Societies and Academies

Abstract

LONDON. Physical Society, Oct. 17.—J. P. Andrews: (1) A simple approximate theory of the pressure between two bodies in contact. The approximation makes use of two principles: (a) The displacement at the centre of the circle of contact is twice that at its edge, and (6) for the purpose of calculating the stresses we may replace the two bodies by a single sphere of which the circle of contact is a diametral section, and write the strain at any point as the ratio of the displacement of that point to the length of the line drawn from the point to the sphere in the direction of displacement. When the elastic modulus by which this is multiplied is taken as that appropriate to a rod with sides fixed, the agreement with accurate theory is close. Principle (a) remains nearly true for elliptical areas of contact.(2) Experiments on impact. For soft metallic bodies and impact of equal spheres, for small velocity of approach v, duration of contact varies inversely as t1/5, while the coefficients of restitution e are unity for all speeds below a value characteristic of each material. Duration of contact has no effect upon the size of the permanent deformations. For variation of duration of contact t with mass of sphere at high speeds of approach, t varies as the square root of the mass, as theory predicts. (3) Observations on percussion figures. Steel ball on glass blocks. Diameter of innermost circular or part-circular crack remains constant for one specimen of glass, and is independent of the maximum pressure exerted by the ball on the glass; diameter of outermost circular or part-circular crack varies with the maximum pressure in a manner which suggests that the crack tends to keep to the outer edge of the area of contact. No crack is formed until the pressure exceeds a value characteristic of the glass.