Dirac’s modified wave equation which successfully accounts for many of the phenomena interpreted as due to the spin of orbital electrons, also predicts that the free electron should have a spin. On this basis each electron wave is characterised by a definite direction other than that of propagation, and an electron beam should be capable of exhibiting polarisation. A method for the production and detection of a polarised electron beam is suggested by the double scattering experiments for the production and detection of polarised X-rays, especially in view of the similarity between diffraction phenomena for electrons and electromagnetic waves. Double scattering experiments have been performed by a number of investigators and it has been well established that no observable effect is found with electrons having energies in the neighbourhood of 100 volts.* With very much higher energies, however, an asymmetry in the intensity distribution of the secondary scattering appears to exist, although the evidence is somewhat contradictory and incomplete. This paper gives an account of a double scattering experiment in which electrons were successively reflected at approximately 90° from thick polycrystalline tungsten targets. The results extend the region in which the asymmetry in the secondary scattering is known to be less than 1 per cent, to electron energies of 10 kilovolts.