The paper by P. G. Saffman discusses the lift force experienced by a small sphere moving through a viscous liquid in a slow shear flow. The sphere's translation velocity is parallel to the streamlines, and the lift force acts perpendicular to the flow direction, deflecting the particle towards the streamlines moving in the opposite direction to the translation velocity. The lift force is given by \(81.2 \mu V a^2 \kappa^4 / \nu^4\) plus smaller terms, where \(a\) is the sphere's radius, \(\kappa\) is the velocity gradient, \(\mu\) is the viscosity, and \(\nu\) is the kinematic viscosity. The relevance of this result to observations by Segré & Silberberg (1962) of small spheres in Poiseuille flow is discussed, and the problem of a sphere in a parabolic velocity profile is also addressed. The functional dependence of the lift force on various parameters is derived, and the analysis is compared with experimental results. The paper highlights the importance of inertia in the motion of rigid spherical particles in shear flows and provides a quantitative understanding of the lateral migration observed in such flows.The paper by P. G. Saffman discusses the lift force experienced by a small sphere moving through a viscous liquid in a slow shear flow. The sphere's translation velocity is parallel to the streamlines, and the lift force acts perpendicular to the flow direction, deflecting the particle towards the streamlines moving in the opposite direction to the translation velocity. The lift force is given by \(81.2 \mu V a^2 \kappa^4 / \nu^4\) plus smaller terms, where \(a\) is the sphere's radius, \(\kappa\) is the velocity gradient, \(\mu\) is the viscosity, and \(\nu\) is the kinematic viscosity. The relevance of this result to observations by Segré & Silberberg (1962) of small spheres in Poiseuille flow is discussed, and the problem of a sphere in a parabolic velocity profile is also addressed. The functional dependence of the lift force on various parameters is derived, and the analysis is compared with experimental results. The paper highlights the importance of inertia in the motion of rigid spherical particles in shear flows and provides a quantitative understanding of the lateral migration observed in such flows.