  We present a reinterpretation and extension of the reciprocal theorem for
swimmers, extending its application from the motion of a single swimmer in an
unbounded domain to the general setting, giving results for both swimmer
interactions and general hydrodynamics. We illustrate the method for a squirmer
near a planar surface, recovering standard literature results and extending
them to a general squirming set, to motion in the presence of a ciliated
surface, and expressions for the flow field throughout the domain. Finally, we
present exact results for the hydrodynamics in two dimensions which shed light
on the near-field behaviour.
