In three papers (1, 2, 3) Bhabha has set up a new theory for relativistic particles of any spin, and has suggested that a particular wave equation of half-odd spin, classified as (, ½), may be applicable to the proton. It is therefore of interest to study this equation and to calculate results which could perhaps be compared with experiment; since in the non-relativistic limit the particle obeys Dirac's equation, it is sufficient to consider the behaviour at energies large compared to the rest mass. Here the important problem is the calculation of scattering cross-sections for cosmic-ray processes.