## Abstract

The motion of a body through a viscous fluid at low Reynolds number is considered. The motion is steady relative to axes moving with a linear velocity, U$_{\text{a}}$, and rotating with an angular velocity, $\Omega _{\text{a}}$. The fluid motion depends on two (small) Reynolds numbers, R proportional to the linear velocity and T proportional to the angular velocity. The correction to the first approximation (Stokes flow) is a complicated function of R and T; it is O(R) for T$^{\frac{1}{2}}\ll $ R and O(T$^{\frac{1}{2}}$) for T$^{\frac{1}{2}}\gg $ R. General formulae are derived for the force and couple acting on a body of arbitrary shape. From them all the terms O(R+T) or larger can be calculated once the Stokes problem has been solved completely. Some special cases are considered in detail.