320 



NATURE 



{Feb. 4, 1886 



troubled himself with impossible distributions of load 

 over impossible surfaces, but toolv the problems of 

 mechanics as they occurred practically, and solved 

 them for practical purposes. This tendency on his part 

 was no doubt greatly due to his training as an engineer. 

 He was Ingtfnieur-en-chef des Fonts et Chaussdes ; he 

 had been Professeur de Genie rural a I'lnstitut agrono- 

 mique ; he had built lock-gates and improved the gutters 

 of Paris ; he was an authority on agricultural drainage, 

 and had investigated the best form of the ploughshare ; 

 he designed a bridge for the Creuse, and planned a 

 method, afterwards adopted, for drying up the vast 

 marshes of the Sologne. Yet with all this he was a great 

 master of analysis, and knew how to make his analysis 

 fruitful in practice. 



It is not our purpose here to give a bibliographical 

 account' of Saint-Venant's works ; we wish only to sketch 

 the general scope of his researches, and shall confine our- 

 selves to indicating the more important advances he has 

 made in his own peculiar subject — that of elasticity. The 

 first important work by Saint- Venant is the " Cours 

 lithographee " of 1837. This consists of lithographed 

 sheets given to the students of the Ecole des Fonts. A 

 few years previously Vicat had made his crushing attack 

 upon the accepted mathematical — the BernouUi-Eulerian 

 — theory of beams. Here we find this attack justified and 

 replied to by the introduction of the neglected slide 

 {glissement) into the theory, and its application to a 

 number of practical problems. Here, too, we see for the 

 first time the true limit of elasticity expressed by a strain, 

 and not a stress, maximum. This is a correction of the 

 old theory which is of primary practical importance, 

 although the old theory is still to be found in many Englibh 

 practical books, and even in such a theoretical authority 

 as the German Clebsch. 



A thorough appreciation of the true relation of theory 

 to practice is evidenced by the following lines, which 

 should be taken to heart by every technical teacher : — 



"L'usage des mathdmatiques cessera de s'attirer des 

 reproches si ^on le referme dans ses vrais limites. Le 

 calcul pur est siraplement un instrument logique tirant 

 des consequences rigoureuses de prifmisses posees et 

 souvent contestables. La mc'canique y joint bien quel- 

 ques principes physiques que I'expe'rience a mis hors de 

 contestation, mais elle laisse aux experiences particulieres 

 le soin de tleterminer quelles forces sont en jeu dans 

 chaque cas, et il r^gne toujours a cet dgard plus oumoiiis 

 d'incertitude qui affecte ndcessairement les rdsultats. Ces 

 re'sultats ne doivent point etre considerds comme les 

 oracles, dictant infailliblement ce que Ton doit d&ider ; 

 ce sont de simples renseignements, comme les depositions 

 de te'moins ou les rapports d'experts dans les affaires 

 judiciaires, mais des renseignements extremcment prdcieux 

 et dont on ne doit jamais se priver, car il est extremement 

 utile ^ la di^termination que Ton a a prendre, de connaltre 

 la solution exacte d'un probleme fort rapproche de celui 

 qui est propose, et de pouvoir se dire, par example, ' si 

 les efforts etaient exactement telsoutels, les dimensions a 

 donner seraient telles ou telles.' De cette maniere le 

 champ de I'appriciation insti)ictive se trouvera' reduit 

 aux differences qui ne peuvent pas etre le sujet du calcul 

 thdorique ; et Ton voit que ces deux mdthodes, loin de 

 s'exclure, peuvent concourir ensemble, se supplier et 

 s'aider mutuellement, se controler meme quelquefois, — 

 enfin contracter sous les auspices du bon sens, une alhance 

 fdconde en rdsultats utiles sous le double rapport de la 

 convenance et de I'economie." 



These words represent exactly the spirit with which 

 Saint- Venant entered upon the important investigations 

 of later years. Of other earlier work of Saint-Venant, we 



' A bibliography of his memoirs relating to elasticity and the strength of 

 materials will be given in the " History of Elasticity." A complete bibho- 

 graphy to 1864 will be found in " Notice sur les travaux . . . de M. de 

 Saint- Venant," Paris, 1864. This is brought up to 1885 with partial complete- 

 ness in the copy presented to us by Saint-Venant himself. 



may especially note the series of papers in the Comptes 

 retidus for 1840-50. These contain the rectification of 

 the theory of elastic rods by the introduction of the third 

 moment in the case of inertial Eeolotropy in the section,' 

 the complete equations for spiral springs, and the first 

 rectification of the theory of torsion by the discovery of 

 the distortion of the primitively plane section. These 

 researches are all epoch-making in the theory of elasticity. 

 To the next decade belong the classical memoirs on 

 " Torsion " and " Flexure," the complete treatment of 

 torsion on the basis of the distortion of the plane sections, 

 and the complete treatment of flexure by the considera- 

 tion of slide. The beautiful diagrams of the contour lines 

 are known to all students of physics, if not from the 

 original memoirs, at least from the " Treatise on Natural 

 Philosophy" of Thomson and Tait. The very perfect 

 plaster models prepared under the direction of Saint- 

 Venant to illustrate flexure, torsion, and resilience, are less 

 generally known,- but for teaching purposes they are of 

 even greater value than the diagrams. In addition to 

 these opera maxima we may mention the important re- 

 searches on impact, belonging to the same period (Socidtt^ 

 Philomatique, 1853 and 1854). The decade received its 

 final touch in the first volume of Saint-Venant's edition of 

 Navier's " Leqons." This volume presents the first history 

 of elasticity in the brief but luminous " Historique abrdge." 

 The last period of Saint-Venant's work contains the all- 

 important memoirs on the distribution of elasticity in 

 a;olotropic bodies, on the various types of homogeneity, 

 further researches on longitudinal impact, the tract on 

 the undulatory theory of light, the second volume of 

 Navier's " Legons," the treatise on elasticity in Moigno's 

 " Statique," and, amid a variety of opiiscula, to crown the 

 work of a life, the annotated edition of Clebsch's " Theorie 

 der Elasticitat." The original "Clebsch" contains 420 

 pages, the annotated translation with a much larger page 

 has more than 900 pages. When will an English elastician 

 arise, who will annotate Saint-Venant as Saint-Venant has 

 annotated Clebsch.'' 



One word more with regard to Saint-Venant's position 

 as an elastician. In England the controversy over the 

 number of elastic constants seems to have been decided 

 in favour of multi-constancy. Saint-Venant was, and 

 remained to his death, a supporter of the French, or 

 rari-constant, hypothesis. The experiments, he argued, 

 upon which the multi-constant elasticians based their 

 theory were not made on truly elastic bodies, or were 

 made upon bodies like wires and plates which are not 

 isotropic. Into his treatment of such bodies he intro- 

 duced, not the two constants of isotropy, but the constants 

 of a cylindrical or planar distribution of homogeneity. 

 Being written to last September on this point, he 

 replied : — 



"Vous voulez bien me demander si je conserve les 

 menies opinions que j'ai exprimees et longuement deve- 

 lopp(^es a I'appendix V. de mon edition de Navier, 

 il savoir, la reduction des coefficients des formules d'cflas- 

 ticite h. un sen! (oil X = /x dans les formules de Lame) ; ce 

 qui conduit d'apres le meme principe que chaque action 

 entre deux molecules est fonction de leur seule distance 

 mutuelle, a rdduire pour la contexture hdtdrotrope le plus 

 generale, et k ne reconnaitre que 15 coefficients distincts 

 et non pas 21. 



" Je reponds out pour les vrais solides (supposes iso- 

 tropes) comme sont les metaux ordinairement, ainsi que 

 le marbre, le verre ; mais 71011 si Ton veut absolument par 

 un motif quelconque cjue je ne consols guere, appliquer 

 les formules de I't^lasticitt^ au caoutchouc, aux gommes 

 molles, aux geMes, et aux autres corps mous et dlastiques, 

 car ces corps-L'i ne sont que des melanges de tissues 

 cellulaires, de membranes dlastiques, et de fluides vis- 

 queux que leurs cellules contiennent." 



^ He shares the honour of this discovery with Bellavitis. 



^ We have a copy of the whole collection at University College. 



