PROGRESS IN NINETEENTH CENTURY 31 



Hence even if the literary references may be given in print with 

 some fullness, it is impossible to refer verbally to more than the chief 

 actors, and quite impossible to delineate sharply the real significance 

 and the relations of what has been done. Moreover, the dates will in 

 most instances have to be omitted from the reading. It has been my 

 aim, however, to collect the greater papers in the history of physics, 

 and the suggestion is implied that science would gain if by some 

 august tribunal researches of commanding importance were formally 

 canonized for the benefit of posterity. 



Elastics 



To begin with elasticity, whose development has been of such 

 marked influence 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 concep- 

 tion of a modulus, and who seems to have definitely recognized the 

 shear, there were merely the experimental contribution of Galileo 

 (1638), Hooke (1660), Mariotte (1680), the elastic curve of J. Ber- 

 noulli (1705), the elementary treatment of vibrating bars of Euler 

 and Bernoulli (1742), and an attempted analysis of flexure and tor- 

 sion by Coulomb (1776). 



The establishment of a theory of elasticity 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 po- 

 tential energy (1822-1827); yet this startling advance 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 

 principal strains, the ellipsoids, and other of the indispensable con- 

 ceptions 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. Contemporaneous with Cauchy's results are certain in- 

 dependent 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 system 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 equations with twenty-one constants 

 for the seolotropic medium reducing to two in the simplest case. 



