EXPLANATION Enter Table 2 with the course S. 65° E. and distance 362'. in the distance column and the corresponding number in the latitude column 153'.0 will be the proper difference of latitude, which subtracted from the latitude left gives the latitude of the ship. From Table 3 take the meridional parts for the latitudes to the nearest mile and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. With the course S. 65° E. and the meridional difference of latitude 183”.6 S. enter Table 2 and find the meridional difference of latitude in the latitude column and the difference of longitude 393”.7 will be opposite in the departure column, which subtracted from the longitude left gives the longitude of the ship. EXAMPLE NUMBER 4 Both latitudes, one longitude and course to find the distance and longitude in: A ship was sailed S. 56° W. from a point in latitude 34° 21' 12" S. and longitude 18° 29' 26" E. to latitude 37° 10' 25" S. Find the distance and longitude of the ship. - 2183'.7 2391 .0 207 .3 S. Lat. left – 34° 21' 12" S. Mer. parts 18° 29' 26" E. Dif. long. 307'.6=- 5 07 36 W. Long. ship 13 21 50 E. Co. S. 56° W. Prop. dif. lat. 169'.2 S. j = distance 302.5. EXPLANATION Find the difference of latitude by subtracting the latitude left from that of the ship and name it south because the ship is south of the point left. From Table 3 take the meridional parts for the latitudes to the nearest mile and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. Enter Table 2 with the course S. 56° W. and meridional difference of latitude 207'.3 S. and the corresponding number in the departure column 307'.6 will be the difference of longitude, which subtracted from the longitude left gives the longitude of the ship. Enter Table 2 with the course S. 56° W. and find the proper difference of latitude 169'.2 in the latitude column and the corresponding number in the distance column 302'.5 will be the distance. EXAMPLE NUMBER 5 Both latitudes, one longitude and distance to find the course and longitude in: A ship was sailed 392'.o easterly from a point in latitude 55° 58'41" S. and longitude 67° 16' 15" W. to latitude 57° 05' 30" S. Find the course, latitude and longitude of the ship. EXPLANATION Find the difference of latitude by subtracting the latitude left from that of the ship and name it south because the ship is south of the point left. From Table 3 take the meridional parts for both latitudes and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. Enter Table 2 with the proper difference of latitude 66'.8 S. in the latitude column and where it agrees with the distance 392'. E. in the distance column will be found the course S. 80° E. Enter Table 2 with the course S. 80° E. and the meridional difference of latitude 120'.3 in the latitude column and the corresponding number in the departure column will be the difference of longitude 681'.4 E., which subtracted from the longitude left gives the longitude of the ship. In this example the error of 13'.9 in the difference of longitude is due to the difference of i'.o between the course found by logarithms and that by inspection, and shows that logarithms should be used if an accurate result is wanted, and particularly so when the elements fall beyond the limits of Table 2. EXAMPLE NUMBER 6 One latitude, one longitude, course and departure to find the distance, latitude and longitude in: A ship was sailed S. 67° 30' W. from a point in latitude 40° 37' 02" N. and longitude 69° 37' 05" W. making 342'.o departure. Find the distance, latitude and longitude of the ship. Co. S. 67° 30' W. l_ {= Dif. lat. 141'.8. = Lat. left 40° 37' 02" N. Mer. parts 2656'.0 Dif. 141'.8=- 2 21 48 S. Lat. ship 38 15 14 N. Mer. parts - 2472.8 Dif. 183.2 S. Co. S. 67° 30' W. l. Mer. dif. 183.2 ] = dif. long. 442.5 W. Long. left. 69° 37' 05" W. Dif. 442.5= + 7 22 30 W. Long. ship 76 59 35 W. Co. S. 67° 30' W. L Prop. dif. lat. 141'.8 S.) = 0 {= distance 370'.o. EXPLANATION Enter Table 2 with the course S. 67° 30' W. and find the departure 342'. W. with 67o and the corresponding number in the latitude column will be the difference of latitude. Using 68°, find the difference of latitude in the same manner and add together and divide by 2 and the result will be the proper difference of latitude 141'.8 S., which is subtracted from the latitude left because the ship has sailed south, and gives the latitude of the ship. From Table 3 take the meridional parts for both latitudes and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. Enter Table 2 with the course 67o and 68° and the meridional difference of latitude 183'.2 in the latitude column and the mean of the corresponding numbers in the departure columns will be the difference of longitude 442'.5 W., which is added to the longitude left, giving the longitude of the ship. With the courses 67o and 68° find the proper difference of latitude 141'.8 in the latitude columns and the mean of the corresponding numbers in the distance columns 370'.o will be the distance. 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 214.0 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. Dist. Dep. 428'. S. L - Prop. dif. lat. 370'.7 S. 1 Co. S. 30° E. 1233 0 Lat. left 20° 15'00" N. Mer. parts Dif. - 846.9 386.1 S. 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'.o E., which subtracted from the longitude left gives the longitude of the ship. |