The object of this paper is to describe, in principle, a method of reducing astronomical sights, of plotting the resulting position lines and of calculating a position from two or more sights. The method, which is thought to be new, requires neither a calculator nor extensive tables and appears to possess some advantages over more conventional methods. After a general description, and illustrations of two variations, the method is analysed in sufficient detail to indicate that its practical realization, to meet any specific requirement, is a straightforward matter of detailed design.

No attempt is here made to translate the principles of the method into a form for practical use. The paper is mainly addressed to those interested in the theory of astronomical navigation; the description, together with the analysis and the illustrations, is available for use as a basis for a practical method of sight reduction – should anyone consider that there is a requirement! The treatment is intended to be rigorous, though much elementary mathematical detail has been omitted; in a practical application some care may be required near the singularities.