NAVIGATION. DEFINITIONS, ETC. (1.) Two distinct methods are used for navigating a ship from one place to another; the first is an application of the common rules of plane trigonometry; the other requires a knowledge of spherical trigonometry, and of the principal definitions and facts in astronomy. The latter is for this reason called Nautical Astronomy; the characteristic name of the former being Navigation or plane sailing. P. (2.) The necessary angles and measurements in the first method are supplied by means of the compass and log-line; in the second and more exact method they are obtained by astronomical observations. &c., at the same angle. This common angle is called the course from A to F, and the arc AF (in nautical miles) is called the distance. Draw the parallels of latitude AN and FO; the arc AU is the latitude of A, and Fz the latitude of F; UZ, or the angle APF, is the difference of longitude. between A and F. The arc OA is the difference, or, as it is called in Navigation, the true difference of latitude between A and F. Suppose the intermediate meridians PV, PW, &c. to be drawn through points B, C, &c. taken on the arc AF indefinitely near to one another, and through B, C, &c., suppose arcs of parallels BH, CI, &c. to be drawn; on this supposition the elementary triangles ABH, BCI, &c. may be considered as right-angled plane triangles, of which the sum of the sides AB, BC, &c. is the distance, the sum of the sides AH, BI, &c. is equal to the true difference of latitude, and the sum of the sides BH, CI, &c. is called in Navigation the departure. A The chart used at sea for marking down the ship's track, and for other purposes, exhibits the surface of the globe on a plane on which the meridians are drawn parallel to each other, and therefore the parts BH, CI, DK, &c., arcs of parallels of latitude, are increased and become equal to the corresponding parts of the equator UV, VW, &c. Now, in order that every point on this plane may occupy the same relative position with respect to each other that the points corresponding to them do on the surface of the globe, the distance between any points a and o, and a and F must be increased in the same proportion as the distance Fo has been increased. The true difference of latitude, AO, is thus projected on the chart into what is called the meridional difference of latitude, and the departure, BH+CI+DK+.. into the difference of longitude. A chart constructed in this manner is called a Mercator's Chart. From these definitions and principles are deduced certain trigonometrical formulæ, and these expressed in words form the common Rules of Mercator and Parallel Sailing. For the proof of these formulæ and rules, the student is referred to the author's volume of "Astronomical Problems and their Solutions," (p. 122.) PRELIMINARY RULES IN NAVIGATION. Rule (a). To find the true difference of latitude, having given the latitude from and latitude in.* (1.) When latitude from and latitude in have like names, that is, are both north or both south. Under the latitude from, put down the latitude in, take the difference and reduce the same to minutes; place N. or S. against the result according as the latitude in is north or south of the latitude from; the remainder is the true difference of latitude. (2.) When latitude from and latitude in have unlike names, that is, one north and the other south. Take the sum of the two latitudes, reduce it to minutes, and attach N. or S. thereto according as the latitude in is north or south of the latitude from; the result is the true difference of latitude. EXAMPLES. 1. Find the true difference of latitude, having given latitude from = 42° 10′ N., and latitude in 50° 48' N. lat. from 42° 10' N. lat. in 50 48 N. 8 38 60 T. D. lat. 518 N. * The latitude of the place left is called the latitude from; the latitude of the place arrived at is called the latitude in. 2. Find the true difference of latitude, having given latitude from 3° 42′ N., and latitude in 2° 50′ S. lat. from 3° 42' N. lat. in 2 50 S. 6 32 60 T. D. lat. 392 S. Find the true difference of latitude in each of the following examples: To find the meridional difference of latitude, having given the latitude from and latitude in. Take the meridional parts for the two latitudes from the table of meridional parts; subtract, if the names be alike, and add if the names be unlike; the result is the meridional difference of latitude, N. or S. being attached thereto according as the latitude in is north or south of latitude from. EXAMPLES. 9. Find the meridional difference of latitude, having given latitude from 42°10'N., and latitude in 50° 48' N. lat. from 42° 10′N. lat. in 50 48 N. mer. parts 2795.2 N. mer. parts 3549.8 N. mer. diff. lat. 754.6 N. 10. Find the meridional difference of latitude, having given latitude from 3° 42′ N., and latitude in 7° 32′ S. lat. from 3° 42' N. lat. in 7 32 S. mer. parts 222.2 N. mer. parts 453.3 S. mer. diff. lat. 675.5 S. |