5. Using the compa.s.s, log and lead in a fog or in unfamiliar waters.

1. Cross bearings of two known objects.

Select two objects marked on the chart, so far apart that each will bear about 45 off your bow but in opposite directions. These bearings will be secured in the best way by the use of your pelorus. Correct each bearing for Variation and Deviation so that it will be a true bearing.

Then with the parallel rulers carry the bearing of one object from the chart compa.s.s card until you can intersect the object itself and draw a line through it. Do exactly the same with the other object. Where the two lines intersect, will be the position of the ship at the time the bearings were taken.

[Ill.u.s.tration]

Now supposing you wish to find the lat.i.tude and longitude of that position of the ship. For the lat.i.tude, measure the distance of the place from the nearest parallel with the dividers. Take the dividers to the lat.i.tude scale at the side of the chart and put one point of them on the same parallel. Where the other point touches on the lat.i.tude scale, will be the lat.i.tude desired. For the longitude, do exactly the same thing, but use a meridian of longitude instead of a parallel of lat.i.tude and read from the longitude scale at the top or bottom of the chart instead of from the side.

2. Bearing and distance of a known object, the height of which is known.

Take a bearing of, say, a lighthouse the height of which is known. The height of all lighthouses on the Atlantic Coast can be found in a book published by the U.S. Dept. of Commerce. Correct the bearing, as mentioned in case No. 1. Now read the angle of the height of that light by using your s.e.xtant. Do this by putting the vernier 0 on the arc 0, sliding the limb slowly forward until the top of the lighthouse in the reflected horizon just touches the bottom of the lighthouse in the true horizon. With this angle and the known height of the light, enter Table 33 in Bowditch. At the left of the Table will be found the distance off in knots. This method can be used with any fairly perpendicular object, the height of which is known and which is not more than 5 knots away, as Table 33 is not made out for greater distances.

3. Two bearings of the same object, separated by an interval of time and with a run during that interval.

Take a compa.s.s bearing of some prominent object when it is either 2, 3 or 4 points off the bow. Take another bearing of the same object when it is either 4, 6 or 8 points off the bow. The distance run by the ship between the two bearings will be her distance from the observed object at the second bearing. "The distance run is the distance off."

A diagram will show clearly just why this is so:

[Ill.u.s.tration]

The ship at A finds the light bearing NNW 2 points off her bow. At B, when the light bears NW and 4 points off, the log registers the distance from A to B 9 miles. 9 miles, then, will be the distance from the light itself when the ship is at B. The mathematical reason for this is that the distance run is one side of an isosceles triangle. Such triangles have their two sides of equal length. For that reason, the distance run is the distance off. Now the same fact holds true in running from B, which is 4 points off the bow, to C, which is 8 points off the bow, or directly abeam. The log shows the distance run between B and C is 6.3 miles. Hence, the ship is 6.3 miles from the light when directly abeam of it. This last 4 and 8 point bearing is what is known as the "bow and beam" bearing, and is the standard method used in coastwise navigation.

Any one of these methods is of great value in fixing your position with relation to the land, when you are about to go to sea.

4. s.e.xtant angles between three known objects.

This method is the most accurate of all. Because of its precision it is the one used by the Government in placing buoys, etc. Take three known objects such as A, B and C which are from 30 to 60 from each other.

[Ill.u.s.tration]

With a s.e.xtant, read the angle from A to B and from B to C. Place a piece of transparent paper over the compa.s.s card and draw three lines from the center of the compa.s.s card to the circ.u.mference in such a way that the angles secured by the s.e.xtant will be formed by the three lines drawn. Now take this paper with the angles on it and fit it on the chart so that the three objects of which angles were taken will be intersected by the three lines on the paper. Where the point S is (in my diagram) will be the point of the ship's position at the time of sight. To secure greater accuracy the two angles should be taken at the same time by two observers.

5. Using a compa.s.s, log and lead when you are in a fog or unfamiliar waters.

Supposing that you are near land and want to fix your position but have no landmarks which you can recognize. Here is a method to help you out:

Take a piece of tracing paper and rule a vertical line on it. This will represent a meridian of longitude. Take casts of the lead at regular intervals, noting the time at which each is taken, and the distance logged between each two. The compa.s.s corrected for Variation and Deviation will show your course. Rule a line on the tracing paper in the direction of your course, using the vertical line as a N and S meridian. Measure off on the course line by the scale of miles in your chart, the distance run between casts and opposite each one note the time, depth ascertained and, if possible, nature of the bottom. Now lay this paper down on the chart which can be seen under it, in about the position you believe yourself in when you made the first cast. If your chain of soundings agrees with those on the chart, you are all right. If not, move the paper about, keeping the vertical line due N and S, till you find the place on the chart that does agree with you. That is your line of position. You will never find in that locality any other place where the chain of soundings are the same on the same course you are steaming. This is the only method by soundings that you can use in thick weather and it is an invaluable one.

Put in your Note-Book this diagram:

10 8.30A.M. | 12 9.00A.M. | 13 10A.M. | 13-1/2 10.30A.M. | 14 11A.M. | 14-3/4 11.30A.M. |

a.s.sign for Night Work, Review for Weekly Examination to be held on Monday.

Add an explanation of the Deviation Card in Bowditch, page 41.

Put in your Note-Book:

Entering New York Harbor, ship heading W 3/4 N, Variation 9 W. Observed by pelorus the following objects:

Buoy No. 1--ENE 1/4 E " " 2--E 1/2 N " " 3--NE 1/4 E " " 4--NW 1/4 N

Required true bearings of objects observed.

Answer:

From Deviation Card in Bowditch, p. 41, Deviation on W 3/4 N course is 5 E. Hence, Compa.s.s Error is 5 E (Dev.) + 9 W (Var.) = 4 W.

C. B. C. E. T. B.

ENE 1/4 E 70 4 W 66 E 1/2 N 84 4 W 80 NE 1/4 E 48 4 W 44 NW 1/4 N 318 4 W 314

WEEK II--DEAD RECKONING

TUESDAY LECTURE

LAt.i.tUDE AND LONGITUDE

[Ill.u.s.tration]

We have been using the words Lat.i.tude and Longitude a good deal since this course began. Let us see just what the words mean. Before doing that, there are a few facts to keep in mind about the earth itself. The earth is a spheroid slightly flattened at the poles. The axis of the earth is a line running through the center of the earth and intersecting the surface of the earth at the poles. The equator is the great circle, formed by the intersection of the earth's surface with a plane perpendicular to the earth's axis and equidistant from the poles. Every point on the equator is, therefore, 90 from each pole.

Meridians are great circles formed by the intersection with the earth's surface of planes perpendicular to the equator.

Parallels of lat.i.tude are small circles parallel to the equator.

The Lat.i.tude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place. It is measured by the angle running from the equator to the center of the earth and back through the place in question. Lat.i.tude is reckoned from the equator (0) to the North Pole (90) and from the equator (0) to the South Pole (90). The difference of Lat.i.tude between any two places is the arc of the meridian intercepted between the parallels of Lat.i.tude of the places and is marked N or S according to the direction in which you steam (T n').

The Longitude of a place on the surface of the earth is the arc of the equator intercepted between the meridian of the place and the meridian at Greenwich, England, called the Prime Meridian. Longitude is reckoned East or West through 180 from the Meridian at Greenwich. Difference of Longitude between any two places is the arc of the equator intercepted between their meridians, and is called East or West according to direction. Example: Diff. Lo. T and T' = E' M, and E or W according as to which way you go.

Departure is the actual linear distance measured on a parallel of Lat.i.tude between two meridians. Difference of Lat.i.tude is reckoned in minutes because miles and minutes of Lat.i.tude are always the same.

Departure, however, is only reckoned in _miles_, because while a mile is equal to 1' of longitude on the equator, it is equal to more than 1' as the lat.i.tude increases; the reason being, of course, that the meridians of Lo. converge toward the pole, and the distance between the same two meridians grows less and less as you leave the equator and go toward either pole. Example: TN, N'n'. 10 mi. departure on the equator = 10'

difference in Lo. 10 mi. departure in Lat. 55 equals something like 18'

difference in Lo.

The curved line which joins any two places on the earth's surface, cutting all the meridians at the same angle, is called the Rhumb Line.