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or at m, and tangents the 55th parallel at about 28° E, or at r, the second great-circle track commences at about 73° E, or at y, crosses the 50th and 45th parallels at n and s, or in 105° E and 117° E, respectively. These positions, together with those of A and B, are then plotted on a Mercator's chart, as shown in Fig. 20, and through the points A, m, r and y, m, s, B thus found curves are drawn that will coincide with the 55th parallel at x and y.
83. In a similar way the great-circle track A V B, Fig. 19, may be transferred to the Mercatorial chart by plotting on it the positions of a, b, c, d, l', e, f, g, h, ś, and then connecting all places by a curve, as shown in Fig. 20.
84. Solution by Trigonometry.-Problems in composite sailing may also be solved by means of spherical trigonometry, as shown in the following example.
ExAMPLE.—A ship in latitude 30° S and longitude 18° W is to sail for a place in latitude 38° 49' S and 19ngitude 145° E. It is decided to utilize the great-circle route, but not to go farther south than the 55th parallel. Required the initial and final course of the composite track, the total distance to be run, and the number of miles to be run on the parallel.
Solution.—Let P, Fig. 21, represent the south pole, A the place of departure, B the place of destination, and m a y n the 55th parallel; also let the arcs .4 r and By represent, respectively, the great-circle tracks drawn from A and B to the parallel. Now, in the triangles PA+ and PBy we have the sides
A P=90°–p =90°–30° =60°,
and Pa- Py =90°–55° =35°.
The angles A a P and By P are each 90°, since the great circles tangent the parallel at r and y, and are, therefore, at right angles to the meridians passing through these places. Hence, the triangles are right-angled, and to find the initial course PA at and the final course P By we therefore use the formulas sin PA ar=sin Por cosec A P, sin P B y=sin Py cosec B P.
initial course=S 41°29' E, final course=N 47° 24' E. Ans. To find the distance A or and By on the respective great-circle tracks, we use the following formulas: cos A or=cos A Psec Par, cos By =cos B P sec Py.
The total distance on the composite track is therefore 3,143+1,415 +2,404=6,962 mi. Ans.
85. The formulas used in the preceding example may serve as guides in any case of composite sailing.
86. When, from any cause, a ship has deviated from the original great-circle track, it is not necessary to resume it; a new track should then be laid out from the actual position of the ship to her port of destination, or any other desired point.
EXAMPLES FOR PRACTICE.
1. A ship in latitude 40° S and longitude 16° E is ordered to proceed to a place in latitude 48° S and longitude 147° E. She is to follow the great-circle track. Required the initial and final courses, and the highest latitude reached.
Final course = N 35° 44' E. Highest Lat. = 67° S. 2. Find the initial and the final course, also the distance and position of vertex of the great-circle track between a place in latitude 15° 55' S and longitude 5° 44' W, and another in latitude 55° 59' S and longitude 67° 16' W.
1. By reason of the peculiarity of his profession, the navigator should, above all others, possess a good practical knowledge of meteorology—the science that treats of the conditions and changes of the atmosphere.
A good insight into the navigational phases of this science will be found not only very valuable, but it will materially aid him in successfully navigating his vessel. Under this heading, therefore, we shall present a few of the most important facts and principles of what may be termed ocean meteorology.
2. Extent of Atmosphere.—Our planet is entirely enveloped by a gaseous body known as the atmosphere. The height of this atmosphere is far greater than any height to which we can attain, though we can ascertain to some degree its approximate limit. By measuring the thickness of the penumbra that surrounds the shadow of the earth on the moon at the time of an eclipse of the moon, the height of the atmosphere is estimated to be from 50 to 60 miles. It covers everything on the earth's surface with a pressure of nearly 15 pounds per square inch. The density of the atmosphere is a maximum at the surface of the earth, and gradually diminishes until the confines are reached, where the density is zero.
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3. Composition of Atmosphere.-The atmosphere is composed of air just as the ocean is composed of water. The chief ingredients of air are oxygen and nitrogen; of these, oxygen is the most important, because its inhalation by human beings and animals is essential to life.
4. Heat.-Heat is not a substance, but may be considered as a form of energy. It is due to the rapid motion of minute particles, called molecules, of which all bodies are composed. Thus, when a person feels cold, he may, by rapid motion, for instance, by running, increase the warmth of his body.
5. Temperature.-The different states that a body is in, according to the amount of sensible heat it possesses, are indicated by the word temperature. We thus say that the temperature of a body is high or low, according as the body is hot or cold.
6. Measurement of Temperature.—The instrument used for making accurate measurements of the temperature of bodies is called a thermometer, or heat measurer. In this instrument the effects of heat on bodies are made use of in ascertaining the temperature. The most common method is to utilize the expansive effect of heat on liquids. The liquids used are mercury and alcohol—the former being used because it boils only at a very high temperature, and the latter because it does not solidify at the greatest known cold produced by ordinary means.
7. Description of the Thermometer.-In Fig. 1 is shown a mercurial thermometer with two sets of graduations on it. The one on the left, marked F, is the Fahrenheit thermometer, so named after its inventor, and is the one commonly used in this country and in England; the one on the right, marked C, is the centigrade thermometer, and is used by scientists throughout the world on account of the graduations being better adapted for calculations.