A new equivalent-optical system consisting of three lenses is proposed to represent the electron-optical system of a cathode-ray-tube gun. The image formation by these lenses is discussed. It is concluded that the fluorescent spot is an image of the cathode and that its size is almost independent of the value of the final anode voltage EAif lens errors can be disregarded. The solid angle of the electron beam proceeding from the second lens to the main focusing lens contracts in inverse proportion to the final accelerating voltage, as expressed by the formula r2EA=constant, r being the radius of the electron beam. Measurements on a number of cathode-ray tubes of widely different design confirm these predictions. The new theory is compared critically with the earlier "cross-over" theory which led to different predictions. Some applications of the new conception to practical, cathode-ray-tube design are briefly discussed.