The majority of transmission-type electron microscopes use magnetic electron lenses because of their superiority with respect to resolving power as compared with that of electrostatic lenses. The axial field distribution of magnetic lenses customarily in use can be approximated very closely by the analytical expression H(z) = H0/[I+(z/a)2]. H(z) is the field strength along the optical axis z. H0is the maximum field strength at the point z = 0. 2ais the so-called half width of the field curve, i.e., H(±a) = H0/2. The paraxial-ray differential equation can be rigorously solved for such a field. On the basis of this solution, it is possible to calculate accurately all optical constants which are of interest in the design and performance of a microscope. Previous measurements and calculations are summarized and extended to give a complete description of the behavior of this type of electron microscope.