Book excerpt: Using the trajectory-tracing technique, the asymptotic directions and cut-off rigidities for Palestine, Dallas, and Midland, Texas were calculated as a function of various zenith and azimuth angles. Continuation of the trajectory-tracing process below the Stormer cutoff allows an evaluation of the reentrant albedo showing that the invariant latitude of the guiding center of the trajectory at the albedo origin is the same as the invariant latitude of the guiding center of the particle trajectory at the specified zenith and azimuth angle of the detection point. Tables of asymptotic directions, cutoff rigidities, and the location of the reentrant albedo for each of these locations are given. Summaries of cutoff rigidity calculations as a function of zenith and azimuth directions for some miscellaneous locations are also included.