Dep. = Lat. point 37° 55'25” N. Mer. parts 2447'.5 Lat. ship – 35 57 25 N. Mer. parts - 2300.5 Dif. 118.0= 1 58 00 S. Dif. 147.0 S. 216'.5 E. 2.33546 Prop. dif. lat. 118.0 S. – 2.07188 Co. S. 61° 24' E. tang. 0.26358 Prop. dif. lat. 118.0 2.07188 Co. S. 61° 24' E. sec. .31994 Dist. 246'.5 2.39182 Mer. dif. 147'.0 2.16732 Co. S. 61° 24' E. tang. t .26358 Dif. long. 4° 29' 42" E. = 269'.7 = 2.43090 Long point 74° 56' 22" W. Dif. 269'.7 =- 4 29 42 E. Long. ship 70 26 40 W. EXPLANATION Find the difference of latitude by subtracting the latitude of the ship from that of the point left, convert it into miles and name it south, because the ship is south of the point sailed from. 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. From the logarithm of the departure 216'.5 E. subtract the logarithm of the proper difference of latitude 118'.0 S., which gives the logarithm tangent of the course S. 61° 24' E. To the logarithm of the proper difference of latitude 118'. add the logarithm secant of the course S. 61° 24' E., which gives the logarithm of the distance 246.5. To the logarithm of the meridional difference of latitude 147'.0 add the logarithm tangent of the course S. 61° 24' E., which gives the logarithm of the difference of longitude 269':7, which is subtracted from the longitude of the point sailed from and gives the longitude of the ship. EXAMPLE NUMBER 3 One latitude, one longitude, course and distance to find the latitude and longitude of the ship: A ship sailed S. 65° E. for 362'.o from a point in latitude 35° 15' 17" N. and longitude 75° 31' 16" W. Find the latitude and longitude in. Dist. 362.0 2.55871 Co. S. 65° E. cos. t. 9.62595 Prop. dif. lat. 2° 33' oo" S. = 153".0 = 2.18466 Lat. left 35° 15' 17" N. Mer. parts 2249'.1 Dif. 153.05- 233 oo S. Lat. ship 32 42 17 N. Mer. parts - 2065.5 Dif. 183.6 S. Mer. dif. 183'.6 2.26387 Co. S. 65° E. tang. t .33133 Dif. long. 6° 33' 42" E. = 393':7 = 2.59520 Long. left 75° 31' 16" W. Dif. 393.7 — 6 33 42 E. Long. ship 68 57 34 W. EXPLANATION To the logarithm of the distance 362'.o add the logarithm cosine of the course S. 65°. E., which gives the logarithm of the proper difference of latitude 153'.o. From the latitude left subtract the difference of latitude 153'.0, which gives the latitude of the ship. From Table 3 take the meridional parts for both 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. To the logarithm of the meridional difference of latitude 183'.6 add the logarithm tangent of the course S. 65° E., which gives the logarithm of the difference of longitude 393'-7 E., which subtracted from the longitude left will give 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. Lat. left — 34° 21' 12" S. Mer. parts — 2183.7 Lat. ship 37 10 25 S. Mer. parts 2391 .0 Dif. 169'.2= 2 49 13 S. Dif. 207 :3 S. Mer. dif. 207*.3 2.31660 Co. S. 56° W. tang + I7IOI Dif. long. 5° oz' 18" W. = 307'3 = 2.48761 Long. left 18° 29' 26" E. Dif. 307'.3=- 5 07 18 W. Long. ship 13 22 08 E. Prop. dif. lat. 169'.2 2.22840 Co. S. 56° W. cos. - 9.74756 Dist. 302'.6 = 2.48084 EXPLANATION Find the difference of latitude by subtracting the latitude left from that of the ship, convert it into miles and name it south, because the ship has sailed south. 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. To the logarithm of the meridional difference of latitude 207'.3 add the logarithm tangent of the course S. 56° W. and the result will be the difference of longitude 307'.3 W., which is subtracted from the longitude left and gives the longitude of the ship. From the logarithm of the proper difference of latitude 169'.2 subtract the logarithm cosine of the course S. 56° W., which gives the logarithm of the distance 302'.6. 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. Lat. left - 55° 58' 41" S. Mer. parts – 4052'.7 Lat. ship 57 05 30 S. Mer. parts 4173.0 Dif. 66'.8= I 06 49 S. Dif. 120.3 S. Prop. dif. lat. 66'.8 S. 1.82478 Dist. 392 .0 E. – 2.59329 Co. S. 80° 11' E. = cos. 9.23149 Mer. dif. 120'.3 2.08027 Co. S. 80° II' E. tang. t .76188 Dif. long. 11° 35' 18" E. = 695'.3 = 2.84215 Long. left 67° 16' 15" W. Dif. 695'.3=-11 35 18 E. Long. ship 55 40 57 W. EXPLANATION Find the difference of latitude by subtracting the latitude of the point left: from that of the ship, convert it into miles and name it south, because the ship has sailed south. 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. From the logarithm of the proper difference of latitude 66'.8 subtract the logarithm of the distance 392'.o and the result will be the logarithm cosine of the course S. 80° 1' E. To the logarithm of the meridional difference of latitude 120'.3 add the logarithm tangent of the course S. 80° 11' E. and the result will be the logarithm of the difference of longitude 695'.3 E., which is subtracted from the longitude left and gives the longitude of the ship. 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 342.0 departure. Find the distance, latitude and longitude of the ship. |