acute angle, formed between it and the meridian, will be the course made good. From the 6uter 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.

1

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 177 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. SbW. or one point, distance 25 gives 245 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 14 northing, and 69 easting. And S. distance 10 miles is all southing. The difference between the total southing and the total northing is 67'4 southing; and the difference between the total westing and the total easting is 186 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 the numbers.

The course, therefore, is S. 15 W. distance 70 miles, difference of latitude 674 miles N. departure 186 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 NWb W. 73 miles, WN W. 40, SS W. 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?

VOL. II.

PP

Computation.

With 49 miles northing, and 115 miles westing, seek for course and distance in the table of difference of latitude 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, NW/W. 30 miles, SSE. 36 miles, SEE, 58 miles. Required her course, distance, difference of latitude and departure made good..

Ir 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 latit ude and longitude, by applying the difference of latitude,

found

found by these principles, to the latitude, and the differ ence of longitude to the longitude of the place, from which the ship sails. This difference of longitude is found, either by parallel sailing, middle latitude sailing, or Mercator's sailing.

PARALLEL SAILING is the method of finding the differ ence of longitude made by a ship, when her course and distance, on a known parallel of latitude, are given; and the contrary.

The computations in parallel sailing depend on the following

THEOREM.

On the globe, the difference of longitude between any two meridians is to the distance between those meridians, measured on any parallel of latitude, as radius to the cosine of the latin.de.*

in the ratio of their radii AQ, BC.

But AQ, the radius of the equator, is the sine of the are PQ, a quadrant, and BC, the radius of the parallel of latitude, is the sine of the arc PC, the complement of the latitude of the

place