Professor M'Pherson's paper on ‘Education and the Sea’ does somewhat less than justice to the non-university sector of the British educational system; his Appendix A lists only two university undergraduate courses in nautical—maritime studies, whereas six such courses are offered by polytechnics and the first of these was approved ten years ago.

More recent developments have included a B.Sc. in Fishery Science; a number of degree courses in Environmental Studies and Geography, which contain substantial elements of meteorology, oceanography, cartography and marine surveying; and post-graduate courses in Shipping Management and in Hydro-graphic Surveying. These courses gain awards of a first degree or the diploma of the Council for National Academic Awards—a body which deserves much credit for encouraging experimentation in many ‘new’ areas of study.

In my article (this Journal, 1, 290, 1948) on The Provision for Astronomical Navigation at Sea I called attention (p. 302) to the possible advantages of dividing the standard PZS triangle of astronomical navigation into two right-angled (or quadrantal) triangles by a perpendicular (or quadrantal arc) from the pole P to ZS, or ZS produced. In particular I wrote ‘the method is one which might be further explored,…’; it is only recently that I have had occasion to do so. As far as I have been able to discover from the material available to me (including, by courtesy of Captain Charles H. Cotter, a copy of the typescript of his A History of Nautical Astronomical Tables), the only published method or tables using this principle is ‘Tables for the Abbreviated Computation of Zenith Distance and Azimuth of Celestial Bodies’, by Frane Flego (Split, 1957). Unfortunately, as pointed out by W. A. Scott and myself in a review article (this Journal, 11, 207, 1958), Captain Flego failed to overcome some of the technical difficulties of the method.

On 29 October 1969, taking the chair at a Duke of Edinburgh Lecture, the great educator Lord Butler commented, ‘…in my view, it would do a great deal of good if navigation could be considered an educational subject’. Indeed, we know that by 1700 the discipline was being taught in ordinary schools in this country, and it is perhaps worth repeating Isaac Newton's remarks on the Christ's Hospital syllabus: ‘he that is able to argue nimbly and judiciously about figure, force and motion is never at rest until he gets over every rub’.

The inclusion of navigation in the curricula of schools during the 17th century was for financial rather than for educative reasons. In those days, the master of a ship was responsible for its navigation and invariably had a stake in the marine enterprise. Thus he might make a small fortune in a single voyage. By 1800, the introduction of the limited liability shipping company and the growth of marine insurance were beginning to relegate the captain to the status of a hired servant paid the minimum wage. Navigation rapidly disappeared from ordinary schools and was taught only in the specialized nautical establishments. Nevertheless, it is worth noting that today, the mariner, the submariner, the pilot and the astronaut have restored to the subject its original lustre and the yachting explosion has given the discipline a wide appeal.

The idea of an ‘Altitude-Azimuth’ almanac is not new though most effort (see this Journal, Vol. 1, 185, 1948; Vol. 2, 285, 1949) has been concerned with the Sun and planets rather than the stars. For the stars the simple problem is that observations are recorded in mean time (say G.M.T.) whereas the positions of the stars depend on sidereal time (L.H.A. Aries) given by: L.H.A. Aries = G.H.A. Aries + west longitude. A full account of star tables (and diagrams) using a mean-time argument (and thus avoiding using the Almanac to give G.H.A. Aries) is given in ‘The Genesis of the E. A.N.T.s’ (this Journal, Vol. 6, 333, 1953).

If I may continue Mr. Harrison's analogistic extravaganza for only a moment, I would like to say that whatever smoke, haze or fog there may have been in his vicinity it has prevented him from identifying the target at which I and my colleagues have been firing. I must also say that his bland assumption of the superiority of his own gunnery is hardly complimentary to the highly qualified and experienced support without which, as he well knows, no simple sailor would venture into such a technical action.

None of my comments made upon this subject thus far have denied the existence of errors, cyclic or otherwise, in the sources from which the radar data is drawn; nor have I disagreed with the evidence and the theories about the size and character of such errors, and the resulting prediction errors they might cause, which have been adduced by the various experts (in electronics), under the conditions and within the limits which they postulate.

Most professional navigators would agree that navigation could play a useful role in general education. How are teachers to be convinced of this and how are they to be persuaded that its introduction is desirable ? If navigation is to be introduced as an academic subject into the school curriculum we must endeavour to remove the mystique with which it is often surrounded and dispel the suggestion that it is an art rather than a science. The notion that successful sailormen must have a seafaring background has been proved wrong time and again; let us also dispense with the misconception that good navigators are born with a gift similar to that of a homing pigeon. Man has a natural instinct to explore and find his way; the purpose of navigation in education should be to exploit and develop this natural instinct to the full.

Anyone who has read articles by the present writer about automatic radar plotters but has not handled at sea one of those systems in which the vector lengths are time-correlated and have a fine (minute-by-minute) adjustment, might think that they tend to exaggerate its importance as an aid to realistic and rapid appraisal. I hope that the pictorial presentation which follows may serve to reverse such opinions even though, with still pictures, it is difficult to create the sense of a continuous and rapid series of brief manual movements and mental assessments.

Far from needing elimination, as suggested by Riggs (Journal, 28, 143), the rapidly extensible vectors lend apparent acceleration to the radar picture, which always changes so slowly on the PPI, and thus convey with verisimilitude a sense of the predicted movement of the entire complement of echoes in their proper mutual relationship. Further, in situations demanding particular care or perhaps a change of course or speed, they can be used to give a rapid forecast of the probable duration of the emergency.

The use of the traverse table for plotting a bearing from an object outside the coverage area of the chart, as described by Pesi Sorab, suggests a graphical solution that might be preferred by some navigators. The method is analogous to advancing a position line by advancing the position of the object observed.

Well developed states have aircraft following airways in an orderly fashion under full positive A.T.C. control with good v.h.f. communications. The least developed states on the other hand are overflown by aircraft each on its own desired track with little if any control or communications. Many emergent states have taken the simplest step on the road to civilization in the air; they have specified mandatory airways or routes. In the most primitive situation aircraft, usually few in number, are protected against the risk of collision by natural dispersion. In other words the sky is so big and aircraft are so small that, provided they are spread out, there is very little risk of collision. The broadcasting of position reports by aircraft by v.h.f. on 126·9 m enables pilots to resolve any potential encounters that may occur. This situation occurs over the western Sahara.

The author's personal experiences under operational conditions have been with the CBM (Commodore Business Machines) S.R. 4148R, which has proved quite adequate for position comparisons in a surface warship fitted with a Magnavox satellite navigation system primarily used as a DR recorder. It is fed with ship's course and speed, corrections to the positions found being up-dated from satellite passes. Occasionally the criteria for up-dating from a satellite pass are not met and the system may run on DR for several hours without up-dates. Since the system is unable to compensate automatically for tidal or current drift and set or for leeway, the accuracy of the DR will deteriorate with age. The possibility of component malfunction, albeit temporary, may also contribute to DR error. In such conditions a series of astronomical observations is made; the calculator is capable of finding the average of such a series if required.

The small-craft navigator is beset by a number of problems in taking sextant observations; of these wave motion is foremost for the constantly changing height of eye makes the dip correction uncertain. One alternative is to take a number of sights and average the times and altitudes; but averaging angles, and especially times, is an error-prone occupation and if one of the sights is badly in error it will probably not be noticed, and will bias the resulting average. This would be avoided if all the sights were individually reduced and plotted, but the work involved is prohibitive. The method here described permits several sights to be taken and the individual position lines plotted, but requires practically no increase in work over a single sight. Inspection of the position lines will give a very accurate average and also indicate immediately if one of the sights was in error either in recorded altitude or time.

Charles Henry Lane was born at Hereford about the year 17J4 and at the age of 17 joined the Buckingham, 70 guns, Captain John Symons. In this ship he went to India, spending about four years in her, the first two as able seaman and the second two as midshipman. Returning home he joined the Enterprize, 28, Captain Sir Thomas Rich, spending about two years in her in the Mediterranean. Of these the first three months were as able seaman and the rest as midshipman.

In July 1777 he successfully passed his examination for lieutenant and in September received his commission to the Royal Oak, 74, initially as 5th lieutenant but rising to 3rd before, in April 1778, he was appointed 1st lieutenant of the Surprize, 28, Captains Robert Linzee and later Samuel Reeve. In that ship he served just over three years, each year making a voyage to Newfoundland and back from about June to November. While in those waters on the third voyage he was transferred to the Portland, 50, Captain James Luttrell. Then in September 1782 Vice-Admiral John Campbell promoted him to Commander and placed him in command of the sloop St Johns, which had been purchased locally. Exactly a year later the St Johns was paid off and Commander Lane returned home and was placed on half-pay.

When the scale readings of a sextant are suspected of error, or if an assurance of scale accuracy is needed, optical equipment for establishing angles is rarely available. Comparison with another sextant is possible, but if the arc between two stars were measured by bringing them into coincidence this could be compared with the calculated angular distance. To calculate the distance from a spherical triangle, knowing the stars' declinations and right ascensions, would be laborious and the refraction corrections would be difficult to apply—as they were in the old lunar distance methods. It is far simpler, in the northern hemisphere, to take Polaris as one of the two stars. If the other is within an hour of its meridian passage, so that the measured arc is approximately vertical, the usual corrections for refraction are sufficient. Also the calculated angular distance will then be simply 90° – δ, where δ is the declination of the star selected. This calculated distance is therefore subject to two corrections:

(i) refraction corrections for both stars,

(ii) a correction for Polaris not being exactly at the pole.

Mr. Podmore's article1 will certainly cause several people to write to you, as he is not suggesting the best use of the HP-35. One advantage of the Hewlett-Packard calculators is that one does not need to convert degrees and minutes to degrees and fractions of a degree before beginning the problem. Also one should use the cosine law again to find the azimuth. The usefulness of the calculator is that it can find with ease, both the calculated zenith distance and azimuth (no more tables!).

In an earlier paper the present writer drew attention to the distinction between mixed and aggregated distributions. Incidentally, two minor mis-statements in that paper should be corrected. The first sentence in the last paragraph of section 2 (page 72) should read ‘As σ2/σ1 (=k say) tends to either zero or infinity, X/σ increases indefinitely; whilst for k nearer unity, X/σ is smaller’. Also the last line of the Appendix should not terminate with ‘X/σ = 3·724’ but with ‘X/σ→∞’.

Mixed distributions arise when for example an error occurs either from one distribution with probability p, or from another with probability 1–p, as in a set of position line errors due sometimes to one and sometimes to the other of a pair of observers of differing precision. An aggregate distribution occurs when the error consists of, say, two sub-errors, one from each of the two distributions; as when Captain Flint marks the chart and Long John subsequently reads it.

Not surprisingly much of the work that has been done on collision at sea has involved the study of collisions which have actually occurred. There must however be a wealth of untapped data relating to ‘near misses’ judging by the hair-raising stories often told by ships' officers. These accounts, sometimes of ships passing one another so closely in fog that human sounds have been heard, are doubtless subject to embellishment but are, nevertheless, the stuff that nightmares are made of.

An interesting point which (perhaps predictably) features in many such stories is that the navigator presents himself as a victim of circumstances rather than one who has suffered the effects of a wrong decision. Curiously the ‘other ship’ sometimes shares this diplomatic immunity. Discounting ‘acts of God’ then, is there room for a category of encounter in which blame is minimized or even ruled out? In the discussion following a recent paper Captain F. J. Wylie states that between 1948 and 1966 most of the collisions he had studied which had come to court had, according to the Judge, been due to personal error (generally related to the Rules or misinterpretation of radar information). This no doubt reflects the situation in a true light provided one accepts that it may occasionally be necessary to distinguish between ‘personal error’ and blame. The two might not go together, for example, when the error is due to overloading of the human system or under-exposure to congested waters—a view which appears to be gaining support in some quarters.

Jocobrad (devised by K. D. Jones, G. R. Cowap and M. R. Bradshaw) has been devised in the light of research into the reactions and responses of mariners to various computer-based radar plotting and forecasting systems. It is a new concept in computer-based radar plotting systems which allows the operator to ascertain very quickly a safe manoeuvre in any encounter, having regard to every other target in the vicinity and to the time period associated with a contemplated manoeuvre. The system assumes that some means of echo filtering, acquisition and tracking is available and that a simple program calculates the true course and speed of every target which approaches within radar range. Automatic acquisition and plotting of every such target is essential as manual acquisition would detract from the more important features of JOCOBRAD. JOCOBRAD can be operated in one of three separate modes; useful information being conveyed by interswitching between true and relative motion while operating in two of the three.