When a fluid flows through a stationary curved pipe, a secondary flow is set up, the fluid in the middle of the pipe moving outwards and that near the wall inwards. Dean showed that the dynamical similarity of this flow depends on a non-dimensional parameter , where wm is the mean velocity along the pipe, v is the coefficient of the kinematic viscosity, and 2α is the diameter of the pipe which is bent into a coil of radius R. This conclusion has been verified experimentally. Dean also analysed the secondary flow and calculated the resistance to the main flow for small values of k. The present work deals with the motion when k is large. It assumes that the flow consists of a non-turbulent core moving slowly outwards, surrounded by an inward moving boundary-layer. This conception leads to the prediction that the effect of curvature is to increase the resistance coefficient γc of the curved pipe relative to the coefficient γ5 of the same pipe if it were straight and that approximately