PBOKY, OASPARD CLAIR-FRANCOIS DB. 



PROPERTIUS, SEXTD8 AURELIOa 



1, an introduction, containing the analytical formula! and the mode of 

 using tin t !.! ; '.', lu,uOO natural sine* to 35 place* of decimal*, with 

 seven and eight column* of difference*; 3, the logarithm* of 100,000 

 line* to 14 plaote of decimal* and 6 column* of difference*; 4, the 

 logarithm* uf the ratio* of the first 6000 line* to their corresponding 

 arc* to 14 decimal plaow; 5, a aiinilar table of the ratio* of the 

 tangents to their an* ; 6, the logarithm* of 100,000 tangent* ; 7, the 

 logarithm* of number* from 1 to 100,000 to 19 decimal place*, aud 

 from 1 00 to 200,000 to 1 4 decimal places, with 5 columns of difference*. 

 In 1820 a distinguished member of the Board of Longitude, Loudou, 

 was instructed by our government to propose to the Board of Longitude 

 of 1'ari* to print an abridgment of these tables at the joiut expense of 

 the two countries : 60004. was named as the sum which our govern- 

 ment was willing to advance for this purpose ; but the proposal was 

 declined, aud the great 'Tables du Cadastre' are fctill confined in 

 manuacript to the library of the Paris Observatory. 



Prony was appointed profeeaor of mechanic* to the Kcole Polj Uch 

 nique in 17W4, the year of its institution, and the same year he became 

 Directeur-Gcuc'ral des Fonts et Chaucsees. As professor to the Kcolo 

 1'oly technique he was indefatigable in endeavouring to bring the 

 researches of modern mathematicians within the comprehension of his 

 pupil*. This was the object of his ' Mucauique PhUoaophique,' 4 to, 

 Par., 1800. It is an analytical synopsis of mechanics, hydrostatics, and 

 hydraulics. The right-hand pages are each divided into four columns, 

 headed notation, definition, theorems, problems; while those to the 

 lelt are occupied with so much of investigation and reasoning as is just 

 sufficient to connect the several results in the mind of the student. 



In 1798 Napoleon invited him to become a member of the Institute 

 of Egypt, which however he declined, and bis refu-al was never 

 entirely forgotten or pardoned. Nevertheless, after Napoleon's coro- 

 nation a* king of Italy (1806), Prony was charged with the engineering 

 operations for protecting the province of Ferraru IV.. m the further 

 inundations of the Po; and about the same time, or earlier, he was 

 employed in superintending the work* then carried on by the French 

 government in the ports of Genoa, Ancona, Poln, and in the Gulf of 

 Upezzia, including some very intricate investigations connected with 

 the tides, currents, and deposits of the Adriatic and canals within the 

 Venetian territory. Napoleon's animosity towards Prony appear* to 

 have been counteracted only by a regard for his abilities. \Ve are told 

 by Arago that Prouy's researches relative to the thrust of embank- 

 ment* (' pouatce des terres '), and on the proper dimensions of lining- 

 wall* (' rnurs do revetemect ), 4to, Paris, 18U2, with the obvious 

 practical utility of the results to which they led, were the meonx of 

 securing Napoleon's suffrage. On a later occasion, when the emperor 

 was distributing the new dignities which he had created, a seer, tni y 

 of itate reminded him of Prouy, to which he merely replied, "II ne 

 faut pa* mettro son rabot en dentelles ; on ne pourrait plus s'en scrvir 

 pour rabotor." 



In lalu he was appointed (in conjunction with Count Fossoinbrouo 

 of Florence) chief of the Commissions de 1'Agto Romano, which had 

 for its object the more effectual drainage and improvement of the 

 I'ontiue Mann**. " The results of hu labours iu this very important 

 tek, which be prosecuted with extraordinary zeal and success, were 

 embodied in his ' Description Hittorique et Hydrographique des Marais 

 Pontin*,' which appeared in 1823, and which contains a very detailed 

 account of the past, present, and prospective condition of those pesti- 

 lential regions, aud a very elaborate and scientific description of the 

 principle* which should guide us in all similar cases in order to effect 

 their permanent restoration to healthiness and fertility." (' Edinburgh 

 Journal of Science,' xv., p. 627.) 



After the restoration he continued to be employed in various 

 important works, among which was the formation of extensive embank- 

 meuU near the mouth of the Rhone. In 1817 he became a ineuib. r of 

 the Bureau de Longitude ; the following year he was elected one of 

 the fifty foreign members of the Royal Society, London : in 1828 he 

 was created a baron by Charles X., aud in 1835 a peer of France. He 

 died at Aoniena, near Paris, the latter end of July 1839. 



In his profeuional character Prony waa the reverse of imperious. 

 lie gave hi* opinion on all occasion* with exemplary frankness. Those 

 who were associated with him in any of his undertakings continued 

 ever after hi* friend*, and there is no instance of a pupil claiming hi* 

 rapport without it* being cordially granted. That he was mindful of 

 hi* obligation* to other* is shown by hi* calling on Arago in 1837, 

 and desiring him not to omit in hi* ' Eloge of Carnot,' then about to 

 be published for the fint time, that the latter had saved hi* (Prony'*) 

 life in 1798. A* a mathematician and philosopher, though inferior to 

 ome of the gr. at men of hi* day, he was certainly one " of whom hi* 

 country my justly be proud, whether we consider the extent and 

 character of his 'scientific attainments, or the variety of important, 

 practical, and useful labours in which his life was spent." 



The fol. owing works, with those already mentioned, will, we 

 believe, nearly complete the list of Prouy'* literary labours: 1, 

 ' Experimental and Analytical Essay on tbe Law* of Expansion 

 observed by Elastic Fluid*, and on the Expansile Forco of the 

 Vapour* ot Water and Alcohol at dillerent Terujieraturai,' Par. 4to, 

 1704 (also printed in the first volume of the 'Journal de 1' Kcole 

 PolyUchuiquu ') ; 2, ' Plan of Instruction for the Students of the 

 National School des Pont* et Cliaus.ce*, for the year vii./ Par. 1795; 



3, Analysis of the ' Exposition du Syitctue du Monde ' of Laplace, 

 Par. 8vo, 1801; 4, 'Plan of Instruction for the Polytechnic 

 o far as regard* the Kqaflibriam of Bodies,' Par. 4lo, Isol ; 5. 

 'Report made to the Mathematical and Physical Class of the National 

 Institute, upon divers inventions of Jean Pierre Drox, relative to the 

 Art of Coining,' Par., 4to, 1801 ; 6, 'Report on the Memoir of Ducros 

 relative to the supply of Water requisite for Canals,' Par. 8vo, Isul ; 

 7, ' Results of Experiments for determining the Relation between the 

 French Metre aud the English Foot,' 1'ur. 1-02; 8, ' On the Supply 

 of Water requisite for the Canal Saint Queutin ' ('Surle Jau^uage 

 del Eaux Courante* qui doivent alimeuter le basain du passage du 

 Canal Saint Queutin') Par. 4 to, 1802; 9, ' Phybico-Mathematical 

 Researches in the Theory of Flowing Water*,' Par. 4 to, 1804 ; 10, 

 ' On the Computation of Latitude* and Longitude*,' Par. 4to, . 

 11, ' On the Variations iu the Inclination of the Seine, and its Amount 

 for each day of the years 1788-90, together with the Report m 

 the Academy of Sciences, January 29, 1791, by Lavoisier, Laplace, 

 and Coulomb,' Par. 4 to, 1806; 12, 'Summary of Lessons on the 

 Motion of Solids and on the Equilibrium and Motion of Fluids,' Par. 

 4to, 1809; 13, 'Lesson* iu Analytical Mechanics delivered to the 

 Royal Polytechnic School,' Par. 4to, 1815 ; 14, ' On Breguet's SI 

 Thermometers,' Par. 4to, 1821 ; 15, ' On the work of M. 

 Fontaines relative to the Cubature of Timber,' 4 to, no date; 10, 

 'On Swing Bridges' (Touts a Bascules') 4to, no date; 17, 

 System of Trigonometrical Levelling,' Par. Svo, 1822 ; 18, ' On the 

 large Logarithmic ami Trigonometrical Tables adapted to the New 

 Decimal System of Weights and Measures,' Par. 4to, 1824; I: 1 , ' On 

 the recently iu.-titutcil l'i ofo.-sorship of the Harp iu the Royal . 

 of Music,' Par. 4 to, 1825, 12 pages; 20, 'Synopsis (Uogume) of the 

 Theory and Formula- relative to the Motion of Water iu Tubes aud 

 Canals,' Par. 1825; 21, 'Report on the Old aud New Steam-Engine,! 

 erected at Paris, au Uros Caiilou,' Par. Svo, 182(i ; '2'2, ' Fragments of 

 an unedited Memoir,' Lyon, Svo, 1827 (16 pages); '23, ' Elementary 

 Instructions on the Calculation, of Musical Intervals by assuming 

 either the Octave or the Twelfth Octave as the Unit of Comparison ; ' 

 'Analytical Formulae for calculating the Acoustic Logarithm of any 

 proposed Number, &c., with applications to Musical Instruments,' 

 Par. 4 to, 1832; 24, 'Examination of the proposals for levying a Toll 

 (' Projets de Barrage ') on the Seine near Havre,' Par. Svo, Is31, (also 

 in the ' Annales des Pouts et Chausse'ea ') ; 25, ' On the Inflexion* 

 which, after the lapse of twenty years, hud taken place iu certain 

 straight lines drawn upon the bridge Louis XVI., prior to the removal 

 of the ceuteriug, with Formula) and Tables for calculating the change 

 which settlement (' le tacseuieut ') produces in a circular arc). 

 1832, 20 pages ; 20, ' Formulas pour calculer Ics Hauteurs des Reujous 

 occasioned, soil par des Retrecisseuients, soit par des Barrages 

 (avec ccouleuieuU de 1'ouus) pratiques dons les Lit-. 

 Courantes,' Par. Svo, 1836 (also in the ' Aunales des P. et C.') ; 27, ' On 

 the Measurement of the Dynamical Effects of Rotatory Machines,' 

 Par. 4 to, no date; 28, ' Ou Regulating the Duration of the Oscillations 

 of the Pendulum,' Par. 4to, no date. 



To the 'Recueils de 1'Institut ' be contributed 1, ' Notice of the 

 Life aud Works of Pingre,' torn, i., 1798 ; -', ' Ou the Conversion of 

 Circular Movement into Rectilinear,' ii., ITH'J. To the 'Journal do 

 1'Ecolu Poly technique' 1, 'On a Course of Elementary Analysis, by 

 Lagrange,' torn, i, 1794 ; 2, 'Course of Mechanics for the Yc;.i \ '.. 

 ii., 1795; 3, 'Eloge de Lamblardie,' ib. ; 4, 'On the Principle of 

 Virtual Velocities and the Decomposition of Circular Motions,' ib. ; 

 o, 'Introduction to Pure Analysis and of Analysis as appli 

 Mechanics,' ib. : 6, ' Theory of Rotation about a Free Axis,' ib. ; 7, 

 'On the Particular Solutions of Diiierential Equations anil their 

 Application to Engineering,' ib. 1810; 8, 'On tbe Hydraulic System of 

 Italy,' ib. ; 9, 'Detailed Analysis of the Questions relative to the 

 Moliou of a Body acted upon by any Powers whatever,' ib.; 10, ' Uu 

 the New Sluice of M. de Baucourt,' viii., 1609. See also the ' Bulletin 

 de la SocieUS 1'liilomathique ; ' ' Aunales de* Mines ; ' ' Encyclopedic 

 Moibodique' (' Forets et Bois ') ; ' Conuaiasancs) de* Temps,' after 1800. 

 (DUcourt prononct par M. Arago, It 3 Ao&t 1839, ntr la tombc tic 

 M. de Prony ; BiograjMt det C'ontanporaitu ; Edinburgh Journal of 

 Science, vol. xv. ; Note tur la Publication propose par le (jouvernmtnt 

 Anylait, dagramU Tablet Logaritkmiquet el Trigonometriquet, deM.de 

 Prony, Paris, 1820, quoted by Babbage in hi* Economy of Machinery and 

 Manufacture!, London, 1832 ; Parliamentary /'a;/er, 1823, xv., p. 9, 

 Ac.; Quenrd'a JJictiunnaire Jiiblioffraphique ; The Worlctof Prony, io.) 

 PROPE'RTIUS, SE'XTUS AURE'LIUS, a native of Hispelluui, 

 or, according to others, of Mevauia in Umbria. The year of his birth is 

 not stated by any ancient authority, but he himself (iv. 1, 127, &.C.) says 

 that he took the toga libera (which was generally taken at tbo age of 

 fifteen) at tbe festival of the Liberalia, goon after the battle of Philippi, 

 which was fought in B.C. 42, so that he was most probably born about 

 the year B.C. 66. Clinton fixe* hi* birth however at K.C. 61, and 

 Lachmaun and Hert.isb.rg a* late a* B.O. 48 or 47. His family was of 

 equestrian rank (iv. 1, conip. with 11m., ' KpisU,' vi. 15, aud ix. 22), 

 and when, after the campaign of Philippi, Augustus rewarded his 

 veteran* with assignments of lands, the family of Propertius was, like 

 many other* who had supported the cauao of Antony, deprh 

 their estate*. About thi* time or soon afterward*, young Propertius 

 went to Rome, where he devoted himself entirely to poetry (iv. 1, 



