The object of this contrivance, which may be termed a circular traverse table, is (a) to furnish a ready means of obtaining "distance run" when going at various speeds for odd minutes of an hour (such as between sights or bearings) and (b) to obtain quickly "latitude and longitude in," after steering zigzag courses (such as occur during a war problem or during maneuvering).
To anyone who will notice the construction of .this device and take advantage of the numerous possibilites which a knack in handling the instrument will develop, to him will it be a time and labor saver and an exact servant. He who expects to push a button and have the answer come without any intelligent effort on his part, will find it a source of annoyance and an unnecessary addition to his equipment. This much is claimed for the device: it presents the equivalent of the 90 closely printed pages of traverse tables in a convenient form, with no loss of exactitude and with a gain in every other direction, including the presentation of the functions of the sailing triangle in a lucid way.
The drawing accompanying this article is incomplete and serves only the purpose of illustrating the idea. It is home-made and no more exact than such things usually are; but an interpolation table has been added in each corner (which is unnecessary in the finished product) to aid anyone who wishes to try it out. The complete device consists of 47 concentric circles (only 12 are shown in drawing) properly divided, and a transparent radius arm, fastened and pivoted at the centers, bearing (a) explanatory labels and (b) a line from the outer to the inner circle which, if continued, would pass through the center of the circles. All readings are taken from this line.
The first two circles are divided and labeled like the face of a clock. The next, for convenience, is divided into hundredths. It can be called the distance circle and its divisions can represent anything in the way of distance—miles, half miles, hundredths or tenths of miles.
EXAMPLE—Given Speed and Time. To Get Distance Run.
(a) Ship goes at speed of 12½ knots for 1 hour 24 minutes.
What was run?
When the speed is an integral part of 100 the operation is simply this:
Let 1 mile equal 8 divisions on distance circle (thus making once around the clock equal 12½ miles).
Move arm like minute hand of a clock to 24 minutes.
Circle reads 40, which stands for 5 miles.
Therefore
Answer is 17½ miles.
(b) Ship goes at speed 13½ knots for 2 hours 12 minutes.
What was run?
Of course the complete hours require little mental attention, for it is the fractional part of an hour that always gives trouble. In case there is no convenient way of arranging the speed to exactly fit the circle, let each division equal hundredths of a mile, read your circle accordingly, apply it to the speed and the answer is there.
In this case, swing arm to 12 minutes. It reads 2 tenths. This times speed gives 2.7 which applied to the two whole hours gives 29.7 miles.
It may be well said that in the two cases above, a few scratches with a pencil, together with mental arithmetic, will bring the same answer; but it should be borne in mind that all combinations can be worked accurately as easily by the card and it is a good plan to work easy problems in this way so as to be able to work the awkward ones with equal facility. It is safe to say that the swinging arm will be ahead of the pencil in point of time, anyway—and who does not catch himself making a mistake in multiplication now and then?
All this is aside from the main mission of this card and is simply inserted for anyone who cares to use it. The device was constructed principally to obtain quick readings of “latitude and longitude in,” at the completion of extensive maneuvers, during which the navigator engaged in "shiphandling" has no time to lay down his courses and distances on the chart.
It might be thought that tracing the supposed track of the ship on a chart is an excellent way to show visibly what the ship has done and furthermore it is a custom honored by long practice and consequently hard to break away from. But what virtue is there in this ancient custom, except when actually piloting?
If a ship's position be fixed only by a point on a chart, there can be no illusion as to its being anything but the most probable point on the chart and only as accurate as dead reckoning goes. Its very isolation from nearby reference marks may cause the navigator to question it and serve to remind him to make another operation on his device, correcting for current. If any question arises as to past movements, or, it is required to submit a track of all movements during a war problem, the navigator can, at his leisure, plot in his turning points from his notes and simply run straight lines from one point to the other.
While reading about the operation of this device, it must be remembered that a description of it will, of necessity, be more involved and tedious than the operation itself. Perhaps the easiest way to gain an adequate idea of the simplicity of the device, is to have a light line scribed on the under side of a transparent triangle (such as is furnished with most drawing sets) and to use this as a radius arm on the drawing.
To proceed with the construction of the dead reckoner—what has been called the distance circle is also the 0 degree circle. In other words, nautical miles steamed on course 0 or 180 are simply so many minutes of latitude north or south. The next smaller circle, on the drawing, is the 5 degree course circle (in the completed contrivance, it would be the 1 degree course circle). The graduations on the outer part of this circle represent northing or southing on that course for the distance steamed as represented on the distance circle (and are in the same numerical units) and the graduations on the inner side of this same 5 degree circle represent the corresponding departures (likewise in the same numerical units). The next smaller circle is the 10 degree circle, similarly divided and so on, down to the 45 degree circle.
To get longitude, read the departure as noted, swing radius arm to the same number on the latitude scale of the degree circle corresponding to the latitude the ship is in (or middle latitude if run was great) and the reading on the distance circle gives the longitude.
Example.—Take a short run for illustration.
Took a sight for line of position and established a position point in lat. 40° 15' N. and long. 70° 34’ W., and ship ran 10 miles on course 25° true before the second sight could be taken. Problem: Shift first position point to place of second sight. Or it might be stated thus: Get latitude and longitude of second sight, so that navigator can go ahead with his computation immediately.
Operation.—Swing arm to 10.
The 25° circle reads 9, so jot down 40° 24' N.
The departure scale reads 4:2, so swing arm to 42 on 40° circle. The distance circle reads 55, so note 70° 28.5' W.
Discussion.—If the beginner is not sure whether the departure was 4.2 or 4.3 he can let the scale on the distance circle represent five divisions to a mile. So, swinging the arm to 50, he reads the departure about 21.2, which, divided by 5, gives 4.24 (well clear of 4.3), and, by the way, the latitude here reads 45.3, which, divided by 5, is 9.06.
If his bump of academic research is well developed, he might even swing the arm over to 100, and learn that he actually went 9.063 miles to the northward, and 4.227 miles to the eastward.
Note.—The difference in the second and third departure readings of 0.013 is undoubtedly due to the approximate reading of the "21.2," and to the fact that the drawing is crudely constructed.
It is unnecessary to give more examples, or to show how easily and quickly "course and distance made good" and "course and distance to destination" are obtained, since now that the elements and their positions on the card are known, their relation is clear to anyone who has ever handled traverse tables. One thing further may be added. As the courses pass 45 degrees and approach 90 degrees, the name of the inner and outer scales of each circle changes, and what was the latitude scale is now the departure scale and vice versa. No time need be used to decide which to use, however, for the swinging arm will be lightly etched as shown, all the courses having the latitude scale outside being on the right of the index line and all the others on the left of that line.
In the finished product, it is intended to divide the distance circle into 500 parts; to make use of different colored inks for clearness; to have the subdivisions mechanically exact; and to have a course circle for every degree.
In the drawing, there is no difference between adjacent scales of over nine units, so evidently interpolation between degrees in the final device will be but a matter of a glance.
For those who require a higher degree of exactitude, there will be added a small table of corrections to middle latitude (used when converting departure into longitude) to obtain the precise "latitude of conversion." But this, of course, need not be used when distances involved are inside an ordinary day's run.
In closing, let me state the advantages of the instantaneous dead reckoner over the ordinary method:
It is much quicker.
It is independent of the position of the compass rose on the chart.
It is more accurate when handled properly.
It is as less liable to be handled improperly, as the number of its separate operations compare favorably, with the number of the separate operations necessary in the ordinary method.
It saves labor as well as time.
It makes charts last longer and enables them to be kept cleaner.
It simplifies tracing back past performances for purposes of investigation, etc., from the notes made during maneuvers.