The electron-optical system of the Eindhoven RTM has been designed and constructed with non-stringent alignment and machining tolerances in the order of 0.1-1 mm and 0.1-1 mrad. The alignment and machining errors that are present can and must be counteracted with slightly different settings of the seventeen adjustable parameters (i.e. the excitation currents of the two end magnets and of twelve correction magnets (one at every turn), the beam energy and phase at injection, and the energy gain per turn), otherwise the beam will not be accelerated properly. All the errors are unknown and consequently their effects are unknown. Therefore, twenty-five beam-position monitors (BPMs) have been installed in the RTM (two for each turn and one at the...