. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. e are from the equator, north or south,that is, the greater the latitude we are in, the same departure willcover more longitude. To discover the law for changing departure to difference of longi-tude, we adduce the following figure. Let C be the center of the earth, P thepole, PC a portion of the earths axis. The plane PCB is the plane of onemeridian, and P CA the plane of anothermeridian. AB is a portion of the equator betweenthe two meridians, A CB is a sector int
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. e are from the equator, north or south,that is, the greater the latitude we are in, the same departure willcover more longitude. To discover the law for changing departure to difference of longi-tude, we adduce the following figure. Let C be the center of the earth, P thepole, PC a portion of the earths axis. The plane PCB is the plane of onemeridian, and P CA the plane of anothermeridian. AB is a portion of the equator betweenthe two meridians, A CB is a sector inthe plane of the equator, and DEB. andFQQ are sectors similar to A CB. Observe that DE, FG, &c, are parallels of latitude, that is, theyare parallel to AB, the plane of the equator. The magnitude of DE is called departure, and it corresponds tothe difference of longitude AB. Also, FQ is departure corresponding to the same difference oflongitude AB. The difference of longitude is always greater thanany corresponding departure, that is, AB is obviously greater thanany other parallel distance between the same two PLANE SAILING. 183 Because the two sectors A CB DEH are similar, we have theproportion. AC : DH : : AB : DE (1) Observe that A C is the radius of the sphere, DH is the sine ofthe arc PD, or the cosine of DA, which is the cosine of the lat-itude of the point D. Therefore the preceding proportion becomes, rad. : cos. lat. : : dif. Ion. : , cos. lat. : rad. : : dep. : dif. Ion. In words, The cosine of the latitude is to the radius so is the depar-ture to the difference of longitude. These words are indelibly engraved on the memory of every nav-igator, and they embrace all the rules that can be made for chang-ing departure into longitude, or longitude into departure. When a ship sails east or west, the distance sailed is called de-parture, and is reduced to longitude by the preceding proportion. This is called parallel sailing. EXAMPLES. 1. What difference of
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