Publisher Summary The invention of the electron microscope is closely connected with the development of the cathode-ray oscillograph. At the end of the 1920s, both at the Technische Hochschule in Berlin—Charlottenburg (TH Berlin) and at the AEG Research Institute in Berlin—Reinickendorf, work was being carried out to improve the recording of fast electrical transients. Denis Gabor—who was later to receive the Nobel Prize for the invention of holography—had built such an oscillograph as part of his doctoral thesis at the Electrotechnical Institute of the TH Berlin, with a concentrating coil of novel form. Gabor, from purely practical considerations, replaced the conventional long solenoid by a short solenoid contained within an outer iron cylinder, to reduce the external stray field. This was the first primitive iron-shrouded magnetic electron lens. Gabor did not realize this at the time, nor could he explain satisfactorily, as he admitted in his dissertation, how it worked. A long solenoid does not act as a lens, because there is no radial field component. This became clear in 1926, when Hans Busch delivered the theoretical tool for the newly emerging electron optics. He calculated the trajectories of cathode rays in short, rotationally symmetrical electrical and magnetic fields and found that they behave toward electron beams as lenses do in light optics, with the same formula (lens equation) known from optics.