Summary The formulation and solution of the general equations of motion of pyroclasts in the Earth's atmosphere are described. Ranges of particles ejected from a vent, and times of fall of particles released from an eruption column or ash cloud, are computed for those values of particle radius (0.01 to 100 cm), density (0.5 to 3.5 g cm⁻³), launch velocity (10 to 1000 ms⁻¹), elevation (45, 66 and 87 degrees) and release height (0 to 50km) of practical importance. The values so obtained are presented in tabular and graphical form, and their use in determining the physical parameters of an explosive eruption is described.