Wednesday Lecture
Latitude By Meridian Altitude
A meridian altitude is an altitude 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 altitude of the body by sextant at that instant, the altitude you get is called a meridian altitude. In the case of the sun, such a meridian altitude is at apparent noon. Now latitude is always secured most accurately at noon by means of your meridian altitude. The reason for this was explained in yesterday's lecture. The general formula for latitude by meridian altitude is (Put in your Note-Book):
Latitude by meridian altitude = 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 latitude. 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 altitude of the sun, obtained by your sextant, and 90°. Hence, having secured the true meridian altitude 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:
Find Zenith Distance from Meridian Altitude
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 altitude of the sun at noon, 90°-BC or AB is your zenith distance. If BC measures by sextant 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 altitude 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 latitude 40° N. For that is all latitude 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 latitude and the sun's declination is South. Then the situation would, roughly, look like this:
Observer in N latitude, Sun's declination is S
BC = Altitude 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 illustrating 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 latitude, for the sun's latitude (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 altitude of the sun shortly before noon. By bringing its image down to the horizon, you can detect when its altitude 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 sextant is the meridian altitude of the sun. To work out your latitude, name the meridian altitude S if the sun is south of you and N if north of you.
Correct the observed altitude to a true altitude by Table 46. If the altitude 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 latitude, 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 latitude in, named N or S after the greater. Example:
At sea June 15th, observed altitude of Circle with line under 71° 15´ S, IE - 47´, HE 25 ft. CT 3h 34m 15s P.M. Required latitude of ship.
| Circle with line under | 71° 15' 00 S | IE | - 47' |
| Corr. | - 36 24 | HE | + 10 36 |
| —————— | ——— | ||
| Circle with line through | 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 | ||
| —————— | |||
Assign for Night Work or to be worked in class room such examples as the following:
1. June 1st, 1919. Circle with line under 33° 50' 00" S. G.M.T. 8h 55m 44s. HE 20 ft. IE + 4' 3". Required latitude in at noon.
2. April 2nd, 1919. Circle with line under 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 latitude in at noon.
Assign for Night Work reading also, the following Articles in Bowditch: 344 and 223.