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For the set and velocity of tidal stream proceed as in Art. 24. Thus,

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Hence, the set of the tidal stream met with at 8 A. M. was S 30°12' W, and, assuming it to have affected the ship with a uniform velocity

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1. On November 6, at noon, a departure was taken from a point in latitude 54° 20' S and longitude 6°42' E, which bore by compass S S E A E a distance 12 miles. Deviation for ship's head at time of taking departure 15° W. Afterwards, the following courses and distances were sailed. During the entire period from noon to noon the ship was influenced by a current, the magnetic set of which was S E by E 38 miles. Required the latitude and longitude in at noon, November 7.

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afterwards she sailed as by the following log-book account.

2. On November 29, at noon, a vessel, by astronomical observations, was found to be in latitude 60° 51' N and longitude 20° 54' W,

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the 24 hours from noon, November 29, to noon, November 30, the vessel was affected by a current, the magnetic set of which was SW by S and the drift 13 knots per hour; and between the hours of 8 and 12 P. M. a tidal stream was encountered, the magnetic set of which was N E N, estimated velocity 3 knots per hour. Required the latitude and longitude in on November 30 at noon. Noon, Novem BER 29.

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Lat. in – 61° 35.2’ N. Ans. {{...","...” #ow. 3. On March 5, at noon, a ship was in the following position, determined by astronomical observations: Latitude 39°43’N, longitude 60° 20' W. Afterwards the following courses and distances were sailed according to the log book. A current set S W by S (magnetic) 38 miles during the 24 hours, and a tidal stream was met with at 3 P.M., the magnetic set of which was S 7° W, velocity 2 miles per hour, affecting the ship for 3 hours. Required the latitude and longitude in on March 6 at noon, and find by Mercator's sailing the course and distance from the position thus found to Sandy Hook light ship in latitude 40° 27' N and

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4. Referring to the preceding example, suppose that at 6 o'clock P. M. a ship near by displays signals to the effect that she has lost her reckoning on account of having been tossed about by severe weather and asks as a favor to be given the latitude and longitude in at that hour. What would be the answer?

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40. Plane geometry teaches us that the shortest distance between two places or points is the straight line that joins them; consequently, the shortest path or distance between two places on the earth's surface is the straight line connecting one with the other. This path, however, is denied us, since it would necessarily require the passage through some portion of the earth, while our communications or means of traveling from one place to another is confined to its surface only. Hence, the question is limited to the shortest distance between two places on and over the surface of the earth; and this distance on a globe, or representation of the earth, is evidently found by stretching a thread from one place to the other on its surface; such an arc extended around the entire globe would be a great circle, the plane of which would pass through the center of the globe, and the art of sailing along such an arc is termed by navigators great-circle sailing, and the are itself a great-circle track.

41. The properties of great-circle sailing were known as far back as the 14th century, and in ancient works on navigation it was described as globular sailing. Its general applications for the purpose of practical navigation was, however, not effected until the introduction of steam power had rendered steamships practically independent of the wind, and at the present day of long voyages and great competition, considerable time and distance may be saved by resorting to this method of reaching the port of destination by following the great-circle track leading to it.

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