984 



SCIENCE 



[K S. Vol. XXXVII. No. 965 



of the eloges historiques here collected with 

 annotations from volumes of the Memoires de 

 I'Academie des Sciences de I'Instiiut de 

 France. Nowhere else are such extended ac- 

 counts of the scientific careers of Bertrand 

 (pages 1-60), Perrier (pages 61-115), Her- 

 mite (pages 116-172), D'Abbadie (pages 173- 

 217), and Meusnier (pages 218-262) to be 

 found. 



Joseph Louis Frangois Bertrand (1822- 

 1900) was one of that remarkable group of 

 mathematicians — among them, Poinsot, Pois- 

 son, Cauchy, Poncelet, Chasles, Lame, Le 

 Verrier, LiouviUe, Halphen, Hermite, Poin- 

 care — who were, at least in part, the product 

 of instruction at the Ecole Polytechnique. A 

 child prodigy and boy not to be bound down 

 by the ordinary routine of the lycee he was 

 nevertheless bachelier, licenciee and docteur es 

 science when 17 years of age— the youngest 

 doctor of science whom France has ever pro- 

 duced. He then took the entrance examina- 

 tions for the Ecole Polytechnique. Bertrand 

 has left us some details; Bourdon and Au- 

 guste Comte were the examiners: 



J'ai le souvenir de 1 '^tonnement de M. Bourdon 

 qui, sachant que j 'gtais dooteur 6s sciences, 

 m'avait fait un examen difficile. A la suite de je 

 ne sais quelle reponse, il me dit : ' ' Vous n 'avez 

 done jamais onvert une table de logarithmes ? — 

 Je lui rgpondis: Non, Monsieur, jamais." 11 prit 

 cela pour une impertinence; e'fitait la pure verity. 

 Je n 'avals fait aucun, devoir seientifique ou lit- 

 tSraire, jamais aucun caloul demands par aucun 

 maXtre. 



Bertrand then continues: 



A 1 'Ecole Polytechnique, j 'Stais un problfeme 

 pour mes eamarades. Eecu le premier et gardaut 

 le premier rang dans toutes les gpreuves, je les 

 gtonnais de temps en temps par une ignorance 

 seandaleuse sur des notions qu'on enseigne en 

 septifeme. Beaucoup d'entre eus croyaient a une 

 ignorance affectfie; j 'en Stais tr6s haiteux au con- 

 traire. J'ignorais compl6tement, par example, 

 quelle sorte de mots les grammairiens dSsignent 

 par le terme d'adverbes. 



Bertrand became "repetiteur adjoint d'- 

 analyse " at the Ecole Polytechnique in 1844 

 and professor of analysis in 1856. This posi- 

 tion he held till, by reason of the legal age 



limit, he was retired in 1895, after 51 years 

 of service. On Bertrand, as well as on Poin- 

 care in more recent times, was bestowed 

 the supreme honor which France has in her 

 gift for the elite of her scientists, namely, of 

 election to both the Academic des Sciences 

 (1856) and the Academie Frangais (1884) of 

 the Institut. 



For an account of Bertrand's researches in 

 geometry, analysis, rational mechanics and 

 physics, and of his text-books so popular in 

 secondary education, reference must be made 

 to Darboux's memoir. One may here also 

 find a sketch of his family life and of his per- 

 sonal characteristics. 



Frangois Perrier (1833-1888), another 

 graduate of the Ecole Polytechnique, was em- 

 ployed for nearly a score of years by the gen- 

 eral army staff, before he became a chief of 

 the geodetic survey and professor of geodesy in 

 the Ecole de Guerre, Paris. His extensive sci- 

 entific work was in the field of geodesy. 



Charles Hermite (1822-1901) at the time 

 of his death was ranked first among French 

 mathematicians. It was in connection with 

 algebra and arithmetic that he was essentially 

 inventor and creator; most notable were his 

 contributions to elliptic and Abelian functions, 

 algebraic forms and the theory of numbers. 

 Through his proof of the transcendence of e 

 he may well share with Lindemann (who em- 

 ployed very similar methods in discussing the 

 transcendence of tt) the honor of settling the 

 problem of the squaring of the circle, which 

 had been handed down through the centuries. 

 All these topics and Hermite's career, as pro- 

 fessor at the Ecole Polytechnique and at the 

 Sorbonne, as academician, as friend of mathe- 

 maticians scattered all over the world — are 

 treated at length by Darboux." 



Antoine Thompson d'Abbadie (1810-1897) 



^Disciples of Francis Galton will surely find 

 material of interest in studying hereditary traits 

 of the families of some French mathematicians. 

 For Bertrand was a nephew of Duhamel. Emile 

 Picard and Paul Appell are nephews (the latter 

 by marriage) of Bertrand. Pierre Boutroux is a 

 nephew of Poincare. Picard 's wife was Hermite's 

 daughter and Borel married a daughter of Appell. 



