The estimation of collision danger is often required by harbour authorities and others for planning fairways or for increasing the safety of navigation. Fujii1 gives an approximate formula for the probability of collision in a waterway where the density of traffic, the size distribution of ships and the average speed are known. Fujii's formula is however only applicable where the traffic has been surveyed and traffic patterns are well known. Some simple method is required for estimating collision danger, especially for harbours where traffic patterns are complicated and the information available on marine traffic engineering is comparatively small.