The invention relates to measuring devices of an electrostatic Fourier transform mass spectrometer and measurement methods for the acquisition of mass spectra with high mass resolution. The measuring device includes electrostatic measuring cells according to the Kingdon principle, in which ions can, when appropriate voltages are applied, orbit on circular trajectories around the cylinder axis between two concentric cylindrical surfaces, which are composed of specially shaped sheath electrodes, insulated from each other by parabolic gaps, and can harmonically oscillate in the axial direction, independently of their orbiting motion. In the longitudinal direction, the two cylindrical surfaces of the measuring cell are divided by the parabolic separating gaps into different types of double-angled and tetragonal sheath electrode segments. Appropriate voltages at the sheath electrode segments generate a potential distribution between the two concentric cylindrical surfaces which forms a parabolic potential well in the axial direction for orbiting ions. The ion clouds oscillating harmonically in the axial direction in this potential well induce image currents in suitable electrodes, from which the oscillation frequencies can be determined by Fourier analyses.