NAVIGATION. Although elementary in character, this book is complete enough to enable the student to solve the ordinary problems of navigation. It is, therefore, essential that the student, if he wishes a mate's or a master's paper, thoroughly understand the contents. As the student has already studied arithmetic, geometry and trigonometry, these subjects will not be repeated except in a few cases. This is not a book on seamanship, but is intended for seamen who know little of the subject of navigation. Ignorance of navigation often blocks the way to a position of command. As most navigators have at hand several reference books, such as "American Practical Navigator" by Bowditch and “Wrinkles in Practical Navigation" by Lecky, these books have been referred to for tables, etc. DEFINITIONS. A sphere is a solid body, every part of whose surface is equidistant from a fixed point within, called the center. A diameter of a sphere is any straight line passing through the center and extending in both directions to the surface. A great circle is any circle whose plane passes through the center of the sphere. The center of the sphere is the common center of all great circles. The shortest distance between any two points on a sphere is the arc of a great circle passing through those points. A small circle is any circle whose plane does not pass through the center of the sphere. A spherical angle is the angle or inclination of two great circles of a sphere which meet one another. A spherical triangle is the geometrical figure formed on the surface of a sphere by the intersections of arcs of three great circles. The earth, generally speaking, is a sphere, and revolves about one of its diameters, called the axis, once in every twentyfour hours. The extremities of this axis are called poles, one the north and the other the south pole; in Fig. 1 NS is the earth's axis, N being the north and S the south pole. Equator. This is an imaginary great circle dividing the surface of the earth into two parts, called hemispheres, the north and south. The equator, which is also commonly called the " Line," is represented in Fig. 1 by Q T. Meridians. Fig. 1. These are great circles on the earth's surface drawn through both poles and at right angles to the equator. They are called meridians because they mark the places which have noon at the same time. For instance, N QS of Fig. 1 is a meridian, also NRS, and the other curves drawn through N and S. All places on N RS have noon at the same time. Any two places which lie exactly north or south of each other are said to be on the same meridian. One particular meridian, the one passing through the observatory at Greenwich, England, is taken by the English and American nations to be the first, or prime, meridian. Longitude. The longitude of a place is the distance of its meridian, or the meridian passing through it from the prime meridian; this distance is measured on the equator in degrees, minutes and seconds. Another definition is: longitude is the angle at the pole between the two aforesaid meridians. In Fig. 1 let Y be a place on the meridian N R S, and let N G S be the prime, or Greenwich, meridian; then G R is the longitude of Y and is west of the prime meridian. All places lying between the prime meridian and the 180° meridian in a westerly direction from the prime meridian are in west longitude, and in east longitude when lying between the same meridians in an easterly direction from Greenwich. The 180° meridian is just halfway around the world from the Greenwich meridian. Parallels. Parallels of latitude are small circles parallel to the equator, as A B, C D, etc. (Fig. 1). All places on parallel A B, for instance, are exactly true east and west of each other. Latitude. This is the name given to the distance of a place north or south of the equator, expressed in degrees, minutes and seconds measured on a meridian. In Fig. 1, Y is on the parallel C D, and its latitude, expressed in degrees, minutes and seconds, is the arc R Y of the meridian N RS. We can now see how latitude and longitude determine the position of any ship or other object on the surface of the earth, for longitude fixes its distance east or west of Greenwich and latitude its distance north or south of the equator. The equator, meridians and parallels of latitude are of course purely imaginary lines and are used simply as a means of locating position. The Difference of Longitude between two positions is the distance measured on the equator between their meridians. The Difference of Latitude is the distance between the two parallels of latitude on which the two positions are situated measured on a meridian. The difference of longitude between Y' and Y (Fig. 1) is G R, the difference of latitude is B D, A C, or the distance between the parallels A B and C D measured on any meridian. Departure is the distance in nautical miles made by a ship due east or west, according as it is sailing toward the east or the west, and is commonly called "easting" or "westing." Easting or westing is expressed in nautical miles, and is unlike longitude in this respect. It might seem at first sight that departure and longitude were one and the same thing, but as already stated, longitude is expressed in degrees, etc., while departure is expressed in nautical miles. The difference is this: the distance of length of a degree of longitude grows less as we go north or south from the equator, while the distance of a nautical mile is the same everywhere. The distance of one nautical mile on the equator is equal to one minute of longitude; north or south of the equator the distance of one mile is greater than one minute of longitude. It will therefore be plain that theoretically it is better to make easting or westing in as high latitudes as possible, for the higher the latitude the shorter the distance necessary to sail in order to change the same distance of longitude. OA is the distance sailed, OB the difference of latitude, B A the departure, and the angle B O A the course; similarly, O C is the distance sailed, DO the difference of latitude, C D departure, and DOC the course. Nautical Miles, or Knots. A great circle of the earth is divided into 360 degrees, each degree into 60 minutes, and each minute into 60 seconds. Each minute is 6,080 feet (nearly) in length, or one nautical mile, the statute mile being only 5,280 feet. Rhumb Line. This is the line on which the ship sails as long as her course is not altered; it forms a curve upon the earth's surface which meets every meridian at the same angle. It coin |