The paper is concerned primarily with the electron guns employed in electron microscopy.The position of the image of the cathode, the magnification, and the divergence of the beam leaving the anode are calculated for a three‐electrode electron gun with plane electrodes and circular apertures both for zero and battery bias. The simplifying assumption is made that the electrostatic lenses are thin. The results are compared with the experiments of Johannson. The extension of the results to the gun used in the transmission electron microscope is considered with the aid of electrolytic trough measurements. The case of a gun biased by a cathode resistor is also discussed.