Examination of the requirements for reducing the spherical aberration of an electron lens by modifying the field shows that the hypothetical lens field H(0, z) = γ/zⁿ should have small aberrationsIt is shown that the properties of a certain class of this general field configuration can be described in terms of an exact analysis In particular, the electron optical properties of the γ/z² field are described in detail.The γ/z² field is found to have small aberrations, but practical conditions limit appreciable improvement in resolving power The characteristics of the γ/z³ field are also examined and are found to give little further advantage.