A simple derivation of the second-order Faraday rotation relation is given that shows the contribution of the different effects. A rapid ray tracing program is used to evaluate the errors in first- and second-order relations, and these are plotted under a variety of conditions. A modified form of the second-order relation is suggested to reduce the errors. Magnetoionic path splitting does not affect the Faraday rotation to the third order. The only significant errors are those caused by the high-frequency approximation and by refraction. The first of these is almost independent of zenith angle. The second is zero for magnetically east-west propagation, when accurate results can be obtained to very large zenith angles. The ratio of the Faraday fading rates on 20 and 40 MHz, near the center of the transit, can be used to determine the critical frequency of the ionosphere to within 1 MHz.