4th, The establishment of the Confervatoire des Arts et Métiers, was decreed in the fitting of the 8th of Vendemiaire, in the third year. This confifts of a fpacious hall, in the form of an amphitheatre, and contains the inftruments and the models of machinery connected with the arts, and a defcription of their uses, with every book relating to them. Annexed to this eftablishment are three expofitors and a draughtfman, who explain to the ftudents the use of each inftrument, and who regifter every new discovery, which is prefented to the Bureau de Confultation, to the lyceum of arts, the cidevant academy of fciences, or to the board of

merce.

com

5th, The establishment of the board of longitude was decreed in the fitting of the 7th of Meffidor, third year. It was certainly a difgrace under the monarchy, that an aftronomical and nautical establishment, which had already proved fo beneficial to Great Britain, fhould not have been adopted in France. In confequence of this decree, the French board is now as complete as the English, It confifts of ten members, and has under its jurifdiction the national obfervatory at Paris, and all the aftronomical inftruments belonging to the republic. It correfponds with foreign aftronomers; delivers public lectures on aftronomy and navigation; and its proceedings are annually recited in a public fitting.

6th, The general fchool of the Oriental languages was established by a decree of the 10th of Germinal, in the fourth year. This school adjoins to the national library, and all the books and manufcripts relative to Oriental literature are depofited in it.

7th, The national mufeum of antiquities was decreed in the fitting of 20th of Prairial, fourth year. A fchool of this defcription was fuccefsfully eftablifhed at Vienna, by Eckel; at Gottingen, by Heyne; at Leipfick, by Erneft; and even at Strafburgh, by the celebrated Obeilin Paris was, however, without one. This national archeology, or fcience of antiquity, is divided into nine different claffes: infcriptions, characters, ftatues, bas reliefs, fculptures, paintings, mofaics, medals, civil, religious, and military inftruments. This extenfive eftablishment is under the direction of two principal profeffors; le Confervateur Professeur, et le Confer. vateur Bibliothecaire. The province of the former is to deliver public lectures on the feveral branches of antiquities, to teach the theory of medals and engravings, the hiftory of the arts among the ancients, &c. The duties of the latter are merely of a bibliographical na

ture.

8th, The new modelling of the Grand National Library, was decreed in the fitting of 25th Vendemiaire, in the fourth year. By virtue of this decree, the place of librarian in chief was fuppreffed, and the whole efta. blishment placed under a confervatoire of eight members; of whom two were appointed for the fuperintendance of printed books; two for manufcripts; two for antiquities; and two for engravings. From thefe a temporary director is annually chofen, who fuperintends the whole acts occafionally as prefident of this af fembly, and maintains a regular correfpondence with the constituted authorities relative to the concerns of the library.

9th, The augmentation of the Mufeum of Natural Hiftory, formerly called Le Jardin Royal des Plantes. This establishment was decreed the 15th Brumaire,

third year, upon a report of Thibadeau, in the name Inftitute of the committee of Public Instruction. Befides the addition of large rooms, and various other buildings, there are new collections of natural curiofities and productions; and the library is much increafed. It is open to the public three times a week. At flated periods all the naturalifts in Paris deliver courfes of lectures in the various branches of natural hiftory. The museum is faid to have received greater improvements from this augmentation than from all the labours of Buffon, or from its foundation, fince the time of Tournefort.

10th, The Ecole des Mines was eftablished in the Hotel des Monnaies, and has for its direction the naturalift Le Sage. This inftitution is unrivalled in Europe; and the collection of mineralogical curiofities furpaffes whatever can be conceived.

11th, The fociety of natural hiftory in Paris, defervedly claffes among thofe which have rendered the greateft fervices to the cause of science fince the revolu tion. A lecture of public inftruction is held every ten days, which is generally given by one of the members, and which is open to all the lovers of natural hiftory. Premiums are proposed for differtations; one of which, by the late C. Herman, jun. (whofe early deceafe was a great lofs to the republic of letters) on the apterous clafs of infects, may be faid to conftitute an epocha in the annals of natural hiftory. The fociety has publifhed a volume of memoirs, in folio, entitled, Tranfactions of the Society of Natural Hiftory." It has likewife erected a ftatue to the great Linnæus, in the national garden of plants; and, at the period when every public inftruction was fufpended, gave lectures on the different branches of science belonging to its department. Several intelligent and skilful navigators, among others thofe fent in fearch of the unfortunate La Péroufe, as well as thofe which accompanied Buonaparte on his romantic expedition to Egypt, were members of this fociety.

66

This ftatement of facts relative to the prefent ftate of public instruction, the fciences, the arts, and the progrefs of national literature in France, has been taken from a mifcellany, of which the principal writers are well acquainted with what is doing in that distracted country. They call it a fublime fyitem; and feem to confider the increase of the national library, the improvement of the botanic gardens, and the difcoveries that have been made by the different fchools or infti. tutes, as furnishing a demonftration that the republican government is more favourable to the advancement of fcience, than the monarchical, whether abfolute or li mited. But it fhould not be forgotten, that this fyftem is yet in its infancy; and that in profecuting new fchemes, all men, and more efpecially Frenchmen, are actuated by an enthusiasm which gradually cools as their purfuits become familiar. We thall therefore venture to predict, that the different fchools will not difplay fuch ardour feven years hence as they do at prefent; and that if the republican government continue a dozen of years in France, the progrefs of fcience in that country will not be more rapid than it was under the monarchy. We must remember, too, that the French libraries, mafeums, and picture galleries, have been improved by means which the morals of other governments do not employ-by rapine and robbery.

That fomething may be learned from this fyftem to improve

1

Infurance.

rances in England, which may be feen in Anderfon's Infurance. Hiftory of Commerce, were made in the year 1601. We find by them, that infurers had before that period conducted themselves in fuch a manner, that the utmost confidence was repofed in their honefty, and that on this account few or no difputes had arifen.

Of the various policies for infurance in England, a pretty accurate account will be found in the Encyclopæ dia; but there is one of them, of which our account must be acknowledged to be now defective. This is,

INSURANCE on lives; which is a policy that has greatly increased, in confequence of its utility being more generally underfood. Of the two offices for life-affurances, noticed in that article, the former, entitled the Amicable Society, has extended the number of its fhares to 4000; but, as we have already obferved, the nature of the inftitution is too limited to become of general importance. The latter, entitled, the Society for Equitable Affurances on Lives and Survivorship, is undoubtedly one of the most important inftitutions of the kind, as will appear by the following account, with which we have been favoured by an obliging correfpondent, and upon the accuracy of which our readers may depend:

Inftiute, improve the modes of education in other countries, we admit; and it is for that reason that we have inferted an account of it. But if it contains fomething worthy of imitation, it contains likewife much to be fhunned. We do not think it confiftent with the rights of man to compel parents to fend their children to be educated in particular fchools; efpecially in fchools where not only religious inftruction is omitted, but where, there is reafon to believe, that the profeffors are at pains to raze all religious impreffions from the youthful mind. In a nation denying the truth of Chriftianity, it is not to be fuppofed that the Chriftian religion will be publicly taught; but in a nation of philofophers, as the French call themselves, it might have been expected that the laws of religious toleration would have been fo far regarded, that Chrifiian parents would not have been compelled to fend their children to antichriftian schools! But it is not Chriflianity alone that is neglected in this fublime fyftem of education. Though the legislative body has fome time ago decreed that there is a God, there is not in any one of those schools the fmalleft care taken to inftru& the republican youth in the principles even of natural religion! We might indeed have looked for it under the title Metaphyfics, had not the conftitution of the National Inftitute taught us, that French metaphyfics attend to nothing but the analysis of fenfations and ideas. Yet the legiflators might have liftened on this fubject to a republican as found as themfelves, and who was likewife no friend to fuperftition. "Nam et Majorum insituta tueri facris, ceremoniifque retinendis fapientis eft. Non folum ad religionem pertinet, fed etiam ad civitatis statum, ut fine iis, qui facris publice præfunt, religioni private fatisfacere non pofCicero de Nat. Deorum. INSURANCE, in law and commerce, though an excellent inftitution, is not of high antiquity. The oldeft laws and regulations concerning infurance, with which the indefatigable Beckmann is acquainted, are the following:

fint."

On the 28th of January 1523, five perfons appoint. ed for that purpose drew up at Florence fome articles which are ftill employed on the exchange at Leghorn. Thefe important regulations, together with the preferibed form of policies, which may be confidered as the oldeft, have been inferted, in Italian and German, by Magens, in his Treatife on Infurance, average, and bottomry, published at Hamburgh in 1753.

There is ftill preferved a fhort regulation of the 25th May 1537, by the Emperor Charles V. refpecting bills of exchange and infurance, in which the ftrictly fulfilling only of an agreement of infurance is commanded.

In the year 1556, Philip II. king of Spain, gave to the Spanish merchants certain regulations refpećting in furance, which are inferted by Magens, with a German tranflation, in his work before mentioned. They contain fome forms of policies on fhips going to the Indies. In the year 1598, the Kamer von affurantie, cham. ber of infurance, was established at Amfterdam. An account of the first regulations of this infurance office may be feen in Pontanus's Hiftory of the city of Amfterdam, and in other works.

In the year 1600, regulations refpecting infurance were formed by the city of Middelburg in Zealand. It appears that the firft regulations refpecting infu

The members of the equitable fociety, finding, in June 1777, that their affairs were in a flourishing fitua tion, refolved to reduce their annual premiums one tenth; and in 1782, adopted new tables agreeable to the probabilities of life at Northampton, in lieu of those they had hitherto ufed, formed from the London bills of mortality. But though it was evident, that the new tables were much better adapted for affuring promifcuoufly perfons refiding in the country, or in large towns, it was thought proper, for greater fecurity, to make an addition of 15 per cent. to the real value of the affurances, as computed from the table of mortali.y at Northampton; and with the view of making an ade quate compenfation to the affured for their former payments, which had been fo much higher than would be required by the new rates, an addition was made to their claims of L.1: 10s. per cent. for every premium they had paid. The confequence of thefe meafures proved highly favourable to the society; for its bufinefs increafed fo faft, that in 1785 it was nearly doubled; the fums affured amounting to upwards of L.720,000. At this period, the favourable refult of a minute and very laborious inveftigation of the ftate of the fociety, induced them to take off the 15 per cent. charged upon the premiums in 1782, and make a further addition to the claims of L.1 per cent. for every payment made prior to the 1ft January 1786. A fil greater increase of fuccefsful butinefs determined them, in 1791, to make another addition of L.1 per cent. to the claims; and in the following year, a further addition of L. 2 per cent.; by which the claims upon afurances of the year 1770 were more than doubled; and those of an earlier date increafed in a ftill higher proportion. By thefe advantages to its members, and the honourable and truly equitable manner in which the concerns of the fociety are tranfacted, the augmentation of their bufinefs has been fo great, that on the 31st December 1792, the fums affured (without including the addi tions made to them) amounted to upwards of L.3,000,000; and on the 31st December 1795, to about L. 4,000,000.

The

volution. by a thread unlapped from a cylinder, we do not recollect any thing of the kind among the writings of the mathematicians; and it is to Huyghens alone that we are indebted for this very beautiful and important branch of geometry. It well deferves both of thefe epithets. The theorems which conftitute the doctrines of evolution are remarkable for their perfpicuity and neatnefs. Nothing has fo much contributed to give us clear notions of a very delicate fubje&t of mathematical difcuffion, namely curvature, and the measure and variations of curvature. It had become the fubject of very - keen debate; and the notions entertained of it were by no means diftinct. But nothing can give fuch a precife conception of the difference of curvature, in the different parts of a cycloid or other curve, as the beholding its defcription by a radius continually varying in length. This doctrine is peculiarly valuable to the fpeculator in the higher mechanics. The intenfity of a deflecting force is eftimated by the curvature which it induces on any rectilineal motion; and the variations of this intenfity, which is the characteristic of the force, or what we call its nature, is inferred from the variations of this curvature. The evolution and involution of curve lines have therefore great claim to our attention. But a Work like ours can only propose to exhibit an outline of the fubject; and we must refer our readers to thofe eminent authors who have treated it in detail. Varignon, in the Memoirs of the French Academy for 1706, has been at immenfe pains to prefent it in every form; James Bernoulli has alfo treated the fubject in a very general and fyftematic manner. Some account is given of it in every treatife of fluxions. We recommend the original work of Mr Huyghens in par ticular; and do not hesitate to fay, that it is the finest fpecimen (of its extent) of phyfico-mathematical difcuffion that ever has appeared. Huyghens was the moft elegant of all modern geometers; and both in the geometrical and phyfical part of this work, De Horologio Of cillatorio, he has preferved the utmoft rigour of demonftration, without taking one ftep in which Euclid or Apollonius would not have followed him.

Plate < XXXI.

- juvat integros accedere fontes Atque haurire.

Such authors form the taste of the young mathema tician, and help to preserve him from the almost mechaaical procedure of the expert fymbolical analyst, who arrives at his conclufion without knowing how he gets thither, or having any notions at all of the magnitudes of which he is treating.

There are two principal problems in this doctrine. 1. To afcertain the nature of the figure generated by the evolution of a given curve.

II. To determine the nature of the curve by whose evolution a given curve may be generated.-We shall confider each of these in order, and then take the opportunity which this fubject gives of explaining a little the abftrufe nature of curvature, and its meafures and variations, and take notice of the opinions of mathematicians about the precife nature of the angle of contact. The curve line ABCDEF (fig. 1.) may be confidered as the edge of a crooked ruler or mould; a thread may be fuppofed attached to it at F, and then lapped along it from F to A. If the thread be now led away from A, keeping it always tight, it is plain that the ex

tremity A must defcribe a curve line Abcdef, and Involution. that the detached parts of the thread will always be tangents to the curve ABCDEF. In like manner will the curve line Fdc'b' A' be defcribed by keeping the thread faft at A, and unlapping it from the other end of the mould.

This procefs was called by Mr Huyghens the EvoLUTION of the curve ADF. ADF is called the Evo. LUTE. Adf was named by him the CURVE BY EVOLUTION. It has been fince more briefly termed the EVOLUTRIX, or unlapper. It has also been called the INVOLUTE; because, by performing the process in the oppofite direction fd A, the thread is lapped up on the mould, and the whole space ADFfd A is folded up like a fan. The detached parts Cc, Dd, or Cc, Dd, &c. of the thread, are called RADU OF THE EVOLUTE; perhaps with fome impropriety, because they rather refemble the momentary radii of the evolutrix. We may name them the EVOLVED RADII. The beginning A of evolution may be confidered as the vertex of the curves, and the ends F and ƒ may be called the TERMS.

There is another way in which this defcription of curve lines may be conceived. Instead of a thread Fƒ gradually lapped up on the mould, we may conceive Ff to be a ftraight edged ruler applied to the mould, and gradually rolled along it without fliding, fo as to touch it in fucceffion in all its points. It is evident, that by this procefs the point ƒ will defcribe the curve fd A, while the point F defcribes the other curve Fďa, This way of conceiving it gives a great extenfion to the doctrine, and homologates it with that genefis of curve lines by which cycloids of all kinds are defcribed, and which we may diftinguifh by the name of PROVOLU TION. For it is plain, that the relative motions of the points A and b are the fame, whether the ruler b Bb' roll on the mould ABF, or the mould roll on the ruler: but there will be a great difference in the form of the line traced by the defcribing point, if we fuppofe the plane on which it is traced to be attached to the rolling figure. Thus, when a circle rolls on a straight line, a point in its circumference traces a cycloid on the plane attached to the ftraight line, while the point of the ftraight line which quitted the circle defcribes on the plane attached to the circle another line; namely, the involute of the circle. This mode of defcription allows us to employ a curved ruler in place of the ftraight one bB; and thus gives a vaft extenfion to the the. ory. But at prefent we fhall confine ourselves to the employment of the ftraight line b B, only keeping in mind, that there is an intimate connection between the lines of evolution and of provolution.

By the defcription, now given of this procefs of evolution and involution, it is plain,

1. That the evolution is always made from the convex fide of the evolute.

2. That the evolved radii B b, Cc, D d, &c. are refpectively equal to the arches BA, CA, DA, &c. of the evolute which they have quitted; and that b Bb, Ce', dDd, &c. are always equal to the whole arch ADF.

pa

3. That any point B of the lapped up thread defcribes during its evolution a curve line By rallel to be def; because these curves are always equi diftant from each other.

4. That if the thread extend beyond the mould as a tangent to it, the extremity a will defcribe a parallel or equidiftant