The corrections made to the Hs (sextant altitude) are necessary because the mathematical premise of celestial navigation has the observer taking a sight to the center of the celestial object from the center of the earth. Since we cannot physically replicate that assumption we have to factor in some additional corrections.
I won’t spend time here discussing the dip (height of eye), or the index correction (made on sextant). Suffice it to say that the dip correction is always subtracted and is dependent upon the height of eye of the observer over the visible horizon. During a passage that height usually remains constant provided that the navigator takes sights from the same place on deck.
The index error also usually remains constant (unless of course the sextant is dropped). It is checked every time a sight is taken and it is most important for the navigator to remember the old saw “when you’re on, you’re off.” That is to say that if the sextant is reading on the arc that number is subtracted, and if the sextant is reading off the arc, that number is added. On a good sextant the error remains relatively constant and is not usually more than 2 or 3 feet.
The next set of corrections referred to as altitude corrections, or 3rd corrections, are found on page A2 in the Nautical Almanac. These corrections combine refraction, parallax and semi diameter. All these corrections have to be factored into the Hs in order to “reduce” the sight so that the Ho or observed altitude can be derived. This is what we are seeking. Let’s take a look at each of these corrections.
Refraction: Light is bent as it enters the denser atmosphere of the earth. We all have observed how a pencil looks bent when placed in a glass of water — it is the same phenomenon with the light arriving from a celestial body. The effect is that the celestial object appears to be higher above the horizon than it actually is. The correction for refraction is therefore always negative. On page A2, refraction corrections are listed for stars and planets in different sections than for the sun.
Semi diameter: This correction applies to the sun and moon. The moon tables are at the rear of the Nautical Almanac and are a subject of another newsletter. Because of the elliptical shape of the Earth’s orbit, the semi diameter of the sun is subject to change.
It varies roughly between 15.8 to 16.3 feet over the course of a year. An examination of the daily sun pages at the bottom of the page shows the daily semi diameter labeled SD.
There are two columns in the altitude correction tables noting the months of the years when the sight is taken. A mistake in entering these tables would only yield an error of 0.2 feet.
Semi diameter must be factored because navigators are not observing the center of the sun, but instead sight either the upper or lower limb of the sun. Usually a lower limb sight (LL) is preferred since it is easier to “rock the sextant.” As for a moon sight, the observed limb is dependent on the phase. Semi diameter is always added if the lower limb is observed and subtracted for the upper limb. These differences are made obvious by the apparent altitude correction tables, which list both upper and lower limb sights.
Parallax: This is the third correction, which is basically the change in position of a celestial object as seen from two different locations. These locations can be said to be the center of the earth and the place on the surface on the earth where the navigator took his sight. The moon has the largest parallax. There is a table on page A2 for Venus and Mars, the two closest planets.
Let’s put all this together now by doing an example. The day of a lower limb sight of the sun is Dec. 21, 2010. The Hs of the sun is 35° 27.5’. Index error is 2 feet on the arc. The height of eye (dip) is 10 feet. Find the Ho.
Hs 35° 27.6’
app alt 35° 22.5’
The apparent altitude, also known as the Ha, is now applied. It is the 3rd correction, which includes refraction, semi diameter and parallax.
app. Alt 35° 22.5’
+ 3rd corr 14.9’
Ho 35° 37.4’
Note: Altitude correction tables are known as “critical tables.” There are two possible choices. Always choose the higher number. If a mistake is made here it is not that damaging. The wrong choice will only throw the accuracy of the sight out by 0.1 foot.