The importance of line-of-position work in ocean navigation has resulted in the appearance of numerous tables for facilitating the computation and the laying down of the line of position from one or more measured altitudes of the sun or other celestial objects. Whatever method may be employed, whether that of St. Hilaire, Aquino, H.O.203 tables, or that recently advanced by Lieutenant Commander Weems, a point on the line must first be plotted on a Mercator chart and a line then drawn through this point at right angles to the sun’s true bearing. The large charts usually provided for this purpose are cumbersome, and though, of course, universal in their longitude scale, are necessarily limited in their latitude scales. This necessitates carrying a whole series to cover the range in latitudes which may be required, although only a small part of each chart may actually be utilized. The problem of handling and stowing the used and unused charts presents no small difficulty, especially in cramped quarters such as submarines, subchasers, or aircraft. Furthermore the graphical work on the large charts can never be filed with the observational data and therefore the ship’s log to this extent contains a missing step in the actual deduction of the required fix.
The plotting board, illustrated herewith, is designed especially to obviate such troubles by providing in a compact kit (twelve inches by fifteen inches by one and one-fourth inches) a universal chart table and a compartment for the storage of the plotting sheets, and the temporary filing of the records until removed to a book or file where they may be permanently preserved with the numerical records.
The plotting sheets, which are printed without scales in either latitude or longitude, are attached to the metal drafting surface by means of hinged clips near the four corners of the board, and the paper preserved in the proper position and orientation by short lugs or dowels nicely fitting perforated holes in the paper.
The longitude scale is etched on a rule constructed similarly to a draftman’s T-square, the T-head fitting closely on the left hand edge of the plotting board.
The longitude scale is graduated both in arc and in time. The latter graduation makes possible the plotting of a given longitude in terms of time without the necessity for conversion into the arc equivalent as in the usual procedure.
The necessary latitude scales needed to make the plotting sheets universal are etched on the surface of a rotating cylinder recessed in a compartment at the left side.
The various latitude scales with which the rotating cylinder is provided are brought into view successively by a slight turn of a knurled knob, conveniently located at the upper left-hand corner of the board.
Only one latitude scale, covering a range of two or three degrees, is visible at any one time. It may be read through a suitable opening adjacent to the left-hand margin of the plotting sheet.
A small cog engages a tooth gear which automatically stops the roller at the proper point and holds it firmly until it is again intentionally turned.
It will be recalled that in the determination of a ship’s line of position from an observed altitude of the sun at sea, it is necessary to assume a given latitude and longitude with which, by means of appropriate tables, a line of position can be drawn at right angles to the sun’s true bearing or azimuth. In some of the newer methods of navigation, an even degree of latitude for the ship is assumed, and an even degree of altitude of the sun is taken nearest the value observed by the sextant. From computation or the use of appropriate tables, such as H.O. 203 and 204, a longitude corresponding to the assumed latitude and altitude will be found, which gives a point on the circle of equal latitudes, a small portion of which in the vicinity of the ship will appear as a straight line, the line of position or the Sumner Line. The Sumner Line for this position, therefore, will be drawn through this point at right angles to the sun’s azimuth, which will be taken directly from the tables. If, as is usually the case, the actual altitude observed by the sextant is greater or less than the assumed altitude, this line of position is moved toward or away from the sun in the direction of the sun’s azimuth by as many nautical miles as there are minutes in the difference between the observed altitude and the assumed altitude. The line is moved toward the sun if the observed altitude is greater than the assumed, or away from the sun if the observed altitude is less than the assumed.
For the purpose of laying out quickly and accurately the line of position, there are printed on the plotting sheets a 0°-360° protractor. With the plotting board is provided a rectangular device of celluloid, called the “line locator,” on which are ruled two sets of parallel lines spaced at convenient intervals.
The line locator is placed on the plotting sheet in such a way that one of the ruled lines passes through the center of the compass protractor and extends in the direction of the sun’s true bearing or azimuth as taken from the tables. The celluloid protractor is then slid along this line until the short edge of the protractor at right angles to the line just described, passes through the point in question. A pencil line is then drawn along this short edge of the celluloid protractor. It is the line of position required, being automatically at right angles to the sun’s azimuth. This procedure eliminates the necessity of the numerical computation of the complement of the sun’s azimuth before laying down the direction of the line of position, and thus a small source of numerical error is eliminated.
The plotting papers are provided in quantity and are housed within the cabinet contained just below the main surface of the board. Access to this compartment is given by a special spring door on the right-hand edge of the box which is opened by a press of the finger and closes automatically when released. The compartment chamber is sufficiently large to contain the T-square and the celluloid protractor, besides a supply of plotting sheets, and the dividers.
The use of the plotting board in working a practical example in navigation follows.
A ship is known to be in the vicinity of 430 00' north latitude, and 610 07' west longitude. An altitude of the sun is observed by the sextant from which it is desired to plot the ship’s line of position.
Let us assume that the ship is in latitude 430 and that the corresponding longitude from the observed altitude and this latitude has been found by computation or tables to be 4h 06m 10s. The sun’s azimuth is computed or found from tables to be 130°.
First, we will prepare the plotting board by attaching one of the sheets and label the heads of the three indicated meridians, numbering in degrees from right to left, 60° 61 °, 62°. It will be convenient to have the time equivalents for each meridian written on the chart. As this can be marked with the greatest ease, we will label the respective meridians in hours and minutes as indicated, 6o° being the equivalent of 4h, 61 °, 4h 04™, and 62°, 4" 08m. We are now prepared to lay out the line of position. By means of the thumb nut at the left-hand edge of the board, the latitude cylinder is rotated until the region containing 420, 430, and 440 is visible. As our longitude is derived directly in “time,” we will make use of the lower edge of the T-square containing the time scale for plotting longitudes. Placing the head of the T-square in juxtaposition with the left-hand edge of the plotting board, we set the lower edge of the T-square at 43°. Next we find our longitude corresponding to 4h 06m 10s on the scale of the T-square, and make a pencil dot at the required point. The line of position will now pass through this pencil point at right angles to the sun’s azimuth. In drawing the line of position, the celluloid locator is laid over the printed protractor on the plotting sheet so that one of the long ruled lines passes through the central point and the 130° division, and in such a position that the end edge of the celluloid passes through the point just plotted. A line is then ruled along this edge which is the line of position on which the ship may be found. It will be observed that this line of position is effectively drawn at right angles to the sun’s true bearing without computation.
It should be noted that if H.O. 203 (or 204) is used, the line of position may be laid down as in the above problem for the nearest degree of latitude and the corresponding longitude found from the tables opposite the nearest degree of the observed altitude, entailing no logarithmic computation whatever. The azimuth given in H.O. 203 indicates the direction of the sun at right angles to the line of position.
If, as would usually be the case in practice, the observed altitude differs from the assumed altitude, a distance is stepped off toward the sun for an observed altitude greater than the computed altitude or away from the sun if the observed altitude is less than the computed altitude. The distance stepped off in miles is exactly equal to the number of minutes of arc in the difference between the observed and computed altitudes. These amounts would commonly be stepped off with dividers, taking the scale from the latitude scale at the left of the board. Through this point so laid out, a line is drawn at right angles to the sun’s azimuth (130° in the above problem) which line will be the required line of position, say for an a.m. sight.
This a.m. line may be carried forward for a run of the ship on any given course by means of the printed protractor and the celluloid device just as would ordinarily be done with parallel rulers. With the a.m. line thus carried forward an intersection may be formed with the noon latitude line or a subsequent p.m. line, in accordance with the usual custom, thus determining the fix of the vessel. Of course an ideal fix is obtained from the simultaneous observation of two or more stars suitably selected.
It is to be remarked that the above procedure in plotting is essentially the same whether a “time sight,” Marcq St. Hilaire, H.O. 203, or any of the newer methods of navigation are used for determining a point in the ship’s line of position. The sheet should be removed from the board as soon as the fix has been determined and a new one substituted. The unused sheets are blocked for convenience in stocks of fifty. The used sheets may be temporarily kept in the receptacle of the apparatus. By making use of the perforations in the top margin, and by folding the sheet once, the used records may be clipped into any standard two-ring binder and become a permanent part of the ship’s log.