Published online by Cambridge University Press: 24 October 2008
1. Introduction. The historical basis for the work in this paper lies in a remarkable fact discovered by Dean in 1948. He found that time-periodic surface waves in an ideal fluid experience no reflexion when they encounter normally a fixed, submerged, right-circular cylinder. We might reasonably ask if a similar non-reflective property carries over to different geometrical configurations of submerged objects, for example, two or more cylinders. This question motivates the investigation which follows.