1796.] Lyceum of Arts and Republican Lyceum. is its bafis, in various ftates of decompoition. No. VI. MINERALOGY. 6c fpecimens of marbies, granites, and ancient porphyries, collected in Italy. 130 ditto of marble, from Norway, Denmark, Germany, and Brabant. 3 ditto of gold, with the ore still attached to the quartz. 3 ditto of filver, from Peru. 3 ditto of fine cryitals. Impreffion of fishes, plants, &c. &c. No. VII.-LIST OF REMARKABLE MSS. SENT FROM COLOGNE. Catholicon Joban a Fanua; grand folio, 1407. The capitals adorned with miniatures, and enriched with gold. The penmanship very fine. Biblia facra, 4 vols. vellum; atlas fize. Hieronimus fuper Ezechielam & de locis Hebraicis; vellum: folio. Fons Poetarum Richardi de Polla & alia poëmata: 8vo. Fabula Alphonfis regis: folio. Tabula magna omnium poëtarum; Cypriani opufcula, vellum; folio. fine penmanship. folio.. Very Liber de diftin&tione metrorum; folio. Speculum bumana falvationis; vellum; folio, with miniatures; two copies. Via Alexandri Magni, & alia opufcula; folio. Biblia M. Hebræa; vellum; 3 vols. folio. Stobæi ecloga apophtegmatum, Græce ; folio. Liber logicus, O&avii Orticiani & alia ad rem medicam pertinentia; folio, in vel lum. Catalogue de la bibliothèque des Jéfuites de Cologne; folio. No. VIII.-LIST OF THE PRINCIPAL PRINTED BOOKS SENT FROM CoLOGNE. Hieronimi epiftola, Maguntia; Scheffer, 1470; folio. Fortalitium fidei; folio, no date. Biblia facra; Nuremberg, 1477, folio. Catbolicon Job. Jannenfis, Nuremberg, 1486, folio. Biblia facra, vulgatæ editionis, Rome; 1590; folio. (This is the bible of Sixtus V.) Biblia vulgata, Colonie, 1479; folio. Platonis opera, Venetiis, Aldus, 1513, in folio. The margins are full of variations, and manuscript notes. Leonardi de Elfino fermones; folio, no date. Suetonius Mediolani, 1595; folio. 717 For the Monthly Magazine. ACCOUNT OF TWO RECENT NA TIONAL ESTABLISHMENTS, IN PARIS; THE LYCEUM OF ARTS; AND THE REPULICAN LYCEUM. THE LYCEUM of ARTS was founded in the year 1792. A paffage in the writings of the celebrated Abbé Raynal, intimating, "that the arts and industry require the moft powerful fuppert during the convulfions which agitate the ftate,' gave rife to this establishment. Over it prefides M. DESAUDRAY, prefident alfo of the Bureau de Confultation, and fellow of a number of learned focieties. To this gentleman the Lyceum is indebted for the original plan and diftribution of the building, the complete organization of the establishment in general, and the appointment of its directory, to whom he has been nominated the general fecretary. This great public edifice is divided into the following compartments: 1. A covered gallery and the first veftibule. 2o. A fecond interior veftibule, with a fpacious ftair-cafe. 3o. A Gothic périftile of 50 square feet dimenfions. 4. A third communicating veftibule. 5. An oblong gallery, 500 feet' in length.. 6°. An extenfive faloon, for the collection and exhibition of the arts, large enough to contain 3000 perfons. 7°. A fplendid hail, for mufical concerts and dances. 8. A library and a literary cabinet. 9°. Four halls, ufed as fchools. ioo. An additional hall, for a dépôt des arts, or exhibition of arts. 11°. A Vauxhall, for nocturnal affem blies. And 12°. Various apartments for baths, billiard-rooms. coffee-houfes, &c. The general plan of the Lyceum contains four leading objects: 1. The encouragement of ufeful arts. 2°. The encouragement of agreeable and polite arts. 3. Public instruction. IV. General Phyfics. Natural History LIN, GILLET, Anatomy NELIER, and SUE. 4. The publication and diffufion of V. Experimental Phy recent difcoveries. The directory establishment includes all the profeffors engaged in the feveral branches of inftruction; the affemblage of commiffaries, felected from all the learned focieties; and a certain number of enlightened citizens, in public repute for their inventions and other works. The primary butinefs of the directory is to inveftigate every ufeful object laid before them, and to make their reports and obfervations concerning the fame to the fociety. The contents of thefe reports are recited in the public fittings, every feventh day (feptid:) at five o'clock in the evening. At the clofe of these fittings, bounties are diftributed to the inventors, &c. The great mafs of materials for the Journal of Aris, is alfo furnished by the members of the directory: the Journal containing an accurate account of all the interefting tranfactions of the fitting. The following is the method adopted in the feveral courfes of inftruction: 1. Political Economy. Profeffor DE SAUDRAY. The Social Arts (Agriculture 1. Rural Economy. Melioration of Soils Profeffor METS. DESCE III. Mathematical Sci Forefts 1. General Mathema tics Algebra Geometry Trigo- fics. Profeffor VI. The Polite Arts. VII. The Belles Let- PINE. VIII. Technology. FRATZ. The inventors of difcoveries, &c. are The always allowed to be prefent when their rights are the fubject of difcuffion. The decrees of the Lyceum are invariably adminiftered, according to this equitable mode of judging and deciding. premiums are fometimes a brafs medal, with an honorary infcription, or a laurel crown; but confift, for the most part, of the honourable mention, &c. The meanest artificers are fometimes feen crowned, by the fide of the moft celebrated scholars. In the literary cabinet is depofited an extenfive collection of elementary treatifes in the different arts and fciences. In the fchools are 400 feats, where perfons may attend gratis. Every course of inftruction comprifes 36 lectures. The foregoing is the outline of this grand national eftablishment; an inftituapplication-Aftro- tion fo much the more praife-worthy, as nomy-- Fortification it has been planned and executed at a --Tactics-Nautical time when the arts and fciences were fubjects. Profeffors fuppofed to be in France in a state the 2. Particular Mathe- moft critical. DUMAS, matics-Arithmetic Foreign ExchangeBanking Bookkeeping. Their application.--General ence. JARGE, THE REPUBLICAN LYCEUM. Foreigners not well informed of the literary cftablishments in France, are apt frequently to confound the Lyceum of Arts Mechanics-Statics with the Republican Lyceum. Thefe, how-Dynamics Op- ever, it fhould be obferved, are very d ferent inftitutions. Pies. y dif The 1796.] Proceedings of the Lyceum of Arts. The REPUBLICAN LYCEUM was founded in the year 1785, and may be faid to bear some resemblance to the Athenian Portico, where the most learned philofophers lectured in their refpective branches of learning. The general plan of this Lyceum is by no means fo comprehive as that of the Lyceum of Arts, being folely appropriated to the culture of the fciences. The courses are of eight months' duration. One night in every decade is allotted to extraordinary fittings. The ladies, in numerous parties, frequent this Lyceum. There is a particular hall in it, with musical inftruments, for their accommodation. There is alfo a lecture-hall, a conversation-hall, and a library. The following is a lift of the profeffors, in their refpective faculties : DEPARCIEUX. LA HARPE. BROGNIART. SUE HASSENFRATZ. GARAT. FOURCROY. TONNELIER. MENTELLE. SILVESTRE Philofophical Grammar, SICARD. PROCEEDINGS OF THE FIRST AND SECOND PUBLIC SITTINGS OF THE LYCEUM OF ARTS, AT PARIS. AT the FIRST PUBLIC SITTING of the Lyceum of Arts, held on the 30th Germinal (April 19) DARCET made a report concerning feveral manufactories eftablished by citizen OLIVIER, in the Fauxbourg of St. Antoine. Among the valuable articles he manufactures, is a new kind of earthen-ware, of the most beautiful colours; ornaments of metallic earth, as fonorous as bronze; black por celain, equal to English, for Etrufcan vafes; and glazed` earthen-ware, which is not fubject to crack, proper for the common purposes of the kitchen. He alfo gave an account of a new procefs which will exempt all manufactories of earthen-ware from the ruinous carriage and expenfive ufe of the Nevers fand, hitherto deemed indifpenfable. A crown was adjudged to him as the reward of his labours. MALHERBE made a report concerning the invention of an economical me 719 thod of fpinning, in country places, and concerning an improvement of the double crane, proper for unloading fhips in port, both by citizen TREMELLE. He obtained a medal. LE GRANGE and VAUQUELIN made a report concerning SEGUIN's new way of tanning, by means of which the fame operations may be performed for the best kinds of leather in a decade or two, that ufed to require two or three years. The manufactory of the above-mentioned artift, eftablished at Sevres, is now capable of tanning, every year, fifty thousand ox-hides and two hundred thousand calffkins, befides dogfkins and horfe-hides. Two or three others, upon the fame plan, are already fet up in different departments. A crown was adjudged to citizen SEGUIN. A report was made by DESAUDRAY, concerning the art of dividing fwarms of bees, of removing them eight or ten leagues without deranging them, of inuring them to different climates, of parting the hives at will, and and of cleaning and emptying them without killing or hurting their inhabitants; by citizen BARDON, a farmer. Rewarded with a medal. Some new experiments of FourCROY and VAUQUELIN, upon the means of producing detonation by contact, (détonation par le choc) were executed by LEGRANGE, upon mixtures of fuperoxygenated muriate of pot-afh, with fulphur and charcoal. The effects of thefe experiments were terrible enough to ferve as a leffon of prudence to thofe who may be defirous of operating upon the fame fubftances. Time and experience alone can teach us the useful purpofes to which the above mixtures may be applied. In the SECOND PUBLIC SITTING of the 20th Prairial (June 8) a report was made by LEFEBURE concerning fome improvements made by citizen JABARIN, in Vaucanfon's reel for winding off the filk from the cocoons.-A medal. A report was made, by BIENAIME, upon citizen SAUMON's fimplification of the hand-mill for grinding corn, and another, by DIZE, upon an incorruptible cement, or plafter (maftic, incorruptible) for privies, refervoirs of water, and stone terraces. invented by citizen PAROISSE, who, as well as citizen Saumon, was rewarded with a medal. The reft of the fitting was of little importance to the arts. MATHEMATICAL (Fig. II.) Let E be the earth, C the Comet, in its perihelion, and HSG the fun draw ECO through the earth, the Comet, and the centre of the fun, O; and let H, G be the points where the right line EO meets the furface. Then By the rule (§ VII) the heat communicated to the earth, at E, is to the heat communicated to the comet, at C, as XOG EG pxoG XH. Log. to XH. L. EO EH CO Log. CH Now on December 8th, when the comet was in its perihelion, the distance thereof from the centre of the fun was to the diftance of the earth from the fame, as 6 to 1009 pearly; therefore, if EO=100000, OG, the fun's femidiameter, will be = 467.6, and CO, the Comet's diftance = 600. Hence, EG-100467.6 CG=1067.6 EH= 99532 4 CH 132.4 and the heat at E to the heat at C, as 100467.6 to 100000 × Log. 99532.4 600 × Log. 1067.6 132.4 But Log. EG=Log.100467.6=5.002026 Log. EH Log. 99532.44 997965 EG Log. =0.004061 EH 600 EG EH IX. Therefore, the heat of the fun on the earth was at that time to the heat of the fun on the comet, as 2.4366 to 90652.1; that is, as 1 to 37204. But according to the obfervations of Sir Ifaac Newton, the heat of boiling water is about three times greater than the heat which dry earth acquires from the fummer fun; and the heat of red-hot iron about three times greater than the heat of boiling water: therefore, the heat which dry earth on the comet, while in its perihe lion, might have received from the rays of the fun, was about 4000 times greater than red-hot iron, which is one-third greater than the deduction from Newton's hypothefis. From this calculation is derived one of the many strong arguments to prove that the bodies of comets are folid, compact, fixed, and durable, like the bodies of the planets: for if they were nothing elfe but vapours or exhalations, in its paffage by the neighbourhood of the fun, it would have been immediately diffipated. In a fimilar manner may the comparative heats of the planets be determined, which will differ confiderably from Newton's computations+. X. Let us now fuppofe both the bodies to be regular folids, generated by the rotation of given curves about their axes. Let P be the centre of gravity of the body which communicates the heat; HFG (Fig. 1) the generating curve of the other body; HG its axis; A any point in its circumference; AD a perpendicular on the axis and let AP, CP, and CA be joined. Then if the whole body be fuppofed to act in communicating the heat, its action upon the paint A will be given by § III; and, confequently, its action upon the convex fuperficies of a fegment of a fphere, whofe axis (or thicknefs), DE, and centre P. Let this action, and 4x dAP will be *This proportion is probably too great, as it is the equatorial heat we thould reckon as the CO Log. = 2.4366 fun's true heat at our orbit. equal 796.] Mathematical Correfpondence. equal to the differential of the action on the part AHBA of the folid. 721 = × Hyp. Log. +412 R2 r A XI. For example, let the two folids x Hyp. Log. (x2-R2)+C. But when be fpheres, whereof the radii are R, r,, this integral ought to be =0; therefore the complete integral is equal 4pRr [(+R) Hyp. Log. (x+R)+ Jet (R being that of the fiery folid); and and X dAP= Hyp. Log. x+R 2pR 7(42-R2) Hyp. Log. * R A (R) Hyp. Log. (x-R)-(s+R−1) Hyp. Log. (4+R~r)—(R—4+r) H. Log. (4--R)]. If we fuppofe that part only of the furface of the fiery globe, contained between the tangents drawn from any point ¿ but DE in the furface of the other globe, to act upon that point, the whole action upon the fegment AHBA will be just onefourth of the action on the other hypothes that is, its action will be equal pRrx [(x+R) Hyp. Log. (x+R)† ; therefore, XdAP=4/2R (y2°— (s—x)2)dx p2r2 dx (x2-R2) +12dx(x2—R2)(1—‚x') 2 Hyp. Log. =2pRx -R A Log. -R' the integral of which, when =A+r, will give the whole action of the fiery globe upon the other. XII. But if the furface only be fup pofed to communicate the heat, the effect upon the point A will be given by § V; and if this effect, the action upon the circumference of a circle whofe radius =AD, will be px 2px AD, and the action upon the furface of the fegiment AHBA=.2pqXAD × dAH. Let the two bodies be spheres, then will x Hyp. Log. Let x denote the firft man's money; then will +4 be the fecond man's; +1 the third man's; and 2x+4 the fourth man's. The fum of thefe, by the question, is equal to 90; that is, 4x+9=90, or 9x+18=180; hence x+2=20, and x=181. the first man's money, confequently, 18+4=22, the fecond man's; 1+1=10, the third man's; and 18x2+4=400 the fourth man's. 2 This Queftion was alfe anfwered by Meffrs. George Fox, Liverpool; Wm. Adams; Academicus; N. Bosworth; L-t Cr; W. Clavery; F; J. H. Juvenis, Laycey; Chriftopher Mann; John Richter, jun.; Wm. Roufe; T. S--k; T. Salmon; and J. W. NEW MATHEMATICAL QUESTIONS. QUESTION XX.-By J. FY THEOREM. If through any point of a great circle two other great circles be described, at right angles to each other; and from two other points of the first mentioned great circle, one on each fide of the point of interfection, perpendiculars but by the be raised to meet the interfecting circles; the the rectangle of the tangents of the perpendiculars will be equal to the rectangle of the fines of the fegments of the arc intercepted between the perpendiculars.-Required, demonftration. 2pR rdPD AD × Hyp. Log. = x+R_4p2R +R -R and dPD= APX dAP Therefore, 2p9xAD×dAH= x+R × Hyp. Log The in-R tegral of this expreffion is evidently = 4 Rrx x+R 8p2R2rx dx x H. Log. -R QUESTION XXI.-By L. W. D. 2 What is that number, whofe fquare root is equal to the fum of the two digits of which it is compofed; and if from the faid numbers be fubtracted the product of the fum and difference of its digits, they will be inverted, and +(42-R2) represent my age in years? NEW |