This paper was written in 1946 when Mr. Kiewiet de Jonge was a student at Harvard College Observatory. Subsequent developments in astronomical navigation, particularly the publication by the U.S. Hydrographic Office of H.O.249, have overshadowed the practical advantages of the three-star position tables. But the principles of the method, which have not previously been described in print, are of sufficient importance and novelty for permanent record.

In this paper we will develop a fast tabular solution of the position deduced from three ‘simultaneous’ sights. This is achieved in a novel way, through principles not generally associated with the traditional approach to the problem. The solution is based on the fact that the measured altitudes of a set of three stars uniquely define the most probable position of the observer projected on the celestial sphere.