Some experimental results are presented for the motion of small rigid spherical particles suspended in a Newtonian viscous liquid flowing under steady laminar conditions in a vertical tube of circular cross-section. When the particles were neutrally buoyant, the Segré & Silberberg (1961, 1962) effect was confirmed, the particles moving into a narrow annular zone with a diameter about two-thirds of the tube diameter. When the particles were slightly denser than the fluid, they migrated relatively rapidly to the wall of the tube for downward fluid flow and to the axis of the tube for upward fluid flow. Individual particle trajectories were obtained (necessarily approximately) from photographic records, and statistical techniques used to obtain ‘universal’ paths for given flow conditions. A complete set of relevant dimensionless parameters is given by the tube flow Reynolds number, the ratio of the tube diameter to the particle diameter, and the ratio of the Stokes free-fall velocity of the particle to the maximum fluid velocity. An attempt has been made to study the dependence of the trajectories on each of these parameters, the ranges being 10–200, 10–20 and 0–0.2 respectively. Detailed results can be found in Jeffrey (1964). Some comments are made on the relevance for this situation of certain theoretical solutions given elsewhere.