The present paper gives an account of measurements on some close collisions of fast β-particles with electrons, photographed by the Wilson cloud method. These measurements afford a direct test of the applicability of the principles of the conservation of momentum and energy and the principles of relativistic mechanics to individual atomic phenomena. On the basis of Newtonian mechanics, if one particle collides with another which is initially at rest and the two particles are of equal mass, the angle between the directions of motion of the two particles after collision is equal to 90° for all angles of scattering of the incident particle. On relativistic mechanics, however, this angle becomes a function of the angle of scattering and the velocity of the incident particle, and in particular, it becomes smaller and smaller as this velocity approaches that of light. Qualitative evidence has already been given by Wilson, Bothe and others that this angle is less than 90° for the collisions of fast β-particles with electrons, but up to the present no quantitative study has been made of the general relation between the whole angle after collision, the angle of scattering, and the velocity of the incident particle. Assuming that momentum and energy are conserved in the collision the following calculation may be made.