Although Mercator's chart is the navigator's chart par excellence the writer proposes in this article to present a few "wrinkles" towards increasing the value and popularity of the Plane Chart, as far as plotting lines of position is concerned.
The "true spirit" of modern navigation requires the plotting of lines of position on a chart and, unless this is done, the best results cannot be obtained, especially when the altitude of the observed body is over 75° or when it is desired to eliminate to a certain extent the systematic and accidental errors. A glance at the lines of position on a chart will immediately show the influence of any one of the component parts of these errors.
Our "protractor diagram" (shown for the first time in the PROCEEDINGS No. 147, September 1913, page 1035) represents a plane chart in its most convenient form, because it has a protractor around the border, to facilitate the plotting of lines of position by Sumner's or Marcq St. Hilaire's methods and, if desired, to serve as a substitute for the Plane Traverse Tables.
PLANE CHART DIFFICULTY OVERCOME
In a recent contribution to the pages of the Nautical Magazine for October, 1913, page 313, a high authority said:—"The initial difficulty in connection with a chart extemporised by means of squared paper is of course this, that different units have to be employed for measuring latitude and longitude respectively, whereas the side of a square only furnishes a single unit. If for instance we adopt the side of a square as representing so many minutes of latitude, it will be no longer adapted for measuring off minutes of longitude. We require, in fact, two scales, one for measuring longitude, the other for latitude or distance run."
This difficulty is overcome in a very simple way by means of our "graduated triangle," as will be seen later on.
AQUINO'S GRADUATED TRIANGLE
After a careful study of the advantages and disadvantages of Fontoura's T Square, a description of which appeared in the September 1913, issue of the PROCEEDINGS, page 1042, the writer came to the conclusion that a "graduated triangle" would answer just as well the purpose and be more suitable from a constructional point of view.
He therefore ordered from Messrs. Keuffel and Esser, of New York, one of their well-known 12-inch 30° x 6o° xylonite triangles graduated on the edges to be used in connection with his "protractor diagram," as shown on appended engraving.
Its use is easily understood, not only for facilitating the plotting of lines of position by Sumner's or Marcq St. Hilaire's methods, but also for solving a number of problems usually solved by means of the Plane Traverse Tables. The divisions on the edges are the same as those on the diagram. By means of the "diagram" and the "triangle" any plane triangle can be formed and solved.
The adjustment of the triangle on the diagram corresponds to a line of position AA' from a body whose azimuth is S 30° E (150°) and an intercept OA= +20’.0. The line of position AA' can be immediately drawn once the triangle is properly adjusted. It is not necessary to draw the intercept OA.
With the divisions on the edges it is not necessary that the triangle should be of xylonite or transparent material. It can be of boxwood or rubber and any triangle made from these substances may be graduated and made to answer the purpose.
"DIAGRAM" TRANSFORMED INTO MERCATOR CHART
Our "diagram" can be rapidly transformed into a Mercator chart, if desired, simply by drawing a straight line with an inclination to the line 0°-180° equal to the observer's latitude. If the latitude was 30° the line 0-30° (will the reader kindly draw this line?) will show a scale of latitude or of miles for this latitude, each mile being the part of the inclined line comprised between two successive horizontal lines (those parallel to the line 90°-0-270°). This is the method usually followed in France. Each side of a square would then represent one minute of longitude.
"DIAGRAM" always A PLANE CHART
The author believes, however, that it is simpler to consider the "diagram" always as a plane chart by adopting each side of a square as a minute of latitude or a mile of distance run.
The distances taken in a North and South direction would be equal to the difference of latitude and those taken in an East and West direction would be equal to the departure, which could be immediately transformed into difference of longitude by multiplying the departure by the secant of the latitude, by means of the diagram or the Plane Traverse Tables, as usual.
LONGITUDE SCALE ON "DIAGRAM" AS PLANE CHART
This transformation is not necessary, however, as the longitude scale, for a given latitude, say 30°, may be immediately obtained by simply adjusting the "graduated triangle," as on engraving. Place the long graduated edge of the triangle so as to pass through the center 0 of the diagram and the graduation 30° of the "protractor." Then the other graduated edge AA' will be the longitude scale for latitude 30°.
The "diagram" shows that A (17 miles south of 0) is 10 miles in departure East of 0 and the lower graduated edge of the "triangle" shows that A is 11.5 miles East of 0 in longitude.
The "diagram" shows that A' (27 miles south of 0, or 10 miles south of A) is 17 miles West of A in departure and the lower graduated edge of the "triangle" shows that A' is 19.6 miles West of A in longitude and 8.1 miles West of 0 in longitude.
The difference of longitude can be reckoned from any particular meridian. Draw the line AA' (after adjusting the triangle as indicated above) across the diagram, and slide the side AA' of the triangle along the line AA' until A is on the meridian from which we want to reckon the difference of longitude. When the longitude is West use the short side of triangle AA'. When it is East use the long side of triangle OA.
Example. If the latitude of A is 30° N and the longitude 20° W of Greenwich, the longitude of 0 would be 20° 11’.5 W and that of A', 20° 19'.6 W.
In this very simple way both scales for latitude and for longitude are immediately available, just as they are on Mercator's chart.1
BLANK MERCATOR'S CHART
The United States Hydrographic Office issues a blank Mercator chart No. 3000 in ten parts extending only from latitude o° to 53° N or S, but the writer believes the general solution given above to be more convenient from a practical and economical standpoint.
The distinguished writer already quoted from the Nautical Magazine (loc. cit.) sums up the advantages of the use of our "diagram" as follows: "Amongst the advantages that may be claimed for this special form of chart are the following":
(I) "The work is done more quickly since we have not to hunt for a protractor, but the chart is complete in itself."
(2) "The bearings, by reason of the very clear divisions on the edge, rendered possible by the liberal dimensions of the chart, can be laid off more accurately."
(3) "For the same reasons the work is effected with much less strain upon the eyesight."
1In ordinary practice A, the zero of the longitude scale, could be made to coincide with 0, the center of the diagram; not only for reckoning the difference of longitude from the center 0, but also for facilitating the plotting of lines of position by Sumner's method. The triangle was placed as it is, on the engraving, to enable us to demonstrate also its use in plotting lines of position by Marcq Saint Hilaire's method.