Of the 293 papers published in the Journal, eighty-two, or 28 per cent, have been concerned with astronomical navigation. This, however, gives a false impression of its present-day importance. There was a time when conventional astronomical navigation provided the only means of determining position, in the absence of recognizable landmarks; and it still provides the only fundamental method independent of man-controlled devices. But there has been no change in principle since accurate time became available through the combination of radio time-signals and chronometers. The papers have dealt with techniques only. The large number is evidence of the abiding interest in astronomical navigation; but it also indicates the realization that, while the principles of astronomical navigation are unchanged, the conditions of its application have undergone radical change. Techniques have had to be improved under the pressure of necessity, so that the practice of astronomical navigation is now simpler than it has ever been.

The problem of the determination of the observer's position on the Earth can be most easily solved in terms of the equatorial coordinates of the observer's zenith. From Fig. 1, in which the inner circle represents the Earth and the outer circle the celestial sphere, it can be seen that the zenithal point on the celestial sphere is its intersection with the prolongation of the radius to the observer's position. The geographical latitude of the observer is equal to the declination of the observer's zenith, and the geographical longitude is equal to the difference between Greenwich sidereal time (G.S.T.) and the right ascension of the observer's zenith. We can obtain G.S.T. by interpolation from a nautical almanac or directly from a separate watch or clock set to keep sidereal time.

Squadron Leader Bower gives some data regarding the accuracy of astronomical navigation in high-speed aircraft. No attempt was made to assess the absolute accuracy of astro-navigation, but the distance, when plotted on the chart, between pairs of sights taken on the same star was measured, with the following results.

The average spread between beam shots is consistently greater than that between fore and aft shots, and it is possible that acceleration errors, which can be sizable for high-speed aircraft, are responsible for this.

Errors Due To Aircraft Accelerations. Errors due to the combined effect of the aircraft's movement and the Earth's rotation give rise to errors in the position line.

Many of the major ports of the British Isles, including two of the most important, London and Liverpool, are situated at or near the head of sand-filled bays or estuaries. Their continued utility depends not only on the provision of adequate berthing facilities within the harbour area itself but also on the maintenance of a deep-water approach channel through the shoals of the outer estuary. In some cases the latter requisite is the more difficult of the two to achieve, especially where the bottom configuration is liable to considerable change over a relatively short period of time.

The problems connected with a changing sea-bed configuration come within the scope of loose-boundary hydraulics, a branch of flow mechanics which has only begun to be investigated. Some success in this direction has already been achieved using scale models of specific areas but many unsolved problems remain and much remains to be done.

We are told by Captain Greenvile Collins that Charles II was ‘A great lover of the noble art of navigation’. I think his brother, James, Duke of York, who became the Lord High Admiral at the happy Restoration in 1660, shared the same enthusiasm. Members of the Royal Society, including distinguished seamen, studied mathematics, mechanics and optics. The time was ripe for improvements to be tried out, under royal patronage, in ship design and construction as well as in the navigation of ships. English methods began to be regarded as not only the best but even as unnecessarily exacting, and we are told that Davis's backstaff was known as the English Quadrant by the French, and the English log and log-line for estimating a ship's speed through the water was better than the simpler methods popular with Spanish, Portuguese and Dutch mariners.

The growing complexity and variety of navigator techniques and equipment, associated with a marked increase in aircraft speed, necessitates a more detailed investigation of the navigator's task. Despite an increase in the range and automaticity of navigational aids, the demands made upon him are changing their character, and are in danger of being excessively high.

A detailed recording of navigator activity in flight seems the only practical approach to this problem. The knowledge gained by such a task analysis would be expected to furnish information on the following aspects:

(a) Objective evidence of fatigue effects.

(b) The effects of experience on the navigator's work pattern.

(c) The need, if any, for the modification of training methods.

(d) Equipment layout and design in relation to efficiency.

(e) Practical specification of the navigator's layout.

(f) Indications of specific situations which may with advantage be subjected to laboratory investigation.

A novel instrument for use in chartwork has been devised combining a ruler with the principle of the square Douglas protractor, and permitting immediate indication of direction to be read without ambiguity. A prototype of this instrument, which will probably be known as the Harries Course and Bearing Indicator, is illustrated in Fig. 1. It is constructed of Perspex, and the basic ruler component has engraved upon it a long double-ended arrow, emphasized as the line AA in the illustration. Centrally pivoted above this arrow is an approximately rectangular ‘aligning plate’, B, on which are engraved equally-spaced lines, C, parallel to the 180°/360°, or north /south, line of a circular compass rose.

To obtain the direction of a course laid off on a chart, the bevelled edge, D, of the ruler is placed along it. The aligning plate is then rotated until the north/ south lines on it are seen to be parallel to any adjacent meridians (Fig. 2). The true course can then be read off directly from that degree of the compass rose lying directly over the appropriate arrow head—an action which can be carried out on a folded map or chart held on the knee.

Thomas Hariot's recently discovered manuscript ‘The Doctrine of Nauticall Triangles Compendious’ was the subject of a paper in this Journal by Professor Taylor and D. H. Sadler which poses but leaves unanswered the intriguing question of the method he employed in his computation. Sadler shows that the method depends on the fact that if sequences of meridional parts are in arithmetic progression the corresponding values of tan (45° − ½φ) will be in geometric progression. This is at once obvious from the modern formula for meridional parts:

But how did Hariot, writing before 1596, discover the relationship when neither logarithms nor the integral calculus had yet been invented; and was he able to prove it? It is the purpose of the present paper to supply a proof which requires neither logarithms nor the calculus. It is not claimed that this was necessarily the method that Hariot employed, although the manuscript reveals several points of similarity.

During the last few years much has been learned about the navigational developments and techniques of the English pioneers of colonization in the New World. This has been made possible in some measure by the formation in America of a private library of the books relating to the art of navigation as practised by the Elizabethan and early Stuart seamen. It was in the course of forming his remarkable collection of early Americana that Mr. Henry C. Taylor of New York, purchased copies of Captain John Smith's An Accidence or The Pathway to Experience. Necessary for all Young Sea-men, or those that are desirous to goe to Sea … first published in London in 1626, and A Sea Grammar, with The Plaine Exposition of Smiths Accidence for Young Sea-men, enlarged … first published in London in 1627, subsequent editions of this latter work being entitled The Sea-mans Grammar, etc.