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MIDDLE LATITUDE SAILING BY INSPECTION Having the latitudes and longitudes of the two points between which the course and distance is wanted, find their differences and name them after the direction the point lies to which the course is to be found. As the miles of longitude are not the same as those of latitude, the middle latitude is found by adding together the two latitudes under consideration and dividing their sum by 2, which will be the middle latitude, the nearest degree of which is used for converting the difference of longitude into departure by entering Table 2 with it as if a course and finding the difference of longitude in the distance column and the corresponding number in the latitude column will be the departure. The departure may be used in a similar manner for converting departure into difference of longitude.

Enter Table 2 with the difference of latitude and departure, and where they agree, or nearly so, the course and distance will be found.

EXAMPLE NUMBER I

Both latitudes and longitudes to find the course and distance: A ship is in latitude 36° 51' 00" N. and longitude 70° 55' 45° W. Find the course and distance to Barnegat light in latitude 39° 45' 52" N. and longitude 74° 06' 24" W.

Lat. ship - 36° 51'00" N. Long. ship. — 70° 55' 45" W.
Lat. Barnegat 39 45 52. N. Long. Barnegat 74 06 24 W.
Dif. 174.9= 2 54 52 N. Dif. 190'.65= 3 10 39 W.
Lat. ship 36° 51'00" N.
Lat. B. + 39 45 52 N.

2)76 36 52
Mid. lat. = 38 18 26=18°, dif. long. 190ʻ.65= dep. 150'.5 W.
Dif. lat. 174.9 N.} =Course N. 41° W., distance 230'.O.
Dep. 150.5 W.) — Course N. 41 W., a

EXPLANATION

Find the difference of latitude by subtracting the latitude of the ship from that of Barnegat light, convert it into miles and name it north because Barnegat light is north of the latitude of the ship.

Find the difference of longitude by subtracting the longitude of the ship from that of Barnegat light, convert it into miles and name it west, because Barnegat light is west of the longitude of the ship.

Add together the latitude of the ship and that of Barnegat light. Then divide by 2, which will give the middle latitude, the nearest degree of which is 38°.

With 38° enter Table 2 and find the difference of longitude, which to the nearest mile is 191'.0, which is found in the distance column, and the corresponding number in the latitude column will be the departure, 150'.5 W.

Enter Table 2 with the difference of latitude 174.9 N. and departure 150'.5 W. and they will be found to agree nearly, giving the course N. 41° W. and the distance 230'.o.

EXAMPLE NUMBER 2 Both latitudes, one longitude and departure to find the course and distance, and longitude in: A ship left a point in latitude 37° 55' 25" N. and longitude 74° 56' 22" W. and arrived in latitude 35° 57' 25" N., the departure being 216'.5 E. Find the course and distance and longitude of the ship. Lat. point 37° 55' 25" N. Long. point 74° 56' 22" W. Lat. ship – 35 57 25 N. Dif. 271'.o=- 4 31 00 E. Dif. 118.0= 1 58 oo S. Long. ship. 70 25 22 W. Lat. point 37° 55' 25" N. Lat. ship +35 57 25 N.

2)73 52 50 Middle lat. = 36 56 25=37° dep., 216'.5 = dif. long. 271'.0 E. Dif. lat. 118'. S. lDep: 216.5 E.

{=Course S. 61° E., distance 247'.c.

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 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, the nearest degree of which is 37°.

With 37° enter Table 2 and find the departure 216'.5 E. in the latitude column, and the corresponding number in the distance column will be the difference of longitude, 271'.0 E., which is subtracted from the longitude of the point left, because the ship has sailed east and in doing so has decreased the longitude.

Enter Table 2 with the difference of latitude 118.0 S. and departure 216'.5 E. and they will be found to agree nearly, giving the course S. 61° E. and distance 247'.

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. Co. S. 65° E.) | Dif. lat. 153.0 S. Dist. 362'.o

Dep. 328.0 E. Lat. left 35° 15' 17" N. Long. left 75° 31' 16" W. Dif. 153'.=- 233 oo S. Dif. 396'.0=- 6 36 00 E. Lat. ship. 32 42 17 N. Long. ship. 68 55 16 W. Lat. left 35° 15' 17" N. Lat. ship + 32 42 17 N.

2)67 57 34 Middle lat. = 33 58 47 = 34° dep. 328'.o dif. long. 396'.0 E.

EXPLANATION Enter Table 2 with the course S. 65° E. and distance 362'.o and take out the difference of latitude 153'.0 S. and departure 328'.o E.

Subtract the difference of latitude from the latitude left and the result will be the latitude of the ship.

Add together the latitude of the point left and the latitude of the ship. Then divide by 2, which will give the middle latitude, the nearest degree of which is 34o.

With 34o enter Table 2 and find the departure 328'.o in the latitude column, and the corresponding number in the distance column will be the difference of longitude 396'. E.

Subtract the difference of longitude from the longitude left and the result will be 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' 15" S. Find the distance and longitude of the ship. Lat. left – 34° 21' 12" S. Long. left 18° 29' 26" E. Lat. ship

37 10 25 S. Dif. 310'.5 W.=-5 10 30 W. Dif. 169'.2= 2 49 13 S. Long. ship 13 18 56 Co. S. 56° W.

L S Dep. 251'.2 W.
Dif. lat. 169'.2 ) - Dist. 303 .O
Lat. left 34° 21' 12" S.
Lat. ship + 37 10 25 S.

2)71 31 37 Middle lat. = 35 45 48 = 36° dep. 251'.2= dif. long. 310'.5 W.

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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 if south because the ship has sailed south.

Enter Table 2 with the course S. 56° W. and the difference of latitude 169'.2 in the latitude column, and find the departure 251'.2 in the departure column and the distance 303".0 in the distance column.

Add together the latitude of the point left and the latitude of the ship. Then divide by 2, which will give the middle latitude, the nearest degree of which is 36o.

With 36o enter Table 2 and find the departure 251'.2 in the latitude column, and the corresponding number in the distance column will be the difference of longitude 310'.5 W., which is subtracted from the longitude of the point left because the ship has sailed west and in doing so it 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.

Lat. left
Lat. ship
Dif.

- 55° 58' 41" S.

57 05 30 S. 66'.8 = I 06 49 S.

Long. left 67° 16' 15" W.
Dif. 699' =- II 39 00 E.
Long. ship 55 37 15 W.

IT 39

Dist. 392'.o 1 - S Co. S. 80°E.
Dif. lat. 66.8 S.) - Dep. 386'.o E.

Lat. left 55° 58' 41" S.
Lat. ship + 57 05 30 S.

2)113 04 II Middle lat. = 56 32 05= 56° 1/2 dep. 386.0=dif. long. 699'. E.

Middle lat. -2) 113 94 u

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