This year the Royal Society celebrates the third centenary of its foundation. In this paper Sir Harold Spencer Jones, the late Astronomer Royal, who was the Institute's first President, describes the early years of the Society and shows how closely some of its work was related to navigation.

For some two thousand years, until well into the seventeenth century, the writings of the ancient Greek philosophers, and in particular those of Aristotle, were regarded as the supreme fountain of wisdom and the source of all knowledge. The break with the Aristotelian dogma may be said to have started with the publication by Copernicus in 1543 of his De Revolutionibus Orbium Coelestium whereby the Earth was displaced from proud position as the centre of the Universe, fixed and immovable, and asserted to be not only rotating around an axis but also to be merely one of a system of planets revolving around the Sun as a centre. Copernicus had refrained for thirty years from publishing his theory as he knew that it would be received with ridicule, not merely because it was not in accordance with Aristotelian dogma but also because it would be held to be against the Scriptures. The Copernican theory met, in fact, with widespread opposition and more than a century elapsed before it came to be generally accepted; for long it was regarded as merely a convenient mathematical representation of the motions of the planets without any true physical basis.

When the problem of collision in the air is discussed, it is usual to start by pointing out the enormous closing speed of two modern aircraft meeting head-on, and to conclude from this that avoidance on the ‘see and be seen’ principle has ceased to be possible. The fact is, however, that the great majority of mid-air collisions (about 85 per cent) occur within five miles of an airport and the typical case is not the head-on one, but the case in which the two aircraft crab into one another from a direction which may be anywhere around the whole enclosing sphere. Since the field of view of the aircrew covers only about 20 per cent of the enclosing sphere, the aircrew of colliding aircraft seldom see each other. It would seem, therefore, that the ‘see and be seen’ principle never did afford much protection, even when speeds were low. In other words, the fact that the number of mid-air collisions in Europe has hitherto been small is not primarily due to seeing and evading, although this sometimes happens, but to the fact that the airspace is very large compared to the volume of all the aircraft in it at any given time. However, as traffic densities go up, the risk rapidly increases, and in congested airspace, such as that around New York, the problem of avoiding collision has already become acute. In the period 1948–57, there were 159 mid-air collisions in the United States, and many of these made headlines in the world press. One can imagine the public outcry if two large transports were to collide over a housing estate; but unless something effective is done, something like this will presumably happen eventually. At very high altitudes the ‘see and be seen’ principle certainly fails, by day, because the speed will be high, and in addition, the range at which a pilot can see an object the size of an aircraft may be less than 1½ miles due to what is sometimes called ‘high-altitude myopia’.

The paper describes the system developed and used by the United States Hydrographic Office for selecting the optimum track for transoceanic crossings by applying long-range predictions of wind, waves and currents to a knowledge of how the routed vessel reacts to these variables. Over a period of two years, over 1000 optimum ship routes were provided to one authority, with an average reduction in travel time of 14 hours.

I must forewarn you that this lecture will deal only with very elementary mathematics. Its subject is what may be termed the preparatory school stage in the education of the navigator. Nevertheless, it is a subject of particular interest and importance because it is in the field of navigation that we first meet with mathematics quite outside learned academic circles. It was among sailors that the process was begun (and it is not yet complete) of transforming the craftsman—whose skill rests on tradition and experience—into the technician—who works on established scientific principles. For the scholar, mathematics is like poetry—an end in itself.

The expansion of air traffic in the United States continues at a forceful rate and shows no signs of decelleration. The Federal Aviation Agency (F.A.A.) traffic control statistics of Fig. 1 show total yearly operations and their relative growth. The graphs distinguish between the three major airspace users, i.e. the scheduled air carriers, the military activity at F.A.A. controlled airfields, and general aviation. The term ‘general aviation’ combines all non-military and non-scheduled airline operators, such as business fliers and private individuals who operate their own airplanes. In addition to the total trend the most significant aspect to note is the high percentage of general aviation activity and its explosive growth rate.

In 1955, following certain discussions within the Technical Committee, arising largely from a suggestion put forward by Mr. A. J. Moline, a member of the Australian Institute of Navigation, the Institute decided to set up a Working Party to go into the philosophy underlying current practices of fuel reserve calculation for aircraft. Because it would have been inappropriate for the Institute to attempt to lay down any sort of recommended code of practice, the Council paid particular attention to the precise terms of reference of the Working Party. It was agreed that its function would be: ‘To examine the requirement for reserve fuel and the factors governing its determination; to ascertain whether common parameters obtain, and to assess their application to future aircraft operation’.

The Chairman of the Working Party, and author of the following report, which has been discussed and agreed by the other members, was Mr. Jack Vivian, of British European Airways Corporation. The other members were Captain R. C. Alabaster (British Overseas Airways Corporation), Wing Commander D. Bower (Royal Air Force), Wing Commander M. C. Bunting (Royal Air Force), Mr. D. O. Fraser (English Electric Aviation Limited), Mr. J. P. Meade (Meteorological Office), Mr. J. E. D. Williams (then of El Al Airlines), and Mr. D. A. Blake (Ministry of Aviation). All members served in a personal, not an official capacity.

The report has been forwarded to the Aeronautical Research Council of the Ministry of Supply.

The analysis of low-altitude observations of celestial bodies specially made for the purpose, indicates that no significant amendment is required to the refraction corrections published in the (Abridged) Nautical Almanac.

In recent years there has been an increasing interest in low-altitude astronomical sights, particularly in regard to the accuracy of observation and of the corrections to be applied for atmospheric refraction. As a result of the analysis of many thousand observations made under different conditions, Professor C. H. Smiley had deduced tabular refraction corrections which differed significantly from those in current use and also from those deduced from modern theories. Suspecting some systematic error in Smiley's results, possibly associated with the phenomenon of irradiation, Dr. G. M. Clemence of the U.S. Naval Observatory undertook an independent investigation using observations made at his request by ships of the U.S. Merchant Navy. Although the number of observations was rather small, leading to a fairly large uncertainty in the deduced refractions, there was little possibility of any source of systematic error; the observed values agreed with the theoretical values well within their observational uncertainty, and differed significantly from those of Smiley. A systematic difference between the observed altitudes of the upper and lower limbs of the Sun was ascribed to irradiation (the spreading of a bright image on the retina of the eye, making the diameter of a bright object appear larger than it is) and, taken in conjunction with a similar phenomenon depressing the visible horizon, was allowed for by subtracting 1.2 from the observed altitudes of the Sun's upper limb and leaving those of the lower limb unchanged. This correction was later incorporated in the altitude correction tables of the (Abridged) Nautical Almanac.

The basic values for dead reckoning, course and speed, are ascertained by inadequate references. The log does not measure the ground-speed but the speed relative to the water. The accuracy of magnetic compasses is limited by the instability of variation and deviation; gyro-compasses are better, but neither does away with steering errors. All classes of position-fixing permit the derivation of course and speed from two fixes but are influenced by the errors inherent in the methods. An astro fix is subject to irregularities of dip and the inefficiency of artificial horizons. The uncertainty of course and speed errors in running fixes is estimated and does not give very satisfactory results for astronomical and radio fixes, with the exception of methods giving an accuracy of 1 n.m. (e.g. Decca). Standard errors are referred to throughout.

This paper briefly reviews some of the research findings with respect to factors which affect the efficiency of radar operation. One of the most important factors in determining whether or not a radar target will be visually detected is the brightness of the radar scope. A simple method is described for setting optimum scope brightness. Visual search habits are discussed and the implications of such habits for the design of radar displays are pointed out. Reference is made to some of the design factors which determine the accuracy with which target range and bearing are reported. It is shown that human monitors perform less efficiently as a watch progresses and factors which impair or aid their vigilance are described. Finally, a brief account is given of illusions on radar displays.

Development of Dead Reckoning in the Air. Air navigation is the child of sea navigation. Hence navigation across the skies tended to follow the pattern of navigation across the oceans. It was built around the dead-reckoning plot, into which was fed all varieties of information. At take-off and landing, there was also a little pilotage, but this was hardly mentioned in polite air navigation circles.

In a previous paper (Journal, 11, 180), the author gave assessments of the forecast wind errors likely to be met with at any point on the globe by an aircraft flying for one hour. The present paper follows this up by giving the probable errors of 24-hour wind forecasts over routes of any length, and thereby assesses the probable unpunctuality of aircraft owing to wind forecast errors.

The paper outlines some of the factors to be considered in the design of any complete airborne automatic navigation and control system. It is pointed out that such a system should lower the work-load on the pilot or navigator as well as contributing to flight safety. Modern engineering techniques have produced a wide range of navigation devices, and their safe and economical use in a complete system involves the consideration of a control loop including the displays and the human navigator. The paper examines this navigation loop in some detail. Some simple and some more complex methods of securing safe operation are suggested.

Shortly after merchant marine radar came into use as a navigational aid, it was felt that some consideration should be given to the development of electronic aids for vessels too small to use radar, such as tugs and fishing vessels. It was obvious that the use of the microwave frequencies of radar would best suit the development of a small directionfinding receiver. The final system developed by the National Research Council used a compact 3-cm. pulse transmitter on a shore site, such as a lighthouse, or harbour breakwater. The antenna was designed to radiate energy across the water from all angles of approach.

The receiving equipment was built into a case on the back of a small radar antenna consisting of a six-inch slotted waveguide at the focal plane of a parabolic cylinder. The receiver used a radar crystal detector and transistorized audio amplifier for reception on phones or a speaker. The receiver could be hand held or mounted on a pelorus head, and rotated around the horizon to take a bearing on the shore transmitter. The signal from the shore is audible over an arc of only about six degrees, and can be maximized with an accuracy of ± 1 degree.

After the radar altimeter came into use at the end of the second world war, the combination with a pressure altimeter made it possible to measure horizontal pressure gradients, which enabled the navigator to estimate the geostrophic wind. The pressure gradient is directly related to the component of the wind at right angles to the track by means of the geostrophic relation and the navigator is thus provided with a method of evaluating one component of the drift. A position line of pressure combined with another position line (Loran, astro, &c.) enables the position of the aircraft to be determined.

This account of the recent International Conference on Safety of Life at Sea, has been written for the Journal jointly by Captain J. H. Quick, C.B.E., the Professional Officer and Chief Nautical Surveyor to the Ministry of Transport, who was a delegate to the conference, and Captain F. J. Wylie, R.N., the Director ofthe Radio Advisory Service of the Chamber of Shipping and Liverpool Steam Ship Owners' Association, who was an advisor to the British delegation. The account concentrates on those parts of the conference's work which will be of most interest to the seafarer, and in particular on the revision of the International Regulations for Preventing Collisions at Sea.

The Final Act of the conference, with Annexes, including the texts of the revised International Convention for the Safety of Life at Sea and revised International Collision Regulations, will be published shortly by the International Maritime Consultative Organization, from Chancery House, London.

The International Conference on the Safety of Life at Sea (1960) concluded on the 17th June. Forty-five governments had sent delegations and in addition ten other governments were represented by observers. The purpose of the conference was to revise the International Convention for the Safety of Life at Sea (1948) and the International Collision Regulations.

Dr. Ahrens's paper, which was presented in a more extended version at the meeting in Paris, describes a number of ways in which automatic processes may be applied to, or operated from, echo-sounders.

Knowledge of the depth of water is of secondary navigational value to the surface ship since (as compared with the submarine), she has no changes of course to make in the vertical direction. The present state of development of surface navigation systems makes the use of the depth as a method of navigation superfluous in all cases in which sufficient water is available, where there is no danger of grounding. It can, however, when the topography of the sea-bottom is known from accurate charts, be employed for checking and confirming the data determined by other forms of navigation.

This paper describes and discusses some of the techniques by which a moving inertial platform may be aligned by using external velocity measurements and also presents some of the major problems and error sources affecting such alignment. It is based upon the results of a 3-year study, of inertial and doppler-inertial navigation at the Naval Ordnance Test Station, China Lake, California, and, in general, applies to inertial navigation systems which erect to either the local level or the mass-attraction vertical. Although rudimentary derivations are made of the alignment techniques, the paper is largely nonmathematical for ease of reading. Emphasis is placed upon the major errors affecting the alignment. This paper describes and discusses some of the techniques by which a moving inertial platform may be aligned by using external velocity measurements and also presents some of the major problems and error sources affecting such alignment. It is based upon the results of a 3-year study, of inertial and doppler-inertial navigation at the Naval Ordnance Test Station, China Lake, California, and, in general, applies to inertial navigation systems which erect to either the local level or the mass-attraction vertical. Although rudimentary derivations are made of the alignment techniques, the paper is largely nonmathematical for ease of reading. Emphasis is placed upon the major errors affecting the alignment.

This account of the problems of navigating the Hustler, the Convair B-j8 supersonic bomber, was presented at the sixteenth Annual General Meeting of the American Institute of Navigation, held at the United States Air Force Academy in Colorado Springs on 16, 17, 18 June. It is published with the kind permission of that Institute.

In navigating high-performance vehicles with the precision required to get acceptable results, the individual is limited in his ability to assess all the data available about heading, speed, instrument readings, &c, and to act upon this information in sufficient time to get the job done. The same limitations apply to pilots when flight conditions approach the design limits of the aircraft. For these reasons the manual tasks required of the crew of the B-58 have been automated to the extent that transition to a missile environment seems almost complete.

The view is taken in this paper that an automatic navigation system should be capable of weighing up data and issuing instructions, in the same manner as a human navigator. Conventional information tends to offer static rather than dynamic data.

It is suggested that there are several stages of development towards completely automatic navigation: (i) a dynamic interpretation of the existing navigational situation, (ii) the automatic prediction of future situations, (iii) automatic navigational advice, (iv) automatic control of a ship under the supervision of a navigator. Such control would not take care of all situations but would be particularly suited to some; a list of the information likely to be required for presentation is given.

For entirely automatic navigation to be feasible, the whole of the process of transport at sea may have to be reviewed. It is suggested that the trend should be towards presenting error, rate of change and forecast data.