A recently discovered ‘Navigational Notebook’ contains an interesting account of day-to-day navigation during the early part of the eighteenth century. The document was brought to light by Mr. J. R. Timms, a student at the School of Navigation of Southampton University, whose father discovered it in a bank at Ventnor, Isle of Wight, its depositor long deceased and no longer known or traceable. The date of the manuscript is uncertain but references to John Robertson's Elements of Navigation and Archibald Patoun's Epitome seem to place it after 1730. However the account of actual navigation is given in the journal of a voyage, in 1704, from the Lizard to Madeira, which is reproduced in the Notebook. It seems likely that the author, John Wilson, eventually came ashore as an instructor in navigation (and probably mathematics) and copied out the journal from one of his earlier voyages for the benefit of his pupils. Whether this is a later work by the John Wilson referred to in E. G. R. Taylor's The Mathematical Practitioners of Tudor and Stuart England is not clear.

In December 1940 some 500 captured allied seamen, including the author, were transferred from a German commerce raider to an ex-Norwegian tanker under the command of a German prize crew, with the original crew still aboard. The ship was in the Southern Indian Ocean—in about S. 32°, E. 70°—just cruising about aimlessly; apparently awaiting orders to proceed. The captured Chinese and Indian ratings were accommodated aft somewhere, the shipmasters and passengers were housed amidships; and the rest were forward.

This vessel was very effective for the purpose to which it was being put as it was easy to position machine guns to cover all ways of approaching the midship house; in particular the fore part of the bridge was a solid wall right up from the foredeck to the high dodgers. Nothing could be seen of those on watch and no bells were struck, so that the officer prisoners were denied the sight of anything which might help them to guess what was happening, and any sound to give them an idea of the passage of ship's time.

Although no details of the proposed artificial satellites are yet available, the idea is by no means new, and it seems likely that any successful experiment of this kind must follow the plans already outlined by Professor S. F. Singer of Maryland University. At the Astronautical Conference at Zürich in 1953 he gave details of a small spherical satellite, weighing only 100 lb., which would revolve about the Earth in a period of 90 minutes at a height of 190 miles above the surface. In collaboration with Arthur C. Clarke and A. V. Cleaver of the British Interplanetary Society, Singer called this instrument MOUSE (Minimum Orbital Unmanned Satellite Earth) and proposed that it should be launched as a three-stage rocket with an initial all-up weight of about 35,000 lb., and a thrust of 65,000 lb., which is very little different from the performance of the V2 rocket. The first step would take the rocket vertically through the lower atmosphere and then turn over to begin the inclined part of its flight; the second stage would come into action when the first had burned out, and complete the climb to give the correct altitude and direction of motion. The third stage would merely give sufficient boost to attain the required speed, which is about 17,400 m.p.h. At the moment of cut-out (controlled from the ground) the nose tip would open and release the satellite. This would take the form of a sphere, about three feet in diameter, spinning so as to maintain a constant orientation, and packed with instruments. The spin axis, parallel to the Earth's surface and perpendicular to the direction of motion, would point to the Sun, so that one half of the sphere would be strongly heated by the Sun's rays, and the other hemisphere would be extremely cold. Power would be obtained from a new type of solar battery, and the readings of the instruments would be radioed continuously to Earth.

The first scientific instrument to be designed specifically for use at sea was the mariner's astrolabe. The cross-staff or Jacob's staff had been used by astronomers since the Middle Ages, and the magnetic compass used by navigators had long been familiar as an aid to land travel, a means of setting portable sundials, and in the east, a device for divination.

In June 1955, Canadian Pacific Airlines inaugurated a regular scheduled service between Vancouver and Amsterdam via the polar route. The Company had a wealth of northern experience which was of immense operational value on the polar route. In addition to its overseas services, C.P.A. has operated regular flights for many years to far northern parts of Canada and some of the group of companies which amalgamated to form C.P.A. in 1942 had arctic experience dating from the days when commercial aviation was in its infancy. One aspect of navigational experience which has helped its navigators on many occasions has been the map reading talents of the former bush pilots who show an astonishing ability to locate themselves visually over country which is mostly water, and where one lake looks much like every other lake.

When, over twenty years ago, Admiral J. A. G. Troup wrote his admirable book On the Bridge, he said that he had searched his soul to find a reason for burdening even one of his brethren with his observations on handling ships. That his diffidence was quite unfounded is, of course, proved by the fact that his book, at any rate in naval circles, has become a near classic. The fact is that there is remarkably little real opportunity for junior officers at sea to gain experience in the actual manœuvring of ships in restricted waters, and aspiring shipmasters will seize with avidity any crumbs of knowledge which may fall from the table of the experienced. And, while it is clearly true that much practical experience is essential, that experience will be dearly bought and largely wasted if the underlying principles are not clearly understood, and unless the practitioner learns what he must look for, and what will affect the issue. How often has one made, or heard others make, some such remark as ‘and then the wind caught her bows and I couldn't do a damn' thing about it’. But on reflection one realized that the observation should have been qualified by the admission that one had got into what, in sailing parlance, is known as ‘the hopeless position’, and should never have been there at all if a proper appreciation of the problem had been made.

Lieutenant-Commander Bini's interesting paper on the use of bisectors shows the trap open to the believer in the 3-line fix and goes on to show the M.P.P. when four lines are used. However, as the ideal for the four lines is to have each at 90° apart, an error in either one or two lines provides the observer with an ellipse for the M.P.P. and is for practical purposes but a variation of the 3-line cocked hat circle of M.P.P. and little appears to have been gained by the working of the fourth line.

Throughout the history of aircraft design, a trend that has remained quite constant up to the present time is the steady increase of wing loading with successive types. This feature with its consequent raising of stalling speed, and therefore landing and take-off distances, has resulted in techniques rather more scientific than those used in the early days of civil flying. With take-off distances of anything up to 6000 feet, the pilot in deciding whether a particular airfield is adequate for a given aircraft is no longer the sole arbiter; the rule of thumb must give way to the slide rule.

The pilot is, of course, still responsible for the safety of a particular operation, and to help him in this respect, performance information for his particular type of aircraft is supplied in graphic form with the safety factor already built in. It is the purpose of this paper to explain why and how this is done.

I am of the opinion that the figures in Mr. Durst's paper have been obtained primarily from the main civil operators and that the results are not necessarily valid for military aircraft. Before accepting Mr. Durst's paper as a reference work for all aircraft it would be necessary to know the answers to the following questions:

(a) Were the navigating officers of each aircraft experienced practising navigators or were they perhaps ‘third officers’ occupying the seat to obtain navigational experience?

(b) Were the aircraft equipped with and did the navigators use Loran equipment? If so, were the operators adept at using sky-wave signals?

(c) Were the aircraft fitted with air mileage units and air position indicators?

(d) Were the aircraft fitted with remote indicating compasses with performance characteristics equal to those of the G3 and G4B (CL2)?

(e) Were the radio compasses swung at regular intervals?

When I was a member of the Transport Command Examining Unit (1949–51) one of my tasks was to assess logs and charts of experienced navigators flying the main trunk route from the United Kingdom to Australia. I can say quite confidently that as far as the 200 kt. aircraft are concerned a D.R. error of 8 n.m. per hour proved to be an excellent working approximation. Seldom did circles or ellipses of errors around fixes and D.R. positions not intersect or give a ‘sensible’ wind.

Air traffic controllers separate aircraft on the North Atlantic with reference to dead reckoning (D.R.) positions of aircraft. Two such D.R. positions are transmitted to a.t.c. regularly from each aircraft, one usually 10 to 30 minutes following a fix, the other one hour's run farther ahead. The accuracy of these positions is important, since it has a direct bearing on horizontal separation standards and optimum time between position reports.

‘The Earth is an ellipsoid’, says the Admiralty Navigation Manual firmly, although in a later volume the expression is softened to ‘approximately ellipsoidal’, For in fact, as was implied by Captain Topley, the exact shape of the Earth is not yet known. Nevertheless, for nautical purposes it appears sound teaching practice to consider it a perfect sphere and then explain the departures of the nautical mile or minute of arc from its mean value. Nor need one quarrel with the Manual's statement that ‘to regard certain small triangles as plane is not to disregard the initial decision to regard the Earth as a sphere’. But the writer next indulges in an historical aside which cannot be allowed to pass. ‘This assumption (he says) gives rise to the expression plane sailing, which is popularly referred to as if plane were spelt plain and the sailing were free from difficulty’. But this is to put the cart before the horse. ‘Plain sailing’ was the original term, and it was only sophisticated into ‘plane sailing’ during the eighteenth century by teachers of navigation among whom John Robertson was the chief. Robertson was master at the Mathematical School of Christ's Hospital towards the middle of the century, and afterwards taught at the Portsmouth Naval College, finally becoming Librarian to the Royal Society. His Elements of Navigation was considered authoritative and ran into many editions, a later master at the Hospital, James Wilson, prefixing to it a Dissertation on the history of navigation which was also accepted as definitive. It is in this volume that we read: ‘Plane sailing is the art of navigating a ship upon principles deduced from the notion of the Earth's being an extended Plane. On this supposition the meridians are esteemed as parallel right lines…’, and the author goes on to what he terms the Plane Chart, with its equally-spaced meridians. There is little doubt that his passage is the source of the theory taught to modern sailors that ‘Plain Chart’ is a corruption of ‘Plane Chart’, while the latter was drawn by people who believed the Earth was flat. Actually we have only to go back a generation from Robertson to find an almost identical description of the chart—actually an equal-spaced conventional cylindrical projection of the sphere—but with the addition of the words ‘The rectangle formed by these meridians and parallels they (i.e. mariners) call the Plain Chart’. This was said in 1714 by John Wilson, a teacher in Edinburgh.

With modern sight reduction tables, new techniques of working out astronomical observations and the recent changes in the Abridged Nautical Almanac, it has been found that many of the hitherto necessary mathematical tables included in the majority of the nautical tables are now no longer used in the Royal Navy. An analysis in the Royal Navy's navigation school, H.M.S. Dryad, has revealed that only about a third of the tables in each of the three most used books of nautical tables, Burton's, Inman's and Norie's, are used in the Royal Navy.

The method described in Schütte's paper is very ingenious and evidently simple in its application; it depends on solving two pairs of equations of identical forms (in terms of different variables) by simple inspection of diagrams constructed in accordance with the first pair of equations. In his paper the author states, with reference to a figure and without proof, the two pairs of equations referred to. It is obvious that the fourth of Schiitte's equations (p. 310) is inconsistent with the figure and with the example he gives on the determination of altitude and ‘azimuth’ (pp. 312, 313). The trouble arises partly from misconception as to the use of the term azimuth. The method deserves a more detailed explanation of the derivation of the formulae and their application.

The parallel cursor and disc. In the Royal Navy manœuvring problems are normally worked out on the Battenburg Course Indicator which gives a mechanical solution of the speed/distance triangle (Fig. 1). A similar device for direct use on the PPI face can be made by engraving parallel lines on the rotatable PPI mask and attaching two perspex vector arms to the centre. Although developed primarily for manœuvring purposes this idea can be put to several purely navigational uses and from it have sprung two valuable adjuncts to the PPI: the parallel cursor and the fixed plotting surface (or disc).

I think Professor Taylor and I are at cross-purposes in our discussion of the influence of scientists upon the art of navigation before the nineteenth century. Dr. Freiesleben expressed the view that until 1800, ‘when our technical age began’, there was a big gap between what interested scientists and what the seaman could understand and apply, that men of science were too remote from practical requirements. The implication was that scientists were not concerned with seamen's problems nor seamen with obtaining scientific help. I pointed out that whatever the situation in the eighteenth century might have been, in the sixteenth and early seventeenth centuries improvements of a radical nature were made by scientists, working with and for seamen, in the means of practising the art of navigation, in particular by English scientists working in the latter part of the period under the aegis of Gresham College and the East India Company. This is historical fact, little known perhaps, but none the less fact. I certainly never intended it to be understood that the seaman-scientist relationship peculiar to this period and resulting in such important developments typified, to use Professor Taylor's expression, ‘the degree of cooperation between sailor and scientist prior to the nineteenth century’. I intended it to be understood as being descriptive of the situation or relationship peculiar to the period in which it occurred, roughly 1550–1640 and more particularly 1598–1637.