Having some time ago been requested to design a sundial for the Hydrographic Institute of Genoa (Fig. 1) I went through various books and found that the methods indicated for drawing sundials were all based on graphical constructions. Although quite interesting these methods have the inconvenience of all graphical solutions, that they require constructions which, besides being complicated, turn out to be rather inaccurate, especially when lines cross at small angles, as inevitably happens outside a limited central area of the drawing. To avoid this I worked out a numerical system, related to the familiar methods of astro-navigation, which, by means of simple formulae, gives the coordinates of the points necessary to design a sundial. As the bibliography I examined is, of course, limited, I am not in a position to state whether this method of calculation is new or not; I describe it here hoping it may interest people who have sometimes wondered how sundials are made.

Whilst steaming westwards at night along the coast of South Africa, echoes were received on the radar screen that gave the impression the vessel was about twelve miles off the coast. At the time, the vessel was about thirty miles S. by W. of Seal Point.

The radar set, a Decca Mk. 12, was operating on the twenty-five mile range. It was receiving strong echoes from a sighted ship seven miles away on the port quarter. The set had been switched on to clear an unlit buoy fitted with a radar reflector. The position of the buoy was about ten miles WSW. of the vessel's position.

Captain Wylie begins his paper by evoking a philosophic vision: a planet full of colliding ships, all staffed by mathematicians. He concludes by rejecting, on behalf of mariners, the help of the mathematicians. The maritime record also evokes a vision: the colliding ships are somewhat fewer, but the main difference is that every one is staffed by persons other than mathematicians. The latter vision rather implies a need for help from somewhere.

Recently I was asked to assist the engineers in my company (a Canadian electronics firm) devise a method for using radiation from the Sun to check the alignment of heavy ground radar sets to within very fine tolerances. The degree of accuracy would have to be better than five minutes of arc in azimuth for search antennas, and three minutes of arc in elevation angle for height finding antennas. Solar radiation in the microwave region of the radio frequency spectrum would be used as a reference. The antenna reflector would be rotated in azimuth and elevation until maximum solar radiation was reflected into the waveguide horn and thence to the radar receiver. The moment peak detector current was obtained, the antenna would be locked in position and the exact G.M.T. noted. Normal astro-navigation calculation methods and tables would then be used to calculate the Sun's true azimuth and elevation angle, which would be compared with that measured by the antenna to determine its accuracy.

Since none of the engineers had previous navigation experience, they had run into difficulties when they tried to devise a method for calculating the Sun's position to within the requisite accuracy limits.

The first difficulty was the fact that most antenna calibrations would be performed by field technicians having no knowledge of astro-navigation tables and calculation methods. They would be at extremely remote radar stations across Canada and thus would not have an opportunity to ask questions if our instructions proved ambiguous.

As Mr. Sadler points out, there can be no conflict between mathematicians and navigators, provided the mathematicians have adequately fulfilled their job. If, however, the navigators fail to follow the mathematics, or even to check the results by taking a few examples, then there will be plenty of misunderstandings; to bring ‘philosophy’ into the discussion is to return to the attitudes of the Middle Ages, and to obscure technical issues which are perfectly clear and simple.

Passenger and cargo liners sailing on regular routes follow tracks for a given voyage, taking account of the various seasonal conditions which may apply, and masters of these ships, with many years experience in a particular trade, can decide without great difficulty the most advantageous track for their ship when planning a voyage for a given time of year.

In the transport of oil, on the other hand, it is not common to employ ships on regular voyages, and the great majority of tankers are employed in world-wide trading, so that although a particular oil company may have a number of ships constantly voyaging on a particular route, a high degree of flexibility is maintained and ships are regularly changed from one route to another. This means that the tanker master is called upon to consider the requirements for optimum routing of his ship on any ocean voyage. Further, he is often given his orders with fairly short notice and, in some cases, he may have his destination changed either at the last moment or during the voyage, leaving him little time to consider the many factors which have to be taken into account when planning the best route for the voyage to be undertaken.

The imaginary question I propose to answer in this address is—how does it come about that a person with such a very ordinary sort of intellect, and certainly with no particular flair for mathematics, should be the author, or nominal author, of such an imposing publication as a volume of nautical tables?

To build up the background to the story briefly let me explain that in my training ship days I received the impression that a ship's position was found by mathematical calculations. True, we knew that sextants and chronometers were necessary instruments in the scheme of things; but they only seemed to supply certain ingredients to the calculations that ultimately produced one of the components, latitude or longitude. It was when I was consigned to a stretch of service on the North Pacific in 1927 that, for something to do, I decided to try and improve my limited understanding of astronomical navigation. In the volume of Raper's Tables which I had always used there was an appendix by the Naval Instructor William Hall which explained what was then called by the Navy ‘The New Navigation’, and gave four-figure cosine-versine tables for the work. It was in reading, and re-reading, and thinking about Hall's marvellously lucid explanation of the St. Hilaire process that the light suddenly burst upon me.

‘The mark of a good navigator is not so much his ability to obtain accurate information as his ability to evaluate and interpret correctly the information available to him.’ So writes Captain Alton B. Moody, U.S.N.R. in the course of an interesting correspondence in the February number of the U.S. Naval Institute Proceedings. In the August 1961 number (page 132) Captain Robert Lee Rhoads, Jr., a shipmaster, suggests that the ‘cartwheel’ set of astro-sights, where four position-lines intersect each other at angles of about 45°, is inferior to the square where the position-lines intersect at approximately 90°, which gives a more reliable fix. One of Captain Rhoads's illustrations shows a case of a 4-minute systematic error in a ‘cartwheel’ fix giving a position 6 miles in error, where the same error would have had no effect on the position interpolated from four sights taken at 90° to each other.

Over a decade ago there was some controversy about the selection of an international standard airfield approach lighting system. At a very late stage, the R.A.E. produced a visual simulator of great simplicity on which any administrator could fly approaches using any of the rival systems. His performance could be checked but, what is far more important, he obtained personal and realistic visual experience. If this simulator had been available in 1945 it might have saved many millions spent on the flight evaluations of the rival systems and years of international conferences.

In the present controversy on collision avoidance regulations in the air and at sea, time and wealth could be saved by the creation of a visual and dynamic simulator in which all persons attending symposiums on collision problems could obtain synthetic visual experience of the present day avoidance regulations and of the new conventions proposed by E. S. Calvert and S. H. Hollingdale.

Curiously enough, such a simulator would not be very costly. It would consist of a very large hangar and a number of small electric two-seater cars somewhat similar to those known as ‘Dodgems’ often seen at Funfairs.

It would be used quite effectively for simulating air traffic as a high percentage of all near-misses occur in the horizontal plane but it would be desirable to gimbal the cars so that they can bank when turning.

Simulation of nocturnal traffic requires only black-out and navigation lights.