A machine is described which solves the equations of motion for a charged particle in a two‐dimensional magnetic field. Its accuracy is not limited by the steepness or the asymmetry of the field. Guided by remote control, the mechanism moves continuously over a contour map just as a particle would move through the field itself. The operator matches position, or local field value, with a parameter of the steering control, or curvature of the trajectory. He is able to interpolate continuously between lines of constant field value, thus speeding the process of solution and increasing the accuracy. In five minutes a 40‐inch orbit can be drawn over which the field values vary through 23 000 gauss. Five minutes are required for introducing initial conditions, including momentum. For regions in which the field is more than half maximum, the orbits of the mechanical particle and the electromagnetic particle coincide in their radii of curvature to within 0.5 percent. Accuracy is less for low field values. The performance characteristics have been determined from a working instrument which is fully described. An alternative computer design to the one already in use is also discussed.