[en] A detailed description of a Tret'yakov-type magnetic β-spectrometer with electrostatic acceleration is presented. The instrument is being used for high precision measurements of the β-spectra of various isotopes and to search for neutrino mixing and heavy neutrinos with masses up to 100 keV/c². The relative momentum resolution, obtained with an extended source (3x2 cm²) and a large silicon strip detector, is δp/p=6.9x10^-4 (FWHM). The width of the energy band, which can simultaneously be measured with this resolution, is typically 50 times larger than the corresponding width of the energy resolution. The detector delivers pulse-height and one-dimensional position information. The read-out electronics provides a separate channel for each detector strip, allowing measurements to be made with high count rate and small dead-time losses. The detection of scattered electrons was minimized by the arrangement of baffles and by the use of materials with small atomic number. Experimentally, scattering in the spectrometer was investigated by accelerating photoelectrons up to 60 keV energy. A system for measuring the corresponding high voltage is described. Extensive Monte Carlo simulations of scattering in the spectrometer have been performed. Good agreement with the experimental data was obtained and there was no need to adjust any scattering cross section to the particular experimental situation. We conclude that calculated scattering probabilities can reliably be used in the analysis of experimental β-spectra, which is important as otherwise scattering would constitute a major uncertainty