will reach from 125, the diff lat towards the right, on the line of numbers, to 146, the distance.

Hence the course is S 30° 58′ W, and the distance 145.8 miles.

EXAMPLES FOR EXERCISE.

1. If a ship sail from Oporto, N WW 315 miles, required her departure, and the latitude she has arrived at ?

Answer, dep 233.4 miles W, and lat 44° 41′ N. 2. If a ship sail from lat 55° 1′N, SE b S, till her departure is 45 miles, required the distance she has sailed, and her latitude?

Answer, dist 81 miles, and lat 53° 54′ N. 3. A ship from lat 36° 12′ N sails southwestward till she arrives in lat 35° 1′ N, having made 76 miles of departure, required her course and departure ? Answer, course S 46° 57′ W, and dist 104 miles. 4. A ship from lat 40° 5' N sails SWS till she arrives in lat 36° 7′ N, required her distance and departure?

Answer, dist 307.9 miles, and dep 195.3 miles W. 5. A ship from Funchal sails between the south and west, till her diff lat is 114, and her dep 97 miles, required her course, distance, and latitude?

Answer, course S 40° 24′ W, dist 149.7 miles, and lat 30° 43′ N. 6. A ship sails from the Cape of Good Hope southeastward till she arrives in lat 40° 10' S, having run 700 miles, required her course and departure? Answer, course S 60° 51′ E, and dep 611.4 miles E. 7. If a ship sail N N W2 W, 123 miles, from lat 18° 2′ N, required her departure and latitude arrived at ?

Answer, lat 19° 47′ W, and dep 63.2 miles W. 8. If a ship from Halifax sail SEE till her dep is 128 miles, required her latitude and distance?

Answer, lat 42° 51′ N, and distance 165.6 miles. 9. If a ship sail from Cape Finisterre S S W W 234 miles, required her latitude and departure?

Answer, lat 39° 31′ N, and dep 200.7 miles W.

10. If a ship from lat 50° 16′ N sail southeastward till her distance is 137, and her departure 112 miles, required her course and latitude come to? Answer, course S 54° 50′ E, and lat 48° 57′ N. 11. If a ship sail N W b WW from lat 30° 14′ N till her departure is 204 miles, required her latitude, and the distance she has sailed? Answer, distance 231·4 miles, and lat 32° 3′ N. 12. A ship from lat 12° 17' N sails NEN 201 miles, required her latitude and departure? Answer, lat 14° 46', and dep 135 miles E. 13. A ship sails from the North Cape, in Lapland, 200 miles, and it is then found that she is to the westward of the Cape, and 125 miles south of it, required her course, latitude, and departure ?

Answer, course S 51° 19′ W, lat 69° 5′ N, dep 156.1. 14. A ship from the east point of St. Mary, Azores, sails E NEE till she arrives in the lat of Lisbon, required her distance and departure? Answer, dist 361-7, and dep 346·1.

15. A ship leaving Charleston light sails N eastward 128 miles, and is then by observation found 39 miles north of the light, required her course, latitude, and departure?

Answer, lat 33° 22′ N, course N 72° 16′ E, and dep 122. 16. A ship sails from Cape St. Roque N E N, 7 miles an hour from 3 P м till 10 a м, required her distance, departure, and latitude arrived at? Answer, lat 3° 27′ S, dep 84.38, and dist 133. 17. A ship from lat 41° 2′ N sails N N W W, 5 miles per hour for 2 days, required her distance, departure, and latitude arrived at ? Answer, lat 45° 45′ N, dep 1697, and dist 330.

18. If a ship sail from lat 48° 27' S, NW b W, 7 miles an hour, in what time will she reach the parallel of 50° S? Answer, 23 914 hours. 19. If a ship sail from Cape Horn due south 121 miles, and then due west 121 miles, required her course and distance, and the latitude which she has arrived at?

Answer, course S W, dist 171'1, and lat 58° 0'S. 20. If after a ship has sailed from lat 40° 21' N to lat 46° 18′ N she be found 216 miles to the eastward of the port from whence she has sailed, required the course she has sailed, and the distance she has made? Answer, course N 31° 11' E, and dist 417.3.

TRAVERSE SAILING.

WHEN a ship is obliged to sail on different courses, the crooked line which she describes is called a traverse, and the method of finding a single course and distance, which would have brought the ship to the same place, is called resolving a traverse.

A traverse is resolved by finding the difference of latitude and parture corresponding to each course and distance, and entering

them in a table, of which the form will be found in the first of the following examples; taking care when the ship steers southward to enter the difference of latitude in the column marked S, but in the column marked N, when the course is northward. In like manner when the course is easterly or westerly, the departure must be entered in the column marked E, or W, accordingly.

Thus if the course is S Eb S the difference of latitude must be entered in the column S, and the departure in the column E; if the course is WN, the difference of latitude must be entered in the column N, and the departure in the column W; when the course is exactly E, W, N, or S, the whole distance will, of course, be entered in the corresponding column E, W, N, or S. Then the difference between the sum of the numbers in the column marked N, and the sum of those in the column marked S, will be the whole difference of latitude, and of the same denomination with the greater sum; and in like manner the difference between the sum of the numbers in the columns marked E and W will be the whole departure, and of the same denomination with the greater sum.

Having then obtained the whole difference of latitude and departure which the ship has made, the corresponding course and distance may be found either by inspection, or by any other method,

EXAMPLE,

A ship from Cape Clear sails SSEE 16, ESE 23, S W b W W 36, W N 12, and SE bE E 41 miles, required the equivalent course and distance, and the latitude of the place which the ship has arrived at?

BY CONSTRUCTION.

N

d

ESE. 23.

Take A for the place sailed from, and draw the vertical line NASC to represent the meridian. About A, as a centre, with the chord of 60°, describe a circle cutting N C in N and S; then N and S will represent the north and south points of the compass. Take 2 points from the line of rhumbs, and apply it from S to a, join A a, and on it take A D = 16, from a line of equal parts. Then D will be the place of the ship at the end of the first course. From S set off Sb 6 points from the line of rhumbs; join A b, and through D draw D E parallel to A b, and make it equal to 23 from the same scale of equal parts that A D was taken from.

Then E will be the place of the ship at the end of the second course.

WN./2

G

SE

Dist

Diff Lat 59'6"

.........

C
Dep 19.6m

716

E

W. 36.

B

Make S c = 5 points, N d 7 points, and Se 5 points taken from the line of rhumbs. Through E draw E F parallel to A c, and make it equal to 36 from the scale of equal parts; through F draw F G parallel to A d, and make it equal to 12 from the scale of equal parts; through G draw G B parallel to A e, and make it equal to 21 from the scale of equal parts. Demit B C a perpendicular on the meridian N C, and join A B; then B will be the place of the ship, AB her distance from the place which she left, A C her difference of latitude, B C her departure, and BAC the course which she has made on the whole. Now A B, A C, and B C being measured on the scale of equal parts from which the distances were taken, we have AB 627, A C = 59'6, and B C 19.6 miles. And the arc included by A C and B C, if measured on the line of chords, gives about 18° for the measure of the course B A C.

Whence the course is S 18° 12' E, and the distance 62.75 miles.

BY INSPECTION.

Under 18° in Table 2, and adjacent to 59.9 in the lat column, stands 19.5 in the dep column, and 63 in the column of dist, whence the course is nearly 18°, and the distance nearly 63 miles.

BY GUNTER'S SCALE.

The extent from 59'6 to 19'6 on the line of numbers, will reach from 45° on the line of tangents to the course about 1840, and the extent from the complement of course to radius on the line of sines, will reach from the diff lat 596 towards the right, to the distance 63, on the line of numbers.

EXAMPLES FOR EXERCISE.

1. A ship sails from Cape Clear S b W 23, W SW 40, S W W 18, W&N 28, SbE 12, and S S E E 16 miles, required her course, distance, and latitude come to?

Answer, course S 45° 47′ W, dist 102.4, and lat 50° 14′ N. 2. If a ship sail from Porto Sancto ENE 18, NEE 40, NE 13, NW W 16, and NEN 23 miles, required her course, distance, and latitude?

Answer, course N 34° 30′ E, dist 88.1, and lat 34° 16′ N. 3. A ship from lat 41° 12′ N sails S Wb W 21, SWS 31, WS W S16, SE 18, SW W 14, and WN 30 miles, required her course, distance, and latitude arrived at?

Answer, course S 52° 49′ W, dist 1117, and lat 40° 5' N. 4. A ship from the equator sails N 48, W 37, NW 18, NE 70, N NE 24, and E 32 miles, required her course, distance, and latitude in? Answer, course N 17° 12′ E, dist 138.6, and lat 2° 12′ N. 5. If a ship sail from lat 10° 6' S, N N E 86, N 74, E b N 53, NNW N 40, and E N EN 21 miles, required her course, distance, and latitude in?

Answer, lat in 6° 34′ S, course N 23° 25′ E, and dist 231 miles. 6. A ship sails from lat 4° 5' N, SS W 112, SbE 86, Sb W 86, SSE 112 miles, required her course, distance, and latitude arrived at ?

Answer, lat in 2° 11′ S, course S, dist 375'6 miles, being the same as the diff lat.

7. Last noon we were in lat 28° 46′ S, and since then we have sailed S WW 62, S b W 16, W S 40, S W2 W 29, S bE 30, and SE 14 miles, required the course and distance which we have run, and our present latitude?

Answer, lat in 30° 41' S, course S 43° 14' W, and dist 158 miles. 8. If a ship sail from lat 51° 12′ S, W 68, N 70, N W 120, and