This paper presents the following two velocities in terms of nondimensional factors : (a) The mean suspension velocities of single freely-suspended spheres in a pipe v₁, (b) The terminal velocities of single spheres falling through still water in a pipe v₂ . The experiments were carried out with changes in sphere diameter d, specific gravity of sphere γ_s, pipe diameter D and inclination angle of pipe Θ. The results obtained are summarized as follows : (1) v₁ is not always identical with v₂, (2) v₁/v_t = 1.024 - 1.329In(d/D + 1.0), (1) (3) v₂/v_t = 1.0 - 2.130(d/D)^2.462 (2) for the spheres falling straighly along the pipe axis, or v₂ /v_t = 0.817 - 2.390(d/D)^2.462 (3) for the spheres falling with oscillation in the pipe, where v_t is the terminal velocity of single spheres in unbounded fluid, , (4) v₂/v₁ = 1.10 - 1.35, in the case of Eq . (2) and v₂/v₁ = 0.90 - 1.03, in the case of Eq . (3) .