5. A ship from Cleveland, Ohio, bound to Buffalo, N. Y., after passing the most seaward crib, latitude 41° 32.7' N and longitude 81° 45′ W, stationed outside of Cleveland Harbor, steers the following compass courses and distances:

The wind is NW by W. Find the latitude and longitude of the position arrived at.

Ans.

(Lat. in
Long. in

42° 10.6' N.
80° 46.5' W.

=

6. From the position arrived at in the preceding example, find compass course and distance to Port Stanley, Ont., latitude the 42° 39.5' N and longitude 81° 13′ W, assuming the variation to be 4° W and the deviation 60 E.

LAKE NAVIGATION

(PART 4)

TO FIND THE DEVIATION OF THE COMPASS BY BEARINGS OF THE SUN

EXPLANATION AND PRINCIPLES

1. We have previously discussed at some length the methods of ascertaining the deviation of the compass by means of terrestrial objects, the magnetic bearings of which were known. The difference between the magnetic bearing and the bearing by compass, we know, is the deviation for that particular point, or the direction in which the ship is heading at the time of taking the bearing. At sea, however, and when out of sight of land, the utilization of terrestrial objects for determining the deviation of a compass is out of the question, and the navigator must then resort to methods by which the deviation of his compass may be found by the bearing of celestial objects. Of these methods there are several, but only those in most common use will be considered here, viz., the amplitude and the time-azimuth methods.

2. The principles of both methods are essentially the same as for the methods in which the bearings of terrestrial objects are used, the only difference being that in dealing with celestial objects the true bearing of the object is compared with its compass bearing. Hence, the result obtained by taking their difference is not the variation of the compass, as it is sometimes erroneously termed, but the total compass error, or, in other words, the combined effect of both variation and deviation.

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Now, since the variation of the compass for any particular part or locality of the sea is conveniently found on charts, it is evident that by allowing for same the required deviation is readily deduced. The change of magnetic variation is so inconsiderable as to be barely appreciable from year to year, and once determined and registered for any place it will, with a slight moderation, serve for a considerable period. Thus, the value of the variation given on the chart facing page 28 is good until 1906. It should be noticed that on this chart the line of no variation is indicated by a heavy black line, westerly variation by continuous fine lines, and easterly variation by dotted lines.

3. How Bearings Are Obtained. — In all methods of determining the deviation of a compass at sea, the true bearing of the celestial object is either calculated by means of spherical trigonometry, or it is obtained by inspection from tables especially prepared for this purpose, and the compass bearing is taken directly from the standard or navigating compass. In this Course, however, the method by tables only will be considered.

Before going any further, it becomes necessary to explain certain terms in connection with these methods.

EXPLANATION OF ASTRONOMICAL TERMS

4. The amplitude of a celestial body is its angular distance measured along the horizon from the east or west point at the time of rising or H' setting. Thus, in Fig. 1, if

H

FIG. 1

HH' represents the sea horizon, E the true east point, S the sun, and O the place of an observer, the angle E OS is the amplitude. It is expressed east or west so many degrees north or south. Thus, when

the amplitude is E 15° S, it means that when the sun is rising its center is 15° south of the true east point, and when

the amplitude is W 20° N, it means that the sun's center at setting is 20° north of the true west point of the horizon.

5. The azimuth of a celestial body is the arc of the horizon intercepted between the north or south point, and a point on the horizon vertically below the body. Thus, in Fig. 2, if NES W represents the visible horizon, N the

north point, S the south point, S, a celestial body, and ca point vertically below S1, the arc Nc of the horizon intercepted between N and c is the azimuth of the body S1.

In expressing the azimuth of a celestial object, it is necessary to state whether it is measured from the north or south point, and whether it is measured east or west. For example, if the azimuth of a body is 35°, measured from the north toward the east, it should be written as N 35° E. Sometimes the azimuth is reckoned up to 179°. Thus, in Fig. 2, if the arc Nc is 60° and the azimuth, reckoned from the north point, is N 60° E, the same azimuth may be expressed as 180° 60° S 120° E.

=

6. It is evident that the amplitude of a body is the complement of the body's azimuth. Thus, in Fig. 2, if the azimuth of the body S, is N 60° E, its amplitude will be 90° 60° E 30° N. The amplitude, however, is considered only when the body is on the horizon.

7. The declination of a celestial body, for instance the sun, is its angular distance north or south from the extended

The declination is north, if

plane of the earth's equator. the body is north of the equator, and south, if south of the equator. Thus, in Fig. 3, if N. P. represents the north pole, S. P. the south pole, E E' the equator, A B C the plane of the equator extended, and S a celestial body, the angular

distance a S is the declination of that body, and is northerly because the body is north of the equator. The declination of the body S, is south because S, is south of the equator; when the body is at B, or exactly on the plane of the equator, its declination is zero.

8. Limitation of the Sun's Declination. As stated before, the declination of a celestial body may be either north or south and is named accordingly. The declination of the sun, which is given in Table I, can never exceed 23° 27' 30" in either direction. On March 21 or 22, the sun is on the equator, and its declination is zero. From this date to June 21 the sun's declination is north and increasing; from June 21 to September 22 or 23 it is north and decreasing. On September 22 or 23 the sun is again on the equator and its declination is zero. From this date to December 21 the sun's declination is south and increasing; and from December 21 to March 22 it is south and decreasing.