23° of leeway, the variation of the compass being 12° E., and the deviation 7° E.; required her true course.

(194.) A ship sailing N. 73° W. on the starboard tack makes 26° of leeway, the variation of the compass being 10° E., and the deviation 12° W.; required her true course.

(195.) A ship sails S. 48° W. on the port tack, and makes 28° of leeway, the variation of the compass being 17° E., and the deviation 9° E.; required her true course.

CHAPTER V.

ON PLANE SAILING.

178. In Plane Sailing, the surface of the earth is considered as a plane, the meridians as parallel straight lines, and the parallels of latitude as straight lines cutting the meridians at right angles. It is not, however, strictly correct to consider any part of the earth's surface as a plane, yet when the operations to be performed are confined within the distance of a few miles, the results thus obtained will be sufficiently correct to serve many useful purposes.

179. Plane Sailing requires a knowledge to some extent of Plane Trigonometry, and proposes the solution of the following problems: 1. Given the latitude and longitude of two places, required the course and distance from one to the other; and 2. Given the course and distance sailed, and the latitude and longitude of the place sailed from, to find the latitude and longitude of the place arrived at.

180. A RHUMB LINE is a curve line on the earth's surface, which cuts all the meridians which it crosses at the same angle; this is therefore the track described by a ship while she continues to sail on the same course, and the length of this rhumb line is called the DISTANCE SAILED.

181. DEPARTURE is the distance due east or due west which a ship has made good from the meridian from which she first started.

182. A ship's COURSE is the angle which her direction makes with a meridian line, and is measured from the north or south towards the east or west, either in points of the compass or in degrees.

183. In the figure in the margin, let A represent the place from which a ship sails, AC a portion

of a meridian passing through the place, AB the line on which the ship sails, and B the point at which she has arrived; then AB represents the distance sailed, AC the difference of latitude she has made, BC the departure made from the first meridian AC, and the angle BAC is called the

course.

DIST.

DIFF. LAT.

COURSE

B

DEPT.

184. In constructing a figure to represent the conditions of any problem in plane sailing, it is customary to make the top of the figure, as A, the north, and the bottom, as BC, the south, the line AC being north and south, the right-hand side of AC being the east, and the left-hand side being the west. The figure above therefore represents a ship sailing from the north point A along the line AB towards the SW., making a difference of latitude to the south represented by AC, and a departure to the west represented by BC, and a course to the west of the south represented by the angle BAC contained between the meridian AC and the line AB, along which the ship sails.

185. Applying now the principles laid down in Arts. (122130), and observing that the departure is there represented by a, the difference of latitude by b, and the distance by c, as in these articles, when any two of the four parts, dist., course, dif. lat., and dept. are given, we will be enabled to find the other two by Plane Trigonometry.

186. Using now the Navigation names instead of the letters

a, b, c, we have the Arts. (122-127) changed into the following:

multiply by dist. ; .. dept. = dist. × sin. course.

multiply by dist. ; .. dif. lat. = dist. x cos. course.

multiply by dif. lat. ; .'. dist. = dif. lat. × sec. course.

multiply by dept. ; ... dist. = dept. × cosec. course.

Problem VIII.

187. Given the course and distance sailed, to find the difference of latitude and the departure from the meridian.

Example.

A ship from latitude 49° 57′ N. sails SW. by W. 488 miles; required the latitude she is in, and the departure she has made from the meridian sailed from.

BY CONSTRUCTION.

Draw the line AC to represent the meridian of the place A

AB, which make equal to the distance 488; draw BC parallel to E and W points to cut the meridian in C. Then will AC be the difference of latitude 271.1 miles, and BC the departure = 405.8 miles.

Now as the ship is in north latitude, and has sailed southward,

her difference of latitude made is south; hence