Although the use of bisectors to select the most probable position determined from astronomical observations is well known, the system seems to have received insufficient recognition in current navigational literature. In what follows an attempt is made to assess the problem practically.

When, last year, you did me the honour of electing me your President you gave me the duty, and the privilege, of composing and delivering a Presidential Address. It does not lie within my abilities to make a grand survey of the present state of any great and important navigational development—such as might fittingly form the central theme of such an Address, and which has, in fact, been so admirably treated by my predecessors in this office. I have, however, been privileged to serve on the inner councils of the Institute since the earliest days of its conception, and feel that I may be in a position to take the Institute of Navigation itself as a central theme. I do so at this time particularly because the by-laws of the Institute quite rightly operate to ensure that no one person shall remain on the Council indefinitely and I must be the last to have such continuous service since the foundation. But there is a more cogent reason: the Institute was founded in the enthusiasm of the immediate post-war application of war-time navigational methods to civil use, and its precise role was deliberately left vague. It will be my object this afternoon to examine the extent to which the Institute is fulfilling its initial purpose and, on the basis of seven years' experience, how it can best play its part in the future.

In 1953 an Institute working party was set up to investigate the accuracy of dead reckoning in air navigation and to attempt to produce error data covering a wide range of operational conditions. Dead reckoning errors fall into two categories, those due to wind finding and forecasting, and those due to instruments. Mr. Durst's paper surveys the whole problem, laying particular emphasis on the meteorological aspects, and represents the main progress in this subject to date.

The error of a dead reckoning position in the air will depend on the accuracy of the initial position from which the departure is made, the accuracy of the course steered (compass error), the accuracy of distance flown (airspeed-indicator or engine-revolution error), and the accuracy of the wind used (forecast error, found-wind error, &c). These quantities can be expressed mathematically, as is done in Appendix I, and it will be seen that if a pair of fixes is available it is possible to derive the dead reckoning error. The standard error that will arise when a large number of D.R. positions have been calculated on different occasions using a large number of aircraft and observers can be written symbolically; the expressions are fairly simple provided that the errors made in the different classes listed above (e.g. the errors in compass and distance run) are not closely correlated.

The purpose of the S-diagrams is to give a rapid and convenient solution of the chief problems in astronomical navigation; they are especially simple for determination of altitude and azimuth. The solution is obtained without logarithms and by referring to no more than two pages of the diagrams. The diagrams are less expensive and more accurate than the Astronomisches Rechengerät (ARG), and are, without any doubt, less difficult to use than the Astronomische Rechenatlas. The method, which was recently mentioned in a paper by H. C. Freiesleben, may, therefore, be discussed here in some detail.

Powered research ships are the basic vessels from which the science of oceanography is conducted. For the investigation of certain surface water problems, however, a large, powered vessel is not the most suitable platform, for, while affording ample accommodation and working space, she may have fundamental faults. Her deck may be far above sea-level so that in bad weather direct observation of marine life is impossible. More important, her mere presence may alter the very characteristics, both physical and biological, which are being studied. Thus her hull, rolling, pitching and threshing in a seaway may appear to some animals as a fearsome intruder. The throbbing of her propeller sets up low-pitched vibrations powerful enough to alert the fish for miles around. The sea close to the engine room becomes warmed and to it is added hot water from the condenser. There is violent water mixing by the bow wave. These factors in combination effectively alter both the sea temperature and the thermal stratification. The ship's wash, thrown away from the sides, may set up a heavy cross sea which distorts the shape of nearby waves, particularly in regard to their steepness and height.

It is not possible at this stage to do more than hint at the possible alterations in navigational procedures which the new knowledge contained in Mr. Durst's paper on the accuracy of dead reckoning in the air logically leads to. This is so for two reasons. First, existing navigational procedures differ so widely between civil and military users (and amongst civil users themselves) that detailed modifications to existing procedures require separate consideration in the light of the different current navigational drills at present used. Secondly, only two particular areas of the world, the North Atlantic and Central Africa, were considered in the paper, though these are fairly representative of extra tropical and tropical latitudes (there will, of course, be variations from place to place owing to the known variability of the general circulation of the atmosphere). Nevertheless, the data obtained by the meteorological statisticians is of such interest and importance that certain broad applications suggest themselves.

On 26 November 1954 The Mathematical Practitioners of Tudor and Stuart England by E. G. R. Taylor was published for the Institute by Cambridge University Press. Dr. Derek Price, of the Whipple Museum of the History of Science at Cambridge, here describes the book for the Journal.

During the last twenty-five years there has been a revolution in writings on the history of science. Now, just as the profits are beginning to materialize, a second great change has occurred.

Dr. Atkinson here proposes a type of radar plot which was not actually considered in the Institute working party's recent report. It would be useful to have some comment, particularly from sea, on the effectiveness of this type of plotting.—Ed.

The current discussions on radar plotting at sea appear to have rather overlooked one plot which may have quite important advantages: this is the pure time-distance plot, ignoring bearings almost completely. One would use ordinary squared paper (say quarter-inch squares or some similar coarse mesh), with distance increasing upwards, time increasing to the right, and both scales permanent ones; pre-printed scales would be useful, but not essential of course, and one might suggest an inch to a mile and an inch to four minutes.

The name of John Dee (1527–1608) is one which every navigator, whether seaman or airman, has good cause to respect. For he was the first to try to teach unscholarly English sailors the use of the spherical triangle to find the distance and direction of some desired haven on the globe. Nor was that his only contribution to nautical science. Yet historians have treated him slightingly, dubbing him astrologer and alchemist, by which words they understand ‘charlatan’. Consequently the popular picture of him is of a servile, ignoble figure, eager to dupe the first Elizabeth and her courtiers. The acclaimed mathematician, and the ever-ready instructor are forgotten. It is true, of course, that Dee cast horoscopes, and that he hoped to find the formula for transmuting the baser metals into gold. It is true, besides, that in middle age he took to crystal-gazing, believing that he conversed with angelic spirits. Hence when in 1583 he went abroad at the invitation of the Polish Prince Lasky, a mob broke into his house at Mortlake and wrecked his library, which contained over 4000 books and manuscripts, besides scientific instruments. But by this date his work on navigation had come to an end. Yet his simple account of his meeting with the medium Edward Kelly (who was indeed a cheat) reveals him as a sincere man. Kelly at once asked to see what feats he could perform, but, says Dee, ‘I truly excused myself therein, as not in ye vulgarly accounted magic either studied or exercised. But… I brought forth to him my stone in ye frame … and said to. him that I was credibly informed that to it, after a sort, were answerable aliqui boni Angeli—certain good Angels.’ We should perhaps echo, therefore, the judgment of Disraeli—Dee's imagination often predominated over his science—but science he had.

In modern air navigation, fuel consumption and cruise control present problems inseparable from those of pure navigation. Captain Majendie's paper, which was prepared for another purpose (but has not previously been published), is therefore of particular interest to navigators, because of the light it sheds on these related matters.

Instruments are to a very real extent the basic tools of both the pilot and navigator of a civil transport aircraft, and it is difficult to draw any clear line between their respective requirements. The following notes have been put together to try to give a survey of some of the most useful lines of development in this field. Clearly, such a survey must be in very general terms, but it is hoped that it may be of value in setting the various problems discussed into some sort of general perspective.

Waves, tides and ocean currents might not be expected to produce electric currents, but by moving water, as a conductor, through the Earth's magnetic field they do in fact produce measurable voltages and flows of electricity. Young, Gerrard and Jevons, who made the first detailed study of this phenomenon, thought it conceivable that measurements of electric potential gradient might be used to estimate the drift of a ship at sea, and Von Arx showed how indications from electrodes towed behind the Research Vessel Atlantis were used to keep her on a direct course from Bermuda to Woods Hole, across the Gulf Stream. In recent years the method has been used extensively in studies of ocean currents and more ships might use it if the necessary equipment were readily available.

A country that frowns on rich men must be content to let its rare books cross the ocean. Certainly it will lose all those which make no appeal to the literary man, and those to which the devotee of ‘pure’ science is indifferent, since these are the two groups who might be consulted before such a transference, or whose protests would be listened to. Hence it is that, because only a tiny minority has as yet been interested in the crude beginnings of applied science and technology, a discerning American member of the Institute, Mr. Henry C. Taylor, has formed a collection of about one hundred and fifty books which tell the story of how skippers and pilots were taught to set course and make port during the Great Age of Discovery and Colonization. Nearly half of these books are in English, and this is understandable, for although the pioneers of the new methods of navigation were the Portuguese, the English sailor took pride of place after the defeat of the Spanish Armada. Mr. Taylor appears at one time to have been satisfied with the breezy statement of Captain Smith of Virginia in 1626 that the seaman was sufficiently equipped if he had his Almanack, his Waggoner, a manual or two, and knew a good instrument-maker like Master Bates on Tower Hill. But one book leads to another, and, having got together these half-dozen books, he began to study them.

The Rhine which has a length of about 900 km. (approximately 560 statute miles) carries perhaps a greater volume of traffic than any other river in the world. This traffic mainly consists nowadays of high-powered motor vessels varying in size between 300 and 1500 tons, and large tugs towing six to eight non-motorized barges of 500–3000 tons.

We were taught at school that a stone which is thrown forward in a horizontal direction from the edge of a cliff will describe a curved path which is a parabola. The path is in fact an ellipse—but that is not the only thing we were taught at school which turned out to be erroneous in after life. This error arises from the elementary assumption that all vertical lines are parallel; but the vertical in fact is the direction of a plumb line, and all such lines converge towards the centre of the Earth. With a small initial velocity the stone will describe a small ellipse which intersects the surface of the Earth, but with greater speeds the ellipse becomes larger, until it finally clears the Earth completely and returns to the thrower. Although the stone is now circling the Earth, it is still ‘falling’ freely in a gravitational field, and from this point of view all such orbits are referred to as ‘free orbits’, the stone being in a state of ‘free fall’.

Scandinavian interest in transarctic flying dates back to the successful transarctic flight of the airship Norge under the joint leadership of Amundsen and Ellsworth. The geographical position of Scandinavian countries, of course, makes such interest natural as they have everything to gain from commercial flying across the Arctic. In 1946 when Scandinavian Airlines System was formed, with the primary object of establishing intercontinental routes to the Scandinavian countries, four Stratocruisers were ordered from the Boeing factory in Seattle and plans were made for a non-stop delivery flight from Seattle to Stockholm following the great-circle route across sub-arctic Canada and central Greenland. The object was to gain experience over this route, which might become of strategic importance in the near future. However, the Stratocruisers were sold before S.A.S. took delivery and the plans for the flight were abandoned. The groundwork carried out in connection with navigation was not wasted however.

At the end of the summer of 1952, a series of proving flights were started on B.E.A. routes with the prototype Viscount airliner, the V.700 G-AMAV. One of the objectives of this proving flying was to design operating and flight-planning techniques to be used when normal scheduled services were commenced.

In its essence, navigation in ocean races is the same as navigation on any other voyage; the processes are the same and the drill is not very different. But it is a specialized thing and there are certain interesting problems which demand special solutions and special ways of doing things. To start with, the vessel is propelled by wind and one cannot, in the ordinary course of events, lay off one's mean course and steer it; the course will be continually varying, and the whole of the navigational problem is coloured by this fact. Again, navigation in ocean racing demands a much higher accuracy than navigation in an ordinary sailing vessel, where a landfall within five or perhaps even more miles in good visibility will be quite enough; the difference between spot-on and five miles away may well be the difference between winning an ocean race and otherwise.