In recent years, the most striking development in the philosophy of navigation has surely been the change in attitude towards errors. Ten years ago an error was regarded as something that just did not happen in the best navigational circles; today we accept it as the normal concomitant of observation, and we study to reduce it.

This change in philosophy is really nothing more than theory following in the footsteps of the practical man, for the practical man has always regarded a position plotted on a chart with a certain amount of healthy scepticism. It may therefore be of value to discuss the whole business of errors from the point of view of the practical man, avoiding complicated mathematics and dealing in demonstrations rather than in rigid proofs. Navigation has been described as the business of conducting a ship on its way across the sea or an aircraft on its way across the sky. The word conducting implies safety. Indeed, safety is the keyword in navigation.

Although meteorology probably has a greater influence on marine and air navigation than any other individual science, many users are not fully aware of the problems of present-day forecasting, nor do they make full use of the services available. This paper is intended to give some idea of the value of observers' reports, the importance of communications, and the problems of present-day forecasting. In particular, attention is drawn to the rapid increase in upper air soundings and the interdependence of surface and upper air observations in predicting the elements for all marine and aeronautical services. Arising from the application of upper air data to surface forecasting, the paper emphasizes the value of applying comprehensive analyses and of marine forecasts prepared by weather centrals ashore; in areas where facilities are not available to the marine user, however, knowledge and experience of single-observer forecasting are still needed.

The Institute was planned to bring together not merely the professional navigators, but all who could contribute to the exchange and advance of knowledge bearing on navigation. The founders were wise when they gave effect to the thought that the small-boat sailor and the sailplane aviator could contribute to the progress of our science and art, and could greatly strengthen the hand of the professional provider and the professional user of the processes and material of navigation. The reasons for exchanging and advancing our knowledge are as diverse and yet as closely interacting and mutually reinforcing as are the individual interests of our members.

Every navigator is familiar with the necessity for correcting sextant observations of altitude for the effect of atmospheric refraction. He does this by means of tables which the great majority of navigators are compelled to take on trust, as they would a table of haversines. Unfortunately it is much easier to guarantee the accuracy of a table of a straightforward mathematical function than it is to tabulate accurately an optical effect occurring in a notoriously variable atmosphere. Recent American work based on large numbers of marine observations has to some extent called into question the accuracy of the low-altitude portions of the usual tables, and it therefore seems worth while to give a brief account of refraction theory and also to consider how far it is confirmed by observation. The treatment will be restricted to refraction as it affects marine navigation. This is a considerable simplification. Aerial observations may be made at any level between the ground and the lower stratosphere, so that air navigation involves a much greater range of pressures and temperatures at the position of the observer. Moreover, it involves some occurrence of much more strongly negative altitudes than can be observed from bridge height on a ship, and at such negative altitudes (i.e. zenith distances over 90°) the intrinsic variability of the refraction is large enough to make any table rather unreliable.

During the Antarctic summer season of 1949 the Norwegian sealer Norsel, which had been chartered by the expedition, landed the Norwegian-British-Swedish Antarctic Expedition in Queen Maud Land in the Antarctic. In January 1951 the ship took down relief personnel and stores and for this trip the Admiralty, at the invitation of the planning committee, appointed the author as an observer. The decision to appoint a member of the navigation branch was made partly so that the techniques of ship handling and navigation in ice could be studied; and since the captain of Norsel, Captain Jakobsen, was extremely experienced in every aspect of ice navigation, a great deal of valuable information was acquired. The Institute had also suggested a number of astronomical observations that might usefully be made in polar areas and the Admiralty gave its approval for the observer to make them.

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.

The usual method of using radar for navigation at sea is to transfer the information from the PPI to the chart. In many instances, however, the pilot will con the ship directly from the PPI, using his local knowledge, which is equivalent to using a chart impressed on his mind. In such cases it is necessary to identify immediately and unambiguously the PPI paints, which often bear little resemblance to the shape on the chart of the feature which is producing the echo.

A description is given of the basis and method of calculation of the new table of refraction included in the Air Almanac for 1943 onwards; the table caters for heights up to 55,000 ft. and all altitudes above the visible horizon.

As already announced the Air Almanac and the American Air Almanac will become a single publication, under the title of the Air Almanac, as from 1953. To cater for the greater heights at which aircraft now fly, and for the possible use of observations at very low altitudes, the refraction table has been completely redesigned. The explanation of the table in the Almanac is naturally restricted to instructions for and illustrations of its use, and, in view of the current interest in refraction, especially at low altitudes, it seems desirable to place on record a full description of the theoretical basis of the table and of the method by which it was calculated.

The theoretical determination of a fix from a number of simultaneous, or near simultaneous, positional data has attracted considerable attention during the last five years. A problem is presented whenever the amount of information obtained is more than sufficient to determine the fix, the most common case being when a set of three position lines is obtained. In this instance the size of the triangle of intersection can be used to estimate whether or not the position lines are likely to be consistent with each other; if they are, some central point inside the triangle is accepted as the fix. In doing this the influence of the position provided by the vessel's past history (the dead reckoning position) is ignored; once the fix is decided on, however, a comparison between the two estimates of position may be of value either in enabling a blunder to be detected or, possibly, in selecting some intermediate point as a position from which subsequent navigation should be based. Although the determination of a position from a number of data is, mathematically, a single problem whether these data include the dead reckoning estimates or not, it is usual navigational procedure to consider first the latest positional information. It is the study of this problem that is the object of this article.

The history of marine navigation in the area to the north of Hudson Straits and west of Greenland dates back to Martin Frobisher in 1567, John Davis in 1585 (who reached N. 72° 15′), and William Baffin, who got as far as Smith Sound (N. 77° 45′) in 1616. All of them were searching for a short route to the East. There was little exploration in the area for the next two-hundred years, until, in 1818, the British Government recommended explorations for the Northwest Passage: This activity continued throughout the Franklin era up to 1875, when Captain George Nares proceeded to N. 82° 25′ on the northern end of Ellesmere Island. After this, the role of exploration gradually passed to American hands, largely culminating in 1909 with Robert E. Peary's attainment of the North Pole.

This paper discusses celestial navigation within the Arctic Circle by the use of great-circle position lines. Application of this method in this area is indicated by:

(1) The freedom from need to correct for atmospheric refraction.

(2) The lack of dependence on either D.R. or assumed position.

(3) The simplicity of drawing the great-circle position line.

(4) The freedom from need for making instrumental scale readings and corrections thereto, other than in respect to the time of the observation.

The adequacy of available stars is examined.

The year 1952 is the fourth centenary of the birth of Sir Walter Ralegh. So far from being the great romantic of tradition Sir Walter was a hard-headed practical man, and the first Englishman to engage a scientific and technical expert to advise him on his colonizing enterprises. He brought the brilliant young mathematician Thomas Hariot, some eight years his junior, direct from Oxford to Durham House, his mansion in the Strand, where, setting his instruments up on the leads, Hariot laboured for years at improving observational technique and revising the Ephemerides. Meanwhile he gave instruction in navigation to the officers of Ralegh's ships, himself obtaining practical experience on the voyage to Virginia in 1585, when he was able to observe the seaman's difficulties and the errors to which he was prone. He had already by 1584 written a new Instruction Manual which he entitled Arcticon, but this is unfortunately lost. We have, nevertheless, an epitome of its contents, for Ralegh asked for a ‘refresher course’ on the eve of his departure for Guiana, which was to take place in February 1595, and Hariot's teaching notes in his own (very crabbed) handwriting, besides fair copies of the tables he drew up, are now at the British Museum.

The ocean weather ship. In 1946 an international conference was held in London as a result of which thirteen ocean weather stations were established. In 1949, for reasons of economy, the number of stations was reduced to ten, and that is the situation at present.

A member, Mr. R. G. Bolton, has sent us the following graphic account of refraction, observed from Littlehampton jetty. The ship is a small coaster observed between 1 and 2 p.m. on a hot and sultry summer's day.

H.M.S. Challenger is one of Her Majesty's surveying vessels. She is a ship of 1140 tons and carries a complement of 96 officers and men. Built in 1931, she is named after her illustrious predecessor in which the wellknown world oceanographic cruise was made in the years 1872–6. This expedition brought back a great wealth of chemical and physical data, and a huge collection of plants and animals from the oceans. These were checked and analysed and eventually, under the guidance of Sir John Murray, who had been a scientist on board, the results were published in fifty folio volumes known as the Challenger Reports. These reports still form, the starting point for the study of the oceans and marine life.

No account of the observations described in this paper has previously been published, though they were made nearly eighteen years ago. The author has kindly presented the Institute with all the data he obtained from them and with a detailed description of the investigation. We print here a short account of the observations and of the principal results obtained, which it is felt should go on record.—Ed.

Largely as a result of discussions with Dr. Per Collinder of the Swedish Hydrographic Service and Dr. Knut Lundmark, Professor of Astronomy at Lund, the author undertook, between June and August 1934, a series of sextant observations to determine the degree of refraction at low altitudes, the normal accuracy of sights at sea, the accuracy of twilight and night observations and possible elevations of the horizon at noon. 1908 observations were taken during the period.

In a previous contribution Professor E. G. R. Taylor has reviewed the development of the sea chart up to 1600, the year in which Edward Wright published his celebrated chart of the world on Mercator's projection. Wright's chart represents one of many minor incursions on the part of English cartographers into the field of nautical cartography, which at that time and for the next hundred years was dominated by the flourishing Dutch school of hydrography. It was not until the latter began to decline towards the end of the seventeenth century that the English cartographer really came into his own and began to produce charts to assist the navigator. Thus the evolution of the English nautical chart to its present state of development covers a relatively short span when measured against the whole background of maritime enterprise and endeavour.

The development over the past two hundred and fifty years has been sporadic rather than continuous, being characterized by sudden advances followed by long intervals of consolidation. Factors such as the needs of national defence, the invention of navigational instruments and advances in hydrographic surveying technique, have at various times acted as stimulants to chart evolution. Throughout the period under review responsibility for supplying the navigator with accurate charts has gradually passed from the many private publishing firms to a specially created national department.

To find out the origins of the nautical mile it is necessary to go back to early times, for, like so many other things, it did not spring up in full bloom in a day, but evolved by slow degrees.

Early man, seeking units of measurement, logically looked about him for something in nature that he might use as a standard. For very short distances he used the width of his finger, the width of his hand, his span, the length of his foot, or the length of his forearm. As these varied between men, so the length of the derived units varied. The foot, for instance, varied from 11 to 14 inches. Even greater variation occurred in the length of the cubit, which originally was taken as the length of the forearm, from the elbow to the end of the middle finger. This unit was widely used, but varied from country to country, and was not even constant within various parts of the same country in some instances.

Timed sextant observations of the Moon when it is suitably limbed are obviously as easy to take as those of any other body, and the results obtained are no less accurate or reliable. It is therefore surprising that only about 5 per cent of Merchant Navy navigators appear to take sights of the Moon, and that about 75 per cent of the defaulters seriously believe the Moon to be of small value for navigation, other than for compass checks.

After taking a latitude at noon and obtaining a position, a course and distance to a position nearer the destination is usually required. A course and distance from an estimated noon position may be worked prior to noon and then corrected at noon by the observed latitude and morning position line, by means of a plotting chart, giving reliable results quickly and accurately.

In Fig. 1, BA and CA represent the course and distance from B to A and C to A respectively. BD and EC are arcs of concentric circles with centre A; and AC = AE and AB = AD.

If BD and CD are small in comparison with AB, arcs BD and EC may be considered straight lines and the figure BECD a rectangle. If the rectangle can be solved, the distance AC can be deduced from AB, i.e. AC = AB - DC or AC = AB + DC if C lies the other side of BD.