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(6) A steamer from White Fish Point, in latitude 46° 46.3' N, runs N 40° W a distance of 55 nautical miles. Find her latitude in and the number of miles of departure made.

„Lat. in = 47° 28.4' N.. Ans.

Dep. = 35.4 mi. W. (7) Describe how you would find the index error of a sextant by means of the sea horizon.

(8) Explain how you would read off an angle measured by a sextant.

(9) Suppose that you were to round a cape where outlying hidden rocks and shoals make it necessary to keep at a distance of 3 miles from the shore. On the cape is situated a lighthouse of known height. Describe some method by which the cape may be rounded at the required distance.

(10) (a) In observing vertical danger angles, state how the position of the observer should be in relation to the surface of the sea. (6) Explain the effect on a vertical danger angle, caused by the height of the observer's eye above the water level.

(11) What do you understand by the expression "working a traverse''?

(12) Of what elements are the Traverse Tables composed?

(13) How are the Traverse Tables entered in finding the difference of latitude and departure when the course is greater than 4 points or 45°?

(14) (a) What do you understand by the operation known as taking the departure? (6) How is this departure treated in connection with the determination of a ship's position at sea?

(15) Assume that you are approaching a coast in misty weather, having nothing but the lead, log, and compass to rely on. State how, under such circumstances, you may approximately determine the position of your vessel on the chart.

(16) The bearing of a certain lighthouse at 4 P. M. was NN W; 2 hours later it bore N E by N. The speed of the vessel, having a barge in tow, was 6 miles per hour, and the course steered was west. Find, by construction, and also by the use of proper tables, the distance of the steamer from the lighthouse at the second bearing.

Ans. 13.3 mi.

(17) How do you find the middle latitude of any two places situated in the northern hemisphere?

(18) Explain how you would find the difference of longitude by means of the Traverse Tables when the middle latitude and the departure are known?

(19) On approaching Stannard Rock from the east, the light situated on the pier near the northern end of the rock, is seen just on the horizon. The height of the light, according to the “List of Lights and Fog Signals,” is 102 feet, and the height of the observer above the level of the sea is 35 feet. What is the distance of the ship from the light, expressed (a) in nautical miles; (b) in statute miles, assuming the weather to be clear?

(a18.4 naut. . (6.

Ans. {*) 21.1 stat, mi.

(20) From a place on Lake Erie, situated in latitude 41° 42' N and longitude 81° 41' W, a ship steams the following compass courses and distances:

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The wind is WNW and the mean value of variation for all courses is point west. Find the latitude and longitude

į of the position arrived at.

Ans.

Lat. in 42° 19.9' N. I Long. in = 80° 42' W.

.

(21) The bearing of a certain cape was N W by W. After a distance of 8 miles was run in a W by S direction, the same cape bore N N E. Find by construction, as well as by tables, the distance of the ship from the cape at each observation.

Dist. at 1st bearing = 6.8 mi. Ans.

| Dist. at 2d bearing 5.8 mi.

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(22) Suppose that you are sailing along a coast where two known objects A and B, Fig. I, are in sight; of these A

is the northernmost. According to the chart, the bearing from B to A is NNW (true), and the distance between the two is 4 miles. Outside and nearly midway between A and B lie a number of shoals and

rocks just awash; the outerN most point of C of these shoals

bears S 47° W from A, and
N 70° W from B. You wish to
pass 1 mile outside of that
point. Draw a figure and plot
the positions A, B, and C, using
a scale of 1 inch to a mile.
Then find by construction the
horizontal danger angle.

Danger angle =
Ans.

150°, very nearly.

W 4 miles

(23) When circumstances permit the selection of a vertical and a horizontal danger

angle, which of the two is to be preferred ? State reason for your answer.

FIG. I

(24) A ship has run the following courses: SSEE, 16 miles; E SE, 23 miles; S W by W W, 36 miles; WN, 12 miles; and S E by E À E, 41 miles. Find the course and distance made good.

SCourse S 18° E. Ans.

| Dist. 63 mi.

(25) On September 12, 1901, the lighthouse on Caribou Island, Lake Superior, bore by compass E N E, distance 14 miles. The position of the light according to the chart is latitude 47° 20' N and longitude 85° 49' W. The ship’s head at the time of taking the departure was S W, the deviation for that point being 51° E. From the point of departure the ship ran the following compass courses and distances:

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Ans. {Lat. in

Instead of the small variation of that locality, assume the mean value of the variation for all courses to be 20° E. Find the latitude and longitude of the place arrived at.

47° 54.6' N.

I Long. in = 87° 33' W. NOTE. - In cases where distances are given in fractions of a mile, it is more convenient to find the corresponding difference of latitude and departure by considering the fractions as a whole, and then move the decimal point of the difference of latitude and departure thus found one place to the left. Thus, for a distance of 23.6 miles we find the difference of latitude and departure for 236 miles and shift the decimal point one place to the left.

(26) From the position arrived at in the preceding example, find the compass course and distance to Stannard Rock, latitude 47° 11' N and longitude 87° 14' W, assuming the variation to be 2o E and the deviation 11° W.

SComp. course S 8° E. Ans.

Dist. 45 mi.

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