The penetration of electrons through matter has long been the subject of both theoretical and experimental investigations. Because of simplicity, the investigation frequently deals with a collimated beam of monoenergetic electrons incident normally upon a planar target. Two of the most useful measurements connected with such an experiment concern the range or depth of penetration of electrons in the target, and the intensity of the transmitted beam as a function of incident energy. One object of this research is to determine experimentally range-energy data for thin films. The other object is to measure the transmission of electrons by a thin film and to apply the data to beta-ray spectra obtained using the film as the window in a G-M counter.