I. Elements of a mathematical theory of elasticity

This paper consists of two parts: Part I. on Stresses and Strains; Part II. on the Mechanical Conditions of Relation between Stresses and Strains experienced by an Elastic Solid. Part I.—The terms Stress and Strain are used in accordance with the valuable definitions by which they were first distinctively introduced into the Theory of Elasticity by Mr. Rankine; with only this deviation; that instead of defining a stress as the reactive force exerted by an elastic body when in a condition of strain, the author of the present paper defines stress as “a definite external application of force to a body."