Improvement in the power of resolution is desirable in the multiplication of passages in magnetic fields; our guiding principle is to carry out the operation using a single magnetic prism. In the multipassage process the ions must first turn back after leaving the prism. This turnback is obtained by an electrostatic mirror. We obtain a large enough number of passages by placing two mirrors and two systems with time-varying roles at right angles. These systems are referred to as lens-mirror 1. When they act as mirrors, they enable the particles to circulate in a closed circuit; when they act as lenses, they enable the particles to enter the circuit or leave it. The coupling of two multipassage spectrometers is momentarily possible thanks to lens-mirror 2. The function change results from a change in electrode potential. The requirements for these electrostatic systems and their construction are studied.