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SOLUTION.- First reduce each compass course to true by applying corrections for variation and deviation. Thus,

First Course Compass course = N by W

Or = N 1 point W
Deviation = point E
Magnetic course = N ) point W

Variation A point E
True course = North

Second Course
Compass course = · NW įN

Or = N 3 points W
Deviation - á point E
Magnetic course N 34 points W

Variation À point E True course = N 3 points W

Or NW by N

Third Course

Fourth Course Compass course = N E E Compass course = N by W W Or = N 41 points E

Or = N 13 points W Deviation į point W

Deviation 3 point E Magnetic course = N 3 points E Magnetic course = N 1points W Variation à point E

Variation point E True course N4 points E

True course = N 1 point W
Or NE

Or = N by W
Bearing
Magnetic bearing S i W

Variation I E
True bearing

S by W
Reversed N by E

The true courses, together with the reversed bearing, are then entered in traverse; thus,

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Dep.

3.1'W

For the latitude and longitude in:

Lat. left = 41° 43.5' N
D. Lat. (117.8') 1° 57.8' N

Lat. in 43° 11.3' N. Ans.
Sum of Lats. 85° 25.8
į sum = M. Lat. = 42° 42.9 Resulting D. Long. = 4' W

Long. left 86° 55' W
D. Long. 4' W

Long. in = 86° 59' W. Ans.
Then find the course and distance to the place of destination; thus,
Lat. in 43° 41.3' N

Long. in : 86° 59' W
Lat. Ludington 43° 57.5' N Long. Ludington = 86° 28' W
D. Lat.
16.2 N
D. Long.

31' E Sum of Lats. 87° 38.8

M. Lat. 43° 49.4 Resulting Dep. = 22.3' E.
True course = N 54° E

Or = NEE (nearly)
Variation

ÅE
Magnetic course = Ν Ε ΣΕ
Deviation

W
Compass course NE by E. E. Ans.

Distance = 28 mi. Ans. On the chart of Lake Michigan, Fig. 26, are plotted the courses and distances recorded in the preceding example. By actual measurement on that chart, according to instructions given in Lake Navigation, Part 2, the student will find that the result thus obtained will agree exactly with that obtained by calculation.

EXAMPLE 2.- A steamer coming from St. Mary's River, is bound for Eagle Harbor, Mich., latitude 47° 27.6' N and longitude 88° 9' W. After passing White Fish Point, latitude 46° 46.3' N and longitude 84° 57' W, the light situated at that point is watched for a departure, and just before it goes out of sight its bearing by compass is found to be S 56° E. The range of visibility of the light is 16 statute, or nearly 14 nautical, miles. The deviation of the point on which the ship was headed when the bearing was taken is 12° E, and the variation is 1° W. When the light disappeared from sight, the steamer is put on a compass course N 75° W; the deviation on that point is 151° E and a strong northwesterly wind produces a leeway estimated at point. After a distance of 53 miles has been run on that course, an accident to the machinery compels the ship to be hove-to on the starboard tack and headed S 66° W by compass. On this course a distance of 12 miles is covered, the leeway being 1į points, variation 1° E, and the deviation 8° W. After repairs have been effected, the steamer is headed N 54° W

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Fig. 26

South Haven

88°

86°

1

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by compass, the deviation on that point being 10° E, and the variation 2° E. Find the position of the steamer after a distance of 43 miles has been run on the last course, and find the true course and distance from that point to the port of destination.

SOLUTION. – As before, we reduce the bearing and compass courses to true; thus, Bearing

First Course
Compass bearing = S 56° E Compass course N 75° W
Deviation = 12° E Leeway i point 8°
S 44° E

N 83° W
Variation 1° W

Deviation 151° E
True bearing S 45° E

True course N 671° W
Reversed = N 45° W

Or = WNW
Second Course

Third Course
Compass course = S 66° W Compass course N 54° W
Leeway 14 points 14°

Deviation 10o E
S 52o W

N 44° W
Deviation 8° W

Variation 2° E
S 44° W

True course = N 42° W
Variation 1° E

True course = S 45° W The data in this case, together with the traverse, may conveniently be arranged in the following tabular form:

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S 56° E

1° W 12° E N 45° W 14 9.9
N 75° W 3 point 154° EWN W 53 20.3
S 66° W 11 points 1° E 8° W S 45° W 12
N 54° W

9.9 49.0

8.5 28.8

8.5

2° E 10° E N 42° W 43 32.0

62.2 8.5

8.5 53.7' N

96.2 W Dep.

D. Lat.

Lat. left = 46° 46.3' N
D. Lat. 53.7' N

Lat. in 47° 40' N. Ans.
Sum of Lats. 94° 26.3

M. Lat. 47° 13'

Resulting
D. Long

141' W

Long. left
D. Long.
Long. in

84° 57' W

2° 21' W
87° 18' W. Ans.

For the true course and distance to the port of destination, we proceed as follows: Lat. in 47° 40' N

Long. in = 87° 18' W Lat. Eagle Harbor 47° 27.6' N Long. Eagle Harbor 88° 9' W D. Lat. 12.4' S

D. Long 51' W
Sum of Lats. 91° 67.6'
M. Lat. 47° 33.8

Resulting Dep. = 34.4' W

The nearest degree corresponding to the given D. Lat. and Dep. is 70°. Hence, tiue course is S 70° W, and distance is 37 mi. Ans.

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1. A steamer, after passing the breakwater at Buffalo, N. Y., latitude 12° 52.7' N and longitude 78° 51' W, steers a true course S W by W W. Find the latitude and longitude in after a distance of 48 miles has been covered

Ans.

42'

79° 52' W.

2. Find the true course and distance from Grand Haven, Mich.. latitude 43° 3.2' N and longitude 86° 15' W, to Sheboygan, Wis., Lat. 43° 45' N, Long. 87° 41.2' W.

| True course = N 56° W, or N W by W. Ans.

| Distance 75 mi.

3. The true bearing of the lighthouse on the north end of Devil's Island, Wis., latitude 47° 4.8' N and longitude 90° 43.2 W, is S W, distance 10 miles. From the point where the bearing was taken, the following true courses and distances were run: East 49 miles, and N 60° E 18 miles. Find (a) the ship's position and (6) the true bearing and distance from that position to the lighthouse at Fourteen Miles Point, latitude 46° 59' N and longitude 89° 7.2 W.

„Lat. in 47° 20.9' N.

(a) Ans.

I Long. in 88° 58.2' W. (6)

Į Bearing - S 16° W.

Distance 23 mi.

4. What compass course should be steered from Marquette breakwater, latitude 46° 32' N and longitude 87° 22.7'. W, to the lighthouse on Caribou Island, latitude 47° 20' N and longitude 85° 49' W, assuming the mean value of the variation to be 2o E and the deviation 161o W? How long would it take a steamer making a speed of 10 knots per hour to cover the distance between the two places?

Ans.

Compass course N 67° 30' E, or E N E.
Time required : 8 hr.

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