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EXAMPLE 2.-A ship sails from latitude 26° 17' S, 190' south. Find her latitude in. SOLUTION.

Lat. left=26° 17' S
Diff. of lat. (190') = 3° 10' S (+)

Lat. in=29° 27' S. Ans.
EXAMPLE 3.-A ship from the west end of the Island of Madeira in
latitude 32° 48' N sails north 98'. What is her latitude in ?
SOLUTION.-.

Lat. left=32° 48' N
Diff, of lat. (98') = 1° 38' N (+)

Lat. in=34° 26' N. Ans.

EXAMPLES FOR PRACTICE 1. Latitude left is 0° 10'N; the difference of latitude sailed is 228' north. Find the latitude in. .

Ans. Lat. in=3° 58' N. 2. The latitude of one place is 40° 40' N, of another 33° 42' N. Find the difference of latitude.

Ans. Diff. of lat. =6° 58' or 418'. 3. Latitude left is 2° 48'S; the difference of latitude sailed is 288' north. Find the latitude in.

Ans. Lat. in=2° ON. 4. A ship is in latitude 68° 48' N and another in 38° 30' N; what is the difference of latitude between the two ?

Ans. Diff. of lat.=30° 18' or 1,818'. 5. Latitude left is 3° 42'S; the latitude in is 1° 40' N. Find the difference of latitude sailed.

Ans. Diff. of lat. =322' N. 6. Latitude left is 3° 2 S; the difference of latitude sailed is 190 north. Find the latitude in.

Ans. Lat. in=0° 8'N.

18. The colatitude is the complement of the latitude. Thus, in Fig. 2, the colatitude of the place A is the arc AP, or colatitude=90° — latitude.

19. A nautical mile is reckoned as 6,080 feet, or 1,013 fathoms; it is equal to the mean length of a minute of latitude. A second of arc is, therefore, about 101 feet, or 17 fathoms nearly. A statute mile is less than a nautical mile and contains 5,280 feet, only.

20. The longitude of any place is the distance in arc east or west, measured on the equator from the first meridian to the meridian passing through the place. Thus,

-186° = 174o E, but the former expression is never used. Fig. 3 (6), which represents our globe looking from above the pole P, on the plane of the equator, illustrates very clearly the foregoing statements. Besides being measured in degrees, minutes, etc. of arc, longitude is also measured in time, that is, in hours, minutes, and seconds, each hour being equal to 15°.

22. The difference of longitudes of any two places is the arc of the equator contained between the meridians passing through the places. Thus, the difference of longitude between the two places G and C, Fig. 3 (a), is the arc A D of the equator E E' contained between the meridians PGP and PCP passing through G and C, respectively. When both places are in east, or both in west, longitude, the difference of longitude is the difference between their longitudes, expressed either in arc, time, or nautical miles; if, however, one is in west longitude and the other in east longitude, the difference of longitude is equal to the sum of their longitudes, or the remainder of that sum from 360°.

EXAMPLE 1.–Find the difference of longitude, expressed in minutes of arc, between longitude 5° 3' W and longitude 16° 39' W. SOLUTION.

1st long.

5° 3' W
2d long. = 16° 39 W

Diff. of long.=11° 36'
Expressed in min. of arc= 696'. Ans.

EXAMPLE 2.–The longitude of the Cape of Good Hope is 18° 29' E and that of Tristan da Cunha 12° 2' W. Required the difference of longitude between the two places. SOLUTION.- Long. Cape of Good Hope=18° 29' E

Long. Tristan da Cunha=12° 2' W

Diff. of long. =30° 31'. Ans. EXAMPLE 3.–Find the difference of longitude, expressed in minutes of arc, between New York and Charleston, S. C., the former being in longitude 74° 0 W, the latter in 79° 54' W. SOLUTION.

Long. New York=74° 0 W
Long. Charleston=79° 54' W
Diff. of long.

= 5° 51'
Expressed in min. of arc= 351'. Ans.

EXAMPLE 4.-An observer is stationed in longitude 120° W, another in longitude 79° E; what is the difference of longitude between them? SOLUTION.

1st long. = 120° W
2d long. = 79° E

Sum=1990
Subtract from 360°

Diff. of long.=161° Expressed in min. of arc=9,660. Ans. 23. When a ship in west longitude sails west and in east longitude sails east, she evidently increases her longitude. But when sailing west in east longitude and east in west longitude, her longitude decreases. Therefore, when one longitude and the difference of longitude is known, the longitude arrived at is readily found, as shown in the following examples.

NOTE.-By long. left is understood the longitude of the place the ship sailed from; and by long. in, the longitude of the place arrived at.

EXAMPLE 1.-A ship leaves a place in longitude 97° 45' W, the difference of longitude sailed is 71' east; find the longitude in. SOLUTION.

Long. left=97° 45' W
Diff. of long., 71'= 1° 11' E

Long. in=96° 31' W. Ans.
EXAMPLE 2.-A ship in longitude 1° 20' W changes her longitude
236' to the eastward. Required her longitude in.
SOLUTION.-

Long. left=1° 20 W
Diff. of long., 236'=3° 56' E

Long. in=2° 36' E. Ans.
EXAMPLE 3.-Find the longitude in, having given the longitude
left 160° 20' W and the difference of longitude 2,480 to the westward.
SOLUTION.--

Long. left=160° 20 W
Diff, of long., 2,480= 41° 20 W

Sum=201° 40 W
Subtract from, 360°

Long. in=158° 20 E. Ans. The student will notice that the difference of latitude as well as the difference of longitude is denoted, the former by Nor S, the latter by E or W, to indicate the direction in which the change has taken place.

EXAMPLES FOR PRACTICE 1. Longitude left is 110° 42' W, longitude in is 101° 42' W; find the difference of longitude.

Ans. Diff. of long.=540 E. 2. Longitude left is 2° 30E, the difference of longitude is 126' E; find the longitude in.

Ans. Long. in=4° 36' E. 3. Longitude in is 1° 40.4' W, the difference of longitude sailed is 100.4' W; what was the longitude left? Ans. Long. left=0° 0'.

4. Longitude left is 3° 10 W, the difference of longitude is 380' E; find the longitude in.

Ans. Long. in=3° 10' E. 5. Longitude left is 62° 32' E, the longitude in is 45° 51.5' E; find the difference of longitude.

Ans. Diff. of long. =1,000.5' W. 6. Longitude left is 178° 15' E, the longitude in is 178° 45' W; find the difference of longitude.

Ans. Diff. of long. = 180' E.

24. The ship's course, or the course steered, is the angle between a meridian and the ship's fore-and-aft line.

25. The course made good is the angle between a true meridian and the ship's real track or path through water. Courses are reckoned from north or south toward east or west and are measured either in degrees and minutes, or in points of 11° 15' each.

(a)

FIG. 4

26. The Rhumb Line.—When a ship sails from one place to another in one and the same direction, her course will intersect all meridians at the same angle. Thus, in

Fig. 4 (a), if the ship sails from a to b, the line ab, representing her course or track, will intersect all meridians at the same angle; in other words, the angles Pab, Pa' b, Pa' b, etc. are all equal. Since the meridians all converge toward the pole, it is evident that this line, called the rhumb line, or loxodrome, in its continuity is an unending spiral (see (c) Fig. 4) always approaching the pole, but never actually reaching it. The reason for this is that the geographical pole, bearing due north, cannot be reached on any other course than due north.

27. The distance between two places, or the distance run by the ship on any course, is the length of the rhumb line joining the two places, expressed in nautical miles. It is sometimes termed nautical distance to distinguish it from the shortest distance" on a great-circle track.

28. The departure is the distance made good by the ship due east or west, or the distance between any two

places measured on one of their parallels. The departure is usually expressed in nautical miles.

In order to more fully explain the foregoing terms, the student is referred to

Fig. 5. There, if a Fig. 5

ship sails from a to b, the line ab is the distance, and if the lines x y and 2 v represent meridians running north and south, ac is the difference of latitude; the angle at a, the course; and the distance cb is the departure.

29. The bearing of an object, or place, is the angle that the direction of the object or place makes with the meridian, and is the same as the course toward it. Thus, in Fig. 5, if an observer is standing at a, the bearing of the

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