Gibbs et al. (1971) have derived empirical equations that yield settling velocities in water for spherical grains of approximately quartz density. The present investigation examines the applicability of their relationships to other grain densities, fluids, and to gravity fields other than Earth's. The comparison is with "data" generated from a standard drag coefficient versus Reynolds number curve that is applicable to the settling of spheres in any Newtonian fluid. This comparison shows that the Gibbs et al. relationships cannot be used for gravity fields other than Earth's or for fluids other than water, in each case the errors being extreme. Their relationships do yield good results over the range of grain densities represented by the common heavy minerals settling in water. As the density progressively departs from that of quartz, the amount of error increases, reaching 8.5 percent for densities as high as magnetite. A correction factor is introduced which is a function of grain density, the use of which greatly improves the estimated settling velocities of the common heavy minerals and of low-density materials such as foraminifera shells.