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. . To the logarithm of the difference of latitude 169'.2 add the logarithm tangent of the course S. 56° W., which gives the logarithm of the departure 250'.8. To the logarithm of the difference of latitude 169'.2 add the logarithm secant of the course S. 56° W., which gives the logarithm of the distance 302'.6. Add together the latitude of the point left and that of the ship. Then divide by 2, which will give the middle latitude. To the logarithm of the departure 250'.8 add the logarithm of the middle latitude 35° 45'48" and the result will be the logarithm of the difference of longitude 309'.1, which is subtracted from the longitude of the point left because the ship has sailed west and in doing so has decreased the longitude. 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. Find the difference of latitude by subtracting the latitude of the point left from that of the ship and name it south because the ship has sailed south. From the logarithm of the difference of latitude 66'.8 subtract the logarithm of the distance 392'.0, which gives the cosine of the course S. 80° II' E. To the logarithm of the distance 392'.o add the logarithm sine of the course S. 80° 11' E., which gives the logarithm of the departure 386'.3. Add together the latitude left and that of the ship. Then divide by 2, which will give the middle latitude. To the logarithm of the departure 386'.3 add the logarithm secant of the middle latitude 56° 27' 05" and the result will be the difference of longitude 698'.9, which is subtracted from the longitude of the point left because the ship has sailed east, 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. From the logarithm of the departure 342'.subtract the logarithm tangent of the course S. 67° 30' W., which gives the logarithm of the difference of latitude 141'.7 and is subtracted from the latitude of the point left because the ship has sailed south. From the logarithm of the departure 342'.O subtract the logarithm sine of the course S. 67° 30' W., which gives the logarithm of the distance 370'.2. Add together the latitude of the point left and that of the ship. Then divide by 2, which will give the middle latitude. To the logarithm of the departure 342'.o add the logarithm secant of the middle latitude 39° 26' 11" and the result will be the logarithm of the difference of longitude 442'.8, which is added to the longitude of the point left because the ship has sailed west and in doing so has increased the longitude. 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. 214'. 2.33041 428.0 — 2.63144 = sin. 9.69897 Dep. 2)34 19 18 Middle lat. 17 09 39 cos. 9.93753 428'.0 + 2.63144 = 370.7 = 2.56897 Long. left 74° 08' 01" W. Dif. 224.0=- 3 44 00 E. Long. ship 70 24 01 W. Dep. Middle lat. 17° 09' 39" 214.0 2.33041 sec. + .01978 = 224.0 = 2.35019 EXPLANATION From the logarithm of the departure 214'.O subtract the logarithm of the distance 428'.0, which gives the logarithm sine of the course S. 30° E. To the logarithm cosine of the course S. 30° E. add the logarithm of the distance 428'.0, which gives the logarithm of the difference of latitude 370'.7 and is subtracted from the latitude of the point left because the ship has sailed south. Add together the latitude of the point left and that of the ship. Then divide by 2, which will give the middle latitude. To the logarithm of the departure 214'.o add the logarithm secant of the middle latitude 17° 0' 39" and the result will be the logarithm of the difference of longitude 224'.o, which is subtracted from the longitude of the point left because the ship has sailed east and in doing so has decreased the longitude. 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 course and distance. Lat. ship 4° 32'45" Tr. Long. ship 25° 35' 45" W. Lat. point +1 30 45 S. Long. point — 24 05 15 W. Dif. 363":5=6 03 30 S. Dif. 90'.5 = I 30 30 E. Greater lat. 2)4° 32' 45" Middle lat. 2 16 22 Dif. long. 90'.5 1.95665 Mid. lat. 2° 16' 22" cos. + 9.99966 90'.43 = 1.95631 Dif. lat. 363.5 – 2.56050 Co. S. 13° 58' E. tang. 9.3958I Co. S. 13° 58' E. sec. .01303 Dif. lat. 363.5 + 2.56050 Dist. 374.6 = 2.57353 Dep. |