or at m, and tangents the 55th parallel at about 28° E, or at x; 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, x and y, n, 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 AV B, Fig. 19, may be transferred to the Mercatorial chart by plotting on it the positions of a, b, c, d, V, e, f, g, h, i, 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 longitude 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 mxy n the 55th parallel; also let the arcs Ax and By represent, respectively, the great-circle tracks

drawn from A and B to the parallel. Now, in the triangles PAx and PBy we have the sides

The angles AxP and By P are each 90°, since the great circles tangent the parallel at x 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 and the final course PBy we therefore use the formulas

To find the distance Ar and By on the respective great-circle tracks, we use the following formulas:

According to parallel sailing, the distance on the parallel or ry= D. Long. Xcos Lat. Now, the difference of longitude is measured by the angle at the pole x Py, which is equivalent to APB−(APx +BPy). Or,

x Py=APB-(APx+B Py).

Hence, the value of these angles must be found. Thus,

sin A Px=sin Ax cosec AP,

sin BPy=sin By cosec BP.

log sin 52° 23' = 9.89879

log cosec 60° = 10.06247

log sin A Px= 9.96126

APx=66° 10'

log sin 40° 4' = 9.80867 log cosec 51° 11'=10.10838 log sin B Py= 9.91705 BPy=55° 42'

Inserting these values in the formulas above, we find that x Py, or the D. Long., = 163° — (66° 10′+55° 42′) =41° 8'=2,468'. By parallel sailing we then compute xy as follows:

log 2468 3.39235

log cos 55° 9.75859

log xy=3.15094

xy=1,415 mi. Ans.

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.

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.

Ans.

Initial course=S 34° 12′ W.
Final course=S 75° W.

Dist. 3,662 mi.

Lat. vertex=57° 17' S. Long. vertex=85° 11' W.

3. A ship at Otago Harbor, New Zealand, in latitude 45° 47' S and longitude 170° 45′ E, is about to leave for Callao, Peru, in latitude 12° 4' S and longitude 77° 15′ W. Calculate the initial and final courses, also the distance, using formula given in the note, Art. 61. Initial course=S 65° 45' E. Final course=N 40° 35' E. Dist. 5,764 mi.

Ans.

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OCEAN METEOROLOGY

ATMOSPHERIC CURRENTS

INTRODUCTORY

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.

THE ATMOSPHERE

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.

For notice of copyright, see page immediately following the title page.

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.

THE THERMOMETER

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.