TWO TIONAL IN 1996.] Lyceum of Arts and Republican Lyceum. 7117 is its bafis, in various states of decompo- Philofophorum vitæ, Coburger (the Girion. printer's name) 1477, fol. No. VI.-MINERALOGY. Virgli opera, Nuremburg, 1492, fol. 6c specimens of marbles, granites, Miscbna, Amftelodami, 1698, fol. o vols. and ancient porphyries, collected in Italy. Biblia Germanica, Colonia, 1499, fol. 130 ditto of marble, from Norway, Evang. epift. Mifjel. Nuremburgæ,1484, Denmark, Germany, and Brabant. vellum, small 4to. 3 ditto of gold, with the ore still Tituli quæftionum de XII quodlibet fra: attached to the quartz. tres Tbıma de Aquino, editio Antiq. Printed on vellum: No date. 3 ditro of silver, from Peru. 3 ditto of fine cryttals. Ejusdem fumma de malo, &c. Impressum Impression of fishes, plants, &c. &c. per Arnoldum. Tber. Hern. fol. vellum. No date. No. VII.-List of REMARKABLE Anthologia, Græcè Florentiæ, 1494, 4to. MSS. SENT FROM COLOGNE. Catholicon Joban a Januâ ; grand folio; 1407. The capitals adorned with mini- For the Montbly Magazine. atures, and enriched with gold. The ACCOUNT OF penmanship very fine. RECENT NABiblia sacra, vols. vellum ; atlas size. ESTABLISHMENTS, Hieronimus fuper Ezechielam & de locis PARIS; the LYCEUM OF ARTS, Hebraicis ; vellum : folio. AND THE REPULICAN LYCEUM. Fors Poetarum Richardi de Polla & alia THE Lyceum of Arts was founded poëmata : 8vo. in the year 1792. A passage in the Fabule Alpbonfis regis : folio. writings of the celebrated 'Abbé Raynal;, Tabula magna omnium poëtarum ; folio. intimating, " that the arts and industry Cypriani opuscula, vellum ; folio. Very require the most powerful suppert during fine penmanship. the convulsions which agitate the state, Liber de distinctione metrorum ; folio. gave rise to this establishment. Over it Speculum bumanæ salvationis ; vellum ;' presides M. DESAUDRAY, president also folic, with miniatures ; two copies. of the Bureau de Consultation, and fellow Vila Alexandri Magni, & alia opuscula ; of a number of learned societies. To folio. this gentleman the Lyceum is indebted Biblia M. Hebræa; vellum ; 3 vols. for the original plan and distribution of folio. the building, the complete organization Stobæi ecloga apopbregmatum, Grece; of the establishment in general, and the folio. appointmer hent of its directory, to whoin Liber logicus, O&avii Orticiani & alia hc has been nominated the general lead rem medicam periinentia ; folio, in vel. cretary. lum. This great public edifice is divided into Catalogue de la bibliothèque des Jésuites the following compartments : de Cologne ; folio. 19. A covered gallery and the first veftibule. No. VIII.-LIST OF THE PRINCIPAL 20. A second interior vestibule, with PRINTED BOOKS SENT FROM Co a spacious stair-cafe. 3o. A Gothic péristile of so square Hieronimi epiftolæ, Maguntiæ ; Scheffer, feet dimensions. 4. A third communicating veftibule. Fortalitium fidei ; folio, no date. 50. An oblong gallery, 500 feet' in Biblia sacra ; Nuremberg, 1477, folio. length.. Cattolicon Job. Jannensis, Nuremberg, 60. An extensive saloon, for the col1486, folio. lection and exhibition of the arts, large Biblia sacra, vulgatæ editionis, Rome; enough to contain 3000 persons, 1990; folio. (This is the bible of Sixtus V.) 7o. A splendid hail, for musical con Biblia vulgata, Coloniæ, 1479; folio. certs and dances. Platonis opera, Venetiis, Aldus, 1913; 30. A library and a literary cabinet. in folio. The margins are full of varia: 9°. Four halls, used as schools. tions, and manuscript notes. 10°. An additional hall, for a dépot des Leonardi de Elsino fermones ; folio, no arts, or exhibition of arts. dae. mo. A Vauxhall, for nocturnal aflem Suetonius Mediolani, 1595 ; folio. blies, 4 Y 2 And LOGNE. 1470; folio. GILLET, Anatomy tres. PINE. FRATZ. And. 12o. Varicus apartments for Natural History baths, billiard-rooms. coffee-houses, &c. Zoology Botany Mineralogy tains four leading objects : LIN, 1°. The encouragement of useful arts. LAUMONT, Ton- | Physiology 2o. The encouragement of agreeable NELIER, and SUE. Medicine and polite arts. (Chemistry. 30. Public instruction. (Meteorology 4o. The publication and diffusion of V. Experimental Phy Optics recent discoveries. fics. Profeffor 1 Electricity The directory establishment includes FOURCROY. (Magnetism all the professors engaged in the several Diawing branches of instručijon; the assemblage Painring of commissaries, selected from all the Sculpture İcarned societies; and a certain number VI. The Polite Arts. ; Architectură of enlightened citizens, in public repute Profeffor NEVEU. Engraving for their inventions and other works. Music The primary buliness of the directory is Dancing (The Drama. to investigate every useful object laid before thens, and to make their reports General Gramm and observations concerning the same to VII. 'The Belles Let Languages Rhetoric the society. The contents of thele re Professors ports are recited in the public fittings, LANGLE and Li Geography History every seventh day (leptid:) at five o'clock Antiquities in the evening. At the close of these (Numismatography sittings, bounties are distributed to the inventors, &c. The great mass of ma VIII. Technology. S Arts Profeffor HASSEN- and terials for the Journal of Aris, is also fur Manufactures. nished by the members of the directory: The inventors of discoveries, &c. are the Journal containing an accurate account of all the interesting transactions always allowrd io be present when their of the sitting. rights are the subject of discussion. The decrees of the Lyceum are invariably The following is the inethod adopted adminiftered, according to this equitable in the several courses of instruction: mode of judging and deciding. The premiums are sometimes a brass medal, The Social Arts with an honorary inscription, or a laurel Political Econo- | Art of Government crown; but confift, for the most part, my. Profeffor DE- Law of Nations of the honourable mention, &c. The | Foreign Commerce meanest artificers are sometimes feen (Trade in the interior. crowned, by the side of the most cele. brated scholars. 1). Rural Fcoromy. Melioration of Soils Agriculture In the literarv cabinet is deposited an Profeffor DESCE extensive coilećcion of elementary treaForelis (Horticulture. tises in the different arts and sciences. In the schoois are 400 seats, where 1. General Mathema: perfons may attend gratis. Every course Algebra of intruction comprises 36 le&tures. Geometry - Trigo- The foregoing is the outline of this nometry: with their grand national chablishment; an instituapplication--Aftro- tion so much the more praile-worthy, as nomy-- Fortification it has been planned and executed at a NI. Mathematical Sci --Tactics-Nautical time when the arts and sciences were Piofi lor's subjects. fupposed to be in France in a state the 2. Particular Mathe- most critical. JARCE, DUMAS, and NEVIU. matics-Arithmetic THE REPUBLICAN LYCEUM. Foreign Exchange Foreigners not well informed of the Banking Book literary cftablishments in France, are apt keeping. Their plication. -- General frequently to confound the Loccum of Arts Mechanics Statics with the Republican Lyceum. Thefe, how- Dynamics - Op- ever, it should be observed, are very difpics, ferent inftitutions: The 1. SAUDRAY. MBTS, tics cice, 719 Sue 1796.] Proceedings of the Lyceum of Arts. The REPUBLICAN LYCEUM was thod of spinning, in country places, and founded in the year 1785, and may be concerning an improvement of the doufaid to bear some resemblance to the Arbe- ble crane, proper for unloading ships in nian Portico, where the most learned phi- port, both by citizen TREMELLE. He Losophers lectured in their respective obtained a medal. branches of learning. The general plan LE GRANGE and VAUQUELIN made of this Lyceum is by no means fo com- a report concerning SEGUIN's new way prehmive as that of the Lyceum of Arts, of tanning, by means of which the same being solely appropriated to the culture operations may be performed for the best of the sciences. The courses are of kinds of leather in a decade or two, that eight months' duration. One night in used to require two or three years. The every decade is allotted to extraordinary manufactory of the above-mentioned fittings. The ladies, in numerous parties, artist, established at Sevres, is now capafrequent this Lyceum. There is a par- ble of tanning, every year, fifty thousand ticular hall in it, with musical instru- ox-hides and two hundred thousand calfments, for their accommodation. There ikins, besides dogskins and horfe-hides. is also a lecture-hall, a conversation-hall, Two or three others, upon the same plan, and a library. are already set up in different departThe following is a list of the professors, ments. A crown was adjudged to citizen in their respective faculties : SEGUIN. А report was made by DesaUDRAY, Literature, LA HARPE. concerning the art of dividing swarms of Zoology, BROGNIART. bees, of removing them eiglit or ten Physiology, leagues without deranging them, of inThe Arts, HASSENFRATZ. uring them to different climates, of partHistory, GARAT. ing the hives at will, and and of cleanChemiitry, FOURCROY. Mineralogy, TONNELIER. ing and emptying them without killing Geography, MENTELLE. or hurting their inhabitants; by citizen Rural Economy SILVESTRE BARDON, a farmer. Rewarded with a me.lal. Some new experiments of FourItalian Language, BOLDONI. CROY and VAUQUELIN, upon the means English Language, ROBERT. of producing detonation by contact, (désonation par le choc) were executed by LEGRANGE, upon mixtures of superPROCEEDINGS OF THE FIRST AND SECOND PUBLIC SITTINGS OF THE phur and charcoal. The effects of thele 0.ygenated muriale of poi-ash, with fulLYCEUM OF ARTS, AT PARIS. experiments were terrible enough to At the FIRST PUBLIC SITTING of serve as a lesson of prudence to those the Lyceum of Arts, held on the zoth who may be desirous of operating upon Germinal (April 19) DARCET made a the same substances. Time and expereport concerning feveral manufactories rience alone can teach us the useful purestablished by citizen OLIVIER, in the poses to which the above mixtures may Fauxbourg of St. Antoine. Among the be applied. valuable articles he manufactures, is a In the SECOND PUBLIC SITTING of new kind of earthen-ware, of the most the 20th Prairial (June 8) a report was beautiful colours ; ornaments of metallic made by LEFEBURE concerning some earth, as sonorous as bronze ; black por improvements made by citizen J A BARIN, celain, equal to English, for Etruscan in Vaucanson's reel for winding of tbe filk vafes; and glazed earthen-ware, which from the cocoons.“ Amedal. is not subject to crack, proper for the A report was made, by BIENAIME, common purposes of the kirchen. He upon citizen SAUMON's simplification of also gave an account of a new process the hand-mill for grinding corn, and which will cxempt all manufactories of another, by Dize, upon an incorruptible earthen-ware froin the ruinous carriage cement, or plaster (mastic. incorruptible) and expensive use of the Nevers sand, for privies, reservoirs of water, and stone hitherto deemed indispensable. A crown terraces, inven by citizen PAROISSE, avas adjudged to him as the reward of who, as well as citizen Saumon, was rehis labours. warded with a medal. The rest of the MALHERBE 'made a report concern. fitting was of little importance to the ing the invention of an economical me MATHEMATICAL arts. Log. EO Log. Fig. 2 MATHEMATICAL CORRESPONDENCE. Log. CG= Log. 1067.6=3.028409 Log. CH =Log. 132.4=1.12 1888 CG CH = 0.906521 [Concluded from our last.] EO = 100000 CG A CH = 20652.1 well as of a planet, bears a very small proportion to that of the sun, IX. Therefore, the heat of the sun on the earth was at that time to the heat the preceding rule will serve to determine the heat communicated to the of the sun on the comet, as 2.4366 to comet of 680, which Sir Isaac Newton 90652.1; that is, as I to 37204. But has calculated upon a different hypo according to the observations of Sir Isaac whesis. Newton, the heat of boiling water is about three * times greater than the heat which dry earth acquires from the summer sun; T CH! G 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. (Fig. II.) Let E be the earth, C the lion, might have received from the rays comet, in its perihelion, and HSG the of the fun, was about 4000 times greater fun : draw ECO through the earth, the than red-hot iron, which is one-third comet, and the centre of the fun, O; and let H, G be the points where the greater than the deduction from New ton's hypothesis. right line EO meets the surface. Then From this calculation is derived one of By the rule (VII) the heat communi. the many strong arguments to prove that cated to the earth, at E, is to th: heat the bodies of comets are solid, compact, communicated to the comet, at C, as fixed, and durable, like the bodies of EG PXOG XH. Log. XH. L. the planets: for if they were nothing EO CO else but vapours or exhalations, in its CG EG that is, as CO Log. to EO passage by the neighbourhood of the sun, CH' EH it would have been immediately diffipatCG ed. In a similar manner may the comparative heats of the planers be deter mined, which will differ considerably Now on December 8th, when the from Newton's computationst. comet was in its perihelion, the distance thereof from the centre of the fun was X. Let us now suppose both the bodies to the distance of the earth from the to be regular solids, generated by the fame, as 6 to 1000 pearly; therefore, if rotation of given curves about their axes. EO=100000, OG, the sun's femidi- Let P be the centre of gravity of the ; ameter, will be = 467.6, and Co, the body which communicates the heat comet's distance = 600. HFG (Fig. 1) the generating curve of the other body; HG its axis ; A any Hence, EG=100467.6 CG=1067.6 point in its circumference ; AD a perEH= 99532, 4 CH= 132.4 pendicular on the axis ;- and let AP, CP, and the heat at E to the heat at C, as and CA be joined. Then if the whole 100467,6 600 x Log. to 100000 x Log. body be fupposed to aĉi in communicat99532.4 ing the heat, its action upon the paint 1067.6 A will be given by S III; and, conte132.4 quently, its action upon the convex fuBut Log. EG=Log. 100467.6=5.002026 perficies of a segment of a sphere, whose Log. EH=Log. 99532.4=4 997965 Let this action =%, and $ xdAP will be axis (or thickness). =DE, and centre P. EH * This proportion is probably too great, as it EG is the equatorial heat we thould reckon as the CO Log 2.4366 sun’s true heat at our orbit. equat PXOG to EH Log. CH 600 . __48*Rrx x Hyp. Log. + 4.p2 Rer 2 AT Ara + A4 *-R *+R 1796. ] 721 equal to the differential of the action on *+R the part AHBA of the folid. -R XI. For example, let the two solids X Hyp. Log. (x-R')+C. But when be spheres, whereof the radii are R, r, *=--T, this integral ought to be =0; (R. being that of the fiery solid); and therefore the complete integral is equal et a=co, the distance of their centres : 4pR[(*+R) Hyp. Log. (x+R) + and *=AP. Then will o>3PXDE (R-*) Hyp. Log: (+-R)-(4+R-Y) P(x-R2) (PR x+R Hyp. Log. (+R-r)-(R-4+r) H. X-R and o X DAP= 2 pdxX DE If we fuppose that part only of the surface of the fiery globe, contained be. (12_R) ++R tween the tangents drawn from any point Hyp. Log. but DE= in the surface of the other globe, to ach -R upon that point, the whole action upon 7-(-x)? ; therefore, o X dAP=4j?R the fegment AHBA will be just one fourth of the action on the other hypo(72-(1-x)?)dx p?r? d x (x2-R?) thesis : thai is, its action will be equal Х х paRix *+ p?dx(x2-R2)(1-x)2 [(x+R) Hyp. Log. (*+R) + Hyp. Log. + (R--*) Hyp. Log. (+-R)-(4+R-) ++R Hyp. Log. (4+R-)-(R-Atr) H. Hyp. Log. Log. (4~r~R)]. (r-(4---))x 82,dx(+-R) Aberdeen, June 24. B. CYGNI. A2 QuesȚion XVI (No. V). -- Answered by Log X H. Mr. H. Cox. Let x denote the first man's money; then will Log. -R tặc integral of which, when +4 be the second man's; £xt the third man's; and 2x+4 the fourth man's. The *=4+t, will give the whole action of {um of these, by the question, is equal to 90; the fiery globe upon the other. that is, 44x+9=30, or 9x+18=18n; hence XII. But if the surface only be fup: confequently, 18+4322, the second man's; x+2=20, and x=131. the first man's money, posed to communicate the heat, the effect ti=10, the third man’s; and 18x2+4=409 upon the point A will be given by S V; the fourth maa’s . and if this effect =o, the action upon This Queftion was also answered by Messrs. the circumference of a circle whose radius George Fox, Liverpool ; Wm. Adams ; Acade =AD, will be =px 2px AD, and the micus; N. Bifworth; L- Cr; W. Clovery; action upon the surface of the feginent JF; 7. H. Juvenis, Luycey ; AHBA=1280X ADX DAH. Christophe Mann ; John Richter, juri.; Win. Let the two bodies be spheres, then Rouse; T. S--h; T. Salmon; and J. W. +R New MATHEMATICAL QUESTIONS. 2pR QUESTION XX.--By J. Fr. 200X ADX DAH= X 2PX ADX. THEOREM. If through any point of a great circle two other great circles be described, at right rdPD r+R 4P*RI angles to each other; and from two other pointa · AD X-R of the first mentioned great circle, one on each x+R fide of the point of intersection, perpendiculars DPD x Hyp. Log AR but by the be raised to meet the intersecting circles ; the nature of the circle, PD=- the rectangle of the tangents of the perpen diculars will be equal to the rectangle of the CP2-CATAP APX DAP fines of the segments of the arc intercepted and dPD= 2CP CP between the perpendiculars. Required, a demonstration. Therefore, apo ADXDAH= QUESTION XXI.-By L. W. D. 4pRider +R What is that number, whose square root is X Hyp. Log The in equal to the sum of the two digits of which it tegral of this expreffion is evidently = is composed; and if from the said numbers 4p Rrx r+R be subtracted the product of the sum and diffeX H. Log rence of its digits, they will be invested, and -R (?-R2) reprefent my age in years ? NEW will p = 2PR *R' xdx *-R |