Now, to find what course the ship must steer and what distance she must run in order to reach e her port of destination, lay off from d on a line parallel to W E 116.2 miles, the difference between the departures g c and d f. This will be equal to the departure between d and e. Then from h, on a line perpendicular to hd, lay off 155.9 miles, which is the difference between the two differences of latitude cf and ge. The departure and difference of latitude found, compute the course and distance to be run in order to reach e. Thus, EXAMPLE 4.-Yesterday at noon our latitude by observation was 46° 18′ N and since then we have run the following courses and distances, namely: N 25° W, 50 miles; N 74° E, 64 miles; S 52° W, 36 miles; N 35° E, 40 miles; N 69° W, 75 miles; and S 47° E, 48 miles. Required our present latitude, course, and distance made good. SOLUTION. Arrange a traverse table as before. EXAMPLE 5.-From latitude 51° 30' N a ship making a speed of 8 knots per hour sails the following courses: S 67° W, 3 hours; N 45° W, 2 hours; W, 4 hours; S 33° W, 24 hours, and N WW, 2 hours. Required the course and distance made good and, also, the latitude in. The difference of latitude 2' may be omitted without any practical error. a 20. Cautionary Remarks.-The attention of the student is called to the fact that the balance of the departures made in a succession of courses is not strictly the same as the single departure made in the single course from the place left to that ultimately arrived at by traverse sailing. For instance, if a ship sails in any latitude due east or due west, as from a to bor from b to a, Fig. 12, the total distance a b will also be the departure. But, if another ship were to sail from a lower latitude c on the same meridian to the same place b, it is obvious that her departure cd would exceed E' that of the former ship; and if she sailed from a higher latitude, for instance, from e, her departure ef would be less than a b. In a single day's run the inaccuracy of taking the balance of a set of departures as the departure due to the single course made good E FIG. 12 d is, however, too small to lead to any practical error of consequence. 21. Courses Should Be True.-Hitherto, in the examples given, the courses have been true; in actual practice, however, the courses are compass courses, and must be corrected for leeway, deviation, and variation. In cases where the distances sailed are small and the variation the same for all courses, the magnetic courses, corrected for leeway, may be used in entering the traverse tables, and the result will be the magnetic course made good, but must then be corrected for variation. To avoid mistakes, however, each course should be reduced to true before it is entered in the traverse table. The student should make this an invariable rule. EXAMPLES FOR PRACTICE 1. A ship sails on the following courses: NE, 75 miles; ES, 66 miles; SW by WW, 115 miles; S by EE, 98 miles; WN W, 47 miles. Required the course and distance made good. 2. A ship in latitude 34° 22' S sails SWS, 27 miles; SE by E, 45 miles; SW by S, 48 miles; W, 32 miles; and SSW W, 18 miles. Find the course and distance made good and her latitude in. 3. A cruiser doing patrol duty steams the following courses and distances: S 69° W, 4 miles; S 58° E, 15 miles; S 66° E, 8 miles; S 66° W, 12 miles; S 1° E, 6 miles; S 55° W, 2 miles; N 21° E, 2 miles; S 55° W, 4 miles; S 32° E, 14 miles; S 55° W, 28 miles. Find what course and distance the cruiser made starting point was 44° 10′ N, the latitude in. Ans. good and, if her = SW W, 62 4. From latitude 4° 40′ S, a ship sails as follows: miles; S by W, 16 miles; WS, 40 miles; SWW, 29 miles; Required the course and distance S by E, 30 miles; SE, 14 miles. made good and the latitude in. PARALLEL SAILING 22. Explanation. In the method by plane sailing we regarded the earth as being a flat surface and took account only of the difference of latitude and the distance run east and west. We did not ascertain, however, how much the ship had changed her longitude; in fact, longitude did not enter at all into its calculations. But as soon as the idea of longitude is introduced, we can no longer consider the part of the earth's surface sailed over as a plane and the meridians as being parallel straight lines; we must then take into consideration the sphericity of our globe and the fact that the meridians of each degree of longitude are 60 minutes apart at the equator and meet at the poles; we must also bear in mind that the latitude parallels, being small circles and parallel to the equator, are none of them equal in circumference, radius, or area to the equator. Sailing along a latitude parallel from a to b, or from b to a, Fig. 13, that is, due east or due west, the distance run a b is equal to the departure made good; but this distance or departure is not in length the same as EE', the difference of longitude. Hence, the length of an arc of a latitude parallel E FIG. 13 at some distance from the equator, though intercepted by the same meridians, is not the same as its corresponding arc on the equator. From this it follows that it is only on the equator where a ship sailing 60 miles due east or due west will Lat. alter her longitude just 1°. 23. Relation Between Latitude, Departure, and Difference of Longitude. To form a clear conception of the relation existing between the latitude E'b, Fig. 13, of any parallel, the departure along that parallel, and the corresponding difference of longitude, the student is referred to Art. 42, Navigation, Part 2, where it was shown that an arc of a parallel a b(= Dep.) is to its corresponding arc of the equator EE'(=D. Long.) as the cosine of the latitude E'b(Lat.) is to 1, the radius of the earth being taken as a unit. Dist. 24. Use of Traverse Tables in Solution of Problems. The formulas above solve all questions relating to parallel sailing; and, just as in plane sailing, we may, in this case, also embody the necessary particulars in a right-angled triangle. Thus, in Fig. 14, the side A C may represent the distance or departure sailed, the hypotenuse BC, the difference of longitude (in linear measure), and the angle A CB, subtended by AC and CB, the latitude of the parallel. B Lat. D.Long. From this it is evident that any prob lem in parallel sailing, like problems in plane sailing, can be solved by consulting the traverse tables, and in order to do this the latitude of the parallel is entered as course, the distance sailed as difference of latitude, when the corresponding distance found in the traverse tables will be the required difference of longitude. The perpendicular AB in the triangle has no significance; it serves merely to connect the other parts. FIG. 14 25. To find the distance between two places on the same parallel when the difference of longitude is given. EXAMPLE.-A ship in longitude 64° 30' W, and latitude 40 N, sails due east to a place in longitude 47° 19′ W. Required the distance run. |