Saturday Lecture
Correction Of Observed Altitudes
The true altitude of a heavenly body is the angular distance of its center as measured from the center of the earth. The observed altitude of a heavenly body as seen at sea by the sextant may be converted to the true altitude by the application of the following four corrections: Dip, Refraction, Parallax and Semi-diameter.
Dip of the horizon means an increase in the altitude caused by the elevation of the eye above the level of the sea. The following diagram illustrates this clearly:
Illustration of effect of height of eye above sea level
If the eye is on the level of the sea at A, it is in the plane of the horizon CD, and the angles EAC and EAD are right angles or 90° each. If the eye is elevated above A, say to B, it is plain that the angles EBC and EBD are greater than right angles, or in other words, that the observer sees more than a semi-circle of sky. Hence all measurements made by the sextant are too large. In other words, the elevation of the eye makes the angle too great and therefore the correction for dip is always subtracted.
Refraction is a curving of the rays of light caused by their entering the earth's atmosphere, which is a denser medium than the very light ether of the outer sky. The effect of refraction is seen when an oar is thrust into the water and looks as if it were bent. Refraction always causes a celestial object to appear higher than it really is. This refraction is greatest at the horizon and diminishes toward the zenith, where it disappears. Table 20A in Bowditch gives the correction for mean refraction. It is always subtracted from the altitude. In the higher altitudes, select the correction for the nearest degree.
You should avoid taking low altitudes (15° or less) when the atmosphere is not perfectly clear. Haziness increases refraction.
Parallax is simply the difference in angular altitude of a heavenly body as measured from the center of the earth and as measured from the corresponding point on the surface of the earth. Parallax is greatest when the body is in the horizon, and disappears when it is at the zenith.
Effect of Parallax
When the angular altitude of the sun in this diagram is 0, the parallax ABC is greatest. When the altitude is highest there is no parallax. The sun is so far away that its parallax never exceeds 9". The stars have practically none at all from the earth's surface. Parallax is always to be added in the case of the sun.
The semi-diameter of a heavenly body is half the angle subtended by the diameter of the visible disk at the eye of the observer. For the same body, the SD varies with the distance. Thus, the difference of the sun's SD at different times of the year is due to the change of the earth's distance from the sun.
Illustration of semi-diameter
The SD is to be added to the observed altitude in case the lower limb is brought in contact with the horizon, and subtracted if the upper limb is used. Probably most of the sights you take will be of the sun's lower limb, i.e., when the lower limb is brought in contact with the horizon, so all you need to remember is that in that event the SD is additive.
Now at first we will correct altitudes by applying each correction separately, but as soon as you get the idea, there is a short way to apply all four corrections at once. This is done in Table 46. However, disregard that for the moment. Put this in your Note-Book:
| Dip is -. | Table 14 Bowditch |
| Refraction is -. | Table 20 Bowditch |
| Parallax is +. | Table 16 Bowditch |
| S.D. is +. | Nautical Almanac |
Observed altitude of Sun's lower limb is expressed Circle with line under.
True altitude is expressed Circle with line through.
Remember that before an observation is at all accurate, it must be corrected to make it a true altitude. Remember also that the IE must be applied, in addition to these other corrections, in order to make the observed altitude a Circle with line through altitude. So there are really five corrections to make instead of four, providing, of course, your sextant has an IE.
Examples:
1. June 20th, 1919, observed altitude of Circle with line under 69° 25' 30". IE + 2' 30". HE 16 ft. Required Circle with line through.
2. April 15th, 1919, observed altitude of Circle with line under 58° 29' 40". IE - 2' 30". HE 18 ft. Required Circle with line through.
3. March 4th, 1919, observed altitude of Circle with line under 44° 44' 10". IE - 4' 20". HE 20 ft. Required Circle with line through.
Etc.