Lectures in Navigation Part 12

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Just what a line of position is will now be explained. Wherever the sun is, it must be perpendicularly above the same spot on the surface of the earth marked in the accompanying diagram by S and suppose a circle be drawn around this spot as ABCDE. Then if a man at A takes an alt.i.tude, he will get precisely the same one as men at B, C, D, and E, because they are all at equal distances from the sun, and hence on the circ.u.mference of a circle whose center is S. Conversely, if several observers situated at different parts of the earth's surface take simultaneous alt.i.tudes, and these alt.i.tudes are all the same, then the observers must all be on the circ.u.mference of a circle and _only one_ circle. If they are not on that circle, the alt.i.tude they take will be greater or less than the one in question.

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Now such a circle on the surface of the earth would be very large--so large that a small arc of its circ.u.mference, say 25 or 30 miles, would be practically a straight line.

Suppose S to be the point over which the sun is vertical and GF part of the circ.u.mference of a circle drawn around the point. Suppose you were at B and from an alt.i.tude of the sun, taken by s.e.xtant, you worked out your position. You would find yourself on a little arc ABC which, for all purposes in Navigation, is a straight line at right angles to the true bearing of the sun from the point S. You can readily see this from the above diagram. Suppose your observer is at H. His line is GHI, which is again a straight line at right angles to the true bearing of the sun.

He is not certain he is at H. He may be at G or I. He knows, however, he is somewhere on the line GHI, though where he is on that line he cannot tell exactly. That line GHI or ABC or DEF is the line of position and such a line is called a Sumner Line, after Capt. Thomas Sumner, who explained the theory some 45 years ago. Put in your Note-Book:

Any person taking an alt.i.tude of a celestial body must be, for all practical purposes, on a straight line which is at right angles to the true bearing of the body observed.

It should be perfectly clear now that if the sun bears due North or South of the observer, i.e., if the sun is on the observer's meridian, the resulting line of position _must_ run due East and West. In other words it is a parallel of lat.i.tude. And that explains why a noon observation is the best of the day for getting your lat.i.tude accurately.

Again, if the sun bears due East or West the line of position must bear due North and South. And that explains why a morning or afternoon sight--about 8-9 A.M. or 3-4 P.M., if the sun bears either East or West respectively, is the best time for determining your North and South line, or longitude.

Now suppose you take an observation at 8 A.M. and you are not sure of your D.R. lat.i.tude. Your 8 A.M. position when the sun was nearly due East, will give, you an almost accurate North and South line and longitude. Suppose that from 8 A.M. to noon you sailed NE 60 miles.

Suppose at noon you get another observation. That will give you an East and West line, for then the sun bears true North and South. An East and West line is your correct lat.i.tude. Now you have an 8 A.M. observation which is nearly correct for longitude and a noon position which is correct for lat.i.tude. How can you combine the two so as to get accurately both your lat.i.tude and longitude? Put in your Note-Book:

Through the 8 A.M. position, draw a line on the chart at right angles to the sun's true bearing. Suppose the sun bore true E 1/2 S. Then your line of position would run N 1/2 E. Mark it 1st Position Line.

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Now draw a line running due East and West at right angles to the N-S noon bearing of the sun and mark this line Second Position Line. Advance your First Position Line the true course and distance sailed from 8 A.M.

to noon, and through the extremity draw a third line exactly parallel to the first line of position. Where a third line (the First Position Line advanced) intersects the Second Position Line, will be your position at noon. It cannot be any other if your calculations are correct. You knew you were somewhere on your 8 A.M. line, you know you are somewhere on your noon line, and the only spot where you can be on both at once is the point where they intersect. You don't necessarily have to wait until noon to work two lines. You can do it at any time if a sufficient interval of time between sights is allowed. The whole matter simply resolves itself into getting your two lines of position, having them intersect and taking the point of intersection as the position of your ship.

There is one other way to get two lines to intersect and it is one of the best of all for fixing your position accurately. It is by getting lines of position by observation of two stars. If, for instance, you can get two stars, one East and the other West of you, you can take observations of both so closely together as to be practically simultaneous. Then your Easterly star would give you a line like AA' and the westerly star the line BB' and you would be at the intersection S.

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a.s.sign for reading: Articles in Bowditch 321-322-323-324. Spend the rest of the period in getting times from the N. A., getting true alt.i.tudes from observed alt.i.tudes, working examples in Mercator sailing, etc.

WEDNESDAY LECTURE

LAt.i.tUDE BY MERIDIAN ALt.i.tUDE

A meridian alt.i.tude is an alt.i.tude taken when the sun or other celestial body observed bears true South or North of the observer or directly overhead. In other words, when the celestial body is on your meridian and you take an alt.i.tude of the body by s.e.xtant at that instant, the alt.i.tude you get is called a meridian alt.i.tude. In the case of the sun, such a meridian alt.i.tude is at apparent noon. Now lat.i.tude is always secured most accurately at noon by means of your meridian alt.i.tude. The reason for this was explained in yesterday's lecture. The general formula for lat.i.tude by meridian alt.i.tude is (Put in your Note-Book):

Lat.i.tude by meridian alt.i.tude = Zenith Distance (ZD) Declination (Dec).

Zenith distance is the distance in degrees, minutes and seconds from your zenith to the center of the observed body. For simplicity's sake, we will consider the sun only as the observed body. Then the zenith distance is the distance from your zenith to the center of the sun. Now suppose that you and the sun are both North of the equator and you are North of the sun. If you can determine exactly how far North you are of the sun and how far North the sun is of the equator, you will, by adding these two measurements together, know how far North of the equator you are, i.e., your lat.i.tude. As already explained, the declination of the sun is its distance in degrees, minutes and seconds from the equator and the exact amount of declination is, of course, corrected to the proper G.M.T. Your zenith distance is the distance in the celestial sphere you are from the sun. You know that it is 90 from your zenith to the horizon. Your zenith distance, therefore, is the difference between the true meridian alt.i.tude of the sun, obtained by your s.e.xtant, and 90.

Hence, having secured the true meridian alt.i.tude of the sun, you have only to subtract it from 90 to find your zenith distance, i.e., how far you are from the sun. This diagram will make the whole matter clear:

[Ill.u.s.tration: A | | B (Sun) | / | / | / | / |<- |="" 90="" |/="" |="" +------v----------------------="" c="">

A = Zenith, B = Sun, C = Horizon.]

The arc ABC measures 90. That is the distance from your zenith to the horizon. Now if BC is the true meridian alt.i.tude of the sun at noon, 90-BC or AB is your zenith distance. If BC measures by s.e.xtant 60, AB measures 90-60 or 30. This 30 is your Zenith Distance. Now suppose that from the Nautical Almanac we find that the G.M.T. corresponding to the time at which we measured the meridian alt.i.tude of the sun shows the sun's declination to be 10 N. Well, if you are 30 North of the sun, and the sun is 10 North of the equator, you must be 40 North of the equator or in lat.i.tude 40 N. For that is all lat.i.tude is, namely, the distance in degrees, minutes and seconds you are due North or South of the equator. That is the first and simplest case.

Another case is when you are somewhere in North lat.i.tude and the sun's declination is South. Then the situation would, roughly, look like this:

[Ill.u.s.tration: BC = Alt.i.tude of the sun, AB = Zenith Distance and DB = Sun's Declination.]

In this case, your distance North of the equator AD would be your zenith distance AB minus the sun's declination DB. This diagram is not strictly correct, for the observer's position on the earth 0 appears to be South of the equator instead of North of the equator. That is because the diagram is on a flat piece of paper instead of on a globe. So far as ill.u.s.trating the Zenith Distance minus the Declination, however, the diagram is correct. The last case is where you are, say, 10 N of the sun (your zenith Distance is 10) and the sun is in 20 S declination.

In that case you would have to subtract your zenith distance from the sun's declination to get your lat.i.tude, for the sun's lat.i.tude (its declination) is greater than yours.

Now from these three cases we deduce the following directions, which put in your Note-Book:

Begin to measure the alt.i.tude of the sun shortly before noon. By bringing its image down to the horizon, you can detect when its alt.i.tude stops increasing and starts to decrease. At that instant the sun is on your meridian, it is noon at the ship, and the angle you read from your s.e.xtant is the meridian alt.i.tude of the sun. To work out your lat.i.tude, name the meridian alt.i.tude S if the sun is south of you and N if north of you.

Correct the observed alt.i.tude to a true alt.i.tude by Table 46. If the alt.i.tude is S, the Zenith Distance is N or vice versa. (Note to Instructor: If the sun is South of you, you are North of the sun and vice versa.)

Correct the declination for the proper G.M.T. as shown by chronometer (corrected). If zenith distance and declination are both North or both South, add them and the sum will be the lat.i.tude, N or S as indicated.

If one is N, and the other S, subtract the less from the greater and the result will be the lat.i.tude in, named N or S after the greater. Example:

At sea June 15th, observed alt.i.tude of (_) 71 15' S, IE--47', HE 25 ft.

CT 3h--34m--15s P.M. Required lat.i.tude of ship.

(_) 71 15' 00 S IE -- 47'

Corr. -- 36 24 HE + 10 36 ------------------- --------- -(-)- 70 38' 36" S Corr. -- 36' 24"

-- 90 00 00 ------------------- ZD 19 21' 24" N Dec. 23 17 15 N (G.M.T. June 15--3h 34m 15s) ------------------- Lat. 42 38' 39" N -------------------

a.s.sign for Night Work or to be worked in cla.s.s room such examples as the following:

1. June 1st, 1919. (_) 33 50' 00" S. G.M.T. 8h 55m 44s. HE 20 ft. IE + 4' 3". Required lat.i.tude in at noon.

2. April 2nd, 1919. (_) 12 44' 30" N. CT was 2d 5h 14m 39s A.M., which was 1m 40s slow on March 1st (same CT) and 4m 29s fast on March 15th (same CT). IE -- 2' 20". HE 22 ft. Required lat.i.tude in at noon.

a.s.sign for Night Work reading also, the following Articles in Bowditch: 344 and 223.

THURSDAY LECTURE

AZIMUTHS OF THE SUN

This is a peculiar word to spell and p.r.o.nounce but its definition is really very simple. Put in your Note-Book:

The azimuth of a heavenly body is the angle at the zenith of the observer formed by the observer's meridian and a line drawn to the center of the body observed. Azimuths are named from the lat.i.tude in and toward the E in the A.M. and from the lat.i.tude in and toward the W in the P.M.

All this definition means is that, no matter where you are in N lat.i.tude, for instance, if you face N, the azimuth of the sun will be the true bearing of the sun from you. The same holds true for moon, star or planet, but in this lecture we will say nothing of the star azimuths for, in some other respects, they are found somewhat differently from the sun azimuths. Put this in your Note-Book: