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and confiders the one as alone producing the motion of the 

 body, in the iccoiid inllant, and the other as cmpla\'ed to 

 deitroy that which it had in the tirll. This principle had 

 been applied by M. d'Aleinbert, fo early as the year 1744. 

 to the theory of the equilibrium, and the motion of fluids, 

 (Traitc de I'Equilibre et du Mouvemcnt des Fhiides, 

 Paris, 1744. Ed. 2. 1770.) and the dil'coveiy of it was 

 fucceedcd by a new calculus, the hrll efl'ays of which were 

 publiilied in a " Difeonrfe on the General Theory of the 

 Winds," (Reflexions fur la Caufe Generale desVents, Paris, 

 4to, 1747.) which the academy of Berlin honoured with 

 the prize-medal in 1 746 ; and at the fame time the author 

 was elefted an honorary member. This work was dedi- 

 cated to the king of PrufTia, who was terminating a glori- 

 ous campaign by an honourable peace, in the llu'ee follow- 

 ing Latin verfes : 



" PIxc ego de vcntis, dum ventorum ocyor alls 

 Palantes agit Auilriacos Frederlcus, ct orbi, 

 Inlignis lauro, ramum praetendit olivae." 



*' Swifter than wind, while of the winds I write. 

 The foes of conquering Frederic fpeed their flight ; 

 While laurel o'er the hero's temple bends. 

 To the tir'd world the ohve branch he fends." 



From this time d'Alembert was ranked among the phi- 

 lofophical friends of Frederic. In 1 747 our mathematician 

 applied his new calculus of " Partial Differences," to vi- 

 brating chords, and the propagation of founds. In 17491 

 he fuggefted a method of applying his principle to the mo- 

 tion of any body of a given figure ; and he alfo refolved 

 the problem of the preccfTion of the equinoxes ; determin- 

 ing its quantity, and explaining the phenomenon of the nu- 

 tation of the earth's axis, difcovered by Dr. Bradley, 

 (" Recherches fur la PrccefTion des Equinoxes, et fur la 

 nutation de I'axe de la Terre, dans la Sylleme Newtonien, 

 4to, Paris, 1749.) In 1752 he publiftied a treatife on the 

 " Refillance of Fluids," (" Effais d'une nouvclle Theorie 

 du Mouvement des Fluides, 4to, Paris, 1752."), and about 

 the fame time, in the memoirs of the academy of Berlin, 

 " Refearches concerning the Integral Calculus." In the 

 fame year he pubhfhed " Elements of Mufic," defigncd to 

 explain the principles of Rameau, (" Elemcns de Muflque, 

 Theorique et Pratique, fuivant les principes de M. Rameau 

 eclaires, developpes, et fimplifies, 1 torn. 8vo. a Lyon.") 

 Other pieces, publifhed at various times, in the memoirs of 

 the Academies of Paris and Berlin, were collefted under 

 the title of " Opufculcs Mathcmatiqucs, ou Memoires fur 

 differens fujets de Geometric, de Meehaniqucs, d'Optiques, 

 cTAftrononiie," in 9 vols 4to. Paris, from 1761 to 1773. 

 He alfo wrote " Rcchetches fur differens Points importans 

 du Syfteme du Monde," Paris, 1754 and i7jC), 3 vols. 

 4to. His " Elemens de Philofophie," was printed in 

 1759. Befides thefe feparate publications, the Memoirs of 

 the Academy of Paris contain the following pieces, viz. 

 *' Precis de Dynamique," 1743 ' " Precis de I'Equilibre et 

 de Mouvement des Fluides," 1744; " Methode generale 

 pour determiner les Orbites et les Mouvements de toutes 

 les Planetes, en ayant egard a leur aftlon mutuelle," 1745; 

 " Precis des Reflexions fur la Caufe Generale des Vents," 

 1750 ; " Precis des Recherches fur la PrecefTion deS'EquI- 

 noxes, et fur la Nutation de I'Axe de la Terre duns le 

 Sylleme Newtonien," 1750; " ElTai d'une nouvelle Theo- 

 rie fur la Refiftance des Fluides," 1752 ; " precis des Effais 

 d'une nouvelle Theorie de la Refiftance des I'luides," 1753; 

 " Precis des Recherches furies differens Pomts importans du 

 Syfteme du Monde," 17545 " Recherches fur la Preccflion 



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des Equinoxes.et fur la Nutation dc I'Axe de la Terre, dans 

 I'Hypothefe, de la diflimilitude des Meridiens," 1754; 

 " Reponfe a un Article du Memoire de M. I'Abbe de la 

 Caille, fur la Theorie du Solcil," 1757; "Addition;! ce 

 Memoire," 1757; " Precis des Opufculcs Malhematiques," 

 1761 ; " Precis du troifiirme volume des Opufculcs Mathc- 

 matiqucs," 1764; " Nouvelles Recherches fin- les verre* 

 Optiques, pour fcrvir de fuite a la Theorie qui en a etc 

 doiuiec dans le volume 3' des Opufculcs Matlumatiques," 

 premiere mem. 1764 ; " Nouvelles Recherches fur les vcrrcs 

 Optiques, pour fcrvir de fuitc ;i la Theorie qui en a ete 

 donnee dans le troificme volume des Opufculcs Malhema- 

 tiques," feconde mem. 1 765 ; " Obfervations fur les Lu- 

 nettes Achromaliques," 1765 ; " Suite des Recherclies lur 

 les verres Optiques," troiliemc mem. 1 767; " Rcclierehe-i 

 fur le Calcul Integral," 1767 ; " Accident arrive- par I'ex- 

 plofion d'une meulc d'Eniouleur," 1768; " Precis des 

 Opufculcs de Mathematiques," 4' & 5' vols, leur analyfe, 

 1768; "Recherches furies Mouvemens de I'Axe d'une 

 Planete qnelconque dans I'Hypothefe de la Diflimilitude 

 des Meridiens," 1768 ; " Suite des Recherches fur les 

 Mouvemens, &c.," 1768; " Recherches fur le Calcul In- 

 tegral," 1769; " Memoire furies principes de la Mech." 



The Memoirs of the Academy of Berlin contain the fol- 

 lowing pieces, I'/'z. " Recherches fur le Calcul Integral, l' 

 parte," 1746; " Solution de quelques problemes d'Allrono- 

 " mie," 1747; "Recherches fur leCourbeque forme uneCorde 

 tendue, mifc en vibration," 1747; " Suite des Recherches fur 

 le Calcul Integral," 1748; " Lettre a M. de Maupertuis," 

 1749 ; " Addition aux Recherches fur le Courbe que foinie 

 uneCorde tendue, mife en vibration," 1 750; " Addition- 

 aux Recherches fur le Calcul Integral," 1750; " Lettre a 

 M. le Profeflcur Formey," 1755 ; " Extr. de Differ. Let- 

 tres a M. de la Grange," 1763 ; " Sur les Tautochix>nes," 

 1765 ; " Extr. de Differ. Lettres a M. de la Grange," 

 1769. The Memoirs of Turiti, contain " Differcntcs Let- 

 tres a M. de la Grange, en 1764 & 1765." en tom. iii. of 

 thefe memoirs, and " Recherches fur DifF. Sujets de Math." 

 en tom. iv. 



The numerous and valuable produftions above recited,' 

 entitle d'Alembert to rank among the moil celebrated 

 mathematicians of the age. But he is no Itfs diilinguiflied 

 by his genius, judgment, and tafle, than by bis mathema- 

 tical knowledge ; and he is defcrv'edly regarded in France 

 as one of the lirll writers of that nation. To him the ori- 

 ginal defign of the French Encyclopedia has been generally 

 aferibed ; a work which was begun in 1750 by d'Alembert, 

 Diderot, Voltaire, and many other learned men, ajid which 

 has contributed in a veiy eminent degree to the diHufion of 

 knowledge. Many of the moll valuable articles in mathe- 

 matics, hitlory, and polite literature, were compofed by M. 

 d'Alembert; and the prelinJnary difeourfe,'eonceniing the 

 rife, progrefs, conneiitions, and affmities, of the various 

 branches of human knowledge, will be ever coiilidercd by 

 the befl: judges as the evidence of a well-informed and com- 

 preheniivc mind, as a fpecimcn of judicious arrangement and 

 correct criticifm, and alfo as a model of jull thinking and 

 good writing. Befides the valuable flore with which he 

 furnifhed this treafure of univerfal fcience, his talents were 

 difplayed in many feparate publications on fubjedls of 

 claflical and polite literature. His " Tranflation of fcleft 

 parts of Tacitus, (" Traduftion de divers moiceaux de 

 Tacite,") in 2 vols. izmo. afford, fays one of his biogra- 

 phers, an elegant fpecimen of liis learning : aud his " Me- 

 moirs of Chriflina queen of Sweden," is a mallerlv piece 

 of biographical writing, in which the autiior evinces his 



acquaintaace 



