This paper describes a new method for the continuous development of astronomical position lines, relative to a moving D.R. position. At present the method is restricted to observations of the stars, but it might later be extended to other bodies. A basic requirement is a precomputed ‘star lattice’, which here takes the form of a series of graduated intercept curves drawn so as to be always at right angles to curves of constant altitude. The star lattice may be prepared and printed in advance, or may be constructed by the navigator himself, immediately before observation, from the data in the new tables, Sight Reduction Tables for Air Navigation (Vol. i, Selected Stars).