mindful of his obligations, he printed what he had been preparing for the press during his stay in France; and this composes five volumes in large octavo, and is a treasure of optical and astronomical knowledge. The subjects treated of in these volumes are as follow: A new instrument for determining the refracting and diverging forces of diaphanous bodies; a demonstration of the falsehood of the Newtonian analogy between light and sound; the algebraic formulæ regarding the focuses of lenses, and their applications for calculating thephericity of those which are to be used in achromatic telescopes; the corrections to be made in ocular lenses, and the error of the sphericity of certain glasses; the causes which hinder the exact union of the solar rays by means of the great burning glasses, and the determination of the loss arising from it; the method of determining the different velocities of light passing through different mediums by means of two dioptrical telescopes, one common, the other of a new kind, containing water between the objective glass and the place of the image; a new kind of objective micrometers; the defects and inutility of a dioptrical telescope proposed and made at Paris, which gives two images of the same object, the one direct, the other inverse, with two contrary motions of moveable objects; masses floating in the atmosphere, as hail of an extraordinary size, seen on the sun with the telescope, and resembling spots; the astronomical refractions, and various methods for determining them; various methods for determining the orbits of comets and of the new planet, with copious applications of their doctrines to other astronomical subjects, and still more generally to geometry and to the science of calculation; the errors, the rectifications, and the use of quadrants, sextants, of astronomical sectors, of the meridian line, of telescopes called the instruments of transits, of the meridian, would take occasion to tax him with ingratitude, and hence his reputation would be tarnished. These, and other such thoughts, occasioned a great perplexity of mind, which was followed by a deep melancholy; and this could not be alleviated by the advice and comfort of his friends, because by degrees he became incapable of hearing reason, his ideas being quite confused, and his imagination disordered. To this disagreeable change the state of his health perhaps contributed. A gout had been wandering for some time through his body, and he had caught a severe cold; nor would he admit of medical assistance, of which he had always been very difficult. It may also be that his long and intense application had hurt the organs of the brain, which in some manner are subservient to the use of reason as long as the soul is united to the body. Be that as it will, during the last five months of his life this great man, who had been so far superior in reasoning to his ordinary fellow creatures, was much inferior to every one of them who is endued with the right use of the understanding. He had indeed some lucid intervals, and once there were hopes of a recovery; but he soon relapsed, and an impotency breaking in his breast, put an end to his mortal existence. He died at Milan on the 13th of February 1787, in the 76th year of his age.

He was tall in stature, of a robust constitution, of a pale complexion. His countenance was rather long, and was expressive of cheerfulness and good humour. He was open, sincere, communicative, and benevolent. His friends sometimes regretted that he appeared to be too irritable, and too sensible of what might seem an affront or neglect, which gave himself unnecessary uneasiness. He was always untainted in his morals, obedient to his superiors, and exact in the performance of all Christian duties, as became a Catholic priest, and in the observance of the particular rules of his order. His great knowledge of the works of nature made him entertain the highest admiration of the power and wisdom of their Creator. He saw the necessity and advantages of a divine revelation, and was sincerely attached to the Christian religion, having a sovereign contempt of the presumption and foolish pride of unbelievers; and being fully persuaded that we cannot make a more noble use of our understanding than by subjecting it humbly to the authority of the Supreme Being, who knows numberless truths far beyond the utmost limits of our narrow comprehension, and who may justly require our belief of any of them that he sees fit to propose to us.

The death of our philosopher, who truly deserved that name, was heard with regret by the learned throughout Europe, and more than ordinary respect has been paid to his memory. At Ragusa funeral exercises were performed for him with great solemnity by order of the senate, who assisted at them in a body; on which occasion an eloquent oration in praise of him was pronounced. By a decree of the same senate, a Latin inscription to his honour, engraved on marble, was placed in the principal church of their city. Of this inscription the following is a copy:

N Boscovich This inscription was composed by his friend and countryman the celebrated poet Benedict Stay. Zamagna, another of his countrymen, who had likewise been his fellow Jesuit, published a panegyric on him in elegant Latin. A short encomium of him is to be found in the *Elogio della Litteratura Europea*; and another, in form of a letter, was directed by M. de la Lande to the Parisian journalists, and by them given to the public. A more full eulogy has been written by M. Fabroni; and another is to be met with in the journal of Modena; a third was published at Milan by the Abbate Ricca; and a fourth at Naples by the Dr Julius Bajamonti, of which a second edition was made in the year 1790. Of this last chiefly use has been made here.

But what must secure to Boscovich the esteem of posterity are his works, of the greater part of which we have already taken notice. We have mentioned, 1. His Elements of Mathematics, with his Treatise on Conic Sections; 2. His many dissertations published during his professorship in the Roman college; 3. His account of his Survey of the Pope's Estate; 4. His Theory of Natural Philosophy; 5. His Poem on the Eclipses; 6. His five volumes printed at Baffano.

To these we may add his hydrodynamical pieces. He had made a particular study of the force of running water, and of its effects in rivers; and he was often consulted concerning the best means to prevent rivers from corroding their banks, and from overflowing the neighbouring plains, which often happens in Italy, where the Alps and Apennines pour down so many impetuous streams. He gave a writing on the damages done by the Tiber at Porto Felice; another on the project of turning... It now remains that we give an account of his Theory of Natural Philosophy; and in doing this we shall, in the first place, lay before our readers a view of this system. We shall, in the second place, relate, from what principles and by what steps it was deduced. We shall, thirdly, take notice of the principal objections made to it, and subjoin the author's answers to the same. We shall, finally, shew how happily it may be applied to explain the general properties of matter, as well as the particular qualities of all the classes of bodies, which have been examined according to what it teaches.

I. In this system, therefore, the whole mass of matter, consisting of which all the bodies of the universe are composed, consists of an exceeding great, yet still finite, number of simple, indivisible, inextensible, atoms. These atoms are endowed with repulsive and attractive forces, which vary and change from the one to the other, according to the distance between them, in the following manner: In the least and innermost distances they repel one another; and this repulsive force increases beyond all limits as the distances are diminished, and is consequently sufficient for extinguishing the greatest velocity, and system of preventing the contact of the atoms. In the infiniblable distances, this force is attractive, and decreases, at least sensibly, as the squares of the distances increase, constituting universal gravity, and extending beyond the sphere of the most distant comets. Between this innermost repulsive force and the outermost attractive one, in the infiniblable distances, many varieties and changes of the force, or determination to motion, take place: for the repulsive force decreases as the distance increases. At a certain distance it comes to vanish entirely; and, when that distance is increased, attraction begins, increases, becomes less, vanishes; and the distance becoming greater, the force becomes repulsive, increases, lessens, and vanishes as before. Many varieties and changes of this kind happen in the infiniblable distances, sometimes more rapidly, sometimes more slowly, and sometimes one of the forces may come to nothing, and then return back to the same without passing to the other. For all this there is full room in the distances that are infiniblable to us, seeing the least part of space is divisible in infinitum. Besides these repulsive and attractive forces, our atoms have that vis inertiae which is admitted by almost all modern philosophers. These atoms, endowed with these forces, constitute the whole substance of Bofcovich's system; which, however simple and short it may appear to be, has numberless and very wonderful consequences, as we shall see afterwards. But, that the whole theory may be easily formed, we shall make use of a geometrical figure well accommodated to that purpose. The right line C'AC' is an axis, from which, in the point A', is drawn the plate VI. right line AB at right angles. AB is considered as an asymptote; on each side of which the two curves, quite similar and equal, DEFGHIJKLMNOPQRSTUVWXYZVU on the one side, and DEFG' on the other, are placed. Now, if ED be supposed to be asymptotic, and be extended, it will still approach to BA, but will never come to touch it. This curve ED approaches to the axis CC', comes to it in E, cuts it and departs to a certain distance in F, after which it again approaches the same axis and cuts it in G. In like manner it forms the arches GHI, IKL, LMN, NOP, PQL. At last it goes on in TpV, which is asymptotic, and approaches to the axis; so that the distances from it are in a duplicate reciprocal proportion of the distances from the right line BA. If from any points of the axis, as from a, b, d, we raise the perpendiculars ag, br, db, the segments of the axis Aa, Ab, Ad, are called abscissae, and represent the distances of any two points of matter from one another; and the perpendiculars ag, br, db, are called ordinates, and exhibit the repulsive or attractive force, according as it lies on the same side with D, or on the other side of the axis.

Now it is evident that, in this form of the curve line, the ordinate ag will be increased beyond whatever limits, if the abscissa Aa be lessened likewise beyond whatever limits; that if this abscissa be increased to Aa, the ordinate will be lessened, and will pass into br, which will still be lessened as it approaches from b to E, where it will come to nothing; that then, the axis being increased to Ad, the ordinate will change its direction into bb, and, on the opposite side, will increase at first Before this to F, then it will decrease through I as far as G, where it will again vanish, and again change its direction in Natural Philosophy, m to the former; and that, in the same manner, it will vanish and change its directions in all the sections I, L, N, P, R, until the ordinates o, p, r, become of a constant direction, and decrease, at least sensibly, in a reciprocal duplicate proportion of the abscissas A, B, C. Therefore, it is manifest, that by such a curve are expressed our forces; at first repulsive, and increasing beyond all limits, the distances being lessened in like manner, and which decrease, the same distances being augmented; then vanish, change their direction, and become attractive; vanish again, and become repulsive; till at last, at sensible distances, they remain on the side opposite to D, and are attractive in a duplicate reciprocal proportion of the distances.

We may also observe, that the ordinates may increase or decrease rapidly, as in y v, z t, or slowly, as in v x, w c; and consequently, that the forces may increase or decrease in like manner. We may add, that the curve may return back without intersecting, or even touching, the axis, as in f, and may return after having touched the same axis.

Although this curve expresses very clearly the repulsive and attractive forces of our system, yet, at first sight, it may appear to be a complicated irregular line. But the author shews that his curve is uniform and regular, and may be expressed by one uniform algebraical equation; which it will be necessary for us to consider, in order to give satisfaction to our readers, and do justice to the theory.

Therefore, from what we have seen, the curve must have the following six conditions: 1st, It must be regular and simple, and not composed of an aggregate of arches of different curves. 2ndly, It is necessary that it cut the axis CAC in certain given points only, at two equal distances on each side AE', AE, AG', AG, and so on. 3rdly, That to every abscissa an ordinate correspond. 4thly, That if we take equal abscissas on each side of A, they have equal ordinates. 5thly, That the right line AB be an asymptote, the area BAED being asymptotical, and consequently infinite. 6thly, That the arches terminated by any two intersections may be varied at pleasure, and recede to any distance from the axis CAC, and approach at pleasure to whatever arches of whatever curves, cutting them, touching them, or osculating them, in any place and manner.

In order to find an algebraical formula expressing the nature of a curve line that would answer all these six conditions, let us call the ordinate y, the abscissa x, and let it be made x = z. Then let us take the values of all the abscissas AE, AG, AI, &c. with the negative sign, and let the sum of the squares of all these values be called a, the sum of the products of every two squares b, the sum of the products of every three, c, and so on; and let the product of all of them be called f, and the number of the same values m. All this being supposed, let it be made z = a + az + bz + cz + &c. + f = P. If we suppose P equal to nothing, it is clear that all the roots of that equation will be real and positive; that is, the squares only of the quantities AE, AG, AI, &c. which will be the values of z; and therefore, as it is z = ± √z, because it is z = z, it is likewise clear that the values of z will be both AE, AG, AI, positive, and AE', AG', &c. ne. Boffovich's negative.

This being done, let any quantity be multiplied by z, providing it hath no common divisor with P, left vanishing, it likewise might vanish; and having made x an infinitesimal of the first order, it may become an infinitesimal of the same, or of a lower order, as will be whatever formula z + z + z + &c. + l; which, being supposed equal to 0, may have as many imaginary, and as many and whatever real roots, providing none of them be those of AG, AE, AI, &c., either positive or negative. If then the whole formula be multiplied by z, let this product be called Q.

If we make P - Q = 0, this equation will satisfy the five first conditions above mentioned; and the value of Q being properly determined, the sixth condition also may be complied with.

For, in the first place, seeing the value P and Q are made equal to 0, they have no common root, and therefore no common divisor. Hence this equation cannot be reduced to two by division; and therefore it is not composed of two equations, but is simple, and therefore exhibits one simple continued curve, which is not composed of any others; which is the first condition.

Secondly, The curve thus expressed will cut the axis CAC in all the points E, G, I, &c. G', &c. and in them only; for it will cut that axis only in those points in which y = 0, and in all of them. Moreover, where it will be y = 0, it will also be Q = 0; and therefore, because of P - Q = 0, it will be P = 0. But this will happen only in those points in which z will be one of the roots of the equation P = 0; that is, as we have seen above, in the points E, G, I, or E', G', &c.; therefore, only in those points will y vanish, and the curve cut the axis. Again, that the same curve will cut it in all these points, is clear from this, that in them all it will be P = 0. Wherefore it will likewise be Q = 0; but it will not be Q = 0, seeing there is no common root of the equations P = 0 and Q = 0; it must therefore be y = 0, and the curve will cut the axis; and thus the second condition is satisfied.

Besides, whereas it is P - Q = 0, it will be y = P/Q; the abscissa x being, however, determined, we will have a certain determinate quantity for x; and thus P, Q, will be determined, and the only two of the kind. Therefore y also will be sole and determined; and therefore to every abscissa x, one only ordinate y will correspond. This is the third condition.

Again, whether x be assumed positive or negative, providing it be of the same length, still the value z = nx will be the same, and therefore the values of both P and Q will be the same; wherefore y will still be the same. Taking, therefore, equal abscissas x on both sides of A, the one positive, the other negative, they will have equal corresponding ordinates. This is the fourth condition.

If x be lessened beyond all limits, whether it be positive or negative, z likewise will be lessened beyond all limits, and will become an infinitesimal of the second order; wherefore, in the value P, all the terms will decrease in infinitum, except in y, because all the rest besides it are multiplied by z; and thus the value P will be as yet finite. But the value Q, which has the formula BOS

BOS

being successively put for \( x \), the values of the ordinate Bozovich's \( y \) will be successively be \( N_1, N_2, N_3, \ldots \); and, therefore, that the curve must pass through these given points in those given curves; and fill the value \( Q \) will have all the preceding conditions. For \( x \) being lessened beyond whatever limits, every one of its terms will be lessened beyond whatever limits, seeing all the terms of the value of \( T \) are lessened which were thus assumed, and likewise the terms of the value \( R \) are lessened, which are all multiplied by \( z \); and, besides this, there will be no common divisor of the quantities \( P \) and \( Q \), seeing there is none of the quantity \( P + R + T \).

But if two of the nearest of the points assumed in the arches of the curves, on the same side of the axis, be supposed to accede to one another beyond whatever limits, and at last to coincide, which will be done by making two \( M \) equal, and likewise two \( N \) equal; then the curve sought will touch the arch of the given curve; and if three such points coincide, they will calculate it; nay, as many points as we please may be made to meet together where we please; and thus we may have calculations of what order we please, and as near one another as we please, the arch of the given curve approaching as we please, and at whatever distances we please, to whatever arches of whatever curves, and yet still preserving all the six conditions required for expressing the law of the repulsive and attractive forces. And whereas the value of \( T \) can be varied in infinite manners, the same may be done in an infinite number of ways; and therefore a simple curve, answering the given conditions, may be found out in an infinite number of ways.

What we have said will, we hope, satisfy our readers, and especially those of them who are in the least acquainted with high geometry, that Bozovich's curve is simple, regular, and uniform; and that therefore the law of repulsive and attractive forces, expressed by it, is simple and regular.

II. If this system were a mere hypothesis, it would still be very ingenious, and, from what we shall say afterwards, would still be well adapted for explaining the phenomena of nature. But its author is far from looking upon it as an arbitrary supposition; he affirms us that he was led to it by a chain of strict reasoning, from evident principles. We shall now give an abridgement of that reasoning from his Dissertations on the Law of Continuity, and from his Theory of Natural Philosophy.

He tells us, then, that in the examination of Leibnitz's opinion or the vis viva, he came to consider the theory of the collision of bodies, and took for example two equal bodies, A proceeding with five degrees of velocity, and B following with the velocity of 12; after the collision, they proceed jointly with the common velocity 9. Now, in the moment of collision, it either happens that A passes abruptly from the velocity 6 to the velocity 9, without passing through the velocity 7 and 8, and B passes from 12 of velocity to 9, without passing through 11 and 10; or else there must be some cause which accelerates the one and retards the other before they come to contact. In the first case, the law of continuity is broken; in the second, immediate contact of bodies would be rejected. MacLaurin saw this difficulty, and mentioned it in his work on Newton's Discoveries, I. i. c. 4. He, not having courage to recede from the common opinion, allowed a breach, in such cases, of the law of continuity; but Bozovich maintains Bokovich maintains the universality of the law of continuity; and holds, that no bodies touch one another really and mathematically, but only physically and tentively to us.

The law of continuity is that by which variable quantities, passing from one magnitude to another, pass through all intermediate magnitudes, without ever abruptly passing over any of them. This law Bokovich proves to be universal, in the first place, from induction. Thus we see that the distances of two bodies can never be changed without their passing through all the intermediate distances. We see the planets move with different velocities and directions; but in this they still observe the law of continuity. In heavy bodies projected, the velocity decreases and increases through all the intermediate velocities; the same happens with regard to elasticity and magnetism. No body becomes more or less dense without passing through the intermediate densities. The light of the day increases in the morning and decreases at night through all the intermediate possible degrees. In a word, if we go through all nature, we shall see the law of continuity strictly take place, if all things be rightly considered. It is true, we sometimes make abrupt passages in our minds; as when we compare the length of one day with that of another immediately following, and say that the second is two or three minutes longer or shorter than the former, passing all at once, in our way of speaking, round the globe; but if we take all the longitudes, we shall find days of all the intermediate lengths. We likewise sometimes confound a quick motion with an instantaneous one; thus, we are apt to imagine that the ball is thrown abruptly out of the gun; but, in truth, some space of time is required for the gradual inflammation of the powder, for the rarefaction of the air, and for the communication of motion to the ball. In like manner, all the objections made against the law of continuity may be solved to satisfaction.

But however strong this argument from judgment may appear to be, yet Bokovich goes farther, and maintains, that a breach of this law, in the proper cases, is metaphysically impossible. This argument he draws from the very nature of continuity. It is essential to continuity that, where one part of the thing continued ends and another part begins, the limit be common to both. Thus, when a geometrical line is divided into two, an indivisible point is the common limit of both; thus time is continued; and therefore where one hour ends, another immediately begins, and the common limit is an indivisible instant. Now, as all variations in variable quantities are made in time, they all partake of its continuity; and hence none of them can happen by an abrupt passage from one magnitude to another, without passing through the intermediate magnitudes. As we cannot pass from the sixth hour to the ninth without passing through the seventh and eighth; because, if we did, there would be a common limit between the fifth hour and the ninth, which is impossible; so likewise you cannot go from the distance 6 to the distance 9 without passing through the distances 7 and 8; because, if you did, in the instant of passage you would be both at the distance 6 and at the distance 9, which is impossible. In like manner, a body that is condensed or rarefied cannot pass from the density 6 to the density 9, or vice versa, without passing through the densities 7 and 8; because, in the abrupt passage, there would be two densities, 6 and 9, in the same instant. Before the body must pass through all the intermediate densities. This it may do quickly or slowly, but still it must evidently pass through them all. The like may be said of all variable quantities; and thence we may conclude, that the law of continuity is universal.

But, in creation, is there not an instance of an abrupt passage from non-existence to existence? No, there is not; to this because before existence a being is nothing, and therefore incapable of any state. In creation, a being does not pass from one state to another abruptly; it passes over intermediate states; it begins to exist and to have a state, and existence is not divisible. Do we not, at least, allow of an abrupt passage from repulsive to attractive forces in our very theory itself? We do not. Our repulsive forces diminish, through all the intermediate magnitudes, down to nothing; through which, as a limit, they pass to attraction. In the building of a house or ship, neither of them is augmented abruptly; because the additions made to them are effected solely by a change of distances between the parts of which they are composed; and all the intermediate distances are gone through. The like may be said of many other such cases; and still the law of continuity remains firm and constant.

Let us now apply this doctrine to the case above mentioned of the collision of two bodies. We say that the body B cannot pass from the velocity 6 to the velocity 9 without passing through the velocities 6 and 7; because if it did, in the moment of contact of the two surfaces it would have the velocities 6 and 9. Now a body cannot have two velocities at the same instant. For if it had two actual velocities at the same time, it would be in two different places at the same time; if it had two different potential velocities or determinations to a certain velocity, it would be capable of being, after a given time, in two places at once—both which are impossible. It is therefore necessary that it go through the velocities 7 and 8, and through all the parts of them. What we have said of the bodies A and B may be said universally of all bodies. Therefore no two bodies in motion can come to immediate contact; but their velocities must undergo the successive necessary change before contact. And as the velocity to be extinguished may be increased beyond all limits, an adequate cause to effect this extinction must be admitted.

This naturally leads us to the interior repulsive forces of our system, for the cause retarding the one body forces and accelerating the other must be a force, because by this we mean a determination to motion; and it must be repulsive, because it acts from the body; and it must increase beyond all limits, seeing the velocity of the incoming bodies may be increased beyond all limits. It must likewise be mutual, because action and reaction are always equal, as may be proved by induction.

From these repulsive forces Bokovich deduces the inextensibility of his atoms; for this repulsion being common to all matter, must cause a perfect simplicity in the first elements of body. If these elements were extended, and consequently compounded of particles of an inferior order, these particles might possibly be separated, and then they might meet, and an abrupt passage from one velocity to another might take place, which we have excluded from nature by induction, and by a positive argument.

Besides Besides this, by rejecting the extension of the elements of matter, we get rid at once of all the difficulties arising from continued extension in body, which have always perplexed the philosophers, and have never been satisfactorily explained. If the elements of matter are extended, each of them may be divided in infinitum, and each part may still be divided in infinitum. Can this division be actually made by the power of God or not? Can there be one infinite in number greater than another? Can there be a compound without a simple of the same kind? These difficulties regard not space, which is no real being; but they would regard matter if it had continued extension. All these perplexities are removed by maintaining, as Boscovich does, that the first elements of bodies are perfectly simple, and therefore inextended (A).

With regard to the exterior attractive forces of our system, there can be no question; seeing they constitute universal gravity, the effects of which we see and feel every day. But between the interior repulsive and exterior attractive forces we must admit many transitions from repulsion to attraction, and from attraction back to repulsion, in infinibl distances, which are indicated to us by cohesion, fermentation, evaporation, and other phenomena of nature. And thus we have given, in short, Boscovich's proofs of his whole system.

III. This system has been well received by the learned in Europe, and has contributed much to render its author famous; yet many objections against it have been proposed. Some are startled at the rejection of all immediate contact between bodies; and indeed Boscovich is perhaps the first of mankind who advanced that opinion; but he allows that bodies approach so near to one another, as to leave no sensible distance between them; and his repulsive forces make the same impression on the nerves of our senses as the solid bodies could do. And therefore this opinion of his, however new, is not contrary to the testimony of our senses. He only removes a prejudice which was before universal.

Some say, that they cannot even form an idea of an inextended atom, and that Boscovich reduces all matter to nothing; but certainly extension is not necessary for the essence of a being, as must be allowed by all those who hold that spirits are inextended. Because all the bodies that fall under our senses are extended, we are apt to look upon extension as essential to matter; but this error may be corrected by reflection, and an idea of an inextended atom may be formed, by considering the nature of a mathematical point, which is the limit of any two contiguous parts of a line.

Others again have said, that if the elements of matter were void of extension, there would be no difference between body and spirit. But the difference between body and spirit does not consist in the having or not having extension; but in this, that the atoms of matter are endowed with repulsive and attractive forces, Boscovich's which spirit has not; and spirit has a capacity of thought, volition which bodies have not.

We may here observe, that among the ancients Zeno, and among the moderns Leibnitz, held, that the first principles of matter are inextended points. But both held this opinion with the inconclusiveness, that they maintained the continued extension of bodies, without ever being able to show how continued extension could arise from inextended elements.

It has been objected likewise, that our repulsive and attractive forces are no better than the occult qualities of the Peripatetics. The like objection has been made to Newton's attraction; but the answer is easy. We observe the effects, and take notice of them; for them we must admit an adequate cause, without being able to determine, whether that cause is an immediate law of the Creator, or some mediate instrument that he makes use of for that purpose.

Some are unwilling to give up the idea of motion occasioned by immediate impulse; but can they show a good reason why some distance may not occasion motion as well as no distance? These are the principal objections that have been made against the Boscovichian system.

IV. Before we proceed to the explication of phenomena by means of our theory, we must advert, that in regard to the curve expressing this theory, the abscissas denote the distances between the atoms that are under consideration; the ordinates give the present force, and the area between any two of these ordinates gives the square of the velocity generated between them: the arches are either repulsive or attractive, according as they fall upon the same side with the asymptotic curve EG, or on the opposite side.

We must, in the next place, consider the passages from one side of the axis to the other. Sometimes the passage is from repulsion to attraction, at other times from attraction to repulsion. The first are called limits of cohesion, because a particle removed from that limit returns back to it; because if it is removed to a greater distance it is attracted back, and if it is removed nearer it is repelled back. The second are called limits of non-cohesion; because a particle removed thence to a greater distance is repelled still further, and if removed nearer it is attracted still nearer. Of the first kind are E, I, N; of the second are G, L. Likewise, when the curve touches the axis, it may either be an attractive part of the curve, or a repulsive part. These limits may be nearer one another, or farther away; and the limits of cohesion may be stronger or weaker, according as the forces near them are greater or less.

Boscovich considers minutely the effects of these varieties of limits and forces; first with regard to two points, then with regard to three and four, demonstrating

(A) If a particle of matter is not extended, in what respect does it differ from a point of space? Says Boscovich, it is endowed with attractive and repulsive forces: What is this if before it is thus endowed? Does it then differ from a point of space? We can form no notion of any such difference. But a point of space, considered as an individual, is distinguished from another individual only by its situation; it is therefore immovable, but matter is moveable. Have these forces, then, which make matter an object of sense, any substratum, any thing in which they are inherent as qualities? What are the things which these qualities distinguish from each other as individuals? Bos

Bozovich's theory of the great variety of forces that may arise from these various combinations, and shewing how from simple elements of which they are composed.

Extension of bodies involves figurability; because every extended body must be surrounded by some superficies of a certain figure; but the superficies of bodies can never be accurately determined, upon account of the inequalities in all surfaces. We take, however, that figure for the true one which the body appears to come nearest. Thus we call the earth a globe, notwithstanding the hills and valleys that are on it.

Under the same figure, and of the same magnitude, there may be contained very different quantities of matter. Hence we come to the consideration of density. That body is most dense which contains in the same space the greatest number of atoms, and vice versa.

This density may be increased beyond any given limits by the nearer approach of the atoms to one another. Hence a body of any given magnitude, however small, may come to be divisible beyond any given limits.

Mobility, which is likewise reckoned among the general properties of body, is essential to our system, being an essential part of it consists in forces, which are determinations to motion, at least in certain distances.

Universal gravity in sensible distances is likewise a branch of our theory. On which subject it may be observed, that perhaps our curve, after it has extended beyond the sphere of the comets most distant from the sun, may depart from its asymptotical nature, and approach to the axis, intersect it, and pass to repulsion. This would effectually answer the objection made by some against Newton's attraction, when they allege, that, from his opinion, it would follow, that the fixed stars, and all matter, would be drawn together into one mass. If such a repulsion takes place, it may soon pass again into attraction, and form limits of cohesion; so that our sun may be in such a limit with regard to the fixed stars, and our planetary system make only a small part of the whole universe. And this may suffice concerning the general properties of matter.

Let us now descend to some particular classes of bodies, of which some are fluids, others solid. The parts of fluid bodies are easily separated, and easily moved round one another, because they are spherical and very homogeneous; and hence their forces are directed more to their centres than to one another, and their motions through one another are less obstructed. Between the particles of some of them there is very little attraction, as in fine sand or small grains of seed, which approach much to fluidity. The particles of some others of them attract one another feebly, as do those of water, and still more those of mercury. This variety arises from the various combinations of the particles themselves, of which we have already taken notice. But in air the particles repel one another very strongly; and hence comes that great rarefaction, when it is not prevented by an external force. Its particles must be placed in ample limits of repulsion.

Solid bodies are formed of parallelopipeds, fibres, and of irregular figures. This occasions a greater cohesion than in fluids, and prevents the motion of the parts round one another; so that when one part is moved all the rest follow. Of these bodies some are harder, whose particles are placed in limits which have strong repul- Bos

Some are flexible, the particles of which are placed in limits that have weak arches of repulsion and attraction on each side; and if those arches are short, the particles may come to new limits of cohesion, and remain bent; but if the arches are longer, the former repulsion and attraction will continue to act, and bring back the body to its former position; nay, in doing this with an accelerated velocity, the parts will pass their former limits, and vibrate backwards and forwards, as may be seen in a bended spring. Thus elasticity is accounted for.

Vitreous bodies stand in the middle between solid and fluid. Their particles have less cohesion than the first, and more than the second: they stick to other bodies by an attraction which their particles have from their composition. In like manner water itself sticks to some bodies, and is repelled by others. All which arises from the different composition of the particles, which gives a variety of respective forces.

What appears very wonderful in nature, is the composition of organic bodies. But if we consider that particles may be so formed, that they may repel some and attract others, the whole of vegetation, nutrition, and secretion, may be understood, and follows from our system. And as one particle may attract another in one part only, and repel it in every other situation, hence may be gathered the orderly situation of the particles in many crystallizations. The great variety of repulsive and attractive forces, or limits of cohesion, of the position of atoms, and of combinations of particles, will account for all these phenomena.

The chemical operations, which are so curious in themselves, and so useful to society, are well explained by Bofcovitch's system, and serve as a confirmation of its truth. Of this we shall give some instances. When some solids are thrown into some liquids, there happens to be a greater attraction between the particles of the solid and of the liquid than there is between the particles of the solid itself. Hence the particles of the solid are detached and surrounded by the fluid; this mixture retaining the form of globules, and therefore continuing to be fluid. This is called solution. But when the solid particles are covered to a certain depth, the attractive forces cease on account of the different distances, and no more of the solid is detached. Then the fluid is said to be saturated. If into this mixture another solid be put, the particles of which attract the fluid more strongly, and perhaps at greater distances than the particles of the former; then the fluid will abandon the former and cleave to the latter, diffusing them, and the particles of the former will fall to the bottom in the form of powder, into which they had been reduced by the solution. This separation is called precipitation. Perhaps rain arises from a precipitation of this kind, when the aqueous particles are left by the air, which is more strongly attracted by some other particles floating in the atmosphere.

Fluids of the same specific gravity are easily mixed; and even though the specific gravity be different, the particles of the one attract those of the other, in such a manner that they seem to form one fluid by a kind of solution. Nay, it happens, that two fluids mixed together form a solid, because their particles come to be in the limits of cohesion. They may even occupy less Bofcovitch's space than they did before, by being attracted into less distances between their parts.

Fermentation is a necessary consequence of our system. For when bodies, whose particles, by the variety of their composition, are endowed with different forces, come to be mixed, there must arise an agitation of the parts, and an oscillation among them; sometimes greater, sometimes less, according to the nature of the particles. This agitation is stopped by the expulsion of some particles, by the intrusion of others into vacant spaces, and by the impression of external bodies; but always there is a change in what remains, because there is a new disposition of particles.

Fire consists in a violent fermentation of sulphur, fire and fusous matter, especially when it meets with the matter of light in any quantity. This fermentation agitates strongly the parts of other bodies, separates them from one another, and often throws them into a state of fusion; the cohesion between their parts being broken, and they being thrown into a circular motion. In this state they may be often mixed together, so as to form one body; they may be again separated by the action of the same fire, which evaporates some of them sooner, some later. Hence the art of melting metals.

When, in the agitation occasioned by fire, some of the particles are thrown out into an arch of repulsion, they may fly off and evaporate. Sometimes the whole body may be thrown into a strong repulsion and volatilization; or a sudden explosion take place; when, before the particles are near an equilibrium, a small force may occasion a great change; as the root of a bird may occasion the fall of a great rock, which was before almost detached from a mountain. In evaporation, the bodies that remain assume a particular figure, as all fats do; and this upon account of their particles having certain parts only that attract one another, and consequently occasion a particular disposition. All these chemical operations evidently prove that there are in nature repulsive and attractive forces between the particles of bodies at small distances; which greatly confirms our whole system.

Bofcovitch holds, that light is an effluvium, emitted with great velocity from the luminous bodies by a strong repulsion. He explains all the most remarkable properties of this extraordinary matter according to his own principles, and that with great acuteness. On this subject it is observable, that Newton saw the necessity of admitting repulsive forces for the reflexion of light, which extend at some distance from the reflecting surface, and therefore resemble the repulsive forces of our theory.

Our author gives likewise a probable explication of electricity, according to Franklin's ingenious hypothesis and magnesia, and likewise of magnetism, deducing the whole of both from the appearances from various attractions and repulsions. He supposes that fire and the electrical fluid differ only in this, that fire is in actual fermentation, and not in the electrical fluid.

Finally, he explains our bodily sensations, in which he agrees pretty much with other philosophers; excepting in this, that what they attribute to the immediate contact of bodies, or of certain particles emitted from them, he attributes to attractions and repulsions; which indeed Boscovich's indeed are particularly fit for causing that motion in our nerves, which is supposed to take place in the organs of sensation, and to be thence communicated to the brain.

It is to be observed, that although Boscovich maintains, that the very first elements of matter are void of extension; yet he allows, that these elements, combined in a certain manner, may be formed extended particles of various figures, the parts of which may be so coherent as to be inseparable by any power in nature. By these means the opinion of those philosophers, who are fond of extended particles, may be in so far gratified. Nay, the Peripatetics may, if they please, adopt Boscovich's inextended atoms for their Materia Prima without any inconsistency; and his repulsive and attractive forces may serve for their substantial forms. And as God can make impressions on our senses independently of the atoms, their absolute accidents may in some sense be admitted. Nor would some such extraordinary exertions of Divine Power favour idealism in the ordinary course of nature.

But what is of more consequence, it is more than probable, that had Newton lived to be acquainted with the Boscovichian theory, he would have paid to it a very great regard. This we may conjecture from what he says in his last question of optics; where, after having mentioned those things which might be explained by an attractive force, succeeded by a repulsive one on a change of the distances, he adds, "And if all these things are so, then all nature will be very simple, and consistent with itself, effecting all the great motions of the heavenly bodies by the attraction of gravity, which is mutual between all those bodies, and almost all the less motions of its particles by another certain attractive and repulsive force, which is mutual between those particles." And a little after, treating of the elementary particles, he says: "Now it seems that these elementary particles not only have in themselves the vis inertiae, and those passive laws of motion which necessarily arise from that force, but that they likewise perpetually receive a motion from certain active principles; such as gravity, and the cause of fermentation, and of the cohesion of bodies. And I consider these principles, not as occult qualities, which are feigned to flow from the specific forms of things, but as universal laws of nature, by which the things themselves were formed. For that truly such principles exist, the phenomena of nature shew, although what may be their causes has not as yet been explained. To affirm that every species of things is endowed with specific occult qualities, by which they have a certain power, is indeed to say nothing; but to deduce two or three general principles of motion from the phenomena of nature, and then to explain how the properties and action of all corporeal things follow from those principles, this truly would be to have made a great advancement in philosophy, although the causes of those principles were not as yet known. Wherefore I do not hesitate to maintain the above said principles of motion, seeing they extend widely through all nature." From this passage we may safely conclude, that the great British philosopher would have been highly pleased, had he seen all nature so well explained by the one simple law of forces propounded by the Ragusan.

Boscovich himself was so fully convinced of the truth of his system, that he was wont to make use of the following comparison: When a letter has been written in occult characters, and we are endeavouring to decipher it, we make various suppositions of alphabets; and when we have found one according to which the whole letter comes to have a reasonable meaning, agreeable to all the circumstances of time, place, persons, and things, we can entertain no doubt of our having discovered the true key of the cipher—so, said he, my system explains to well all the phenomena to which it has been properly applied, that I must flatter myself that I have discovered the true key of nature.

The being accustomed to contemplate so deeply the universe and the materials of which it is composed, made of God, Boscovich see most clearly the evident necessity of admitting an all-powerful, intelligent, self-existent Being, for the creation of those materials, and for the arrangement of them into their present beautiful form. He was at a loss to find words strong enough to express his surprize, that there should be any man, not to say anyone pretending to the name of philosopher, who could be so deaf as not to hear the voice of nature loudly proclaiming its Author from all, even the least of its parts. He gives us his sentiments on this, the most important of all subjects, in the appendix to his Theoria, in which he treats of God and of the soul of man.

There, in the first place, he shows the absurdity of their opinion, who maintain that this world may have been the work of chance, the effect of a jumble of self-existent, self-moving atoms; because chance is an empty word without a real meaning. Whatever exists has its determinate cause, and can only be called fortuitous by us on account of our ignorance of that cause. Besides this, though the number of atoms composing this world is finite, yet their possible combinations are many times infinitely infinite; for they may be placed in infinite places of an infinite line; of these lines there is an infinite number in every plane, and of these planes there is an infinite number in space. Again, these points may have an infinite number of velocities in an infinite number of directions. From all this it is evident, that the combinations in which the points of matter may be, is infinite in a high degree, whereas duration can be infinite in only one dimension. Hence it is infinitely improbable that ever the present combination of things could come out by chance. And this is so much the more infinitely improbable, because the disorderly, chaotic combinations, are infinitely more than the regular ones. The whole of matter might roll about in a blind motion for a boundless eternity, without ever being capable to produce one single muthrom.

Moreover, had matter been in motion from all eternity, every atom would have described an infinite line, and then a part of that line would be assignable at an infinite distance from the point of space in which the atom is at present; but an infinite line can never be run over; therefore the atom could never have come to its present place; and therefore the supposition is absurd. Nothing successive can be eternal with a past eternity, though it can continue without end. God alone can be eternal and actually infinite; but his eternity and infinity are beyond our comprehension.

Neither can the world have existed of itself in any thing like to its present form from all eternity; for exalted matter is perfectly indifferent to numberless states, and from eternity.