An experimental study of the migration of dilute suspensions of particles in Poiseuille flow at Reynolds numbers $\hbox{\it Re}\,{=}\,67\hbox{--}1700$ was performed, with a few experiments performed at $\hbox{\it Re}$ up to 2400. The particles used in the majority of the experiments were neutrally buoyant spheres with diameters $d$ yielding a ratio of pipe to particle diameter in the range $D/d \,{=}\, 8\hbox{--}42$. The volume fraction of solids was less than 1% in all cases studied. The results of G. Segré & A. Silberberg (J. Fluid Mech.14, 136, 1962) have been extended to show that the tubular pinch effect in which particles accumulate on a narrow annulus is moved toward the wall as $\hbox{\it Re}$ increases. A careful comparison with asymptotic theory for Poiseuille flow in a channel was performed. Another inner annulus closer to the centre, and not predicted by this asymptotic theory, was observed at elevated $\hbox{\it Re}$. As $\hbox{\it Re}$ is increased, the distribution of particles over the cross-section of the tube at the measurement location, lying at a distance $L \doteq 310 D$ from the entrance, changes from one centred at the annulus predicted by the theory to one with the particles primarily on the inner annulus. The case of slightly non-neutrally buoyant particles was also investigated. A particle trajectory simulation based on asymptotic theory was performed to facilitate the comparison of theory and the experimental observations.