86 



SCIENCE. 



[N. S. Vol. XI. No. 264" 



present insuperable obstacles ; but may not 

 the result be reached by indirect means, or 

 may it not be possible to make the solar 

 system break its Sphinx-like reticence of 

 the centuries and disclose the gravitational 

 mechanism itself? 



Just as the theories of astronomy and 

 geodesy originated in the needs of the sur- 

 veyor and navigator, so has the theory of 

 elasticity grown out of the needs of the 

 architect and engineer. From such prosaic 

 questions, in fact, as those relating to the stiff- 

 ness and the strength of beams, has been de- 

 veloped one of the most comprehensive and 

 most delightfully intricate of the mathe- 

 matico- physical sciences. Although founded 

 by Galileo, Hooke, and Mariotte in the 

 seventeenth century, and cultivated by the 

 Bernoullis and Euler in the last century, it 

 is, in its generality, a peculiar product of 

 the present century.* It may be said to be 

 the engineer's contribution of the century 

 to the domain of mathematical phj'sics, 

 since many of its most conspicuous devotees, 

 like Navier, Lame, Rankine, and Saint- 

 Venant, were distinguished members of the 

 profession of engineering ; and it is a 

 singular circumstance that the first of the 

 great originators in this field, Navier, should 

 have been the teacher of the greatest of 

 them all, Barre de Saint-Venant. f Other 



* An admirable history of this science, dealing with 

 its technical aspects, was projected by Professor Isaac 

 Todhanter and completed by Professor Karl Pearson, 

 under the title "A History of the Theory of Elasticity 

 and the Strength of Materials from the time of Galilei 

 to the present time." Cambridge, at the University 

 Press: Vol. I., Galilei to Saint- Veuant, 1886; ol. VII., 

 Parts I. and II., Saint-Venant to Lord Kelvin, 1893. 



A capital though abridged history of the science is 

 given by Saint-Venant in his annotated edition of 

 Navier's E^sistance des Corps Solides, troisieme Edi- 

 tion, Paris, 1864. 



The history of Todhunter and Pearson is dedicated 

 to Saint-Venant, who has been fitly called ' the dean 

 of elasticiana. ' 



t And this illustrious master has left a worthy 

 pupil in M. J. Boussinesq, Professor in the Faculty 

 of Sciences, Paris. 



great names are also prominently identified 

 with the growth of this theory and with the 

 recondite problems to which it has given 

 rise. The acute analysts, Poisson, Cauchy, 

 and Boussinesq, of the French school of 

 elasticians ; the profound physicists, Green, 

 Kelvin, Stokes, and Maxwell, of the British 

 school ; and the distinguished Neumann 

 (Franz Ernst, 1798-1895), KirchhofiF(1824- 

 1887), and Clebsch (1833-1872), of the 

 German school ; have all contributed heav- 

 ily to the aggregate of concepts, terminology, 

 and mathematical machinery which make 

 this at once the most difficult and the most 

 important of the sciences dealing with mat- 

 ter and motion. 



The theory of elasticity has for its object 

 the discovery of the laws which govern the 

 elastic and plastic deformation of bodies or 

 media. In the attainment of this object it 

 is essential to pass from the finite and 

 grossly sensible parts of media to the infin- 

 itesimal and faintly sensible parts. Thus 

 the theory is sometimes called molecular 

 mechanics, since its range extends to 

 infinitely small particles of matter if not 

 to the ultimate molecules themselves. It 

 is easy, therefore, considering the complex- 

 ity of matter as we know it in the more ele- 

 mentary sciences, to understand why the 

 theory of elasticity should present diflBcul- 

 ties of a formidable character and require a 

 treatment and a nomenclature peculiarly its 

 own. 



While it would be quite inappropriate on 

 such an occasion to go into the mathematical 

 details of this subject, I would recall your 

 attention for a moment to the surprisingly 

 simple and beautiful concepts from which 

 the mathematical investigation proceeds 

 rapidly and unerringly to the equations of 

 equilibrium or motion of a particle of any 

 medium. The most important of these are 

 the concept which relates to the stresses on 

 the particle arising from its connection 

 with adjacent parts of the medium, and 



