Draw the line A D to represent the meridian of Cape St. Vincent, upon which lay off the meridional difference of latitude 323.04; from D erect the perpendicular DE (Prob. II. or XII. Geom.); make it equal to the difference of longitude 475, and draw the line A E; from A to B lay off the true difference of latitude 265, and through B draw B C parallel to D E; then will the angle E AD be the course, measuring 56°, or 5 points nearly, and A C the distance, 471 miles.

60

475'

Course

Diff. of Long.475

Diff. Lat.265 0

M. Diff.of Lat.323

Because the difference of latitude is S. and the difference of longitude is W., hence the true course from Cape St. Vincent to Funchal is S. 55° 47′ W. or S.W. by W. nearly, and the distance 471 miles.

By Inspection.-Seek in the Traverse Table for the meridional difference of latitude 323, and the difference of longitude 475, till they are found together in the latitude and departure columns: the nearest to these are 320 4 and 475 in the page with 56° at the bottom, which is the course; over that course, and opposite the true difference of latitude 265 in its column, is found in the distance column, 474 miles.

Given the Latitude left, the True Course and the Distance, to find the Latitude and Longitude In

A ship from lat. 52° 6′ N., and long. 35° 6′ W., sails N.W. by W. 229 miles. Required her present latitude and longitude.

BY CONSTRUCTION

Draw the line A D, and make the angle D A E equal to the course 5 points; from A to C lay off the distance 229, and from C draw C B perpendicular to A D; then will A B measure the difference of latitude 127; hence the latitude come to is 54° 13', and the meridional difference of latitude 211-86; make A D equal to 211.86, and draw D E parallel to B C; then will the difference of longitude D E measure 317 miles.

By Inspection.-In Traverse Table over the course 5 points, and opposite the distance 229, is the difference of latitude 127.2: hence the latitude arrived at is 54° 13′; then, with the same course and half the meridional difference of latitude 106, in a latitude column, will be found 158.8 in a departure column, which, multiplied by 2, gives the difference of longitude 317.6 miles.

Ans. Lat. in 54° 13′ N.; Long. in 40° 23′ W.

Given the Latitude left, the True Course, and Difference of Longitude, to find the Distance and Latitude In *

A ship from lat. 34° 29′ N. sails S. 41° W. till her difference of longitude is 680 miles. Required her present latitude and distance sailed.

BY CONSTRUCTION

Draw A D, and make A F perpendicular to it, and equal to the difference of longitude 680; draw F E parallel to A D, and A E making an angle with A D equal to the course 41°, meeting F E in E, and E D parallel to FA; then A D will be the meridional difference of latitude equal to 782-3; which, subtracted from the meridional parts of the latitude left, gives the meridional parts of the latitude in; hence the lat. in is 23° 6′, and the difference of latitude 683. Make A B equal to 683, and draw B C parallel to ED; then A C will be the distance, measuring 905

Examples for Practice in Middle Latitude and Mercator's Sailing

1. Required the true course and distance from the Cape of Good Hope, in lat. 34° 22′ S., and long. 18° 24′ E., to the Island of St. Helena, in lat. 15° 55′ S., and long. 5° 45′ W.

Ans. By middle latitude sailing the true course is N. 49° 51′ W., and distance 1717 miles.

*This example cannot be solved by middle latitude sailing.

By middle latitude sailing, using Workman's Table (in Norie's Tables). true course is N. 49° 39′ W., and distance 1710 miles.

By Mercator's sailing the true course is N. 49° 39′ 40′′ W., and distance 1710.17 miles.

2. Required on Mercator's principle the true bearing and distance of Pernambuco, in lat. 8° 4′ S., and long. 34° 53′ W., from Cape Verd, in lat. 14° 45′ N., and long. 17° 32′ W.

Ans. The true bearing is S. 37° 1′ 6′′ W., and distance 1714.6 miles.

3. Required on Mercator's principle the true course and distance from Cape Sierra Leone, in lat. 9° 30′ N., and long. 13° 18′ W., to Cape St. Roque, in lat. 5° 28′ S., and long. 35° 17′ W. If the error of the compass is 10° E., required the compass course.

Ans. The true course is S. 59° 39′ 35′′ W., and distance 1591.9 miles. Compass course S. 45° 40′ W.

4. Required by Mercator's sailing the true course and distance from Cape Palmas, in lat. 4° 24′ N., and long. 7° 46′ W., to St. Paul de Loando, in lat. 8° 48′ S., and long. 13° 8' E. Required also the compass course, the variation being 20° W., and the deviation 17° W.

Ans. The true course is S. 57° 38′ 51′′ E., and distance 1480 miles. Compass course S. 20° 38′ 51′′ E.

5. Required the true course and distance from lat. 26° 38′ S. and long. 15° 08′ E. to lat. 44° 26' N. and long. 63° 33′ W. on Mercator's principle; also the compass course, assuming the variation to be 12° W. and deviation of the compass 4° W.

Ans. True course, N. 45° 29′ 22′′ W.; compass course, N. 29° 29′ 22′′ W. ; distance 6082.4 miles.

6. Required the course and distance from lat. 20° 20' S. and long. 167° W. to lat. 37° 40'S. and long. 170° 30' E. on Mercator's principle; also the compass course, assuming the variation to be 10° E., and deviation of the compass 6° W.

Ans. True course, S. 48° 27' 2" W.; compass course, S. 44° 27' 2" W.; distance 1568 miles.

7. Required the true course and distance from lat. 44° 26' N. and long. 63° 33′ W. to lat. 26° 38′ S. and long. 15° 08′ E. on Mercator's principle; also the compass course, assuming the variation to be 9° W. and deviation of the compass 7° E.

Ans. True course, S. 45° 29′ 22′′ E.; compass course, S. 43° 29′ 22′′ E.; distance 6082.4 miles.

8. Suppose a ship from lat. 9° 10' N., and long. 19° 32′ W., sails in the south-east quarter till she has made 415 miles of departure, and is by observation in lat. 2° 19′ S.; required her true course steered, distance run, and longitude in.

Ans. By Mercator's sailing her true course steered is S. 31° 4′ E., distance run 8043, and long. in 12° 35′ 36′′ W.

9. A ship from lat. 46° 35′ N., and long. 176° 42′ W. sails true N.W. by W. W. till she arrives in lat. 51° 18' N. Required the distance run, and longitude in.

Ans. By middle latitude sailing her distance run is 600.3 miles, and long. in 169° 52′ E.; or, using Workman's Table, 169° 51′ E.

By Mercator's sailing her distance run is 600.3 miles, and long. in 169° 50′ E

10. Required the course and distance from lat. 20° 20′ S., and long. 20° 30′ W. to lat. 37° 40′ S. and long. 30° 20′ E. on Mercator's principle; also the compass course, supposing the variation to be 20° W. and the deviation of the compass 10° W.

Ans. True course, S. 68° 34′ 48′′ E.; compass course, S. 38° 34′ 48′′ E.; distance 2847.7 miles.

II. Find the true course and distance from the Cape of G. Hope in lat. 34° 22′ S., long. 18° 24′ E.; to the Falkland Is. in lat. 52° 21′ S., long. 59° 18′ W. Find also the compass course, the variation being 30° W., deviation 18° E.

Ans. By middle latitude sailing, using Workman's Table, true course S. 72° 9′ 6′′ W., and distance 3520 4 miles, the same as by Mercator's sailing Compass course S. 84° 9′ 6′′ W.

COMPOUND COURSES

To find the DIFFERENCE OF Longitude mADE GOOD UPON COMPOUND COURSES, BY MIDDLE LATITUDE AND MERCATOR'S SAILING

In the preceding cases, both of middle latitude and Mercator's sailing, the ship has been supposed to sail on a direct course; but when she makes a compound course, the several courses, after having been corrected for leeway, and the deviation and variation of the compass, are to be reduced to a single course, as in traverse sailing, and then the difference of longitude may be found either by middle latitude or Mercator's sailing, as shown below. Suppose a ship from lat. 52° 36′ N., and long. 21° 45′ W., has made the following true courses and distances, viz., N.E. 36 miles; N. by W. 14 miles; N.E. by E. E. 58 miles; N. by E. 42 miles; and E.N.E. 29 miles. Required her present latitude and longitude.