Answer, lat in 35° 13′ S, long in 27° 21′ E, course S 66° 24′ E, and dist 2018 miles.

14. A ship from Nootka Sound sails W S WW till her diff long is 387 miles, required her latitude and distance?

Answer, lat in 48° 18′ N, and dist 265 miles.

TO FIND THE DIFFERENCE OF LONGITUDE MADE ON A COMPOUND COURSE.

FORM a traverse table, and find the diff of latitude and departure, latitude arrived at, and course made good, as in traverse sailing. Take the middle latitude between the latitude left and the lat arrived at, and the meridional diff lat between the same two latitudes; then with the departure made by the traverse table, and the middle latitude, find the diff long by middle latitude sailing, or with the course made good by the traverse table, and the meridional diff of latitude, find the diff long by Mercator's sailing, and it always will be of the same name with the departure.

The above method will generally determine the diff long with sufficient exactness in such traverses as can be made in the course of a day; but, in strictness, the diff long ought to be computed for every separate course; and, when the traverse is performed in a high latitude, it may often be expedient to do so.

This may easily be done, by finding the successive latitudes made at the end of every course, the middle latitude between that at the beginning and that at the end of each course, and the meridional diff lat between each pair of successive latitudes. Then, with the middle lat for each separate course, and the departure made on the same course, the diff long made on that course may be found by middle latitude sailing, or with each separate course, and the meridional diff lat made on it, the diff long may be found by Mercator's sailing.

If then the several diff longitudes thus found be entered in two columns, marked E and W, according as the course has been easterly or westerly, the difference between the sum of the numbers in these columns will be the whole difference of longitude made on the traverse, and of the same denomination with the greater

sum.

Note 1. When the course is N or S no diff long will be made; and when it is due E or W the diff long must be found by parallel sailing.

Note 2. In practice, the diff long may in general be determined with sufficient exactness by inspection.

EXAMPLE.

A ship in lat 66° 14′ N, long 3° 12′ E, is bound for Archangel, after sailing NNE E 46, NEE 28, NW 52, NE b E E 57, and E SE 24 miles, required her course and distance to the North Cape?

With the diff lat 129·9, and departure 106·8, the course is found in Table 2. to be about 3910, and the distance 168 miles. With this course, and mer diff lat 337 in the latitude column, the diff long is found in the departure column to be about 278 miles.

Or with the middle lat 67° 19′ as a course, and the departure 106.8 in the lat column, the diff long is found in the distance column to be nearly 279 miles.

To find the diff long made on each course separately by middle latitude sailing.

Successive Lat. Mid Lat. Departure. Diff Long.

With each middle latitude, and the corresponding departure extracted from the previously given traverse table, the diff long is found and entered in the column which is of the same name with the departure, and the difference between the change of long made towards the east, and that made towards the west is 282.8; the whole diff long made on the traverse, differing about 4 miles from that found from the diff lat and departure made on the whole traverse.

To find the diff long made on each course separately by Mercator's sailing.

Courses. Successive Lat. Mer Parts. Mer Diff Lat. Diff Long.

With each course, and the mer diff lat made on that course, the diff long is found and entered in the columns marked E or W, according as the course has been easterly or westerly, and the difference between the sum of the numbers in the E and W columns is 281-7, the diff long, which differs about one mile from that found by middle latitude sailing.

Hence the lat in is 68° 24', and the longitude computed from the result of the whole traverse is 7° 51′; but by computing the diff long for each course separately, the long is between 7° 54′, and 7° 55′ east.

To find the course and distance from the ship to the North Cape.

Hence the course to the North Cape is about N 66° E, 409 miles.

EXAMPLES FOR EXERCISE.

1. If a ship sail from the Naze, W N W 24, N W W 16, SS W 31, SE 12 and S WS 20 miles, required her latitude and longitude?

Answer, course S 56° 24′ W, lat 57° 20′ N, and long 5° 15′ E.

2. If a ship sail from Funchal S 59, W 46, S W W 15, and SW 24 miles, required her latitude and longitude?

Answer, course S 32° 27′ W, dist 109.6 miles, lat 31° 5′ N, and long 18° 7′ W.

3. If a ship sail from the Cape of Good Hope N W 25, NW 21, NNEE 35, N W W 40, and N b E 18 miles, required her latitude and longitude? Answer, lat 32° 37′ S, and long 17° 43′ E.

4. If a ship sail from Fort St. George, in the Island of Grenada, for Kingston, in Jamaica, N W 46, N N W3 W 50, N W b W 70, and WN 21 miles, required her latitude and longitude, and distance from her destination?

Answer, lat 13° 59′ N, long 64° 9′ W, course N 71° 38′ W, and dist 765.5 miles.

5. If a ship take her departure from Cape Matapan, bearing NNE 18 miles, and sail W 13, S W 24, W S WS 20, W N 8, and N W b W 16 miles, required her place, and the bearing and distance of Cape Passaro ?

Answer, lat 35° 49′ N, long 20° 55′ E, course to port N 79° 15′ W, and dist 284 miles.

6. A ship from Toulon sails SS W 48, S b E 34, S W W 26, and E 17 miles, required her course and distance to Port Mahon ?

Answer, lat 41° 32′ N, long 5° 37′ E, course S 30° 43′ W, and dist 117.5 miles.

7. If a ship sail from the Butt of Lewis W SW 26, S W W 42, SS W 13, WbN 29, W 12, S 2 E 18, S E S 10, and W b S 15 miles, required her latitude and longitude, and course and distance to the Peak of Pico?

Answer, lat 57° 18′ N, long 9° 33′ W, course by mid lat S 34° 3′ W, dist 1364 miles, and by Mer S 33° 40′ W, dist 1358 miles.

8. If a ship take her departure from Cape Race, bearing N W 18 miles, and sail SE 32, SE S 16, SE b E 34, E N 40, and E 16 miles, required her place, and the bearing and distance of Corvo, one of the Western Islands?

Answer, lat 45° 39′ N, long 49° 56′ W, course S 66° 44′ E, and dist 906 miles.

9. If a ship sail from Cape Farewell, in Greenland, for Oporto, E 86, E b S 120, and S 39 miles, required her course and distance to her destined port?

Answer, lat 57° 39′ N, long 39° 33′ W, course by Mer S 50° 18′ E, dist 1550, and by mid lat S 50° 40′ E, dist 1562 miles.

and

10. A ship is by observation in lat 24° 14′ N, long 48° 20′ W, sails W S W 24, S W & W 90, SW 24, and W by N 41 miles, required her course and distance to Antigua?

Answer, lat 22° 55′ N, long 50° 50′ W, course to port S 60° 39′ W, and dist 716 miles.