In taking observations of the wind at sea, and in the study of the theory of air-navigation, it is often found difficult to give students a thorough conception of the relative (or apparent) wind. These notes are put forward to help instructors and others interested.

It is recorded that one of England's early Astronomers Royal went sailing on the Thames about 200 years ago, and what he learned that day made an advance in the science of astronomy. The Astronomer Royal was with some professional sailors, who must now be spiritual members of the Institute of Navigation. The learned gentleman was the Reverend Dr. James Bradley, who gave up his vicarage to become a professor of astronomy. The day in question had a wind of force four or five, but it was a steady wind, and the boat was tacking frequently.

At the masthead she wore a pennant, referred to by the doctor as a ‘vane’, and he noticed that it tailed away steadily enough down wind. But every time they went on to the other tack the direction of the pennant altered. The doctor was surprised that the wind should happen to alter every time they put about, but on mentioning this to the sailors he was told that the pennant only showed the direction of the relative wind, depending upon the direction and force of the true wind and the direction and speed of the boat, and their resultant changed every time they went about.

In his detailed and valuable account of the history of the Log (this Journal, 9, 70) Commander Waters is surely at fault as regards the part he ascribes to the Gresham Professor, Gunter. This eminent mathematician delighted in designing instruments with engraved scales, and at first issued the customary Description and Use in Latin, a sufficient indication that he wrote only for fellow scholars. Importuned probably by the instrument-makers, he later published English versions of the tracts (in 1623), and among the numerous ‘uses’ included a couple of chapters on those for navigational purposes.

Captain Wylie's paper on ‘The Region of Collision’ raises some interesting points but if one accepts the view that graphing of some sort is not wholly ‘academic’ the writer feels that there is an alternative graph which Captain Wylie has not mentioned and is worth considering.

As Captain Wylie has shown, the time-distance plot gives very little useful information except that it does keep prominently in mind the distance between the two vessels. The time-bearing plot is much more informative as to the element of danger present in the situation but if the time-bearing is the only plot kept then the fact that it shows no distance between the vessels is a serious disadvantage. The writer suggests that it might be worthwhile considering the advantages of plotting change of bearing against distance between the vessels, especially if this is done on a graph having precomputed curves for various minimum separations between the vessels. The sort of graph obtained is illustrated in Fig. 1 which shows a family of curves for vessels maintaining steady courses and passing at minimum separations of ½, 1 and 1½ miles, curves A, B and C respectively, on the assumption that plotting is begun from the point where the vessels are four miles apart.

Yacht and other small-boat navigators must often wonder what error in a d.f. loop reading on a radiobeacon may be due to heel. The error is in fact quite small, the maximum for a 25° angle of heel being 2°.8 when the bearing is quadrantal to the boat's heading, i.e. when the relative bearing is 45°, 135°, 225° or 315°. When the relative bearing is 0, 90°, 180° or 270°, i.e. when the beacon is ahead or astern or abeam, the error is nil.

Table I gives corrections to the nearest ½ degree, to be applied to the relative bearing of a beacon for 15° and 25° of heel. It makes no difference whether the boat is heeled towards or away from the beacon.

Professor E. G. R. Taylor's review, in the April 1955 issue of this Journal, of my book A History of Marine Navigation has passed unnoticed by me during a long absence, and I beg leave to offer a few comments.

The reviewer's introductory remark is indisputably correct; the title is not an adequate one. The Swedish title, literally translated, is From Noah's Dove to the Gyro-compass: navigational art, ancient and modern. In the earlier chapters I have not followed a chronological sequence but rather proceeded in order of the degree of complication of the methods used. In the later part of the book, I admit that there are many lacunae. However, as the reader will find, there was no ‘final jump’ to electronic navigation; there were several stepping-stones, viz. wind- and current-charts, the gyro-compass, radio-location, and echosounding.

Professor Taylor contends that the expression used to describe a course of action so simple as to leave no room for mistakes is plain sailing; that this is nautical in origin in that it derives from a simple or plain system of navigation based upon the use of a simple or plain (manifestly foolproof) chart; that this system of navigation was known originally as plain (simple) sailing—which expression she traces back to Richard Norwood's Doctrine of Plaine and Sphericall Triangles of 1631, and that it was sophisticated into plane sailing in the eighteenth century in the belief—which she holds to be erroneous—that the expression described a form of navigation based upon the use of a plane or flat chart on which the Earth was drawn as if the Earth and oceans lay in one horizontal plane area and not upon the surface of a sphere or, more accurately, ellipsoid; and, finally, that the Admiralty Navigation Manual is in error in teaching mariners that ‘to regard certain small triangles as plane… gives rise to the expression plane sailing, which is popularly referred to as if plane were spelt plain and the sailing free from difficulty’.

If a ‘sailing’ is defined as a means of finding by calculation, tables or construction, either: (a) the course and distance from one place to another, or (b) the position of arrival after making a given course and distance from a given position, then what is commonly known as ‘plane sailing’ is not in this sense, a sailing at all. ‘Plane’ or ‘Plain’ sailing according to modern as well as early usage involves the arguments, distance, d. lat., departuie and course angle, and in order to solve the problems (a) or (b), d. long., and either meridional d. lat. or ‘middle’ (not ‘mean’) latitude must enter the solution.

In Lieutenant-Commander Waters' paper ‘The Development of the English and the Dutchman's Log' (this Journal, 9, 70) there is an illustration (Fig. 1, p. 73) of the English log, reproduced from Champlain's Les Voyages de la Nouvelle France Occidentale. The device illustrated, though no doubt correct in intention, could not have performed the function stated, namely, of floating ‘vertically in the water presenting its full face to the ship's wake' (p. 74). This raises the suspicion that Champlain had not examined the log minutely enough, if at all, or at least had failed to instruct his draughtsman properly.