Modern {beta}-ray spectrometers are based upon the concept, first introduced by Svartholm and Siegbahn in 1946, of focusing in both the radial and vertical directions. The theory of axially symmetric devices has been carefully studied by a large number of workers, culminating in the analysis, in 1956, of Lee-Whiting and Taylor. These last authors calculate aberrations through the sixth order and show that by appropriate choice of the magnetic field a spectrometer can be designed with a relatively large transmission and a high resolution. The acceptable transmission is remarkable because the second-order 'spherical' aberration in the median plane of the image cannot be made to vanish identically, and consequently the design is forced to a tall thin aperture (or a slightly less advantageous short wide aperture) which a priori would seem to imply a low transmission. It is the purpose of this communication to show that if the arbitrary restriction to axially symmetric fields is removed, then both the radial and the vertical contributions to the 'spherical' aberration can be made to vanish in second order. That azimuthally varying field (AVF) afford the freedom to accomplish this end may well be suspected in view of the technological revolution that the …