Abstract: A sample (2) is mounted in a sample holder (13) with a surface (3) of the sample (2) normal to the axis (4) of a pair of truncated electrically conductive frusto-cones (5, 6) which are coaxial and whose apexes meet at the sample surface (3). An exciting source (7) is mounted within the inner cone (5), which is solid and is maintained at ground potential to serve as a first electrode. The outer cone (6) is made of high transparency metallic mesh and is maintained at a positive potential +V (e.g. 1000 v) with respect to the sample surface (3), to serve as a second electrode. These components of the spectrometer (1) are contained within a vacuum system (15), and the potentials are applied to the cones (5, 6) by a biassing means (14). Electrons generated where the beam from the exciting source (7) strikes the sample are emitted into 2.pi. steradians towards an entrance annulus (8).