An analysis is made of the focusing characteristics of a magnetic spectrometer having an annular magnetic field which varies approximately with 1/r½, thus permitting axial as well as radial focusing of particles of a given energy. By considering the field angle and source location as independently variable, the analysis provides for an instrument more flexible in use than similar existing types.An optical analogy is developed from which a first approximation to the field shape is made, and from which the source and image location, magnification, dispersion and resolution can be readily obtained. Information thus obtained, combined with the results of an investigation into the image shape based on a series expansion, through second order, of expressions for the field strength and particle coordinates, yields more detailed information on the field shape which gives optimum focusing conditions and resolution for any chosen set of initial conditions.Comparisons are made with the homogeneous field spectrometer and with the spectrometer of Svartholm and Siegbahn.