It is proposed that the thicknesses of electron microscope objects be determined by measuring the diminution in intensity of the electron beam caused by the object. Since this method would only be applied to specimens so thin that multiple scattering can be neglected, one need know only the total cross section for single scattering of electrons outside the aperture angle of the electron microscope objective. These cross sections are calculated for fast electrons (energies greater than 10,000 ev) by means of the Born approximation for several cases of practical interest, and the results are applied to some experimental observations.