Once the sextant altitude (Hs) is obtained, corrections must be made to compensate for inaccuracies in the instrument, the atmosphere, the diameter of the celestial body and its proximity to the observer on earth, and the height of the observer above the water's surface.
The first correction is labelled I.C. meaning index correction. This is an error in the sextant itself and can be found by setting the sextant to read exactly zero and observing the sea horizon, a distant mountain top (a reasonably flat one), or a celestial object. At zero reading, the objects observed should appear the same height in the horizon glass and mirror.
If the horizon or object in one side is above or below that in the other side, adjust the micrometer drum or the tangent screw until the objects are level with each other. This is the amount of index correction. If the arrow is to the left of the zero or "on the arc", the I.C. is negative. If
the arrow is to the right of the zero or "off the arc", the I.C. is positive.
An easy way to remember this is to memorize If it's on, it's off. If it's off, it's on. With a plastic sextant, the index correction should be made for each set of sights since plastic
will expand and contract with temperatures and will have different instrument errors. With a brass or aluminum instrument, the index correction should always be the same barring tampering with the mirrors or dropping the instrument.
The next correction is called "dip". It is the angle by which the true horizon differs from the horizon at the eye of the observer so it depends on the height of the observer's eye from the sea level.
Since the angle measured from an eye above the surface of the earth is always greater than that which would have been observed from sea level, the dip correction is always negative. The dip correction table is found inside the front cover of the Nautical Almanac with a shortened version inside the back cover. It is entered with the height of the observer's eye in feet or meters. If the height of eye were 9.5 feet (between 9.2 and 9.8), the dip correction would be -3.0. If the height were 14 meters (between 13.8 and 14.2), the correction would be -6.6. In the case where the height of eye is a critical a value exactly listed in the table, the correction taken is the one toward the top of the page. For example, height of 21.0 feet would give a correction of -4.4. For extremely high or low heights of eye, the column to the right in the table is used. Height of eye of 85 feet would give a value of -8.9. Height of eye of 7.2 feet would give a value of -2.6.
Where dip is expressed in minutes of are, d is the distance in nautical miles to the shoreline being used and h is the height of eye of the observer above the water level, expressed in feet. For convenience, Table 22 in American Practical Navigator by Bowditch can be entered with height of eye and distance to the horizon to obtain the dip correction. These values are to be interpolated when height of eye falls between the values heading the columns. Below the bold stepped line, the dip corrections are equal to those obtained with a true sea horizon. The dip short correction replaces the normal dip correction and is always negative since the land horizon will be lower than the true sea horizon.
The dip short table takes care of the lower land horizon as well as the height of eye. It is entered with the distance to the land horizon (in nautical miles) above which the celestial body appears and with the height of eye. To obtain the distance to the land horizon, we need a chart of the area and the bearing of the celestial body. This bearing can be roughly obtained by a compass or more accurately obtained from the H.O. 229 tables. One result of the H.O. 229 tables is Zn or true bearing of the celestial body to the nearest tenth of a degree. From our dead reckoning position, we layoff the bearing of the land and measure the distance from our DR to the intersection of land and bearing line.
This distance to the nearest tenth of a mile is used to enter the left hand side of Table 22, the correct column is chosen by knowing height of eye. If the height of eye were 15 feet and the distance to land horizon were 2.5 nautical miles, the dip short correction would be -4.4 minutes of arc. If the height of eye were 17 feet, partway between the values listed, and the distance of horizon were 2.5 nautical miles, the interpolated correction would be 2/5 of the way between 4.4 and 5.6 minutes of arc (17 is 2/5 of the way between 15 and 20). The correction then would be negative 4.8 minutes of arc.
The third correction to apply to our sextant altitude air temperature and atmospheric pressure. The alteration of the atmosphere for non-standard temperatures or pressures is only made for low altitude bodies and can be either positive or negative as in the table inside the first page of the Nautical Almanac. Along the top of the table we find temperatures in degrees Fahrenheit or Celsius, along the side are pressures in millibars or inches. By entering the figures, we get a lettered slanted zone. We continue down to the column of the same letter until you arrive at the line of altitude nearest to yours, corrected so far for index error and height of eye. If the temperature were +30° F and the pressure were 30.50 inches, the correct zone would be D. For a low altitude of 10° 15.0, the correction would be -0.4. If the temperature were 35° C and the pressure were 980 millibars, the zone would be M. For altitude of 14° 47.8, the correction would be +0!5. I really don't mess with these corrections
The last correction, callrd "main" is a combination of several factors, with the celestial body observed. One factor, refraction, applies to all bodies. When the light from the body enters the atmosphere its path is bent downward. For an observer on the earth, the celestial body will always appear higher than it really is so the refraction correction is always negative.
A second factor in the "main" correction is semidiameter, applicable to Sun or Moon sights. Since these two bodies we observe either the upper limb or lower limb, we have to correct this altitude to the center of the disk. All positional figures in the Nautical Almanac are based on the disk center. The angular diameter of both the Sun and Moon is close to 30.0 but does vary slightly with the distance of the body from the earth. The Sun is closer to the earth in the northern hemisphere winter so would appear a little larger. If we look at the semidiameter (half diameter) figures at the bottom of the sun column in the Nautical Almanac. The S.D. varies from 15.8 to 16.3. Doing the same for the Moon, W; find a 14.7 to 16.8.
The third factor in the "main" correction is parallax, only for close objects such as the Sun, Moon, and Venus. Since all figures in the Nautical Almanac are based on observation from the center of the earth, a correction must be made for the difference in angle from the center to the surface of the earth, our true observation point. This correction can be over a degree for the Moon, is less than 30 seconds for Venus and less than 9 seconds for the Sun. The parallax correction is always positive and will decrease as the altitude of the body increases.
A fourth factor in the "main" correction is phase, applicable to the Moon, Venus and Mars. This correction is due to the varying of the apparent center of the body from its actual center. Since we observe a limb of the Moon, not its center, we need the phase correction. For Venus and Mars, their image is so small that a limb is impossible to. The phase corrections are listed in the Nautical Almanac for twilight sights only. For daytime observations of Venus, where the relationship between the body and the horizon is different, a formula is solved for this correction. It can be found in the section at the back of the Nautical Almanac which explains altitude correction tables. The values for two unknowns of the formula are also listed there for the particular year. The fifth and last factor in the "main" correction is augmentation of the Moon. As the Moon increases or decreases in altitude, its distance from the center of the earth stays approximately the same, roughly 250,000"miles. We are observing from the surface of the earth, not the center, and the Moon's distance from us will decrease when the Moon is higher in the sky. The semidiameter is larger for higher altitudes since objects appear larger if they are closer to us. The change in semidiameter due to augmentation for the Moon is about 0.3 from horizon to zenith. For the Sun and planets, it is too negligible to be worry about.
For our convenience, all of these factors except phase are lumped together in one "main" correction so we don't have to consider them individually. The corrections for the Sun and planets are found inside the front cover of the Nautical Almanac, those for the Moon inside the back cover.
In the four examples below, we will categorize the celestial bodies in the following manner (1) stars, Jupiter, Saturn (2) Venus, Mars (3) Sun (4) Moon.
STARS AND PLANETS
For the first category, enter the column titled Stars and Planets with the apparent altitude of the body. If it lies between the tabular values, choose the correction that brackets the values. If the apparent altitude is one of the tabular values, choose the correction that lies toward the top of the page. Thus the correction for 12° 30' is -4.3. For 150 30', the correction
is -3.5.
For Venus and Mars, proceed as above for part one of the main correction. The second part of the correction is found in the right half of the Stars and Planets column under the sections labeled Venus and Mars. For an altitude of 25° on 13 Dec., the additional correction
for Venus would be 0.2, for Mars 0.1. Both corrections are positive.
For the Sun, enter one of the two columns in the section depending on the month when sights are taken. Two corrections are available, one for upper and one for lower limb. In January, a lower limb correction for apparent altitude of 150 20' would be +12!8. In July, the upper limb correction for apparent altitude of 11° 05' would be -20.6.
If the altitudes in the above three categories are too low to fit in the column, refer to inside front cover opening on the right-hand page. This table covers altitudes of less than 10° for Sun, stars and planets. For an altitude of 5° 05', corrections are circled in the table to the right. If the apparent altitude lies between tabular altitudes, interpolation is necessary. For instance, for an altitude of 5° 02.5, the correction for a star would be -9.8.
For a lower limb Sun in November, correction would
be +6.5. Sights with such low altitudes are not advised but sometimes are the only ones available.
The main correction for the Moon (fourth category) involves finding a reference number in the daily pages. This horizontal parallax or H.P. is located on the right hand side of the moon column. If we observed the Moon on 5 July 1976 at 1100 Greenwich Mean Time, the H.P. would be 59.4. Remember that this is just a reference number and will not be directly added or subtracted. It has no sign.
Assume our apparent altitude is 37° 28' with H.P. as above. Enter the column inside the back cover which is headed by 35°-39°. Choose the section in that column that is designated by 37°. The minutes within the degree are sectioned by tens in the column to the left and to the right of the page.
Our altitude rounded (interpolation may be necessary in which case the rounding is not done) to the nearest 10 minutes (37° 30') gives a correction of 55.1. (This is entered in the special box on the sight reduction sheet under the sextant altitude correction section.) Continue down the columrl of 35°-39° until it splits in two, one part headed with "L", one with "U". These letters refer to lower and upper limbs. If we sight the lower limb, continue down the "L" column until you come to the line designated by H.P. of 59.4. The second correction would be 6.8. Both corrections are positive and are added together for the main correction.
If we had observed an upper limb, the first correction would be found in the same manner as above. The part of the column entitled "u" would then be followed until the line for H.P. is reached. The second correction would be 4.5. The first and second corrections would be added and then 30' subtracted from the sun. If the first two corrections add to less than 30', the main correction may be negative. Remember that the Moon is roughly 1/2 degrees wide. All corrections are based on the lower limb and then adjusted for upper limb by applying the 30'. Both upper and lower limb sights have to be corrected to get the altitude of the center of the Moon. The same is true of the Sun,the large difference in the altitude corrections for the two limbs there.
Assume our apparent altitude is 37° 28' with H.P. as above. Enter the column inside the back cover which is headed by 35°-39°. Choose the section in that column that is designated by 37°. The minutes within the degree are sectioned by tens in the column to the left and to the right of the page.
Our altitude rounded (interpolation may be necessary in which case the rounding is not done) to the nearest 10 minutes (37° 30') gives a correction of 55.1 (This is entered in the special box on the sight reduction sheet under the sextant altitude correction section.) Continue down the column of 35°-39° until it splits in two, one part headed with "L", one with "U". These letters refer to lower and upper limbs. If we sight the lower limb, continue down the "L" column until you come to the line designated by H.P. of 59.4. The second correction would be 6.8 Both corrections are positive and are added together for the main correction.
If we had observed an upper limb, the first correction would be found in the same manner as above. The part of the column entitled "u" would then be followed until the line for H.P. is reached. The second correction would be 4.5 The first and second corrections would be added and then 30' subtracted from the sun. If the first two corrections add to less than 30', the main correction may be negative. Remember that the Moon is roughly 1/2 degrees wide. All corrections are based on the lower limb and then adjusted for upper limb by applying the 30'. Both upper and lower limb sights have to be corrected such that we finally get the altitude of the center of the Moon. The same is true of the Sun, the large difference in the altitude corrections for the two limbs there. I know this sounds confusing but when you do get a good sight and it all works good it really makes you feel good.
