This paper describes two methods by which lines of position may be obtained by observation of stars (in pairs) without the use of instrumental scale readings either for altitude or for azimuth. These lines of position represent arcs of great circles of the Earth. An instantaneous observation is proposed.

Great circles determined by star positions form, on the celestial sphere, a lattice which is not deformed by precession. Whether or not he be at rest relative to the rotating Earth, the observer's zenith traverses this lattice, which thus may serve in celestial navigation precisely as does a well-marked terrain in contact flying over land, or as do ranges and markers in coastal and harbour navigation. Observation of the zenith-transit of an element of this lattice is akin to the process of noting the moment when an aircraft crosses a coastal line or other visible terrestrial mark or to the recognition of when a vessel near shore is on a certain range. Observation of this type is as rapid as the navigator may be able to make it since it is the observation of the occurrence of an instantaneous situation.