In 1877 a two-volume book, Nouvelle Navigation Astronomique, edited by the astronomer Villarceau and a naval officer, Magnac, was published in Paris. The book, which may be considered the most comprehensive work on astronomical position lines up to date, covers completely the theoretical treatment of circles of equal altitude on Mercator projections and their practical evaluation, and considers the effects of possible mistakes and errors. In the present writer's view these factors have not yet been sufficiently appreciated. It is surprising that similarly detailed descriptions of the other position lines used for navigation have not yet been published; although, apparently, the attitude towards these questions has altered since that time. The change in methods of navigation, particularly with the introduction of radio aids, has brought a variety of other position lines to the fore, and the predominance of Mercator's projection is not as universal as it was eighty years ago. In order that these premises may be clarified, a summary of the various position lines in use today is here given.