BOSCOVICH

BOSCOVICH (Roger Joseph), one of the most eminent mathematicians and philosophers of the present age, was born, of virtuous and pious parents, on the

Boscovich. the 11th of May 1711, in the city of Ragusa, the capital of a small republic of the same name, lying on the eastern coast of the Adriatic Sea. At baptism, the name of Roger was given him, to which he added that of Joseph when he received the sacrament (A) of confirmation.

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 shewed 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; whither he was sent in the year 1725, and entered the noviceship with great alacrity. This noviceship 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 condisciples 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 ripe 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

Boscovich, 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 Boscovich'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 comic 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 Boscovich 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 oscillators; 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 solid of greatest attraction; a new method of using the observation of the phases in the lunar eclipses; the cycloid; the logistic and certain other curve lines; the forces that are called living; 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 ca-

toptries, certain conditions of its motions being given; Boscovich 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 above-mentioned dissertations that Boscovich 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 Boscovich; in which, among other things, he with great sagacity discovers errors in optics into which De Dominis, 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 Boscovich. 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 falseness of the mathematical prejudice, 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 beneficent patron of learned men, was not ignorant how valuable a subject Rome possessed in Boscovich; and this pope gave him many proofs of the esteem he had for him. Two insures which had been perceived in the cupola of the church of St Peter's on the Vatican had occasioned some alarm. The pope desired Boscovich and some other mathematicians to make their observations and give their opinion on the same. They obeyed, and their opinion was printed. They shewed 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,

French 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 Boscovich 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 Condamine, 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 Boscovich in Italy, where he had occasion for him, and could by no means consent to part with him.

Accordingly a commission was given to Boscovich by Benedict to correct the maps of the papal estate, and to measure a degree of the meridian passing thro' 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. Boscovich 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 visitors. They therefore insisted that Boscovich 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 1757 the republic of Lucca entrusted Boscovich 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 stability of the Cæsean 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 sea-faring, and much employed in the carrying trade; and therefore it would have been inconvenient for them to have caused any disgust against them in the principal maritime power. Their countryman Boscovich 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.

Boscovich 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 refracted from the atmosphere of the earth by the shadow of the moon, which happens

Boscovich 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 explanation 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 drefs, 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 baylors 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 comprises 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 diaphonous 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 the sphericity 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 these 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, of sextants, of astronomical sectors, of the meridian line, of telescopes called the instruments of transits, of the meridian,

Boscovich, meridian, and of the parallaxic machine; the trigonometrical differential formulae, which are of so much use in astronomy; the use of the micrometrical rhombus, extended to whatever oblique position; the error arising from refractions in using the astronomical ring for a fundial, and the correction to be made; the appearing and the disappearing of Saturn's ring; the methods of determining the rotation of the sun by means of the spots, proposed formerly by the author, and now perfected; the greatest exactness possible in determining the length of a pendulum oscillating every second of middle time by the comparison of terrestrial and celestial gravity; a compend of astronomy for the use of the marine, containing the elements of the heavenly motions, and of the astronomical instruments to be explained to a prince in the course of one month; a method for determining the altitude of the poles with the greatest exactness, by means of a gnomon alone, where other instruments are not to be had; the determination of the illuminated edge of the moon to be observed on the meridian; a method of using the retrograde return of Venus to the same longitude, for determining the less certain elements of her orbit; a method for correcting the elements of a comet, of which the longitude of the node is given, and the inclination of the orbit has been found nearly; another method for the same purpose, and for finding the elliptical orbit, when the parabolic one does not agree with the observations; a method for correcting the elements of a planet by three observations; the projection of an orbit inclined in the plane of the ecliptic; the projection of an orbit inclined in any other plane; the calculation of the aberration of the stars, arising from the successive propagation of light; some beautiful theorems belonging to triangles, which are of great use in astronomy, reduced to most simple demonstrations.

After having seen the impression of these five volumes finished, Boscovich left Bassano, made an excursion to Rome, and visited his old friends there and in other places of Italy. He then took up his abode at Milan, and applied to the revising of some of his old works, and to the composing of new ones. He set himself particularly to prepare annotations and supplements to the remaining two volumes of Stacy's Modern Philosophy, which he had not had time to publish sooner, and which he lived not to publish.

He was happy at Milan in the neighbourhood of Brera, where was his favourite observatory; and in the company of many friends, who were become the more dear to him by his long absence from them. But he began to consider, with grief, that his two years of absence were drawing to an end. He was very unwilling to leave Italy and return to France. He thought of applying for a prolongation of his absence; he thought of making interest at the Imperial court for some honourable commission, which might be a pretext to him for remaining at Milan; but he was afraid that the proposal of never returning to France might appear indecent and ungrateful to a nation from which he was receiving considerable pensions. He apprehended that those persons at Paris who had before opposed him,

would take occasion to tax him with ingratitude, and Boscovich, that 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 diffident. 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 endowed 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 imposthume 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 unstained 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 through Europe, and more than ordinary respect has been paid to his memory. At Ragusa funeral exequies 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:

BOSCOVICHII ELOGIUM RAGUSE,
Marmore Insculptum.