EXAMPLES

of traverses, worked by the table of difference of latitude and departure.

1. A ship sails on the following courses, viz. SW 25 miles, SSW 18 miles, S6W 25 miles, E 4 miles, EbN 7 miles, S 10 miles. It is required to find the course, distance, difference of latitude, and departure made good.

CONSTRUCTION.

Draw

Construct the hori zon with its meridian and parallel. Set off the first course and distance from the centre of the horizon. the rhumb of the second course from the centre of the horizon; and, parallel to this rhumb, from the outer extremity of the first distance set off the second distance. Draw the rhumb of the third course from the centre of the horizon; and,

W

S

parallel to this rhumb, from the outer extremity of the second distance set off the third distance. And proceed, in this manner, till every course and distance of the trav erse be drawn. From the centre of the horizon to the outer extremity of the last distance draw a right line. This right line will be the distance made good, and the Vol. II. Ee

E

acute angle, formed between it and the meridian, will be the course made good. From the outer extremity of the last distance draw a parallel of latitude, falling on the meridian, prolonged if necessary. The east and west line, comprehended between the meridian and the outer extremity of the last distance, will be the departure; and the north and south line, comprehended between the first and last parallels of latitude, will be the difference of latitude.

As the construction of every traverse is performed in the same manner, they will, for brevity, be omitted in

future.

COMPUTATION BY THE TABLE.

Make a table consisting of six columns, and title them course, distance, northing, southing, easting, westing, each column being intended to contain that, which its title de

The courses of the traverse must be entered in the first column, and their respective distances opposite to them in the second. Seek the first course SW, or 4 points, in the table of difference of latitude and departure, and against the distance 25 will be found 17'7 difference of latitude, and 17'7 departure, which enter in the columns of southing and westing, because the course is in the SW quarter. In like manner with the course SSW, or two points, against distance 18 is found 16-6 difference of latitude, and 6'9 departure, which are likewise southing and westing. S6W, or one point, distance 25 gives 24 5 southing, and 4'9 westing. E distance 4 miles, need not be sought out, as the distance is all easting, and must, therefore, be entered in the E column. EbN, or 7 points, distance 7 gives 1'4 northing, and 6.9 easting. And S distance 10 miles is all southing. The difference between the total southing and the total northing is 674 southing and the difference between the total westing and the total easting is 18'6 westing. With these numbers, in the table of difference of latitude and departure, the distance is found 70, and, at the top of the page, 15 degrees for the course, which is in the SW quarter, the course being taken from the top and not the bottom of the page, because the titles of lat. dep. at the top agree with the nature of numbers.

The course therefore is S 15 W distance 70 miles, difference of latitude 67'4 miles N, departure 18'6 W.

2. A ship in 17° 12′ N latitude, bound to a port in 18° 40′ N latitude, and 220 miles to the westward, sails NW6W 73 miles, WNW 40, SSW 18. What is her present latitude and departure made good, and what are the bearings and distance of the port, to which she is bound?

With 49 miles northing, and 115 miles westing, seek for course and distance in the table of difference of lati tude and departure, which being found N 67 W distance 126, are the required bearing and distance of the port, according to the principles of plane sailing.

3. A ship sails on the following courses, SE 40 miles, NE 28 miles, SW6W 52 miles, NW6W 30 miles, SSE 36 miles, SEE 58 miles. Required her course, distance, difference of latitude, and departure made good.

IT has already been observed, that sailing on the principle of the plane chart is too erroneous, when applied to the surface of a sphere, to be used in any but small distances, or between the tropics, where the meridians have but little convergency, and the rhumb lines do not widely differ from portions of great circles. In all sea reckonings, the principles of the plane chart are supposed to be exact enough for the distance of a day's run; and, at the end of every 24 hours, the ship's place is determined in latitude and longitude, by applying the difference of latitude,