September 22, ]905.] 



SCIENCE. 



.3.55 



enee throughout the whole of physics, we 

 note that the theory is virtually a creation 

 of the nineteenth century. Antedating 

 Thomas Young, who in 1807 gave to the 

 subject the useful conception of a modulus, 

 and who seems to have definitely recognized 

 the shear, there were merely the experi- 

 mental contribution of Galileo (1638), 

 Hooke (1660), Mariotte (1680), the elastic 

 curve of J. Bernoulli (1705), the elemen- 

 tary treatment of vibrating bars of Euler 

 and Bernoulli (1742), and an attempted 

 analysis of flexure and torsion by Coulomb 

 (1776). 



The establishment of a theory of elas- 

 ticity on broad lines begins almost at a 

 bound with Navier (1821), reasoning from 

 a molecular hypothesis to the equation of 

 elastic displacement and of elastic potential 

 energy (1822-1827) ; yet this startling ad- 

 vance was destined to be soon discredited, 

 in the light of the brilliant generalizations 

 of Cauchy (1827). To him we owe the six 

 component stresses and the six component 

 strains, the stress quadric and the strain 

 quadric, the reduction of the components 

 to three principal stresses and three prin- 

 cipal strains, the ellipsoids and other of 

 the indispensable conceptions of the present 

 day. Cauchy reached his equations both 

 by the molecular hypothesis and by an 

 analysis of the oblique stress across an 

 interface — methods which predicate fifteen 

 constants of elasticity in the most general 

 case, reducing to but one in the case of 

 isotropy. Cotemporaneous with Cauchy 's 

 results are certain independent researches 

 by Lame and Clapeyron (1828) and by 

 Poisson (1829). 



Another independent and fundamental 

 method in elastics was introduced by Green 

 (1837), who took as his point of departure 

 the potential energy of a conservative sys- 

 tem in connection with the Lagrangian 

 principle of virtual displacements. This 

 method, which has been fruitful in the 



hands of Kelvin (1856), of Kirchhoff 

 (1876), of Neumann (1885), leads to equa- 

 tions with twenty-one constants for the 

 ffiolotropic medium reducing to two in the 

 simplest case. 



The wave motion in an isotropic medium 

 was first deduced by Poisson in 1828, show- 

 ing the occurrence of longitudinal and 

 transverse waves of different velocities; 

 the general problem of wave motion in 

 feolotropic media, though treated by Green 

 (1842), was attacked with requisite power 

 by Blanchet (1840-1842) and by Christof- 

 fel (1877). 



Poisson also treated the case of radial 

 vibrations of a sphere (1828), a problem 

 which, without this restriction, awaited the 

 solutions of Jaerisch (1879) and of Lamb 

 (1882). The theory of the free vibrations 

 of solids, however, is a generalization due 

 to Clebsch (1857-58, 'Vorlesungen,' 1862). 



Elasticity received a final phenomenal 

 advance through the long continued labors 

 of de St. Venant (1839-55), which in the 

 course of his editions of the work of 

 Moigno, of Navier (1863), and cf Clebsch 

 (1864), effectually overhauled the whole 

 subject. He was the first to adequately 

 assert the fundamental importance of the 

 shear. The profound researches of de St. 

 Venant on the torsion of prisms and on the 

 flexure of prisms appeared in their com- 

 plete form in 1855 and 1856. In both cases 

 the right sections of the stressed solids are 

 shown to be curved and ' the curvature is 

 succinctly specified; in the former Coul- 

 omb's inadequate torsion formula is super- 

 seded and in the latter flexural stress is re- 

 duced to a transverse force and a couple. 

 But these mere statements convey no im- 

 pression of the magnitude of the work. 



Among other notable creations with a 

 special bearing on the theory of elasticity 

 there is only time to mention the invention 

 and application of curvilinear coordinates 

 by Lame (1852) ; the reciprocal theorem 



