Having read with great interest the comments of Captain F. J. Wylie in the July 1973 issue of the Journal, and moreover found himself in complete sympathy with the views expressed, the present writer, who shares Captain Wylie's disappointment and apprehension with respect to the construction of the 1972 Rules, offers some further comments as follows.

There is no doubt that visibility influences the probability of collision and stranding and even a full moon, which gives a brightness of only 0·2 lux, seems to reduce the probability compared with a dark night; there is a much greater difference in the brightness by day (several thousand lux even with cloud) and at night. However the number of accidents in a seaway is influenced by many factors, such as traffic density, average speed, encounter condition, visibility, the helmsman's skill, availability of information &c. Of these factors, traffic density has most influence on the probability and this influence must be removed in order to study the influence of brightness. The present writer has shown that the danger of collision is roughly proportional to the square of the traffic density, and therefore proportional to the square of the traffic volume. Diurnal changes in the number of accidents and in traffic volume are therefore used to estimate the ratio of the danger by day and by night.

Captain Wylie's extensive and detailed criticisms of the Sailing and Steering Rules in the new Collision Regulations (Journal, 26, 365) were published in the January number of Navigation, the journal of the French Institute of Navigation, with an editorial note by Professor Hugon. The note and Captain Wyile's reply are given below.

The visual sense supplies a major part of the information necessary for avoiding traffic accidents and fog impedes this channel of information, even though the invention of radar has removed the limitation to a considerable extent. The closure of airports is caused mainly by reduced visual range and partly by low cloud, or by typhoons in Japan. The length of signal sections on the Japan National Railway (600 m) was determined from a study of the frequency of visual ranges. Nishikura and others have studied the influence of visibility on the probability of marine traffic accidents and conclude that the ratio of the collision danger with a visibility less than 1 km and more than 1 km is in the range of from 30 to 100. Wheatley et al. have also shown the risk of traffic accidents to be high in bad visibility in the Dover Strait.

The comments of Captain Maybourn on collision-avoidance systems in his paper ‘The Pay-off from Improved Navigational Aids’ (27, 133) prompt me to make a number of observations. What information, in principle, are we able to extract from a radar display ? This information will, of course, be degraded by the system errors, but that is another matter. Some of the following comments may appear trivial but it seems to me that they are of fundamental importance and escape sufficient emphasis.

When in 1877 Clements R. Markham edited The Voyages of Sir James Lancaster Kt to the East Indies he remarked that the first log-book with printed headings was that used by Captain Reddell on his voyage in the Samuel & Anna in 1702–3. He does not say that this became standard practice in the ships of the East India Company but it would seem that some of his readers thought that this must have been the case. In The Art of Navigation in England in Elizabethan and Early Stuart Times David W. Waters refers to the Samuel & Anna log and follows it with the comment: ‘The logs of British warships were still ruled and captioned in manuscript in the eighteenth century.’

While a great many areas in the world which contain shipping focal points have been designated as routing areas, and in most cases very successfully organized to ensure a safe flow of vessels through them, one area remains outstanding without any attempt having been made to regulate or control the traffic. This is the stretch of waterway in the Malacca and Singapore Straits from One Fathom Bank, lying some 28 miles to the westward of Port Swettenham, to Remunia Shoals off the SE. corner of Malaysia, a route containing many navigational hazards ranging from shoal-water to periods of seriously reduced visibility, and being used by high density traffic including vessels of every type and size.

In G. R. Spooner's interesting if not important article (27, 265), a situation was described wherein a risk of collision was created by basic non-adherence to the Rules. Firstly, the intention of the officer-of-the-watch to alter course to port was wrong, whilst that of the Master, substantially to alter course to starboard, was right. Secondly, the action of the non-burdened vessel was in error in as much as she should have stood on in anticipation of the burdened vessel making a decisive turn to starboard. The fact that at the precise moment of ordering this turn the other ship altered to port need not have necessarily prevented the burdened vessel from altering to starboard and ‘taking a turn out’—a procedure adopted in many such instances as that under discussion.

The prudence of determining the best windward and running courses for sailing yachts can be seen from Fig. 1 in which the heart shaped curve represents a polar diagram of yacht performance with respect to the true wind direction. It is a diagram of yacht velocity V and the angle α between the yacht's track and the true wind direction. The gap in the curve dead to windward is an area over which no performance is possible, whereas any destination lying outside this zone can be reached directly; there is only one sailing angle at which a destination lying between X and Y can be reached the quickest. A similar situation occurs on the running point of sailing where the curve may have an inflexion, i.e. there is profit in tacking a course downwind.

In the old Cunard Line the log-books on the passenger steamers had a K and an F column on the left-hand page of each opening. This was taken to mean, and in fact was so used, as Knots and Fractions (not fathoms as in W. E. May's article, p. 116, Vol. 27).

Each noon the junior third officer filled in the columns for the previous 24 hours, and each hour had the nautical miles and the fraction thereof expressed in cables which had been steamed, entered in the appropriate box. Thus the figures in the F column never exceeded 9.

As part of their navigational outfit many of the ships in service today are equipped with Sight Reduction Tables (A.P. 3270 = H.O. 249), and many navigating officers include amongst their personal kit a Rude Star Identifier (H.O. 2102), or some similar device according to individual preference, for the purpose of obtaining the approximate altitude and azimuth of a selected body as a preliminary to making observations, particularly for star sights. However, for the benefit of those without such means at their disposal and as a matter of interest for others, the use of ABC tables for this purpose is suggested. The origin and author of this method are not known and it does not appear to be included in any of the navigational manuals which have been in circulation in recent years, but there was reference to it by Capt. S. T. Lecky in his General Utility Tables first published in 1897, a reference for which I am indebted to Capt. C. H. Cotter.

Of immense importance to nautical astronomers are tables of trigonometrical functions. The history of these begins with the table of chords first suggested by Hipparchus two centuries before the beginning of the Christian Era. The earliest table of chords extant is that computed by Ptolemy (fl. c. 150 a.d.) whose table, true to the sexagesimal tradition, is based on the division of the radius of a circle into sixty parts. The first table of half-chords, or sines, is supposed to be of Indian origin and to date from the sixth century; but credit for being first to use a table of half-chords for solving spherical triangles belongs to the Arab mathematician Albategnius who flourished during the tenth century. The first printed table of sines, according to De Morgan, is a small work giving sines to each minute of arc from 0° to 90°, undated and unsigned but evidently published before 1500.

It is some considerable time since the questions associated with irradiation were considered in the pages of the Journal. Indeed the interesting and practical paper by Captain Brett Hilder is the latest considerable contribution to the Journal and this appeared no less than twenty years ago. It is only in comparatively recent times that nautical astronomers have been provided with an authoritative irradiation correction of any sort. This, which applies only to observations of the Sun's upper limb, was incorporated in the altitude correction table for the Sun and appeared annually in the Nautical Almanac after 1953, the year of Hilder's paper, but was discontinued after 1969.