24 G. H. KNIBBS. 



are similarly indebted to mechanics, to the theory of elasticity, to 

 thermodynamics and to like departments of applied mathematics, 

 for their extraordinary development. Wherever in applied 

 science, the mathematical method is relevant, its application 

 seems to transform every conception and render it fruitful. 



At the beginning of the century, viz., in 1804, Poinsot [1777 - 

 1859] published his 'Elements of statics,' the earliest introduction 

 to synthetical mechanics, and to the idea of a couple. In elasticity 

 particular problems had been solved before the beginning of this 

 century by Jakob and Daniel Bernoulli, Lagrange and Euler. In 

 the early part of the century Thomas Young [1773-1829] in 

 England, J. Binet in France, and G. A. A. Plana [1781 - 1864] 

 in Italy, advanced the subject mainly by criticism and correction 

 of earlier work. The general development of the existing theory 

 of elasticity however, was the work of Navier [1785-1836], 

 Poisson [1781 - 1840], Cauchy, Mademoiselle Sophie Germain 

 [1776-1831], and Felix Savart [1791-1841], among which 

 Poisson and Cauchy were the greatest contributors. St. Yenant 

 [1797 - 1886] developed a theory of flexure which took cognisance 

 of all known relevant phenomena ; Poncelet, theories of resilience 

 and cohesion, and Lame [1795 - 1870], and Clebsch published 

 mathematical theories of the elasticity of solid bodies, adding to 

 the stock of acquired knowledge valuable contributions of their 

 own. Among recent remarkable works touching dynamical 

 problems, Ball's theory of screws, the last memoir of which has 

 quite recently been published, may be mentioned : the theory has 

 been applied by Lamb to the solution of the steady motion of 

 solids in fluids. Stokes introduced, in 1843, the theory of images, 

 of great value in attacking problems in fluid motion, an applica- 

 tion which has since been developed by Hicks and Lewis. In 

 1856 Helmholtz [1821-1894] investigated the properties of 

 rotational motion in an incompressible homogeneous and non- 

 viscous fluid. J. J. Thomson in his well-known treatise on the 

 "Motion of vortex rings," has discussed a peculiar conception of 

 W. Thomson's (Lord Kelvin's) as to the nature of matter, viz. 



