This paper is a sequel to the author's paper under the same title published in the April issue of the Journal.

The estimation of collision danger is often required by harbour authorities and others for planning fairways or for increasing the safety of navigation. Fujii1 gives an approximate formula for the probability of collision in a waterway where the density of traffic, the size distribution of ships and the average speed are known. Fujii's formula is however only applicable where the traffic has been surveyed and traffic patterns are well known. Some simple method is required for estimating collision danger, especially for harbours where traffic patterns are complicated and the information available on marine traffic engineering is comparatively small.

Reduce speed, stop engines, navigate with caution. There can be little doubt that there will be very few legal obligations that are so consistently ignored as Rule 16 of the Collision Regulations at Sea. Yet the circumstance to which Rule 16 applies, reduced visibility, is only one of the causes for reducing speed and the factors involved in the decision to accept delay may prove interesting and revealing. It is the purpose of this paper to stimulate further investigation into the subject, an investigation that will certainly require the cooperation of ship owners associations and master mariner organizations and which could well be carried out by the Marine Science Departments of such advanced educational institutions as for example University of Wales Institute of Science and Technology in Cardiff.

Captain S. T. L. Lecky, in his famous Wrinkles, wrote with derision in his reference to so-called ‘short-methods’. He warned his readers to ‘beware’ of these:

They generally only look short [wrote Lecky] because good care is taken to apply the various corrections beforehand, and the unsuspecting reader is deceived of this device.

As a case in point Lecky considered the ‘small but expensive pamphlet by Mr. Martelli’, to support his derogatory remarks:

When his so-called ‘short-method’ is overhauled and compared with Raper, we get the following startling result:—Martelli, 56 figures and five logarithms, against Raper's 59 figures and five logarithms, required to produce the same result. So that by the first method we have the enormous (!!!) gain of three figures. Furthermore Mr. Martelli's pamphlet contains several glaring errors which makes one rather dubious about the general correctness of the tables, although (for all the writer (Lecky) knows to the contrary) the mathematical principle of his method may be correct enough.

Like any other vehicle a ship needs to be started, stopped and steered safely; the art of doing this is sometimes called ship handling. Successful ship handling depends upon three distinct operations: acquiring the right information, making the right decisions and performing the right manoeuvres. In this paper we assume that the Captain has all the facts and knows the right thing to do, and examine the physical ability of the ship as a mechanism to respond to his will.

Readers of Captain Cotter's very interesting article ‘A Brief History of the Method of Fixing by Horizontal Angles’, may be interested to know that the possible use of the resection or three-point problem was appreciated by English mathematical practitioners of the seventeenth century.

Explanations have been given by John Collins, F.R.S. (1625–83), and Edmond Halley, F.R.S., Master and Commander, later Captain, Royal Navy and Astronomer Royal. It seems probable that Halley actually made some use of the principle when he charted the English Channel.

Dr. Angus Armitage and Dr. A. H. W. Robinson have explained Halley's method.

W. Palmer's note on Standard Time (this Journal, Vol. 25, page 535) may mislead some readers. He tends to confuse ‘Time’, as an abstract philosophical concept, with the measures of time, or time-scales, used in practice by astronomers, navigators, surveyors, physicists, electronic engineers and the general public. Such measures of time may be based on any recurrent phenomenon, whether uniform or not, ranging from the growth of coral to atomic transitions; and, for this reason, those professionally concerned use precise terminology to distinguish the many time-scales in current use. Unlike Mr. Palmer, they do not use ‘Time’ for a particular time-scale; and, for example, they restrict ‘standard’ to its generally understood application to the meridian to which the legal time of a country is referred. There are a number of factual errors arising from this confusion (e.g. G.H.A. Aries is equivalent to sidereal time) which need not be elaborated here.

Recent work on marine traffic engineering in Japan was reviewed in four papers published in this Journal in 1971. In the present paper, which may be regarded as a sequel to these, Professor Makishima offers some theoretical comments.

This paper discusses the drawbacks of observational methods of analysing navigational errors and shows the advantages of a synthesizing technique, whereby the effect of any change in the magnitude and distribution of a component error upon the overall resultant error can be evaluated and examined. To this end a computer program has been developed which is capable of accepting both analytical and numerical statistical distributions, representing errors in the components, and combining them to yield the overall effective error. A new error distribution better representative of many navigational error distributions is introduced. The work described is applicable to the investigation of any error which depends upon the interaction of many component errors and is not restricted to the navigation field. An extension of the method to mixed samples is indicated.

The paper describes the final step in the development of a universal computer program aimed at synthesizing navigational errors in order that they can be used in evaluating their effect on any proposed A.T.C. system. The investigation was commenced at the College of Aeronautics in 1963 and has been the subject of several published papers during the interim period.

As a passenger on the Queen Elizabeth 2 on a westward crossing of the Atlantic in late May 1972, I took sextant sights with my standard marine Plath sextant and also with the ‘bubble’ attachment for this instrument. Inspired by Francis Rogers' discussion of the development of bubble sextants, my project was to compare the accuracy of the bubble sights with that of the conventional marine sextant sights, which require the horizon.

Few will deny the merits of the knot as a unit of speed. It does in one syllable what all other units of speed take three or more to do. It is accepted and used by a great many countries, including those like France which show a general preference for the metric system. Aviation has taken to it as well as shipping. It is not therefore surprising that the full acceptance of the Système International d'Unités (or S.I.) is meeting with some opposition when it offers to supplant the knot.

Details have been given in this Journal (Vol. 25, pages 3 2–42) of the new system of Coordinated Universal Time (U.T.C.) introduced on 1 January 1972. In accord with the agreed recommendations a positive leap-second was introduced at midnight on 30 June 1972 when the value of U.T.1–U.T.C. (DUT1) changed from −0s.64 to + 0s.36. However, the Bureau International de l'Heure has now announced that another positive leap-second is to be introduced at midnight on 31 December 1972, when (according to current estimates) U.T.1–U.T.C. will be about −0s.2; on 1 January 1973 DUT1 will thus be +0s.8, in excess of the maximum permitted value of of 0s.7.

The heart of an inertial navigation system is the Inertial Measuring Unit (I.M.U.) as this carries out the fundamental tasks of measuring the vehicle acceleration and providing a spatial reference. The I.M.U. thus determines the system performance and accuracy; it also accounts for about two thirds of the initial cost of the system and is a major factor in the cost of ownership.

Up to now the majority of IN systems have used a stable platform I.M.U. where the gyros and accelerometers are mounted on a gimbal suspended platform which is servo controlled from the gyros. This has greatly eased the task of developing suitable gyros of the required accuracy, as the gimbal stabilization system isolates the gyros from the angular motion of the vehicle and greatly simplifies the subsequent computation in terms of axis transformations; it provides a direct read out of the euler angles—heading, pitch and roll. However such a system is inevitably mechanically complex and its ultimate reliability is constrained by such components as slip rings, servo motors, synchros, resolvers, encoders, gimbal bearings &c.

Henry Raper (1799–1859) the eldest son of Admiral Henry Raper (1767—1845) retired from active service in 1825, from which time he devoted himself to nautical science. He served repeatedly on the Councils of the Royal Geographical and Royal Astronomical Societies and for many years was Secretary of the Royal Astronomical Society. His Practice of Navigation and Nautical Astronomy earned him the award of the Gold Medal of the Royal Geographical Society.

The velocity of sound in water is a function of temperature, salinity and pressure. When an echo-sounder is used to make depth measurements, the time taken for a pulse to reach the ocean bed and return is measured. The machine is set to a standard sounding velocity, usually 800 or 820 fm/second (1463/1500 m/sec), and a nominal depth is recorded. This depth should then be corrected for the properties of the water. The ‘Tables of Velocity of Sound in Pure Water and Sea Water” by Matthews are commonly used for this purpose. Matthews compiled his tables using soundings taken by a number of research ships all over the world. He divided the oceans into 52 areas, and for each area calculated a set of depth corrections from 200 m to the ocean bottom. Since the tables were published more accurate measurements of velocity as a function of temperature, salinity and pressure have been made. There are also many more observations than were available when the tables were compiled. However, as these tables are in general use, no attempt has been made in this paper to change the corrections, and any computer results are therefore no more accurate than the tables.

When correcting depths manually aboard ship, the following procedure is followed. The depth on the echo-sounder is noted and entered into a log book. The position of the ship is known using some standard method of navigation such as satellite, Decca, Loran or radar.