EXAMPLE NUMBER 7 One latitude, one longitude, distance and departure to find the course, latitude and longitude in: A ship was sailed 428'.o to the southward and departure 214'. E. from a point in latitude 20° 15'00" N. and longitude 74° 08' 01" W. Find the course, latitude and longitude of the ship. Enter Table 2 with the distance 428'.o S. and the departure 214'. E. and where they agree, the proper difference of latitude 370'.7 and the course S. 30° E. will be found. Subtract the proper difference of latitude 370'.7 from the latitude left and the result will be the latitude of the ship. From Table 3 take the meridional parts for both latitudes and find their difference, which takes the same name as the proper difference of latitude. Enter Table 2 with the course S. 30° E. and find the meridional difference of latitude 386'.1 in the latitude column and the corresponding number in the departure column will be the difference of longitude 223'. E., which subtracted from the longitude left gives the longitude of the ship. EXAMPLE NUMBER 8 Both latitudes (one north and the other south) and both longitudes to find the course and distance: A ship is in latitude 4° 32'45" N. and longitude 25° 35' 45" W. Find the course and distance to a point in latitude 1° 30' 45" S. and longitude 24° 05' 15" W. Find the difference of latitude by adding the latitude of the point to that of the ship, convert it into miles and name it south, because the point is south of the latitude of the ship. From Table 3 take the meridional parts for the latitudes to the nearest mile and find their difference by adding, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. Find the difference of longitude by subtracting the longitude of the point from that of the ship, convert it into miles and name it east, because the point is east of the longitude of the ship. Enter Table 2 with the meridional difference of latitude 361'.8 S. and the difference of longitude go'.5 E. and where they are found to agree nearly, the meridional difference in the latitude column and the difference of longitude in the departure column will give the course S. 14° E. Enter Table 2 with the course S. 14° E. and find the proper difference of latitude 363.5 in the latitude column. The distance 374'.7 is found opposite in the distance column. When the places under consideration lie so near the equator it is not necessary to use Mercator sailing unless requested to do so at an examination, as plain sailing, in which the degrees of latitude and longitude are supposed to be equal, will give a result practically the same. MERCATOR SAILING BY LOGARITHMS The course, distance, etc., found by inspection should not be used unless the distance is small and an approximate result will answer. Its most frequent use is in finding the course and distance made good from noon to noon, which should be exact. However, in any case, the elements wanted should be found by inspection first, which not only serves as a check, but saves time in selecting logarithms from Tables 42 and 44. A general description of the various operations is not given here, but in its place an individual explanation follows each example. The following table contains the necessary rules for the solution of any problem by Mercator sailing: and longs. Dep. 3 co. and Ex. Given. To Find. Methods. = sec. co. X prop. dif. lat. = prop. dif. lat. = cos. co. Dep. = prop. dif. lat. X tang. co. Tang. co. = dep. • prop. dif. lat. Dist. = prop. dif. lat. X sec. co. 2 lats. and Dist. Dist. dep. : sin. co. Dif. long. =mer. dif. lat. X tang. co. Dif. long. = (dep. X mer. dif. lat.) = prop. dif. lat. One lat. Dep. Dep. dist. X sin. co. Prop. dif. lat. Prop. dif. lat. = dist. X cos co. dist. Dif. long. Dif. long. = mer. dif. lat. X tang. co. prop. dif. lat. • cos. co. 4 lats. and Dep. Dep. prop. dif. lat. X tang. co. Dif. long. = mer. dif. lat. X tang. co. Cos. co. = prop. dif. lat. • dist. 5 lats. and Dep. Dep. dist, X sin. co. dist. Dif. long. Dif. long. = mer. dif. lat. X tang. co. dep. : sin.co. = mer. dif. lat. X tang. co. dep. Dif. long. Dif. long. (dep. X mer. dif. lat.) → prop. dif. lat. Sin. co. dep. • dist. One lat. 7 dist. and Prop. dif. lat. Prop. dif. lat. = dist X cos. co. Dif. long. = mer. dif. lat. X tang. co. dep. Dif. long. Dif. long. = (dep. X mer. dif. lat.) = prop. dif. lat. Co. |