When in thick weather and trying to fix our position by two bearings and the run between, it is well to take as many radio bearings as practicable and depend on the evidence of several rather than on that of only two of them.
But how best to evaluate this evidence? We cannot well stop the ship to take several bearings at one place, average them, and then run on to repeat it at another Place; and thus get the run between two bearings each of which is the average of several. What we actually get is a series of bearing lines at short and probably irregular intervals; and in most cases the distance offshore obtained by using any two of these lines and the run between them will vary somewhat from the result obtained by using some other pair of them.
Thus the first and second bearings may apparently set us inside our course, the second and third outside of it, and the first and third right on it. So which is right anyhow? In the end we probably use the "seaman's eye" to strike a general average amongst them, or else choose some two lines at the beginning and end of the series at a good angle to each other and pin our faith to them, more or less neglecting the evidence of all the intervening ones. The following simple scheme may be used for evaluating quickly and easily the evidence of a series of such bearings.
Take a piece of transparent celluloid (obtainable from any auto-top repair shop), and cut out a rectangular strip or rule about 2 inches wide and anywhere from 8 to 12 inches long. With fine emery cloth or sandpaper roughen a margin about an inch wide along one edge so that it will take pencil marks without losing its transparency. That is all there is to the rule.
Then use it as we have always been taught to use a piece of tracing paper for establishing position by a line of soundings (for which purpose it will also serve admirably). As each observation is taken plot the bearing with the time on the chart, and in addition make pencil marks on the edge of the rule corresponding in distance from each other to the ship’s run between bearings. Mark these also with the times. When two or three bearings have been taken apply the rule to the chart and adjust it parallel to the course, in and out, forward and back, until the marks and times on the rule are nearest to coincidence with the bearings and times plotted on the chart, thus getting an approximation of your position. As additional bearings are received continue the process, which becomes increasingly accurate as more bearings are included.
A pair of parallel rulers held against the back edge of the celluloid rule will facilitate the operation. The celluloid is easier to handle than tracing paper, and the pencil marks can readily be erased from it after use.
This method will not, of course, correct a constant error in all the bearings, but it will help to throw out wild ones and will utilize the greater accuracy which the mean of several observations generally possesses over that of one or two. A constant error, unless it be of large amount, will not make much difference in our distance abeam of the beacon angled on.
The same method and “gadget” will be equally useful for evaluating any series of bearings; those from a R.C. station ashore, those taken by submarine listening devices, or even those which can often with surprising accuracy be snapped by the pelorus pointed by ear on the wail of some invisible siren or foghorn.