The classical elastic scattering probability function, ƒs (vu',vu), and corresponding speed and angular functions are simply generalized to any arbitrary coordinate system moving with velocity u. Unified consideration leads to new mixed, but equivalent, representations of ƒs(vu',vu) which recover earlier results. The general treatment is concise and maintains the fundamental features of the binary collision in three dimensions. Extension of the analysis to anisotropic scattering is discussed briefly.