The methods used to measure response and performances of an electrostatic spectrometer with an identical apparatus are studied in the case of the 127° cylindrical spectrometer by means of a method of calculation of the electron energy distribution. The distribution given by the monochromator is calculated and its analysis with the identical analyzer is simulated. The three usual methods of analysis are found to give inaccurate results not only for the widths of the energy distribution but also for its profile. It is shown that because of the inherent angular dispersion of the analyzer, it is necessary to carry out the analysis of the beam by narrow angular slices in order to recover the exact profile of the energy distribution yielded by the monochromator.