reversible to the case of side-forces without end-forces. Clebsch[66] extended the research to very thin rods and to very thin plates. Saint-Venant considered problems arising in the scientific design of built-up artillery, and his solution of them differs considerably from Lamé's solution, which was popularised by Rankine, and much used by gun-designers. In Saint-Venant's translation into French of Clebsch's Elasticität, he develops extensively a double-suffix notation for strain and stresses. Though often advantageous, this notation is cumbrous, and has not been generally adopted. Karl Pearson, professor in University College, London, has recently examined mathematically the permissible limits of the application of the ordinary theory of flexure of a beam.
The mathematical theory of elasticity is still in an unsettled condition. Not only are scientists still divided into two schools of "rari-constancy" and "multi-constancy," but difference of opinion exists on other vital questions. Among the numerous modern writers on elasticity may be mentioned Émile Mathieu (1835–1891), professor at Besançon, Maurice Levy of Paris, Charles Chree, superintendent of the Kew Observatory, A. B. Basset, Sir William Thomson (Lord Kelvin) of Glasgow, J. Boussinesq of Paris, and others. Sir William Thomson applied the laws of elasticity of solids to the investigation of the earth's elasticity, which is an important element in the theory of ocean-tides. If the earth is a solid, then its elasticity co-operates with gravity in opposing deformation due to the attraction of the sun and moon. Laplace had shown how the earth would behave if it resisted deformation only by gravity. Lamé had investigated how a solid sphere would change if its elasticity only came into play. Sir William Thomson combined the two results, and compared them with the actual deformation. Thomson, and afterwards G. H. Darwin, computed that the resistance of the earth to
