Nature [April 2G, I 900

614 NATURE [APRIL 2G, I 900

·corresponds to its one degree of freedom on Boltzmann's the adults or larvParis Academy of were:- Sciences. (1) To find one or more species of insects hospitable Joseph Bertrand was born at Paris in 1823, a nd at an to the human Hmathematics and in music, but is never seen in litera• one, and out of 109 of those examined, parasites were ture. We find Bertrand publishing a paper on the theory found in 27. . of electricity in 1839, w_hen he must have been about Some experiments on feeding Anopheles on a patient sixteen years old, and it is hardly surprising in view of with H . malariae gave positive results, several young this to learn that his precocity amazed his masters. In zygotes being found in the gnat. These gnats were 1841 he wrote papers on indeterminate forms, Jacobi's caught in a building where there were .· no fever patients, theorem and differential equations, and from that time and numbers of them had been examined and found free onward he was fairly launched on his career as a writer from parasites. When, however, Anopheles bred from the of mathematical papers, his output being five papers in larv

married the si ster of one of the injured, a :'llademoiselle ":\lccanique analytique," with copious notes, and ril Acloque. At the l'olytechnique, Bertrand acquired a small volume of lectures on electricity, in which I3ertrand knowledge of rnininR, and on leaving he became an in- gives the true origin and reason of Faraday's notion of spector of mines. He was subse4uently appointed pro- "electric flux, " although, being a mathematician, he fessor at the Lycce St. Louis. naturally favoured the rigorous methods of Ampere, for In 1844 he be_came teacher of analysis (r/p/- . whom he expressed great admiration. lilcur d'amzlyse) in the Ecole Polytcchnique; from 11i47 [ l'assing from these standard treatises to the numerous to 1851 he was examiner for admission to the same in- . papers published in scientific journals, a glance down stitution, which raised him to the rank of professor of I the list of these shows that, from the outset, Bertrand in tS;r,, a post which he held till 1895 , just after de,·oted his attention largely to applied mathematics, he had r.ompleted his jubilee as a member of the teach- and to those portions of pure mathematics requirelt ing staff, an e,·ent which was commemorated on May 27, in the solution of problems in applied m;uhematics. 1894, by a committee of his old students, who presented llis early papers deal chiefly with the differen• him with a medal engr;,ved by Chaplain. In 1847 he tial and integral calculus, differential equations, the was appointed deputy professor to Biot in the depart- calculus of variations, analytical mechanics, and in par• ment of physics and mathematics at the College de ticular the integration of the equations of dynamics. France, and on the death of Biot, in I8(>2 , he was ap- His papers on the theory of surfaces, dating from pointed to the chair. From then up till I8<)o he lectured on the principle of similitude in mechanics, on the• regularly, with the exceptions that his work was taken propagation of sound and on capillary phenomena, are• by Darboux in 1867, by ;\Iaurice Levy in 1874-76 and among the best known of his minor writings. i\ftel- 1878-8;, by Laguerre in 188;-86; since 1890 :VJarcel 1864, we find him writing biographical memoirs, com• Ueprez . has rtcted as hrs deputy. \\'e have it on the 1 mencing with Copernicus, Tycho Brahe and authority of 1\1. Caston Paris, that his first course of and followed up in later years with Comte, La,·oisier, 1 lectures was on a comparative study of the theories 1 JL\Iembert ( 1889) and Pascal ( 18<)0 ). In 1868, Bertrand according to which geometers had attempted to account commenced a series of papers on hydrodynamics ; Right for capillary phenomena, his latest lectures being on of birds came unrler his ''ken" in 1871, and in the same electrietty, thermodynamics and theory of errors. From year he turned his attention to lunar theory. In the 1858.to 1862 he was professor of higher mathematics at three years !871-73, he contributed quite a number of the Ecole N ormale Supt:rieure, and he also is stated to papers dealing with electricity and magnetism, including have held a professorship of special mathematics in the the mutual ai,:tion of currents, &c. ln the period 187-t Lycee 1\apolcon. In 18;6 Bertrand was elected a member 1 to 1883, the subjects treated included the sun, figme of of the :\cademie des Sciences at the early age of,thirty- ' the earth, electricity and magnetism, electric four, in place of Sturm ; and on the death of Elie de of power, the Foucault pendulum, the theory of proba• Beaumont, in 187-1, he was elected permanent secretary, I bility. Probability was always a favourite subject with, in which office he had Berthelot as a colleague. He was llertrand. The numerous pitfalls connected with the made officer of the Legion d'Honneur in r\ugust 1867, solution of problems, the remarkable power of prediction and commander in December 1881. In 188-1 he sue- w!-:ich the theory appears to afford, had a great fascina• ceeded jean Batiste Dunt

© 1900 Nature Publishing Group 6r6 .NATURE prizes, we find his name almost invariably appearing on object of 11·hi ch is to assist scientific men and their fam ilies the lists of judges, and he appears to have been no less when in need. Bertrand was one of the fir st to support energetic in drawing up biographical notices of deceased the Society, and his signature figures along with those members. C\evertheless, we find him in till); writing on , of Boussingault, Quatrefages, Becyuerel, Senarmont, a geometrical theorem, and in tSl)6 breaking a lance with j llalarc\, Daubn:e, Frcmy, Deville, Berthelot and Pasteur Boltzmann on that ever-fascinating and never-satisfying 111 all its early records. In 1864 Bertrand was elected theory, the Kinetic Theory of Cases. This is the last on the council, in :\lay r895 he was nominated vice• time that we have been able to find Bertrand's name in president, and in )Jo,·ernber of the same year he sue• the Cfl mpt,·s rcndus as the writer of a paper, though it cecdecl l'asteur as president. The P,tsteur Institute repeatedly figures in other connections. also owes much to his energetic support. Bertrand's countenance and carriage are de,;cribed as :\!athematical investigation is essentially a search for ''characteristic." lie was "short, thick-set, Iivek, truth ; but 1•·ith Bertrand the love of truth and hatred of \'ijo(OTOU S, and ,·ery kind-looking. His fa ce was covered all that false, was not confined to the mathematical with. scars, and his nose had lost its bridge," as we have side of his character; this trait was indeed deeply seen. as the result of the :\Ieudon railway accident, but engrained into his whole existence. \Vhile there was the imprint of misfortune would appear to have a nothing he would not do for those he knew to be tender to his appearanr:e, which seemed to draw deserving, he seems to have p <>sse ssed a happy knack his friends nearer to hun. .-\s a relaxation from work. of effectually disposing of his enemies by a few strokes he is said to have ne1·er tired of reading the of sarcasm, which must have been the more withering of Sir \\'alter Scott, whom he described as ··the greatest because they so completely placed his adversaries in the wrong. Had Joseph Bertrand's life and health been spared a little longer, there can he no clouht that he would have taken a foremost part in the liberal programme of congresses with 11·hich P.uis hopes to attract a distin• guished assembly of .l'tl71

At the funeral, discourses were delivered by :\1. Jules Lemaitre, director of the Academic Fran.; aise; by :\!. :\laurice Le1·y, president of the ,\cademie ; by :VI. Ber• thelot, his fellow secretarv of the .-\ cadcmie des S ciences ; by ,;aston I?arbchnique ;' by :\1. Duclaux, director of the lnstitut Pasteur; hy \1. (;as ton l'aris, admm1strator of the Colll-ge de France: anrl by \1 . < ;eorges !'errol, director of tile Ecole \'ormalc. In endeavounng to portray the life of a man of many and parts l!ke Bertrand, we ha1·e largely drawn on the tnformatton contained in these orations, whir.h are published in the rcndus; but while it tl:u;; been enter 1010 many of the details of Bertrand·s l1fe, h1s

Bertrand. character as an inrlividual can only be appreciated by (From /.,a Yafllrt'.) reading separately the thoughts expressed by those who have known him intimately in his many capaCities. Of novelist that e1·er Ji,·etl." He leaves several >Ons, one these expressions, we can do no better than conclude of whom :\!. ;\hrcel Bertrand, a mining engineer, is with the words of :\1. Georges Perrot :- himself meml:er of the Academy of Sciences, and " ll n'a pas etc moins par lc cn:ur que par rather well known. If Bertrand's mathematical work earned for him the (;,H. respect and adm:r,ttion of men of sr.ience far his philanthropy endeared hun to the smaller cmcle with whom he was more intimately known. The enjoyment NO THS. he derived from his own studies was fully equalled by \VIi notice with regret the announcement that the Duke of his delight at reading the works of others. He con- stantly sought to bring to light fresh workers, and the Argyll die,\ on Tuesday m•>rning, at the age of seventy-seven few words of kind reassurnnce and appreciation, not to years. No definite arrangement has yet been made with regan\ mention the passing on of an idea or the lending a to the funeral, but it is be!ic,·cd the interment will take place helping hand. over a difficulty, so much valued by the I next week. buddin<• mathematician, were never wanting at the d · critical"' moment. In endeavouring to help those less ' Tur-: international conft:rence for the protection of wil am· 1 favoured by furtune than himself, Bertrand would give · mals in Africa, announced last week, was opened at the Foreign much time and thought as to the best way of rendering 1 Office on April 24, and was attended l>y of them assistance. In 1857 Baron Thenard founded the 1 France, Great Britain, Congo Independent States, "Societe des Amis des Sciences," an institution the I Italy, Portugal and Spain. Readers of NATURE hardly need to 1'1:0 I 59 I, VOL. 61 J