In No. 4, 1900, Proceedings of the United States Naval Institute, is described a valuable instrument for the graphic solution of plane triangles devised by Capt. Allan H. Porter for the particular purpose of finding the position in coast navigation. As far as is known to the writer, such instruments are not furnished naval ships, and to make the necessary triple parallel rulers accurately with a ship's appliances might deter officers from an attempt to use the principle of the graphic method. Everything needed for the graphic solution is, however, either now furnished or can readily be made on board ship. A protractor, the cross-section paper marked in tenths furnished to navigators, thumb tacks, a chart board and a ruler are all that is required. It may be found convenient to make a special long ruler with a strip of the cross-section paper pasted on the bevel close to the edge and somewhere near the middle of the length.
In submitting this and what follows nothing particularly new or original is claimed. Simply a very convenient graphic method is pointed out, for which everything is at hand, and by which the information sought can be obtained without computation or the use of tables and can be preserved for comparison with later observations. This graphic comparison is a valuable feature, appealing at once to the eye. No expectation is entertained that navigators will use the method in place of the quick mental process for finding the distance by the bow and beam bearing. With other bearings, however, and particularly in view of the ease and rapidity with which it can be used, and the fact that each record is preserved, the method is believed worthy of trial.
On the cross-section paper assume the position of the landmark at a corner origin of the ruled lines, and assume the course parallel to one edge, which may be called, to distinguish it, the "course edge." As an instance, suppose the landmark first observed when bearing 20° off the bow; from the landmark rule a line making an angle of 20° with the "course edge." After running a distance of 3.1 miles suppose the landmark to bear 30° off the bow; rule a second line making an angle at the landmark of 30° with the "course edge." Move the ruler parallel to the "course edge" until the distance run, 3.1 miles, is just included between the two lines of bearings and rule a line between the two. The distance from the landmark that the ship will pass when abeam, supposing no drift, is seen by inspection before raising the ruler if the latter be long enough to reach the ruled line passing perpendicular to the "course edge" through the landmark. The distance on either bearing from the landmark is found by measuring with the ruler. Practical parallelism with the "course edge"' in fitting the distance run between the lines of bearing is easily attained because of the multiplicity of ruled lines.
Drift, either toward or from the landmark, will be detected if continuous observations be made, and the lines be ruled each time to represent the distances run between the several bearings.
Further, suppose the course be changed before reaching the bearing on which it was intended to make the second, or a later, observation: the drift can still be detected if one bearing and the attendant patent log have been noted. Read the patent log just before the change; the new bearing will be found near enough in the great majority of cases by applying the number of degrees change of course to the bearing just before the turn. Neglecting the transfer in turning, the distance from the landmark just after the change is the same as just before it. If the new bearing be ruled off and that distance from the landmark be marked upon it, drift will be shown at the next observation if the line representing the run between does not pass through the point marked.
The bow and beam or beam and quarter bearing is naturally the particular case of this problem most in use, but circumstances not infrequently arise under which it cannot be used, particularly when the course is changed between. The graphic solution obviates the necessity of waiting for any particular bearing, and, if used continuously, it preserves the value of previous observations, even though the course be changed.
It would be a very inexpensive matter to print and issue to ships special prepared sheets of convenient size, say 12 inches square, with cross lines ruled upon them and with degrees marked on the edges (or with a quadrant drawn from each of two adjacent corners). This would leave nothing to handle but the sheet and ruler. A permanent instrument could easily be made by ruling the lines on plate glass slightly roughened to take pencil marks, though hardly with a ship's appliances.
Examples.
The plain line figure will illustrate the case of a ship passing a landmark without change of course. The first observation was on a bearing of 200 from the ship's head. After a run of 3.1 miles the bearing changed to 300; after a further run of 2.4 miles the bearing became 450; after a further run of 1.8 miles it became 650; and, finally, after a run of 1.6 miles the landmark bore abeam. The plotted lines for run show a consistent drift away from the landmark.
The dotted line figure will illustrate the case where a change of course was made after the first bearing and patent log had been noted. The first observation was made on a bearing of 250 from the ship's head with the intention of getting a bow bearing next, and then a beam bearing. But, after a run of 3.5 miles, the landmark bearing 390 on the bow, the course was changed 17° toward the landmark, bringing the latter's new bearing 220 from the ship's head. The point where the course was changed is at A. Laying off the line of bearing for 22°, the point B, at the same distance from the landmark as A, will now represent the position of the ship on the new course just after the change. After a further run of 3.2 miles the bearing was brought off the bow, and the plotted run, not passing though B but nearer the "course edge," showed an apparent drift toward the landmark. This drift was confirmed when the landmark came abeam after a run of 2 miles.
Note.—My idea of the cross-ruled paper seems to have been adopted in principle by Lieut.-Commander J. B. Blish as far back as 1897 in an instrument devised for the same purpose. The form of his instrument, however, is different, and I am unconscious of ever having seen or heard of Mr. Blish's instrument, which was described in Commander Tanner's report of the cruise of the Albatross, 1897, until my attention was brought to it.—The Author.