Sextant Corrections Explained - Index Error, Dip, Refraction & Parallax

Prerequisites

This lesson belongs to the RYA/MCA Yachtmaster Ocean syllabus ("practical use and care of the sextant at sea"; "sextant corrections"). You should already:

• Hold, or be working towards, Yachtmaster Offshore (or MCA OOW Yachts), the prerequisite for the Ocean exam.
• Understand the basic idea of a sight from the Celestial Navigation lesson: that the true altitude of a body (Ho) gives your distance from its geographical position, and that 1 minute of altitude error equals 1 mile of position error.
• Be comfortable with degrees and minutes arithmetic (60 minutes to a degree, decimals of a minute).

You will need a sextant (a plastic training sextant is fine to start), the current Nautical Almanac (or Reeds Nautical Almanac's astro section) and a notebook.

Learning Objectives

By the end of this lesson you will be able to:

• Name the parts of a marine sextant and explain the double-reflection principle.
• Read a micrometer sextant to 0.1 minute.
• Describe the four sextant errors (perpendicularity, side error, index error, collimation), which can be adjusted by the navigator and in what order.
• Find index error by the horizon and by the sun, and apply it with the correct sign.
• Apply dip, refraction, semi-diameter, parallax and augmentation in the correct sequence to turn sextant altitude (Hs) into observed altitude (Ho) for the sun, stars, planets and moon.
• Use an artificial horizon and understand the bubble sextant.
• Take a good sight at sea and look after the instrument.
• Adjust the sextant step by step, and list the non-instrument errors that limit accuracy.
• Correct planet sights and use a noon sight as a check on the correction routine.

RYA Yachtmaster Ocean syllabus items covered: practical use and care of the sextant; sextant errors and their correction; measurement of altitude; correction of sextant altitude to observed altitude for the sun, stars, planets and moon; meridian altitude latitude; accuracy and limitations of astronomical position lines.

How a Sextant Works

The parts

The marine sextant is a precision instrument for measuring the angle between two objects, in navigation almost always a celestial body and the sea horizon. Its main parts are:

• Frame: a rigid triangular casting (brass or aluminium; plastic on cheaper instruments) carrying the arc, graduated in degrees.
• Index arm: pivots at the top of the frame and carries the index mirror on its pivot. At its lower end are the release clamp, the micrometer drum and often a vernier scale.
• Horizon glass: fixed to the frame. On traditional sextants it is half-silvered (left half mirror, right half clear); "whole-horizon" sextants use a semi-transparent mirror across the whole glass.
• Shades: coloured filters that swing in front of the index mirror (for the sun) and the horizon glass (for glare on the horizon).
• Telescope: usually 3x to 4x magnification. A low-power, wide-field telescope makes finding stars easier; a higher power telescope helps with the sun.
• Handle: on the back of the frame, held in the right hand.

The diagram below shows how the two mirrors combine the reflected body and the direct horizon at your eye.

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Double reflection

Light from the body hits the index mirror, reflects onto the silvered part of the horizon glass, and reflects again into the telescope. Through the clear part (or through the semi-transparent mirror) you see the horizon directly. A law of optics says that when a mirror rotates through an angle, a ray reflected from it turns through twice that angle. So the arc, which is only about 60 degrees of physical arc (one sixth of a circle, hence "sextant"), is engraved to read up to about 120 degrees.

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The great practical benefit is that the reflected body and the horizon are seen together through the same instrument. When the yacht rolls, both images move together, so you can hold them in contact long enough to take a sight. That is why a sextant works on a moving deck where a simple protractor-and-plumb-line would not.

Reading the sextant

1. Read the whole degrees on the arc opposite the index mark on the index arm.
2. Read the minutes on the micrometer drum opposite its index line (0 to 60).
3. Read the tenths of a minute on the vernier beside the drum: the vernier line that best lines up with a drum graduation gives the decimal.

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Example: index mark just past 46 on the arc, drum reads 02, vernier line 5 aligned: 46 02.5.

Readings "off the arc" (to the right of zero, used only for index error) are read differently: the drum must be read as 60 minus the drum figure. If the index mark is just right of zero and the drum shows 57.0, the reading is 3.0 minutes off the arc.

Sextant Errors and Adjustments

There are four instrument errors. The first three are adjustable by the navigator and are always checked in this order, because each adjustment can disturb the next:

Most navigators remove side error and perpendicularity once, then leave a small index error (a few minutes) and simply measure and apply it. Fiddling with the screws to remove index error tends to reintroduce side error, and the adjusting screws wear.

Index error (IE)

Index error is the one correction you must find and apply every time you take sights.

Horizon method (any time of day).

1. Set the sextant to 0 00.0.
2. Look at a clear horizon (a clean, sharp horizon at least a couple of miles away is best).
3. If the direct and reflected horizons form a single, unbroken line, IE is zero.
4. If not, turn the micrometer until they line up and read it.
5. If the reading is on the arc (index mark left of zero, a positive reading), the sextant reads too high: subtract IE.
6. If it is off the arc (index mark right of zero), the sextant reads too low: add IE.

The memory aid is: "If it's on, take it off; if it's off, put it on."

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Take three or four readings, approaching from alternate sides, and average them. Record IE with its sign in the sight book. If IE grows beyond about 5 minutes, or changes suddenly, adjust the instrument or find out why (has it been knocked?).

Sun method (more accurate). With full shades in, set the sextant about 32 minutes on the arc and bring the reflected sun's lower edge to touch the direct sun's upper edge; read it. Then set about 32 minutes off the arc and touch the other edges; read it.

• IE = (off reading minus on reading) / 2. If the result is positive, it is "off the arc" (add); if negative, "on the arc" (subtract).
• Check: (on reading + off reading) / 4 should equal the sun's semi-diameter for the day from the almanac. If it does, your readings are good.

Example: on the arc 31.8, off the arc 32.6. IE = (32.6 minus 31.8)/2 = 0.4 off the arc, so add 0.4. Check: (31.8 + 32.6)/4 = 16.1, matching an almanac SD of 16.1. Readings accepted.

Star method. Set zero and look at a bright star: bring the reflected and direct star into coincidence. If they will not merge but sit side by side, you have side error.

From Hs to Ho: the Correction Sequence

The altitude you read on the sextant (Hs, sextant altitude) is not the true altitude of the centre of the body above the celestial horizon. Several corrections are needed. Apply them in this order:

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Ho = Hs plus or minus IE, minus dip, minus refraction, plus or minus SD, plus parallax

Why the order? Dip and IE are applied first because the almanac's refraction, SD and parallax tables are entered with apparent altitude (Ha), the altitude above the true horizontal as seen by the observer. Enter the tables with Hs and you may pick the wrong line.

Dip

Your eye is above the sea, so the visible horizon lies below the true horizontal through your eye. Every altitude measured from the sea horizon is therefore too large by the dip angle. Dip is always subtracted.

Dip (minutes) = 1.76 x square root of height of eye in metres, or 0.97 x square root of height of eye in feet.

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On a yacht, height of eye changes as you move about the deck and as the boat heels and rises on swells. Pick a standard position (for example standing in the companionway, braced) and measure your height of eye there. Errors of half a metre matter little (about 0.3 minute); the bigger problem in big seas is that the horizon you see may be the crest of the next wave, not the true horizon. Wait until you are on top of a swell for the sight. Cunliffe's rule for a big swell is to estimate the wave height, halve it, and add the result to your height of eye, because you only see the true horizon from the top of a wave and that is where you will be when you take the sight: with 3 m of height of eye and a 4 m swell, use 5 m (dip 3.9 minutes rather than 3.0). Remember too that if you move about the boat for different stars, from the cockpit to the bow to the lee scuppers, the height of eye and the dip change with you.

Abnormal refraction near the horizon (for example warm air over cold water, or vice versa) can make dip differ from the tabulated value by several minutes. This is one reason why star fixes with bodies spread evenly in azimuth are preferred: a dip error moves all lines equally and the cocked hat's centre is unaffected.

Refraction

Light from a body bends as it passes through the atmosphere, curving towards the denser air near the surface. The body therefore appears higher than it really is, and the refraction correction is always subtracted.

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Refraction is about 34 minutes at the horizon, about 5 minutes at 10 degrees, 1 minute at 45 degrees and zero at the zenith. For altitudes above about 15 degrees a good approximation is refraction (minutes) = 0.97 / tan(apparent altitude). The almanac tables assume a temperature of 10 C and a pressure of 1010 hPa; an additional table corrects for non-standard conditions, which matters only for low altitudes (below about 10 degrees) or extreme temperatures. This is the main reason to avoid sights below about 15 degrees.

Semi-diameter (SD)

You cannot judge the centre of the sun or moon against the horizon, so you bring one edge (the limb) into contact with it. The tables, however, are calculated for the centre. The semi-diameter (half the disc's angular width) converts a limb sight to the centre.

• Lower limb (sun sitting on the horizon): add SD.
• Upper limb (sun hanging from the horizon): subtract SD.

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The sun's SD varies from about 15.8 minutes in early July (Earth farthest from the sun) to 16.3 minutes in early January; it is printed at the foot of the sun column on the daily pages. The moon's SD varies from about 14.7 to 16.8 minutes and is also on the daily pages. Stars and planets are points of light: no SD.

Lower limb is normal for the sun. Use upper limb only when the lower limb is obscured by low cloud or haze. For the moon, use whichever limb is fully lit.

Parallax

The almanac gives positions as seen from the centre of the Earth. You stand on the surface, about 3,440 miles from the centre, so a nearby body appears lower to you than it would to an observer at the centre. The parallax correction is always added.

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Parallax depends on the body's distance and is greatest when the body is on the horizon, the horizontal parallax (HP). At altitude h, parallax = HP x cos h.

• Sun: HP about 0.15 minute; correction 0.1 at low altitudes, zero high up. Built into the sun tables.
• Venus and Mars: up to about 0.5 minute; the almanac gives a small "additional correction".
• Stars, Jupiter, Saturn: negligible.
• Moon: HP 54 to 61 minutes, tabulated hourly on the daily pages. At 30 degrees altitude the correction is about 50 minutes, the largest correction in astro. Get it wrong and the line is useless.

Augmentation

As the moon rises, you move closer to it by up to one Earth radius, so its disc appears very slightly larger: the semi-diameter "augments" by up to about 0.3 minute. It is included automatically in the almanac's moon tables.

The almanac's combined tables

The almanac does most of this for you:

• Sun: a combined table (inside front cover) by apparent altitude, giving the total of refraction, SD (a mean value for the half year, October to March or April to September) and parallax, for lower and upper limb.
• Stars and planets: refraction only, from the same page, plus the Venus/Mars additional correction.
• Moon: two tables (inside back cover): a main correction by apparent altitude (parallax for a mean HP, refraction and SD), then a second correction by HP from the daily page, for lower or upper limb. For an upper limb sight also subtract 30 minutes.
• Dip by height of eye, and the additional refraction table for non-standard temperature and pressure.

Worked Examples

All examples use height of eye 2.5 m (dip 2.8).

Example 1: Sun lower limb

Hs 32 14.6. IE 1.8 on the arc. Almanac SD 16.0.

Total correction after Ha: +14.6, which is what you would read from the almanac's sun lower limb table at 32 degrees.

Example 2: Sun upper limb

Same sun, but cloud hides the lower limb. Hs 31 42.6.

Example 3: Star

Sirius, Hs 41 27.3, IE 0.6 off the arc.

Example 4: Moon lower limb

Hs 32 14.0, IE 1.5 on the arc, HP from the daily page 57.0.

In practice you would take the main and HP corrections from the almanac moon tables, which give the same total (about +62.5) in two steps. Note how large the moon correction is; that is why the moon tables are entered carefully with both Ha and HP.

Artificial Horizons and Bubble Sextants

Artificial horizon

When there is no sea horizon (on land, in a fog-bound anchorage, or for practice ashore) a shallow tray of liquid sheltered from the wind makes a perfectly level mirror. You measure the angle between the body and its reflection in the liquid. Because the reflection is as far below the horizontal as the body is above it, the sextant reads twice the altitude.

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1. Apply index error to the sextant reading.
2. Divide by two.
3. Apply refraction, SD and parallax as usual.
4. No dip correction: the reflecting surface is at your level, not a horizon below you.

Water works but ripples; oil (e.g. engine oil) or traditional mercury is steadier. The artificial horizon is excellent for practising sights from a beach or garden, for checking the sextant, and for verifying your chronometer error with a known position. It is useless on a moving deck. The sextant limit of about 120 degrees means you can only observe bodies up to about 60 degrees altitude this way.

Bubble sextant

Aviation (bubble) sextants have an internal spirit level that provides an artificial horizontal. They need no sea horizon (useful at night or in haze) and no dip correction or halving. However, the bubble is very hard to hold steady on a yacht, so individual readings are poor; navigators using one average many readings over a minute or two. They are a curiosity or backup on yachts, not the primary instrument.

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Taking a Good Sight at Sea

Sun sight procedure

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Image: U.S. Navy photo by Photographer's Mate 3rd Class Kevin S. O'Brien, public domain, via Wikimedia Commons.jpg) (downscaled)

1. Check and record IE.
2. Put in enough shades on the index mirror (and the horizon glass if there is glare). Set the shades before raising the sextant.
3. Set the arc to zero, aim directly at the sun, then swing the index arm down while lowering the sextant until the sun appears on the horizon. (Or preset the expected altitude and look along the sun's bearing.)
4. Fine-tune with the micrometer until the lower limb just kisses the horizon.
5. Rock (swing) the sextant gently about the line of sight: the sun appears to swing in an arc. The sextant is vertical when the sun is at the bottom of that arc; adjust so the limb touches the horizon at the lowest point of the swing.
6. Call "Mark!" or press your stopwatch at the instant of contact; note the time to the second, then read the sextant.
7. Take a series of three to five sights over two or three minutes.

Averaging and screening

Plot your series of altitudes against time on a scrap of graph paper. Over a few minutes the sun's altitude changes nearly linearly, so the good sights lie on a straight line; a sight off the line is a bad one and should be rejected. Then use the best sight, or the average of altitudes and the average of times.

Star sights

Preset the sextant to the planned altitude, point along the planned bearing, and the star will appear near the horizon. Alternatively hold the sextant upside down, look at the star through the horizon glass and bring the horizon up to it, then turn the sextant the right way up. Stars are points: bring the star exactly onto the horizon, not just touching it. Use a low-power telescope or none at all for finding stars.

Bracing and safety

Wedge yourself in securely (companionway, against the shrouds, clipped on). One hand for the boat: if you need both hands for the sextant, make sure you are secure before you let go. Never point a sextant at the sun without shades.

Practise ashore

Use of the sextant is the essence of celestial navigation, and the only teacher is practice. Take the sextant to a south-facing beach with a clear sea horizon and shoot the sun until the images come together without thought; then wait for twilight and pull down a few stars, without worrying which they are, just to learn the technique. If you can do it from a beach, a hill or a window with a rooftop as a horizon, you will be able to do it at sea, where, oddly, the motion bothers a sextant far less than it bothers a hand-bearing compass. Soon you will no longer start with the arc at zero: you will guess the altitude, look along the bearing and adjust the image down to the horizon.

Care and Maintenance

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• Rinse with fresh water (or wipe with a damp cloth) after salt spray; dry with a soft lint-free cloth; clean mirrors with lens tissue.
• Store in its box with desiccant, and wedge the box where it cannot fall. Always lift the sextant by its frame or handle, never by the index arm or telescope.
• Never leave it in the sun (heat can distort the frame and shift mirrors) or loose on the chart table.
• Lightly oil the worm gear and rack occasionally; never use force on the micrometer.
• If it is dropped, check all three adjustable errors before trusting it. A bent frame shows as an index error that varies along the arc, or star images that will not merge; at that point, carry on with your spare.
• Carry a spare (even a plastic sextant) on an ocean passage, and record the IE of each instrument separately.

Adjusting the Sextant Step by Step

The table above gives the order; this section gives the practical routine you should be able to describe to an examiner and perform on a training sextant. Always work with the sextant clamped to nothing and held firmly, and use the proper small screwdriver or key supplied in the box. Turn adjusting screws by tiny amounts: a quarter turn can move an image by many minutes of arc.

Perpendicularity of the index mirror

1. Set the index arm near the middle of the arc (about 35 degrees) and hold the sextant flat, arc nearest you, with the frame horizontal at eye level.
2. Look into the index mirror from a position just above the frame, so that you can see both the real arc and its reflection in the mirror.
3. If the reflection of the arc and the arc itself form one smooth continuous curve, the mirror is perpendicular. If the reflection appears to be bent upward or downward relative to the real arc, the mirror leans forward or backward.
4. Use the screw at the back of the index mirror (usually with a locking screw alongside) to bring the two curves into one line, then re-check.

Side error

1. Set the sextant to zero and look at a star, or at a distant well-defined object, through the telescope.
2. Rotate the micrometer back and forth a few minutes either side of zero. The reflected image should pass directly over the direct image. If it passes to one side, there is side error.
3. Alternatively, use the horizon: hold the sextant vertically at zero, then tilt it sideways. If the horizon remains one unbroken line as you tilt, there is no side error. If it breaks into two lines that step apart in one direction, there is side error.
4. Adjust the rear horizon-glass screw (the one furthest from the frame) until the images coincide.

Index error

1. Set the sextant near zero and view the sea horizon (best, in a calm spell) or the sun.
2. Rotate the micrometer until the direct and reflected horizons form one continuous line. Read the arc and drum.
3. If you read zero exactly there is no index error. If you read a small number on the arc, the error is on the arc; if the drum reads a number off the zero end, the error is off the arc.
4. Either remove it by turning the front horizon-glass screw, or (usual practice at sea) leave it and apply it as a correction. Repeat the check several times and take the mean.

A good habit: re-check index error at the start of every session, not just once a voyage. The frame expands and contracts with temperature, and a bump in the box can shift a mirror by a minute or two.

Non-Instrument Errors and Your Error Budget

Even a perfectly adjusted sextant cannot give a perfect altitude. The RYA expects an Ocean candidate to appreciate where the remaining errors come from and how big they are, because it tells you how far to trust a fix and why a three-body fix is better than a single sight.

The practical lesson is that a single sun sight at sea is seldom better than about 2 miles accurate, and a typical yacht position from careful sights is good to 3 to 5 miles. Do not report a position to a tenth of a mile just because the arithmetic has given you one.

Corrections for Planets and the Additional Corrections

Venus and Mars are treated slightly differently from stars. After the normal sequence (IE, dip, refraction) you take the planet's additional correction from the almanac's star and planet table, which allows for parallax and phase. Jupiter and Saturn need no additional correction for yachting accuracy. Because planets have a visible disc you still measure the centre; there is no semi-diameter correction.

Worked example, Venus: Hs 28 41.6, IE off the arc 1.0, height of eye 2.5 m (dip 2.8). Apparent altitude: 28 41.6 + 1.0 = 28 42.6; minus dip 2.8 = Ha 28 39.8. Main correction for 28 40 = minus 1.8 (refraction) giving 28 38.0. Additional correction for Venus (almanac, altitude about 28, month-dependent) say +0.2, giving Ho 28 38.2. The exact figures depend on the almanac edition; the pattern (apply the table's main correction, then the additional correction for the planet) does not.

Meridian Altitude and Why Corrections Matter for Latitude

A noon sight is the simplest application of everything above. The sun's maximum altitude gives latitude directly: zenith distance is 90 minus Ho, and latitude is declination plus or minus zenith distance depending on whether the observer is on the same side of the sun as the equator. Because there is no sight reduction table to hide behind, any error in the corrections goes straight into latitude, mile for mile. If you mistakenly add dip, or apply the lower limb semi-diameter with the wrong sign, you will be about 6 or more miles out immediately. That makes the noon sight a useful practical check on your correction routine. Take the corrections slowly and write down each stage.

Exam Tips: What the RYA Examiner Expects

• Be able to explain, without notes, why the arc reads twice its physical size, and sketch the double reflection.
• Be able to name the sextant errors in order, say which are adjustable, and which are corrected by calculation.
• Show a written correction table: every step on its own line with sign. An answer with the right Ho but unlabelled arithmetic is weaker than a labelled sequence with a small slip.
• Know the mnemonic for IE: "on the arc, take it off"; for dip: always subtract; for refraction: always subtract; for SD: lower limb add, upper limb subtract.
• State the size of each correction to check plausibility: refraction about 1 minute at 45 degrees and about 0.1 at 80 degrees; sun SD about 16 minutes; dip 2 to 3 minutes for a small yacht.
• Be ready to talk about what you would do if the sextant is dropped or the telescope fogs up, and why a spare instrument and a watch check matter.

Common Mistakes

• Wrong IE sign. On the arc, subtract; off the arc, add. Write the sign every time.
• Entering tables with Hs instead of Ha. Apply IE and dip before looking up refraction or the combined correction.
• Adding dip. Dip is always subtracted from sea-horizon sights; and it is zero for artificial horizon sights.
• Wrong limb. Using the lower limb table for an upper limb sight, or forgetting to subtract SD for upper limb.
• Forgetting to halve an artificial horizon reading.
• Moon: forgetting the HP correction or the 30 minutes for upper limb. The moon correction is large; small slips are large errors.
• Sextant not vertical. Failing to rock the sextant gives an altitude that is too large.
• Using a false horizon. In big seas you may be measuring to a nearby crest. Wait to be on top of a swell.
• Very low sights. Below about 15 degrees refraction (and its variability) and dip anomalies grow; avoid unless necessary.
• Using the wrong half-year column in the sun table (October to March versus April to September).

Summary

• The sextant measures angle by double reflection; the arc reads twice its physical size and the body and horizon move together in a seaway.
• Check errors in the order perpendicularity, side error, index error; usually leave a small IE and apply it.
• IE: on the arc subtract, off the arc add. Check it at every sight session.
• Ho = Hs plus or minus IE, minus dip, minus refraction, plus or minus SD, plus parallax (augmentation included for the moon).
• Dip = 1.76 x square root of height of eye in metres; refraction is about 34 minutes at the horizon and zero at the zenith; sun SD about 16 minutes; moon HP 54 to 61 minutes.
• Use the almanac combined tables, entered with apparent altitude.
• Artificial horizon: halve the reading, no dip. Bubble sextant: no horizon or dip, but poor accuracy on a yacht.
• Look after the sextant: rinse, dry, box, never drop it, and carry a spare.

Check Your Understanding

1. Why can the sextant arc, which is only about 60 degrees long, measure angles up to 120 degrees?

Answer: Because of double reflection: when the index mirror turns through an angle, the reflected ray turns through twice that angle, so the arc is graduated at twice its physical angle.

1. In what order should the adjustable errors be checked, and why?

Answer: Perpendicularity, then side error, then index error, because adjusting each mirror can disturb the error that follows it; doing them in this order avoids undoing earlier adjustments.

1. With the sextant set at zero you have to set the drum to 2.4 minutes on the arc to make the horizons line up. What do you do with all your sights?

Answer: Index error is 2.4 on the arc, so subtract 2.4 from every sextant altitude ("if it's on, take it off").

1. Sun method readings: on the arc 31.0, off the arc 33.4. Find IE and check it against an almanac SD of 16.1.

Answer: IE = (33.4 minus 31.0)/2 = 1.2 off the arc, so add 1.2. Check: (31.0 + 33.4)/4 = 16.1, which matches the almanac SD, so the readings are good.

1. What is the dip for a height of eye of 2 m and why is it always subtracted?

Answer: 1.76 x square root of 2 = about 2.5 minutes. The visible horizon lies below the true horizontal, so the measured altitude is too large by the dip angle.

1. Correct a sun lower limb sight: Hs 50 10.0, IE 1.0 off the arc, height of eye 3 m, refraction 0.8, SD 15.9, parallax 0.1.

Answer: 50 10.0 + 1.0 = 50 11.0; minus dip 3.0 = Ha 50 08.0; minus refraction 0.8 = 50 07.2; plus SD 15.9 = 50 23.1; plus parallax 0.1 = Ho 50 23.2.

1. Why is the moon's parallax so much larger than the sun's?

Answer: Parallax depends on the body's distance relative to the Earth's radius. The moon is only about 60 Earth radii away, so the difference between the view from the Earth's centre and from the surface is up to about a degree (HP 54 to 61 minutes); the sun is about 23,000 Earth radii away, so its parallax is only about 0.15 minute.

1. Using an artificial horizon ashore you read 84 36.0 with IE zero. What is the apparent altitude, and which correction is not applied?

Answer: Halve it: 42 18.0. No dip correction is applied, because the reflecting surface is at your own level rather than a sea horizon below your eye.

1. Why must you rock the sextant when taking a sight?

Answer: The altitude is only correct when the sextant is vertical. Rocking makes the body swing in an arc; the bottom of the arc shows the vertical position, so you set the limb to touch the horizon there. A tilted sextant gives too large an altitude.

1. You drop the sextant. What checks do you make before trusting it again?

Answer: Check perpendicularity, side error and index error in turn; look for a star image that will not merge or an index error that varies along the arc, which suggests a bent frame or displaced mirror. If it cannot be corrected, use the spare sextant.

1. A sextant reads 0 03.2 on the arc when the horizon is made continuous. What is the IE and how is it applied to a Hs of 36 17.4?

Answer: The error is on the arc, so subtract: IE minus 3.2. 36 17.4 minus 3.2 = 36 14.2 apparent altitude before dip.

1. Why does a navigator re-check index error at every sight session, and what is the correct order of the first three adjustments?

Answer: Temperature changes and knocks can shift the mirrors; IE changes more easily than the other errors. The order is perpendicularity, side error, index error, because each adjustment can disturb the later ones.

1. Why is the noon sight a good test of your correction routine?

Answer: Latitude comes directly from Ho and declination with no sight reduction tables, so any error in dip, refraction or semi-diameter appears mile for mile in latitude and is easy to spot.