# User s Guide MARK 15 #026 MARK 25 #025 INDEX SHADES INDEX MIRROR. HORIZON MIRROR (Beam Converger on Mark 25 only) ADJUSTMENT SCREW HORIZON SHADES

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1 User s Guide INDEX SHADES INDEX MIRROR HORIZON MIRROR (Beam Converger on Mark 25 only) ADJUSTMENT SCREW HORIZON SHADES TELESCOPE MICROMETER DRUM QUICK RELEASE LEVERS LED ILLUMINATION (Mark 25 only) INDEX ARM STANDARD MARK 15 #026 DELUXE MARK 25 #025

4 To read fractions of a degree: Use the two scales involving the micrometer drum at the side of the index arm. The outer revolving drum scale indicates minutes of arc (one minute equals 1/60 of a degree), while the stationary vernier reads to 2/10 of a minute. To read the number of minutes: Find the single LONG line at the top of the vernier. The line on the drum scale that is opposite this line gives the number of minutes. If the line on the vernier is between two lines on the drum, choose the line of lower value. To read fractions of a minute: 1. Find the SHORT line of the vernier that is opposite to a line on the drum. 2. Count the number of spaces this line is away from the long line at the top of the vernier. Each one equals 2/10 of a minute. Figure 1 In this diagram (Fig. 1), the line on the vernier that is opposite to a line on the drum is two spaces away from the long line at the top of the vernier. The sextant reads '. Note: The micrometer drum scale and its screw mechanism, not the arc, determine the accuracy of your sextant. The arc is stamped with sufficient accuracy to ensure that you are never reading the incorrect whole degree; full accuracy in minutes of arc depends exclusively on the drum scale. For example, when the sextant reads 0 00', the drum scale will be set precisely at zero, while the index line and the zero on the arc may be slightly out of alignment. As you are concerned only with reading whole degrees on the arc, this difference is not significant. Page 2

5 Using the Light on the Davis Mark 25 Sextant The Mark 25 is specially constructed with a solid state light emitting diode (LED) and light guide to allow easy reading of the scales at twilight. To use the light: Make sure that your eyes are dark-adapted before using the light. Press the button at the top of the handle. The light turns off when the button is released. Note: The high-efficiency LED configuration was developed to insure long battery life (as much as ten times longer than with regular bulbs). Nevertheless, all batteries eventually run down. When not using your sextant for long periods of time, remove the batteries by unscrewing the black plastic screw in the handle. Battery contacts can be easily cleaned with a small file or knife blade. Replacements, if needed, are ordinary zinc-carbon or alkaline batteries, 1.5 volt, size AAA. Batteries that start to leak should be removed immediately. After replacing the batteries, be sure to fit the handle together again carefully, and replace the screw snugly but not too tight. Inserting the 3X Telescope Your sextant comes equipped with a high quality 3X telescope. The scope is interchangeable with the hooded sight tube. To remove the sight tube from its mounting bracket on the sextant: Separate the tube from the eye-piece as shown in Fig. 2 below. Figure 2 CAUTION: Do not attempt to snap the assembled sight tube into or out of the mounting bracket. Separate the sight tube from the eyepiece by carefully sliding the eyepiece out of the bracket and from the rear only. Insert the scope from the front only. Page 3

6 Adjusting for and Calculating Built-In Index Error Adjusting your sextant is easy and should be done each time it is used. On a correctly adjusted sextant, the two mirrors are always perpendicular to the frame and become parallel to each other when the body and drum scales read zero. To initially adjust the index mirror so that it is perpendicular to the frame: 1. Set the instrument at approximately Holding the sextant horizontal and about eight inches from the eye, look with one eye into the mirror so that the frame arc is reflected in the mirror. 3. Move the instrument until you can look past the index mirror and see the actual frame arc as well as the reflected arc. The two arcs should appear as one continuous curve (Fig. 3). If they do not, turn the adjustment screw at the back of the index mirror until the two arcs come into alignment. Figure 3 To adjust the sextant for index error: 1. Set the instrument at 0 00' and look at the horizon. 2. Keeping the sextant close to your eye, turn the screw that is furthest from the frame at the back of the horizon mirror until the two horizon images move exactly together (Fig. 4). The two mirror are now parallel. Page 4 Figure 4

8 To adjust the horizon mirror (Mark 15 only): 1. Adjust the horizon mirror (the small, half-silvered mirror) for side error by making it perpendicular to the frame. 2. Holding the sextant in your right hand, raise the instrument to your eye. 3. Look at any horizontal straight edge (the sea horizon or the roof of a building, for example) and move the index arm back and forth. The real horizon will remain still while the mirror horizon will appear only when the body and drum scales read close to zero. 4. Line up the mirror horizon and the real horizon so that both appear as a single straight line (Fig. 6). Figure 6 5. Without changing the setting, look through the sextant at any vertical line (a flagpole or the edge of a building, for example) and slowly swing the instrument back and forth across the vertical line. If the horizon mirror is not perpendicular to the frame, the line will seem to jump to one side as the mirror passes it. To correct this, slowly tighten or loosen the screw closest to the frame at the back of the horizon mirror until the vertical line no longer appears to jump (Fig. 7). Figure 7 Page 6

9 To adjust the Beam Converger horizon mirror (Mark 25 only): 1. Adjust for side error by making the Beam Converger perpendicular to the frame. 2. Holding the sextant in your right hand, raise the instrument to your eye. 3. Look at any horizontal straight edge (the sea horizon or the roof of a building, for example) and move the index arm back and forth using the quick release levers. The real horizon will remain still while the reflected horizon will appear only when the arc and drum scales read close to zero. 4. Line up the reflected horizon and the real horizon with the knob so that both appear together as a single straight line (Fig. 8). Figure 8 5. Without changing the setting, look through the sextant at any vertical line (a flagpole or the edge of a building, for example) and slowly tighten or loosen the screw closest to the frame at the back of the Beam Converger, until the real and reflected vertical lines perfectly coincide (Fig. 9). This is particularly easy since the two images have different colors. It is simply a matter of putting one image exactly on top of the other. Figure 9 Page 7

11 Correcting for the Height of the Eye When measuring the altitude of the sun, you need to measure the angle formed by a ray from the sun and a plane tangent to the earth at the point where the observer is standing. However, due to the height of the eye of the observer, the visible horizon actually falls below this theoretical place (Fig. 11). This requires that a dip correction be made. Figure 11 Due to the height of the eye of the observer, the visible horizon (H) falls below the plane tangent to the earth at the point where the observer is standing (P). To apply a dip correction for the height of the eye: Apply a correction as shown in the table below. Dip correction increases as the eye is raised further above the surface of the water. Height of Eye Dip Correction 5 ft. (1.5 m) 2' 10 ft. (3.0 m) 3' 15 ft. (4.5 m) 4' 25 ft. (7.5 m) 5' 40 ft. (12.0 m) 6' Dip correction must always be subtracted from the sextant reading. Page 9

12 USING SEXTANT READINGS TO CALCULATE LOCATION Before attempting to calculate your location using readings from your sextant, you need to be familiar with the following concepts: A GREAT CIRCLE is a circle on the surface of the earth, the plane of which passes through the center of the earth. The equator and the meridians (perpendicular to the equator) are great circles. See Fig. 12. A SMALL CIRCLE is one whose plane does NOT pass through the center of the earth. Parallels of latitude are small circles which become progressively smaller as the distance from the equator increases. At the poles (90 N or 90 S), they are single points. A great circle. Figure 12 A small circle. A NAUTICAL MILE is equal to one minute of arc of a great circle. Latitude is measured north or south from the equator along a meridian (a great circle). One minute of latitude equals one nautical mile anywhere on the earth. Longitude is measured east or west from the prime meridian (zero degrees) at Greenwich, England. It is measured along a parallel of latitude (a small circle). One minute of longitude equals one nautical mile only at the equator. Approaching the poles, one minute of longitude equals less and less of a nautical mile (Fig. 13). Note: The nautical mile (6076 feet; 1852 meters) is longer than the statute mile used on land (5280 feet; 1609 meters). The earth measures 21,600 nautical miles in circumference. Page 10

13 Figure 13 Finding Local Noon and the Sun s Altitude at the Meridian Passage A meridian is an imaginary line drawn on the earth s surface from pole to pole. A local meridian is one which passes through the position of the observer. When the sun crosses the local meridian, it is at its highest point. It is said to be in meridian passage and the time is local noon. Local noon may vary a half an hour (and in daylight savings time, one and one-half hours) from the noon shown on the clock, due both to the equation of time (to be discussed later) and the fact that our clocks are set to zone time. All clocks in a zone 15 wide show the same time. To find local noon: 1. Follow the sun up with a series of sights, starting about half an hour before estimated local noon. 2. Note the time and the sextant reading carefully. 3. Take a sight about every three minutes until the sun s altitude is no longer increasing. During meridian passage, the sun will seem to hang in the sky for a short period at its highest point, going neither up nor down. 4. Carefully note the sextant reading. This is the sun s altitude at meridian passage. 5. To determine the exact time of local noon, set your sextant at the same altitude as your first sight. Wait for the sun to drop to this altitude, and note the time again. The time of local noon is exactly half way between the times of the two sights. Page 11

14 To locate your position: Record the local time and the sextant reading when the sun was at the highest point. These two readings will serve to locate your position. The time is used to determine longitude and the sextant reading to determine latitude. Calculating the Declination of the Sun Every star and planet, including the sun, has a ground position, i.e., the spot on the earth directly beneath it. Standing at the sun s G.P. (ground position), you would have to look straight up to see the sun; if you were to measure its altitude with a sextant, you would find the altitude was 90. From the earth, the sun seems to move across the sky in an arc from east to west. During certain times of the year, it is moving around the earth directly above the equator. In other words, the sun s G.P. is running along the equator. Declination of the sun at this time is zero. However, the sun s G.P. does not stay at the equator throughout the year. It moves north to a maximum of 23.5 N in the summer of the Northern Hemisphere and south to a maximum of 23.5 S in the winter. The distance of the sun s G.P. from the equator, expressed in degrees north or south, in known as the declination of the sun (Fig. 14). Figure 14 Declination of the Sun In like manner, each star has a ground position and a declination. The declination of Polaris is 89 05'N; it is nearly directly above the North Pole. In the Northern Hemisphere, you can find your approximate position by taking a sight on Polaris. The reading will vary depending upon the time of night, but will never be more than 55 miles off. This is a useful check each evening; the altitude of Polaris will be your approximate latitude without adding or subtracting anything. If you were to find the altitude of Polaris in the evening and again at dawn, your true latitude would be between the two measurements, providing you did not change latitude between the two sights. It is, of course, possible to calculate one s exact latitude from Polaris with the aid of the Nautical Almanac, but such a discussion is beyond the scope of this booklet. Page 12

17 Finding Latitude The altitude of the sun at local noon may also be used to calculate latitude. To calculate latitude: 1. Correct the measured altitude for index error, height of eye, refraction, and semi-diameter. Refraction correction is negligible for altitudes above 25. Semi-diameter correction averages + 0" 16' (semi-diameter correction adjusts the sextant reading from an observation of the lower limb of the sun to one of the center of the sun; 16' equals one-half of the sun s diameter). 2. After the corrections are made, determine the declination of the sun from the Nautical Almanac or from the approximate declination values at the end of this booklet. 3. Calculate latitude by combining the altitude of the sun at local noon with the declination of the sun from the navigation tables. Assuming you are north of the sun, the following formula is used in northern latitudes: Latitude = 90 Corrected Altitude ± Declination of the Sun When the sun is north of the equator, ADD the declination; when it is south of the equator, SUBTRACT the declination. Page 15

18 Diagrams of longitude and latitude calculations The presentations here are commonly used by navigators to help insure the accuracy of their calculations. Longitude Diagram View of Earth looking at South Pole Latitude Diagram View of Earth looking at Equator Figure 16 Figure 17 Position Plot on Chart Page 16

20 4. Line the two suns up by continuing to move the index arm. For a lower limb observation, bring the bottom of the mirror image into coincidence with the top of the image on the liquid. 5. After the observation has been made, apply the index correction. 6. Halve the remaining angle and apply all other corrections (except for Dip or height of eye correction, which is not applicable) to find the altitude of the sun. Figure 18 Note: Since the sextant reading made with an artificial horizon must be halved, the maximum altitude that you can observe with the artificial horizon is equal to one-half the maximum arc graduation on your sextant. There may be several hours around noon during which the sun is too high to take a sextant reading with the artificial horizon, so plan sights for the morning or evening hours. OTHER USES for the SEXTANT Using the Sextant as a Pelorus A pelorus is used to take bearings relative to your ship s heading. 1. Pick out three features on the land. 2. With the sextant held horizontally, measure the angle between the center feature and one of the other features, and note the angle on a piece of paper. 3. As quickly as you can, measure the angle between the center feature and the third feature. 4. Lay out the three angles on a piece of tracing paper so that the angles have a common center point. Page 18

21 5. Move the tracing paper around on the chart until the lines are positioned so as to run through the three features. The point of intersection of the three angles is your position (Fig. 19). Figure 19 Note: Since the sextant does not have a compass, you do not need to worry about variation or deviation. You must use at least three lines of position, however. Using the Sextant as a Heliograph You can use the sextant mirror to flash the sun s rays several miles to attract attention, or to signal another person who is too far away for your voice to reach. If you know Morse code, you could even send a message. 1. Hold the sextant so that the index mirror (the larger of the two mirrors) is just below the eye. 2. With your other arm extended and the thumb held upright, look at the person you wish to signal. 3. Hold your thumb to a position just below the person, so that your eye (with the mirror under it), your thumb, and the person are in a straight line (Fig. 20). Figure Using the mirror, flash the sun on your thumb. The sun flashes simultaneously on the distant person. Page 19

22 REFERENCE: Approximate Declination & Equation of Time The following tables give the approximate declination and equation of time of the sun. Latitude calculated with these values will be accurate to about ±15'. The tables are for study purposes only.

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