‘Surprise has sometimes been expressed by mathematicians who have been led by circumstances to look into the subject of nautical astronomy that no method is practised by sailors for reducing a longitude observation to the prime vertical in the same way that an observation for latitude is reduced to the meridian.’

This quotation forms the opening paragraph of the first of three papers by Mr. H. B. Goodwin, R.N., written in 1904–6 relating to the problem of reduction to the prime vertical. The following description of Goodwin's work in this connection may not be without interest in view of the recent interesting paper by D. H. Sadler in which the author describes the investigations into the same problem made by G. F. Cunningham.

The vast difference, to which Mr. Sadler refers, between proposing and translating into practice, a new navigational table, is exemplified in the case of Goodwin's P.V. Tables. All the intermediate steps between proposing and producing are described with utmost clarity in Goodwin's three papers.