Page:The New International Encyclopædia 1st ed. v. 17.djvu/472

* SAILINGS. 432 SAILINGS. 58° 11' Of." (00° — 1° 48'.n). When the dis- tances sailed are short it is customary to lind the Slim of the departures and piok out (from the table of right triangles) the difference of longitude corresponding to the sum, using the mean of the latitiides of the place left and the place reached. Wliile not so exact, it is suffi- ciently so for ordinary purposes of navigation; in the example under consideration tlie error would be about one-half a minute of longitude. Mercator Saii.i.vg is a more accurate method of determining the latitude and longitude of the place of arrival, or the course and distance be- tween places of which the latitude and longitude are known. A complete demonstration of the method requires too nuich space for insertion in this work. The formula? used are: ? = deosC; L' = L + I; p — dsinC ; m = M' — M ; D = to tanC ; ' = X ± D. In these formulie the sjTn- bols have the same meaning as in the other sailings. In addition, M ami M' are the merid- ional parts or augnwnted latitudes correspond- ing to the latitudes of the point of departure and point of arrival respectively; and X and X' are the longitudes of these points. In the accom- panying sketches Fig. 4 is designed to show the Fia. 4. Fio. 6. actual shape of a segment of the earth in which P is the pole, EQ a portion of the equator, PE and PQ meridians, and AB, GH, and .JK por- tions of parallels of latitude. Fig. 5 represents the same segment of the earth on Mercator's pro- jection. E'Q' is equal to EQ, as are also .J'K', G'H', and A'B'. In Fig. 4 the line EB is a por- tion of a loxodromie curve or rhumb-line passing through E and B and making the same angle with the meridians PE and PG and all the other meridians. In Fig. 5 the angles between the lines E'B' and A'E', and E'B' and B'Q'. are preserved ; and, in order that this condition shall hold — since A'B' is longer than AB, and since A'E' and B'Q' are parallel — it is necessarv that A'E' and B'Q' be longer than AE and BQ." A'E' and B'Q' are called the nuqmented Intitudes of the points A and B; similarly G'E', H'Q', J'E', and K'Q' are the augmented latitudes of the points G, H, J, and K. It follows from the foregoing that the loxodromie line is a straight line when laid down on a Mercator's chart, and this is what makes the charts constructed upon that projection so convenient and so widely used. While Mer- cator's charts are almost universally employed for ocean navigation, Mercator sailing is used very little. The ordinary unavoidable errors of navigation are sufficiently large to render the slight superiority in accuracy over middle lati- tude sailing of no practical value, except where the distances are very great or where the ship's track crosses the equator between the points of arrival and departure. In great circle sailititi a ship is made to follow as closely as practicable the arc of the great circle of the earth passing through the points of departure and arrival. Since the shortest line between any two points of a sphere is the are of a great circle passing through the points, it follows that a ship which moves from one point to another on the earth's surface will pass over the shortest route when she follows the arc of the great circle passing through those points. Theoretically, therefore, ships should always sail on great circles. Practically, this is impossible, and is not even generally desirable. Great circles make different angles with every meridian they cross, so that the course would be constantly changing. To effect this constant change would be dithcult and very troublesome. Furthermore, to follow the great circle rigorously would often lead the ship into bad weather or dangerous localities or into regions where the currents and winds are adverse. The sole advantage is the shortening of the distance sailed. By deter- mining points on the circle and sailing along the rhumb-line from point to point, the distance passed over may be made substantially the same as on the great circle, provided the rhumb-line tracks be made sufficiently short. In many cases it is desiral)!e to follow quite closely the great circle for some distance and then the rhumb- line course to some distant point on the circle, which is again followed quite closely to the de- signed point of arrival. For instance, the great circle from Puget Sound to Yokohama runs through the Aleutian Islands and into a region of fog. For this reason steamers do not follow it throughout, but only as far north as desirable, when they take the rhumb-line course to meet the great circle again (a long distance to the west- ward) in about the same latitude; from this point they follow it in short rhumb-line tracks to the destination. The determination of numerous points upon the great circle involves considerable computa- tion work, and, while not difficult, it is beyond the capacity of rule-of-thumb navigators. To adapt great circle sailing to the comprehension of such navigators and to avoid laborious com- putation, many devices have been invented, such as charts on the gnomonic projection, the sphero- graph, great circle protractors, etc. Of these, the gnomonic charts are decidedly the simplest and most practical. The projection is upon a plane tangent to the earth at some selected point on the surface, and the point of sight is the centre of the earth. As all planes cutting great circles out of the earth pass through the earth's centre, they also pass through the point of sight ; and