GREAT CIRELE or TANGENT SAILING. In order to have a clear idea of the advantages of great circle sailing, it is necessary to re member that the shortest distance between two places on the earth's surface is along an arc of a great circle (see SPHERE), for instance, the shortest distancei between two places in the same latitude is not along the parallel of latitude, but along an arc of a circle whose plane would pass through the two places and the center of the earth. The object, then, of great circle sailing is to determine what the course of a ship must he in order that it may coincide with a great circle of the earth, and thus render the distance sailed over the least possible. This problem may be solved in two ways, either_ by means of an instrument called the "spherograph," or by The first of these methods will be explained The method by computation will be under !Mod from the accompanying diagram: nwsc represents a meridian which passes througk le place p, vexes another meridian through the place x, and pxm a portion of a great ::ircle; let p be the place sailed front, and x the place sailed to, then px is the great circle track, and it is required to determine the length of pa (called the distance), and the merle dpe which it makes with the meridian (called the course). To determine these two, we have three things given: ax, the co-latitude of x; np, the co-latitude of p; and the angle .rnp, which, measured along re, gives the difference of longitude. The problem thus becomes a simple case of spherical trigonometry, the way of solving which will be found in any of the ordinary treatises on the subject of spherical trigonometry.
From the theory of great circle sailing, the following most prominent features arc at once deduced: A ship sailing on is great circle makes straight for the port, and crosses the meridians at an angle which is always varying, whereas, by other sailings, the ship crosses all meridians at the same angle, or, in nautical phrase, her head is kept on the same point of the compass, and she never steers for the port direct till it is in sight. As Mercator's chart (q.v.) is the one used by navigators, and on it the course by the ordinary sailings is laid down as a straight line, it follows, from the previous observations, that the great circle track must be represented by a curve, and a little consideration will show that the latter must al ways lie in a higher latitude than the former. If the track is in the northern
hemisphere, it lies nearer the north pole; if in the southern hemisphere, it is nearer the south pole. This explains how a curve line on time chart represents a shorter track between two places than a straight line does; for the difference of latitude is the same for both tracks, and the great circle has the advantage of the shorter degrees measured on the higher circles of latitude. Consequently, the higher the latitude is, the more do the tracks differ, especially if the two places are nearly on the same parallel. The point of -maximum separation, as it is called. is that point in the great circle which is furthest from the thumb-line on Mercator's chart. 'Since the errors of dead-reckoning (q.v.) pre vent a ship from being kept for any length of time on a prescribed track, and thus neces sitate the calculation of a new path, in practice, time accurate projection of a great circle track on the chart would be a waste of time. In general, it is sufficient to lay down three points—the place sailed from, the place sailed to, and the point of maximum separation, and through these points to draw an arc of a circle. As the rhumb-line and great circle track between two places, one in north latitude and the other in south lati tude, cross each other at the equator, in this case there will be two points of maxt'arum separation, and the course and distance must be calculated for each side of the equator separately. Many ignorantly object to great circle sailing on the ground that, on account of constant change of bearings, a ship cannot be navigated on the correct course; but, in fact, all that is required of a navigator is to sail as near to his great circle track as con venient; and each separate course will be a tangent to his track, and the shorter these tangents are made, the more will the length of a voyage be diminished. We may here mention that a chart constructed on the gnomonic projection (q.v.) represents all great circle tracks as straight lines. See NAVIGATION.