《航海学》课程参考文献（地文资料）CHAPTER 16 INSTRUMENTS FOR CELESTIAL NAVIGATION

CHAPTER 16INSTRUMENTSFORCELESTIALNAVIGATIONTHE MARINE SEXTANTThe index mirror of the sextant is at B,the horizon glass at C1600.DescriptionAndUseand theeye of theobserver atD.Construction lines EFandCF areperpendicular to the index mirror and horizon glass,Themarine sextantmeasures the anglebetween tworespectively.Lines BG and CG are parallel to these mirrorspoints by bringing the direct rayfrom one point and a dou-Therefore, angles BFC and BGC are equal because theirble-reflected ray from theother into coincidence.Itssides are mutually perpendicular.Angle BGC is the inclina-principal use is to measure the altitudes of celestial bodiestion of thetwo reflecting surfaces.The ray of light AB isabovethevisible seahorizon.Itmayalsobeusedtomeasurereflected at mirror B,proceeds to mirror C,where it is againvertical angles tofind therangefrom an object of knownreflectedandthencontinuesontotheeveoftheobserveratheight. Sometimes it is turned on its side and used for mea-D.Sincethe angle of reflection is equal to the angle ofsuring the angulardistance between twoterrestrial objects.incidence,A marine sextant can measure angles up to approxi-mately120°.Originally,theterm“sextant"was applied toABE =EBC,andABC =2EBCthe navigator's double-reflecting, altitude-measuring in-BCF = FCD, and BCD = 2BCF.strument only if its arc was 60°in length, or 1/6ofa circle,permittingmeasurementofanglesfrom0°to120o.Inmod-Since an exterior angle of a triangle equals the sum ofern usagethe term is applied to all modern navigationalthe two non adjacent interior angles,altitude-measuring instruments regardless ofangular rangeABC=BDC+BCD,andEBC=BFC+BCForprinciplesofoperation.Transposing,BDC = ABC-BCD, and BFC = EBC-BCF1601.Optical Principles Of A SextantSubstituting 2EBC for ABC, and 2BCF for BCD in theWhenaplanesurfacereflects alightray,the angle ofrefirst of these equations,flection equals the angle of incidence.The angle between theBDC=2EBC-2BCF,0rBDC=2(EBC-BCF)first and final directions of a rayof light that has undergonedouble reflection in the same plane is twice the angle the twoSinceBFC=EBC-BCF,andBFC=BGC,thereforereflecting surfacesmake with each other (Figure 1601).InFigure1601,AB isarayoflightfromacelestialbodyBDC=2BFC=2BGC.That is.BDC,theanglebetween thefirstand last direc-Ations of the ray of light,is equal to 2BGC,twice the angleof inclination of the reflecting surfaces.AngleBDC is thealtitude ofthecelestialbodyIf the two mirrors are parallel, the incident ray from anyobserved bodymustbeparalleltothe observer's lineofsightthrough the horizon glass. In that case, the body's altitudewould bezero.The anglethatthesetworeflectingsurfacesmakewitheachotherisone-halftheobserved angle.Thegraduations on the arc reflect this half anglerelationship be-tween the angle observed and themirrorsangle1602.MicrometerDrum SextantGFigure1602 shows a modern marinesextant,called amicrometer drum sextant. In most marine sextants, brassFigure1601.Opticalprincipleofthemarinesextantor aluminum comprise theframe,A.Frames come in vari-273

273 CHAPTER 16 INSTRUMENTS FOR CELESTIAL NAVIGATION THE MARINE SEXTANT 1600. Description And Use The marine sextant measures the angle between two points by bringing the direct ray from one point and a dou￾ble-reflected ray from the other into coincidence. Its principal use is to measure the altitudes of celestial bodies above the visible sea horizon. It may also be used to measure vertical angles to find the range from an object of known height. Sometimes it is turned on its side and used for mea￾suring the angular distance between two terrestrial objects. A marine sextant can measure angles up to approxi￾mately 120°. Originally, the term “sextant” was applied to the navigator’s double-reflecting, altitude-measuring in￾strument only if its arc was 60° in length, or 1/6 of a circle, permitting measurement of angles from 0° to 120°. In mod￾ern usage the term is applied to all modern navigational altitude-measuring instruments regardless of angular range or principles of operation. 1601. Optical Principles Of A Sextant When a plane surface reflects a light ray, the angle of re￾flection equals the angle of incidence. The angle between the first and final directions of a ray of light that has undergone double reflection in the same plane is twice the angle the two reflecting surfaces make with each other (Figure 1601). In Figure 1601, AB is a ray of light from a celestial body. The index mirror of the sextant is at B, the horizon glass at C, and the eye of the observer at D. Construction lines EF and CF are perpendicular to the index mirror and horizon glass, respectively. Lines BG and CG are parallel to these mirrors. Therefore, angles BFC and BGC are equal because their sides are mutually perpendicular. Angle BGC is the inclina￾tion of the two reflecting surfaces. The ray of light AB is reflected at mirror B, proceeds to mirror C, where it is again reflected, and then continues on to the eye of the observer at D. Since the angle of reflection is equal to the angle of incidence, Since an exterior angle of a triangle equals the sum of the two non adjacent interior angles, ABC = BDC+BCD, and EBC = BFC+BCF. Transposing, BDC = ABC-BCD, and BFC = EBC-BCF. Substituting 2EBC for ABC, and 2BCF for BCD in the first of these equations, BDC = 2EBC-2BCF, or BDC=2 (EBC-BCF). Since BFC=EBC - BCF, and BFC = BGC, therefore BDC = 2BFC = 2BGC. That is, BDC, the angle between the first and last direc￾tions of the ray of light, is equal to 2BGC, twice the angle of inclination of the reflecting surfaces. Angle BDC is the altitude of the celestial body. If the two mirrors are parallel, the incident ray from any observed body must be parallel to the observer’s line of sight through the horizon glass. In that case, the body’s altitude would be zero. The angle that these two reflecting surfaces make with each other is one-half the observed angle. The graduations on the arc reflect this half angle relationship be￾tween the angle observed and the mirrors’ angle. 1602. Micrometer Drum Sextant Figure 1602 shows a modern marine sextant, called a micrometer drum sextant. In most marine sextants, brass Figure 1601. Optical principle of the marine sextant. or aluminum comprise the frame, A. Frames come in vari￾ABE = EBC, and ABC = 2EBC. BCF = FCD, and BCD = 2BCF

274INSTRUMENTSFORCELESTIALNAVIGATIONous designs,mostaresimilartothis.TeethmarktheouterItismountedontheframe,perpendiculartotheplaneoftheedge of the limb,B;each tooth marks one degree of alti-sextant.The index mirror and horizon glass are mounted sotude.Thealtitudegraduations.C.alongthelimb.markthethat their surfaces are parallel when the micrometer drum isarc.Some sextants have an arcmarked in a strip of brassset at oo, if the instrument is in perfect adjustment.Shadesilver, or platinum inlaid in the limbglasses, K, of varying darkness are mounted on the sexTheindexarm,D.isamovablebarofthesamematerialtant's frame in front of the index mirror and horizon glassas theframe.It pivots about the center of curvature of theThey can be moved into theline of sight as needed to reducelimb.The tangent screw,E, is mounted perpendicularly onthe intensity of light reaching the eye.theendoftheindexarm,whereitengagestheteethoftheThe telescope,L, screws into an adjustable collar inlimb.Because theobserver can move the index arm throughline withthe horizon glass and parallel to theplane of thethe length of the arc by rotating the tangent screw, this isinstrument.Most modern sextants areprovided with onlysometimes called an“endlesstangent screw."Contrastthisonetelescope.When onlyonetelescopeisprovided,itisofwith the limited-range device on older instruments. The re-the“erect imagetype,"either as shown or witha wider“ob-lease, F,is a spring-actuated clamp thatkeeps the tangentiectglass"(farendoftelescope),whichgenerallyisshorterscrew engaged with the limb'steeth.The observer can disen-in lengthand gives a greater field of view.Thesecondtele-gage thetangent screw and movethe index arm alongthescope, if provided, may be the“inverting type."Thelimbfor roughadjustment.The end of thetangent screwinvertingtelescope,having onelens less than the erecttypemounts a micrometer drum, G, graduated in minutes of al-absorbsless light, butat theexpense of producing an invert-titude.Onecompleteturnofthedrummovestheindexarmed image.Asmall coloredglasscapissometimesprovided.onedegreealongthearc.Nexttothemicrometerdrumandtobe placed over the“eyepiece"(near end oftelescope)tofixedontheindexarmisavernier,H,thatreadsinfractionsreduceglare.With this inplace, shade glasses are generallyof a minute.The vernier shown isgraduated into tenpartsnot needed.A"peep sight,or clear tube which servesto di-permitting readings to /1o of a minute of arc (0.1).Somerect the lineof sight of the observerwhen no telescope issextants(generallyof Europeanmanufacture)haveverniersused, maybefittedgraduated into only five parts, permitting readings to 0.2'Sextants are designed to be held in the right hand.The index mirror, I, is a piece of silvered plate glassSome have a small light on the index arm to assist in read-mountedontheindexarm,perpendiculartotheplaneoftheing altitudes.The batteries for this light are fitted inside ainstrument,withthe center of the reflecting surfacedirectlyrecess in the handle, M. Not clearly shown in Figure 1602over the pivot of the index arm.The horizon glass, J, is apiece of optical glass silvered on its half nearer the frame.are the tangent screw, E, and the three legs.Figure 1602.U.S. Navy Mark 2 micrometer drum sextant

274 INSTRUMENTS FOR CELESTIAL NAVIGATION ous designs; most are similar to this. Teeth mark the outer edge of the limb, B; each tooth marks one degree of alti￾tude. The altitude graduations, C, along the limb, mark the arc. Some sextants have an arc marked in a strip of brass, silver, or platinum inlaid in the limb. The index arm, D, is a movable bar of the same material as the frame. It pivots about the center of curvature of the limb. The tangent screw, E, is mounted perpendicularly on the end of the index arm, where it engages the teeth of the limb. Because the observer can move the index arm through the length of the arc by rotating the tangent screw, this is sometimes called an “endless tangent screw.” Contrast this with the limited-range device on older instruments. The re￾lease, F, is a spring-actuated clamp that keeps the tangent screw engaged with the limb’s teeth. The observer can disen￾gage the tangent screw and move the index arm along the limb for rough adjustment. The end of the tangent screw mounts a micrometer drum, G, graduated in minutes of al￾titude. One complete turn of the drum moves the index arm one degree along the arc. Next to the micrometer drum and fixed on the index arm is a vernier, H, that reads in fractions of a minute. The vernier shown is graduated into ten parts, permitting readings to 1/10 of a minute of arc (0.1'). Some sextants (generally of European manufacture) have verniers graduated into only five parts, permitting readings to 0.2'. The index mirror, I, is a piece of silvered plate glass mounted on the index arm, perpendicular to the plane of the instrument, with the center of the reflecting surface directly over the pivot of the index arm. The horizon glass, J, is a piece of optical glass silvered on its half nearer the frame. It is mounted on the frame, perpendicular to the plane of the sextant. The index mirror and horizon glass are mounted so that their surfaces are parallel when the micrometer drum is set at 0°, if the instrument is in perfect adjustment. Shade glasses, K, of varying darkness are mounted on the sex￾tant’s frame in front of the index mirror and horizon glass. They can be moved into the line of sight as needed to reduce the intensity of light reaching the eye. The telescope, L, screws into an adjustable collar in line with the horizon glass and parallel to the plane of the instrument. Most modern sextants are provided with only one telescope. When only one telescope is provided, it is of the “erect image type,” either as shown or with a wider “ob￾ject glass” (far end of telescope), which generally is shorter in length and gives a greater field of view. The second tele￾scope, if provided, may be the “inverting type.” The inverting telescope, having one lens less than the erect type, absorbs less light, but at the expense of producing an invert￾ed image. A small colored glass cap is sometimes provided, to be placed over the “eyepiece” (near end of telescope) to reduce glare. With this in place, shade glasses are generally not needed. A “peep sight,” or clear tube which serves to di￾rect the line of sight of the observer when no telescope is used, may be fitted. Sextants are designed to be held in the right hand. Some have a small light on the index arm to assist in read￾ing altitudes. The batteries for this light are fitted inside a recess in the handle, M. Not clearly shown in Figure 1602 are the tangent screw, E, and the three legs. Figure 1602. U.S. Navy Mark 2 micrometer drum sextant

275INSTRUMENTSFORCELESTIALNAVIGATIONThereare two basicdesigns commonlyused for mountingberesting exactly on the horizon,tangentto the lowerlimband adjusting mirrors on marine sextants.On the U.S.NavyThe noviceobserverneeds practicetodetermine the exactMark3andcertainothersextants.themirrorismountedsothatpoint of tangency.Beginners often err by bringing the imit can bemoved againstretaining or mounting springs withinagedown toofar.its frame. Only one perpendicular adjustment screw is re-Some navigatorsgettheirmost accurate observationsquired.On theU.S.Navy Mark2and other sextants the mirrorby letting the body contact the horizon by its own motion,isfixedwithin itsframe.Twoperpendicularadjustmentscrewsbringing it slightlybelowthehorizon ifrising,andaboveifarerequired.One screwmustbe loosened beforetheothersetting.At the instant the horizon is tangent to the disk, thescrew bearingon the same surface is tightened.navigator notes the time. The sextant altitude is the uncor-rected readingofthesextant.1603.Vernier Sextant1605.SextantMo0nSightsMost recent marine sextants areof the micrometerWhen observing the moon, follow the same proceduredrum type, but at least two older-type sextants are still inas for the sun.Because ofthe phases of the moon, the upperuse.Thesedifferfromthemicrometerdrumsextantprinci-pally in the manner in which the final reading is made.Theylimb of themoon is observed moreoften than that of theare called vernier sextants.sun.When the terminator (the line between light and darkareas)is nearlyvertical, be careful in selecting the limb toThe clamp screw vernier sextant is the older of theshoot. Sights of themoon are best made during either day-two.Inplaceofthemodernreleaseclamp,aclampscrew islight hours or that part oftwilight in which themoon isleastfitted on the underside of the index arm.To move the indexluminous. At night, false horizons may appear below thearm,theclamp screwis loosened,releasingthearm.Whenmoon because the moon illuminates the waterbelow it.the armis placed at theapproximate altitude ofthebody be-ing observed, the clamp screw istightened.Fixed to theclamp screwand engaged withthe indexarm is alongtan-1606.SextantStarAndPlanetSightsgent screw.When this screw is turned,the index arm movesslowly,permitting accurate setting.Movement of the indexUse one of these three methods when making the initialarmbythetangentscrew is limitedtothelengthofthescrewaltitude approximation on a star or planet:(severaldegreesofarc).Beforeanaltitudeismeasured.thisscrew should be settotheapproximatemid-point of itsMethod 1. Set the index arm and micrometer drum onrange.Thefinal reading ismadeonavernierset intheindexO° and direct the line of sight at the body to be observedarmbelowthearc.A small microscopeor magnifyingglassThen,whilekeeping thereflected image ofthe bodyinthefitted to the index arm is used in making the final reading.mirrored halfof the horizon glass, swing the index arm outThe endless tangent screwvernier sextant is identical tcandrotatetheframeofthesextantdown.Keepthereflectedthe micrometer drum sextant, except that it has no drum, andimageof thebodyin themirror untilthehorizon appears inthefine reading is madeby a vernier along the arc, as with th-theclearpartofthehorizonglass.Then,maketheobservaeclampscrewvernier sextant.Therelease is the same as on thetion.When there is little contrast between brightness of themicrometerdrumsextantandteetharecutintotheundersidesky and the body,this procedure is difficult. If the body is"lost"while it is being broughtdown, itmay not be recov-ofthe limbwhichengagewiththe endlesstangentscrewered without starting over again.1604.Sextant Sun SightsMethod 2.Direct the line of sight at thebody whileholding the sextant upsidedown.Slowlymovethe index-Hold the sextant vertically and direct the sight line at thearm out until the horizon appears in the horizon glass. Theninvert the sextant and take the sight in the usual manner.horizondirectlybelowthe sun.After moving suitable shadeglasses into the line of sight,move the index arm outwardMethod 3.Determine in advance the approximate alti-along the arc until the reflected image appears in the horizontude and azimuth of the body by a starfinder suchas Noglassnearthedirectviewofthehorizon.Rockthesextant2102D.Set the sextant at the indicated altitude and face inslightly to the right and left to ensure it is perpendicular. As thethe direction of the azimuth.The image of the body shouldobserver rocks the sextant,the image ofthe sun appears toappear in the horizon glass with a little searching.move in an arc,and theobservermayhaveto turn slightlytoWhen measuring the altitudeof a star or planet, bringpreventthe imagefrommovingoffthehorizonglassits center down to the horizon. Stars and planets have noThe sextant is vertical when the sun appears at the bot-discernible upper or lower limb;observethecenter of thetom of the arc. This is the correct position for making thepointoflight.Because stars and planets havenodiscernibleobservation.The sun's reflected image appears at the centerlimbandbecausetheirvisibilitymaybe limited,themethodof thehorizonglass,onehalf appears on thesilvered part.of letting a star orplanet intersect thehorizon by its ownand the other half appears on the clear part. Move the indexmotion is notrecommended.As withthe sunand moon,armwiththedrumorvernierslowlyuntilthesunappearstohowever,rock the sextant"to establish perpendicularity

INSTRUMENTS FOR CELESTIAL NAVIGATION 275 There are two basic designs commonly used for mounting and adjusting mirrors on marine sextants. On the U.S. Navy Mark 3 and certain other sextants, the mirror is mounted so that it can be moved against retaining or mounting springs within its frame. Only one perpendicular adjustment screw is re￾quired. On the U.S. Navy Mark 2 and other sextants the mirror is fixed within its frame. Two perpendicular adjustment screws are required. One screw must be loosened before the other screw bearing on the same surface is tightened. 1603. Vernier Sextant Most recent marine sextants are of the micrometer drum type, but at least two older-type sextants are still in use. These differ from the micrometer drum sextant princi￾pally in the manner in which the final reading is made. They are called vernier sextants. The clamp screw vernier sextant is the older of the two. In place of the modern release clamp, a clamp screw is fitted on the underside of the index arm. To move the index arm, the clamp screw is loosened, releasing the arm. When the arm is placed at the approximate altitude of the body be￾ing observed, the clamp screw is tightened. Fixed to the clamp screw and engaged with the index arm is a long tan￾gent screw. When this screw is turned, the index arm moves slowly, permitting accurate setting. Movement of the index arm by the tangent screw is limited to the length of the screw (several degrees of arc). Before an altitude is measured, this screw should be set to the approximate mid-point of its range. The final reading is made on a vernier set in the index arm below the arc. A small microscope or magnifying glass fitted to the index arm is used in making the final reading. The endless tangent screw vernier sextant is identical to the micrometer drum sextant, except that it has no drum, and the fine reading is made by a vernier along the arc, as with th￾eclamp screw vernier sextant. The release is the same as on the micrometer drum sextant, and teeth are cut into the underside of the limb which engage with the endless tangent screw. 1604. Sextant Sun Sights Hold the sextant vertically and direct the sight line at the horizon directly below the sun. After moving suitable shade glasses into the line of sight, move the index arm outward along the arc until the reflected image appears in the horizon glass near the direct view of the horizon. Rock the sextant slightly to the right and left to ensure it is perpendicular. As the observer rocks the sextant, the image of the sun appears to move in an arc, and the observer may have to turn slightly to prevent the image from moving off the horizon glass. The sextant is vertical when the sun appears at the bot￾tom of the arc. This is the correct position for making the observation. The sun’s reflected image appears at the center of the horizon glass; one half appears on the silvered part, and the other half appears on the clear part. Move the index arm with the drum or vernier slowly until the sun appears to be resting exactly on the horizon, tangent to the lower limb. The novice observer needs practice to determine the exact point of tangency. Beginners often err by bringing the im￾age down too far. Some navigators get their most accurate observations by letting the body contact the horizon by its own motion, bringing it slightly below the horizon if rising, and above if setting. At the instant the horizon is tangent to the disk, the navigator notes the time. The sextant altitude is the uncor￾rected reading of the sextant. 1605. Sextant Moon Sights When observing the moon, follow the same procedure as for the sun. Because of the phases of the moon, the upper limb of the moon is observed more often than that of the sun. When the terminator (the line between light and dark areas) is nearly vertical, be careful in selecting the limb to shoot. Sights of the moon are best made during either day￾light hours or that part of twilight in which the moon is least luminous. At night, false horizons may appear below the moon because the moon illuminates the water below it. 1606. Sextant Star And Planet Sights Use one of these three methods when making the initial altitude approximation on a star or planet: Method 1. Set the index arm and micrometer drum on 0° and direct the line of sight at the body to be observed. Then, while keeping the reflected image of the body in the mirrored half of the horizon glass, swing the index arm out and rotate the frame of the sextant down. Keep the reflected image of the body in the mirror until the horizon appears in the clear part of the horizon glass. Then, make the observa￾tion. When there is little contrast between brightness of the sky and the body, this procedure is difficult. If the body is “lost” while it is being brought down, it may not be recov￾ered without starting over again. Method 2. Direct the line of sight at the body while holding the sextant upside down. Slowly move the index￾arm out until the horizon appears in the horizon glass. Then invert the sextant and take the sight in the usual manner. Method 3. Determine in advance the approximate alti￾tude and azimuth of the body by a star finder such as No. 2102D. Set the sextant at the indicated altitude and face in the direction of the azimuth. The image of the body should appear in the horizon glass with a little searching. When measuring the altitude of a star or planet, bring its center down to the horizon. Stars and planets have no discernible upper or lower limb; observe the center of the point of light. Because stars and planets have no discernible limb and because their visibility may be limited, the method of letting a star or planet intersect the horizon by its own motion is not recommended. As with the sun and moon, however, “rock the sextant” to establish perpendicularity

276INSTRUMENTSFORCELESTIALNAVIGATION1607.TakingASightthenavigator,and a star or planet is more easilyobservedwhen the sky is relatively bright. Near the darker limit ofPredict expected altitudes and azimuths for up to eighttwilight, thetelescope can be moved out, giving a broaderbodies when preparing totake celestial sights.Choose theviewof the clearhalfof theglass,andmakingthelessdisstars and planets that give the best bearing spread. Try to se-tinct horizon more easily discernible. If both eyes are keptlect bodies with a predicted altitude between 30°and 70°open until the last moments of an observation, eye strainTake sights of the brightest stars first in the evening; takewill belessened.Practicewill permit observationsto besights ofthe brightest stars last in the morning.made quickly,reducing inaccuracy due to eye fatigue.When measuring an altitude,have anassistant note andOccasionally,fog.haze,orothershipsinaformationmayobscurethehorizon directlybelowa bodywhichtherecord thetimeifpossible,witha“stand-by"warningwhennavigator wishes to observe.If the arc of the sextant is suf-themeasurementisalmostready,andamark"atthemo-ficiently long,a back sight might be obtained, using thement a sight is made. If a flashlight is needed to see theoppositepointof the horizonas thereference.Forthis thecomparing watch,the assistant should be careful not to in-observerfaces awayfromthebody and observesthesup-terfere with the navigators night vision.plement of the altitude.If the sun ormoon is observed inIf an assistant is notavailable totime the observations,thethis manner, what appears in the horizon glass to be theobserverholdsthewatchinthepalmofhislefthandleavinghislowerlimb isinfacttheupper limb,and viceversa.Inthefingersfreetomanipulatethetangentscrewofthesextant.Aftercase of the sun, it is usually preferableto observe whatapmaking theobservation,henotes the timeas quicklyas possibleThedelaybetween completingthealtitudeobservation and not-pears to be the upper limb.Thearc that appears whenrockingthesextantforabacksightisinverted:thatis,theing the timeshouldnotbemore than one or two secondshighestpoint indicates theposition of perpendicularityIf morethanonetelescopeisfurnishedwiththe sex1608.ReadingTheSextanttant,theerectingtelescopeisusedtoobservethe sun.Awiderfield of view ispresent if thetelescope is not used.Reading a micrometer drum sextant is done in threeThe collar into whichthe sextant telescopefitsmay bead-steps.The degrees areread bynoting the position ofthe ar-justed in or out, in relation to the frame. When moved in.row on the index arm in relation to the arc.The minutes aremore ofthemirrored half of thehorizonglass is visibletoreadbynotingthepositionofthezero on thevernierwith80whmmO60302055HO505Figure1608a.Micrometer drumsextant setat29o42.5

276 INSTRUMENTS FOR CELESTIAL NAVIGATION 1607. Taking A Sight Predict expected altitudes and azimuths for up to eight bodies when preparing to take celestial sights. Choose the stars and planets that give the best bearing spread. Try to se￾lect bodies with a predicted altitude between 30° and 70°. Take sights of the brightest stars first in the evening; take sights of the brightest stars last in the morning. Occasionally, fog, haze, or other ships in a formation may obscure the horizon directly below a body which the navigator wishes to observe. If the arc of the sextant is suf￾ficiently long, a back sight might be obtained, using the opposite point of the horizon as the reference. For this the observer faces away from the body and observes the sup￾plement of the altitude. If the sun or moon is observed in this manner, what appears in the horizon glass to be the lower limb is in fact the upper limb, and vice versa. In the case of the sun, it is usually preferable to observe what ap￾pears to be the upper limb. The arc that appears when rocking the sextant for a back sight is inverted; that is, the highest point indicates the position of perpendicularity. If more than one telescope is furnished with the sex￾tant, the erecting telescope is used to observe the sun. A wider field of view is present if the telescope is not used. The collar into which the sextant telescope fits may be ad￾justed in or out, in relation to the frame. When moved in, more of the mirrored half of the horizon glass is visible to the navigator, and a star or planet is more easily observed when the sky is relatively bright. Near the darker limit of twilight, the telescope can be moved out, giving a broader view of the clear half of the glass, and making the less dis￾tinct horizon more easily discernible. If both eyes are kept open until the last moments of an observation, eye strain will be lessened. Practice will permit observations to be made quickly, reducing inaccuracy due to eye fatigue. When measuring an altitude, have an assistant note and record the time if possible, with a “stand-by” warning when the measurement is almost ready, and a “mark” at the mo￾ment a sight is made. If a flashlight is needed to see the comparing watch, the assistant should be careful not to in￾terfere with the navigator’s night vision. If an assistant is not available to time the observations, the observer holds the watch in the palm of his left hand, leaving his fingers free to manipulate the tangent screw of the sextant. After making the observation, he notes the time as quickly as possible. The delay between completing the altitude observation and not￾ing the time should not be more than one or two seconds. 1608. Reading The Sextant Reading a micrometer drum sextant is done in three steps. The degrees are read by noting the position of the ar￾row on the index arm in relation to the arc. The minutes are read by noting the position of the zero on the vernier with Figure 1608a. Micrometer drum sextant set at 29° 42.5

277INSTRUMENTSFORCELESTIALNAVIGATION5.Figure 1608b.Vernier sextant set at 29°4230"relationto thegraduations onthemicrometer drum.Thethe index arm and has the small reference mark as its zerofraction ofa minuteis read by noting which mark onthegraduation.On thisvernier,40 graduations coincide with 39vernier most nearly coincides with one of the graduationsgraduations on thearc.Eachgraduation onthe vemnier isequiv-onthemicrometerdrum.Thisissimilartoreadingthetimealentto1/40ofonegraduationof20'on thearc,or0.5,or30"with the hour,minute,and second hands ofa watch.Inboth,In theillustration, theverniergraduation representing 2 1/2the relationship of one part of thereading tothe others(2'3o")mostnearlycoincideswithoneofthegraduationsonthearc.Thereore, thereading is29°42'30",or 29°42.5,asbeshould bekept in mind.Thus, if thehour hand of a watchwere about on“4,"one wouldknowthat the time was aboutfore.When a vernier ofthistype is used,anydoubt asto whichfour o'clock.But if theminutehandwereon"58"onemarkontheverniercoincideswithagraduationonthearccanwouldknowthatthetimewas0358(or1558),not0458(orusuallyberesolvedbynotingthepositionof theverniermark1658).Similarly, ifthe arc indicated a reading ofabout 400oneachsideoftheonethatseemstobeincoincidenceand58'onthemicrometerdrumwereoppositezeroontheNegative readings,suchasa negative index correctionvernier,onewouldknowthatthereadingwas 39o58',notare made in the same manneras positive readings,thevar-40°58.Similarly,anydoubt astothecorrectminutecanbeious figures are added algebraically.Thus, ifthe three partsremoved by noting thefraction of a minutefrom theposiof amicrometer drumreading are(-)1°,56'and0.3,thetion of the vernier.In Figure1608a the reading is 29042.5total reading is(-)1°+ 56'+0.3'=(-)3.7.Thearrowontheindexmarkisbetween29and30the1609.DevelopingObservationalSkillzeroonthevernier isbetween42'and43',and the0.5grad-uation on the vernier coincides with one of thegraduationsonthemicrometerdrumAwell-constructedmarinesextantiscapableofmeasurThe principle of reading a vernier sextant is the same, buting angles with an instrument error not exceeding O.I'.Linesthe reading is made in two steps.Figure 1608b shows a typicalof positionfromaltitudesofthisaccuracywouldnotbeiner-altitude setting.Each degree on the arc of this sextant is grad-ror by more than about 200 yards.However,there arevariousuated into three parts, permitting an initial reading by thesources of error, other than instrumental, in altitudes mea-referencemarkontheindexarmtothenearest20'ofarc.Inthissured by sextant.One of the principal sources is the observer.illustration thereferencemarkliesbetween29°40and30°00The first fix a student celestial navigator plots is likelyindicating a reading between these values.Thereading for theto bedisappointing.Mostnavigators require agreatamountfraction of20'ismade using the vernier,which is engravedonof practicetodeveloptheskill necessaryforgoodobserva-

INSTRUMENTS FOR CELESTIAL NAVIGATION 277 relation to the graduations on the micrometer drum. The fraction of a minute is read by noting which mark on the vernier most nearly coincides with one of the graduations on the micrometer drum. This is similar to reading the time with the hour, minute, and second hands of a watch. In both, the relationship of one part of the reading to the others should be kept in mind. Thus, if the hour hand of a watch were about on “4,” one would know that the time was about four o’clock. But if the minute hand were on “58,” one would know that the time was 0358 (or 1558), not 0458 (or 1658). Similarly, if the arc indicated a reading of about 40°, and 58' on the micrometer drum were opposite zero on the vernier, one would know that the reading was 39° 58', not 40°58'. Similarly, any doubt as to the correct minute can be removed by noting the fraction of a minute from the posi￾tion of the vernier. In Figure 1608a the reading is 29° 42.5'. The arrow on the index mark is between 29° and 30°, the zero on the vernier is between 42' and 43', and the 0.5' grad￾uation on the vernier coincides with one of the graduations on the micrometer drum. The principle of reading a vernier sextant is the same, but the reading is made in two steps. Figure 1608b shows a typical altitude setting. Each degree on the arc of this sextant is grad￾uated into three parts, permitting an initial reading by the reference mark on the index arm to the nearest 20' of arc. In this illustration the reference mark lies between 29°40' and 30°00', indicating a reading between these values. The reading for the fraction of 20' is made using the vernier, which is engraved on the index arm and has the small reference mark as its zero graduation. On this vernier, 40 graduations coincide with 39 graduations on the arc. Each graduation on the vernier is equiv￾alent to 1/40 of one graduation of 20' on the arc, or 0.5', or 30". In the illustration, the vernier graduation representing 2 1/2' (2'30") most nearly coincides with one of the graduations on the arc. Therefore, the reading is 29°42'30", or 29°42.5', as be￾fore. When a vernier of this type is used, any doubt as to which mark on the vernier coincides with a graduation on the arc can usually be resolved by noting the position of the vernier mark on each side of the one that seems to be in coincidence. Negative readings, such as a negative index correction, are made in the same manner as positive readings; the var￾ious figures are added algebraically. Thus, if the three parts of a micrometer drum reading are ( - )1°, 56' and 0.3', the total reading is ( - )1° + 56' + 0.3' = ( - )3.7'. 1609. Developing Observational Skill A well-constructed marine sextant is capable of measur￾ing angles with an instrument error not exceeding 0.1'. Lines of position from altitudes of this accuracy would not be in er￾ror by more than about 200 yards. However, there are various sources of error, other than instrumental, in altitudes mea￾sured by sextant. One of the principal sources is the observer. The first fix a student celestial navigator plots is likely to be disappointing. Most navigators require a great amount of practice to develop the skill necessary for good observa￾Figure 1608b. Vernier sextant set at 29°42'30

278INSTRUMENTSFORCELESTIALNAVIGATIONtions. But practice alone is not sufficient. Good techniquemiddle line. Reject any observation considered unreliableshould be developed early and refined throughout the navi-whendeterminingtheaverage.gator's career,Manygood pointers can beobtained fromexperienced navigators, but each developshis own tech-1610.CareOfTheSextantnique,andapracticethatproves successfulforoneobservermay not helpanother.Also, an experienced navigator is notA sextant is a rugged instrument. However, carelessnecessarily a good observer.Navigators have a natural ten-handling or neglect can cause it irreparable harm.If youdencyto judgetheaccuracyoftheir observations by the sizedrop it, take it to an instrument repair shop for testing andofthefigureformedwhenthelinesofpositionareplottedinspection.When notusing the sextant, stow it in a sturdyAlthoughthis is some indication,it is an imperfect one,be-andsufficientlypaddedcase.Keepthesextantoutofexces-causeitdoesnotindicateerrorsofindividualobservationssive heat and dampness.Do not expose it to excessiveand maynotreflectconstanterrors.Also,it is a compoundvibrationDonotleaveitunattendedwhenitisoutofitsofa numberoferrors,someofwhich arenotsubjecttothecase.Do not hold it by its limb, index arm, or telescopenavigator's control.Liftit by its frame or handle.Do not lift it by its arc or indexLines of position from celestial observations can bebar.comparedwithgoodpositionsobtainedbyelectronicsorpi-Next to careless handling,moisture is the sextant'sloting.Commonsourcesoferrorare:greatestenemy.Wipe the mirrors and the arc after eachuse.If the mirrors get dirty,clean them with lens paper and a1The sextant maynotbe rocked properlysmall amountof alcohol.Cleanthearcwithammonia;nev-2Tangency may not be judged accurately.er use a polishing compound.When cleaning, do not apply3.Afalsehorizonmayhavebeenusedexcessivepressuretoanypartoftheinstrument.4. Subnormal refraction (dip) might be present.Silicagel kept in the sextant case will helpkeep the in-strument free from moisture and preserve the mirrors.5.Theheightofeyemaybewrong.Occasionallyheatthe silicagel toremove the absorbed6Time might be in error.moisture.7The index correctionmayhave been determinedRinse the sextant withfresh water if sea water gets onincorrectlyit.Wipe the sextantgentlywith a soft cotton cloth and dry8.The sextant might be out of adjustment.theopticswith lens paper.9.AnerrormayhavebeenmadeinthecomputationGlassoptics donottransmitall the lightreceivedbe-causeglass surfaces reflecta small portion of light incidentGenerally,itis possibletocorrectobservation techontheirface.Thisloss of lightreduces thebrightness oftheniqueerrors,but occasionally apersonal error will persist.objectviewed.Viewing an objectthrough several glass op-This error might vary as a function of thebody observedtics affects the perceived brightness and makes the imagedegreeoffatigueoftheobserver.andotherfactors.Forthisindistinct.Thereflectionalsocausesglarewhichobscuresreason,apersonal errorshouldbeapplied with caution.the object being viewed. To reduce this effect to a mini-To obtaingreater accuracy,takeanumberof closely-mum, the glass optics are treated with a thin, fragile, anti-spacedobservations.Plottheresulting altitudes versustimereflection coating.Therefore,apply only light pressureand fair a curve through the points. Unless the body is nearwhenpolishingthecoatedoptics.Blowloosedustoffthethe celestial meridian, this curve should be a straight linelensbeforewipingthem sogritdoesnotscratchthelens.UsethisgraphtodeterminethealtitudeofthebodyatanyFrequently oil and clean the tangent screw and the teethtime covered by thegraph.It is best to usea point near theonthesideofthe limb,Usethe oilprovided withthesextantmiddle of the line.Using a calculator to reduce the sightor an all-purpose light machine oil. Occasionally set the in-will also yield greater accuracy because of the rounding er-dexarmofanendlesstangentscrewatoneextremityoftherors inherent in the use of sight reduction tables.limb, oil it lightly, and then rotate the tangent screw overA simpler method involves making observations atthelengthofthearc.Thiswillcleantheteethandspreadoilequal intervals.This procedure is based upon the assump-overthem.Whenstowingasextantforalongperiod,cleantion that, unless the body is on the celestial meridian, theit thoroughly,polish andoil it, and protect its arc with a thinchange in altitude should be equal for equal intervals ofcoat of petroleum jellytime.Observations can be made at equal intervals of alti-If the mirrors need re-silvering,take the sextant to antude or time.Iftimeintervals areconstant, themid time andinstrument shop.the average altitude are used as the observation. If altitudeincrements are constant,the average time andmid altitude1611.Non Adjustable Sextant Errorsare used.Ifonlya small number ofobservationsisavailable,re-The non-adjustable sextant errors areprismatic error,duce and plot the resulting lines of position;then adjustgraduationerror,and centeringerror.them to a common time.The average position of the linePrismatic error occurs when the faces of the shademightbe used, but it is generally better practice to use the

278 INSTRUMENTS FOR CELESTIAL NAVIGATION tions. But practice alone is not sufficient. Good technique should be developed early and refined throughout the navi￾gator’s career. Many good pointers can be obtained from experienced navigators, but each develops his own tech￾nique, and a practice that proves successful for one observer may not help another. Also, an experienced navigator is not necessarily a good observer. Navigators have a natural ten￾dency to judge the accuracy of their observations by the size of the figure formed when the lines of position are plotted. Although this is some indication, it is an imperfect one, be￾cause it does not indicate errors of individual observations, and may not reflect constant errors. Also, it is a compound of a number of errors, some of which are not subject to the navigator’s control. Lines of position from celestial observations can be compared with good positions obtained by electronics or pi￾loting. Common sources of error are: 1. The sextant may not be rocked properly. 2. Tangency may not be judged accurately. 3. A false horizon may have been used. 4. Subnormal refraction (dip) might be present. 5. The height of eye may be wrong. 6. Time might be in error. 7. The index correction may have been determined incorrectly. 8. The sextant might be out of adjustment. 9. An error may have been made in the computation. Generally, it is possible to correct observation tech￾nique errors, but occasionally a personal error will persist. This error might vary as a function of the body observed, degree of fatigue of the observer, and other factors. For this reason, a personal error should be applied with caution. To obtain greater accuracy, take a number of closely￾spaced observations. Plot the resulting altitudes versus time and fair a curve through the points. Unless the body is near the celestial meridian, this curve should be a straight line. Use this graph to determine the altitude of the body at any time covered by the graph. It is best to use a point near the middle of the line. Using a calculator to reduce the sight will also yield greater accuracy because of the rounding er￾rors inherent in the use of sight reduction tables. A simpler method involves making observations at equal intervals. This procedure is based upon the assump￾tion that, unless the body is on the celestial meridian, the change in altitude should be equal for equal intervals of time. Observations can be made at equal intervals of alti￾tude or time. If time intervals are constant, the mid time and the average altitude are used as the observation. If altitude increments are constant, the average time and mid altitude are used. If only a small number of observations is available, re￾duce and plot the resulting lines of position; then adjust them to a common time. The average position of the line might be used, but it is generally better practice to use the middle line. Reject any observation considered unreliable when determining the average. 1610. Care Of The Sextant A sextant is a rugged instrument. However, careless handling or neglect can cause it irreparable harm. If you drop it, take it to an instrument repair shop for testing and inspection. When not using the sextant, stow it in a sturdy and sufficiently padded case. Keep the sextant out of exces￾sive heat and dampness. Do not expose it to excessive vibration. Do not leave it unattended when it is out of its case. Do not hold it by its limb, index arm, or telescope. Liftit by its frame or handle. Do not lift it by its arc or index bar. Next to careless handling, moisture is the sextant’s greatest enemy. Wipe the mirrors and the arc after each use. If the mirrors get dirty, clean them with lens paper and a small amount of alcohol. Clean the arc with ammonia; nev￾er use a polishing compound. When cleaning, do not apply excessive pressure to any part of the instrument. Silica gel kept in the sextant case will help keep the in￾strument free from moisture and preserve the mirrors. Occasionally heat the silica gel to remove the absorbed moisture. Rinse the sextant with fresh water if sea water gets on it. Wipe the sextant gently with a soft cotton cloth and dry the optics with lens paper. Glass optics do not transmit all the light received be￾cause glass surfaces reflect a small portion of light incident on their face. This loss of light reduces the brightness of the object viewed. Viewing an object through several glass op￾tics affects the perceived brightness and makes the image indistinct. The reflection also causes glare which obscures the object being viewed. To reduce this effect to a mini￾mum, the glass optics are treated with a thin, fragile, anti￾reflection coating. Therefore, apply only light pressure when polishing the coated optics. Blow loose dust off the lens before wiping them so grit does not scratch the lens. Frequently oil and clean the tangent screw and the teeth on the side of the limb. Use the oil provided with the sextant or an all-purpose light machine oil. Occasionally set the in￾dex arm of an endless tangent screw at one extremity of the limb, oil it lightly, and then rotate the tangent screw over the length of the arc. This will clean the teeth and spread oil over them. When stowing a sextant for a long period, clean it thoroughly, polish and oil it, and protect its arc with a thin coat of petroleum jelly. If the mirrors need re-silvering, take the sextant to an instrument shop. 1611. Non Adjustable Sextant Errors The non-adjustable sextant errors are prismatic error, graduation error, and centering error. Prismatic error occurs when the faces of the shade

279INSTRUMENTSFORCELESTIALNAVIGATIONglassesandmirrors arenotparallel.Errorduetolack ofpar-The manufacturernormallydetermines themagnitudeof all three non-adjustable errors and reports them to theallelism in the shadeglasses may be called shade error.The navigator candetermine shade error in the shade glass-user as instrument error. The navigator should apply thees nearthe index mirrorby comparing an anglemeasuredcorrection for this error to each sextant reading.whenashadeglassisinthelineofsightwiththesameanglemeasured when the glass is not in the line of sight. In this1612.AdjustableSextantErrormanner,determine and record the errorfor each shadeglass.Before using a combination of shade glasses, deter-The navigator should measure and remove the follow-minetheircombined error.If certain observations requireing adjustable sextant errors in the order listed:additional shading, use the colored telescope eyepiece cov-er.This does not introduce an error because direct and1. Perpendicularity Error: Adjust first for perpendicu-reflected rays are traveling together when they reach thelarityofthe indexmirrorto theframeofthe sextant.Totestforcover and are,therefore,affected equally byany lack ofperpendicularity,place the index arm at about 35°on the arcparallelismof itstwosides.and hold the sextant on its side with the index mirror up and toGraduation errors occur in the arc,micrometer drumward the eye. Observe the direct and reflected views of theand vernier of a sextant which is improperlycut or incor-sextant arc,as illustrated inFigure 1612a. If the two views arerectlycalibrated.Normally,thenavigatorcannotdeterminenot joined in a straight line, the index mirror is not perpendic-whether the arc of a sextant is improperly cut, but the prin-ular.Ifthe reflected image is abovethedirect view,themirrorciple of the vernier makes itpossibleto determine theis inclined forward. If the reflected image is below the directexistence of graduation errors in themicrometerdrumorview, the mirror is inclined backward. Make the adjustmentvernier.This is a useful guide in detecting a poorly made in-using two screws behind the index mirror.strument.Thefirstand last markings on any vernier shouldalignperfectlywith onelessgraduationontheadjacentmi-2.Side Error: An error resulting from the horizon glasscrometerdrumnot being perpendicular is called side error.To test for side er-Centering errorresults if the index arm does not pivotror, set the index arm at zero and direct the line of sight at a star.at the exact center of the arc's curvature.Calculate center-Thenrotatethetangentscrewbackandforthso thatthereflecteding error by measuring known angles after removing allimagepasses alternatelyaboveandbelowthedirectview.If,inadjustable errors. Use horizontal angles accurately mea-changing from one position to the other, the reflected imagesured with a theodolite as references for this procedure.passes directly over the unreflected image, no side error exists.Several readings byboth theodoliteand sextant should min-Ifit passes to one side, side error exists.Figure 1612b illustratesimize errors.If a theodolite isnot available,use calculatedobservations without side error (left)and with side error (right)angles between the lines of sightto stars as the reference,Whether the sextant reads zero when the true andreflected im-comparing these calculated values with the values deter-agesareincoincidenceisimmaterialforthistestAnalternativemined by the sextant.To minimize refraction errors, selectmethod istoobserve a vertical line,suchas oneedgeofthemaststarsataboutthesamealtitudeandavoidstarsneartheho-ofanothervessel(orthesextantcanbeheldonitssideandtherizon.The same shade glasses, ifany,usedfor determininghorizonused).Ifthedirectand reflectedportionsdonotformaindexerror shouldbe used for measuring centering error.continuous line,thehorizonglass is notperpendiculartotheMIRRORLEANINGFOWARDFigure1612a.Testing theperpendicularity of the index mirror.Here themirror is not perpendicular

INSTRUMENTS FOR CELESTIAL NAVIGATION 279 glasses and mirrors are not parallel. Error due to lack of par￾allelism in the shade glasses may be called shade error. The navigator can determine shade error in the shade glass￾es near the index mirror by comparing an angle measured when a shade glass is in the line of sight with the same angle measured when the glass is not in the line of sight. In this manner, determine and record the error for each shade glass. Before using a combination of shade glasses, deter￾mine their combined error. If certain observations require additional shading, use the colored telescope eyepiece cov￾er. This does not introduce an error because direct and reflected rays are traveling together when they reach the cover and are, therefore, affected equally by any lack of parallelism of its two sides. Graduation errors occur in the arc, micrometer drum, and vernier of a sextant which is improperly cut or incor￾rectly calibrated. Normally, the navigator cannot determine whether the arc of a sextant is improperly cut, but the prin￾ciple of the vernier makes it possible to determine the existence of graduation errors in the micrometer drum or vernier. This is a useful guide in detecting a poorly made in￾strument. The first and last markings on any vernier should align perfectly with one less graduation on the adjacent mi￾crometer drum. Centering error results if the index arm does not pivot at the exact center of the arc’s curvature. Calculate center￾ing error by measuring known angles after removing all adjustable errors. Use horizontal angles accurately mea￾sured with a theodolite as references for this procedure. Several readings by both theodolite and sextant should min￾imize errors. If a theodolite is not available, use calculated angles between the lines of sight to stars as the reference, comparing these calculated values with the values deter￾mined by the sextant. To minimize refraction errors, select stars at about the same altitude and avoid stars near the ho￾rizon. The same shade glasses, if any, used for determining index error should be used for measuring centering error. The manufacturer normally determines the magnitude of all three non-adjustable errors and reports them to the user as instrument error. The navigator should apply the correction for this error to each sextant reading. 1612. Adjustable Sextant Error The navigator should measure and remove the follow￾ing adjustable sextant errors in the order listed: 1. Perpendicularity Error: Adjust first for perpendicu￾larity of the index mirror to the frame of the sextant. To test for perpendicularity, place the index arm at about 35° on the arc and hold the sextant on its side with the index mirror up and to￾ward the eye. Observe the direct and reflected views of the sextant arc, as illustrated in Figure 1612a. If the two views are not joined in a straight line, the index mirror is not perpendic￾ular. If the reflected image is above the direct view, the mirror is inclined forward. If the reflected image is below the direct view, the mirror is inclined backward. Make the adjustment using two screws behind the index mirror. 2. Side Error: An error resulting from the horizon glass not being perpendicular is called side error. To test for side er￾ror, set the index arm at zero and direct the line of sight at a star. Then rotate the tangent screw back and forth so that the reflected image passes alternately above and below the direct view. If, in changing from one position to the other, the reflected image passes directly over the unreflected image, no side error exists. If it passes to one side, side error exists. Figure 1612b illustrates observations without side error (left) and with side error (right). Whether the sextant reads zero when the true and reflected im￾ages are in coincidence is immaterial for this test. An alternative method is to observe a vertical line, such as one edge of the mast of another vessel (or the sextant can be held on its side and the horizon used). If the direct and reflected portions do not form a continuous line, the horizon glass is not perpendicular to the Figure 1612a. Testing the perpendicularity of the index mirror. Here the mirror is not perpendicular

280INSTRUMENTSFORCELESTIALNAVIGATIONimages ofthe horizon to come into line.The sextant's readingwhenthehorizoncomesintolineistheindexerror.Iftheindexerror is positive,subtract itfromeach sextant reading.If the in-dex error is negative,add it to each sextant reading.1613.SelectingASextantCarefullymatch the selected sextantto its required usesForoccasional small craft orstudentuse,a plasticsextantmaybeadequate.Aplastic sextantmayalsobeappropriateforanemergencynavigationkit.Accurate offshore navigation re-quires a quality metal instrument. For ordinary use inmeasuring altitudesofcelestialbodies,anarcof90°orslightlyFigure1612b.Testingtheperpendicularityofthehorizonglass.more is sufficient.If using a sextant for back sights or deter-On theleft, sideerrordoesnotexist.Attheright,sideerror doesmining horizontal angles,purchase onewith a longer arc.Ifexist.necessary,havean experienced marinerexaminethe sextantandtest itfornonadjustableerrors beforepurchaseframe of the sextant. A third method involves holding the sex-1614.TheArtificial Horizontant vertically,as in observing the altitudeof a celestial bodyBring the reflected image of the horizon into coincidence withMeasurement of altitude requires an exact horizontal ref-thedirectviewuntil itappearsasacontinuous lineacrosstheho-erence.At sea, the visible sea horizon normally provides thisrizon glass. Then tilt the sextant right or left. If the horizon stireference.If the horizon is not clearly visible,however,a dif-appears continuous, thehorizon glass is perpendicular to theferent horizontal reference is required. Such a reference isframe,but if thereflected portion appears aboveorbelowthecommonlytermed an artificial horizon.If it is attached to, orpart seen directly, the glass is not perpendicular. Make the ap-partof,thesextant, altitudes can bemeasured at sea, on land,propriateadjustment usingtwo screws behindthe horizon glassor in theair,whenever celestial bodies are availablefor obser-vations. Any horizontal reflecting surface will work.A pan ofany liquid sheltered from the wind will serve.Foreign material3.Collimation Error:If the line of sight through theon the surface oftheliquid is likelyto distortthe image and in-telescope is notparallel totheplaneoftheinstrument,a col-troducean error in the readinglimation error will result. Altitudes measured will beTouseanexternal artificial horizon,standor sit in suchgreater than theiractual values.Tocheckforparallelism ofaposition that the celestial bodyto be observed is reflectedthetelescope,insertit in itscollarand observetwostars 90oormoreapart.Bring the reflected imageofone into coinci-intheliguidandisalsovisibleindirectview.Withthesexdence with the direct view of the other near either the righttant.bringthedouble-reflectedimageintocoincidencewithor leftedge of thefieldofview (theupperor lower edge ifthe image appearing in the liquid. For a lower limb obser-the sextant is horizontal).Then tilt the sextant so that thevation of the sun or themoon, bring the bottom of thedouble-reflected image intocoincidencewiththetop of thestars appearnear the opposite edge.If theyremain in coin-cidence, the telescope is parallel to the frame; if theyimage in the liquid.For an upper-limb observation, bringseparate, it is not.An alternative method involves placingthe opposite sides into coincidence.If one image covers thethe telescope in its collar and then laying the sextant on aother,theobservationis of thecenterofthebodyflat table.Sight along theframe of the sextant and have anAfter theobservation, apply the index correction and anyassistantplaceamarkontheoppositebulkhead,in linewithother instrumentalcorrection.Thentakehalftheremainingan-the frame.Place another mark above the first, at a distancegleandapplyall other corrections exceptdip (height of eye)equaltothedistancefromthecenterofthetelescopetothecorrection,sincethis isnotapplicable.Ifthecenter of the sunframe.Thissecondlineshouldbeinthecenterofthefieldormoon isobserved,omitthecorrectionforsemidiameter.of view of thetelescopeif thetelescopeisparallel totheframe.Adjust thecollar to correctfor non-parallelism.1615.ArtificialHorizon Sextants4.Index Error: Index error is the error remaining afterVarious types of artificial horizons have been used, in-the navigator has removed perpendicularity error, side errorcluding a bubble, gyroscope, and pendulum.Of these, theand collimation error.The index mirror and horizon glass notbubblehas beenmost widelyused.Thistype of instrument isbeing parallel when the index arm is set exactly at zero is thefittedasabackupsystemto inertial andotherpositioningsys-major cause of index error.To test for parallelism of the mir-tems ina few aircraft, fulfilling the requirement for a self-rors,setthe instrumentatzero and directthe line of sightatthecontained, non-emitting system. On land, a skilled observerhorizon.Adjustthesextant readingas necessaryto causebothusinga2-minuteaveragingbubbleorpendulum sextantcan

280 INSTRUMENTS FOR CELESTIAL NAVIGATION frame of the sextant. A third method involves holding the sex￾tant vertically, as in observing the altitude of a celestial body. Bring the reflected image of the horizon into coincidence with the direct view until it appears as a continuous line across the ho￾rizon glass. Then tilt the sextant right or left. If the horizon still appears continuous, the horizon glass is perpendicular to the frame, but if the reflected portion appears above or below the part seen directly, the glass is not perpendicular. Make the ap￾propriate adjustment using two screws behind the horizon glass. 3. Collimation Error: If the line of sight through the telescope is not parallel to the plane of the instrument, a col￾limation error will result. Altitudes measured will be greater than their actual values. To check for parallelism of the telescope, insert it in its collar and observe two stars 90° or more apart. Bring the reflected image of one into coinci￾dence with the direct view of the other near either the right or left edge of the field of view (the upper or lower edge if the sextant is horizontal). Then tilt the sextant so that the stars appear near the opposite edge. If they remain in coin￾cidence, the telescope is parallel to the frame; if they separate, it is not. An alternative method involves placing the telescope in its collar and then laying the sextant on a flat table. Sight along the frame of the sextant and have an assistant place a mark on the opposite bulkhead, in line with the frame. Place another mark above the first, at a distance equal to the distance from the center of the telescope to the frame. This second line should be in the center of the field of view of the telescope if the telescope is parallel to the frame. Adjust the collar to correct for non-parallelism. 4. Index Error: Index error is the error remaining after the navigator has removed perpendicularity error, side error, and collimation error. The index mirror and horizon glass not being parallel when the index arm is set exactly at zero is the major cause of index error. To test for parallelism of the mir￾rors, set the instrument at zero and direct the line of sight at the horizon. Adjust the sextant reading as necessary to cause both images of the horizon to come into line. The sextant’s reading when the horizon comes into line is the index error. If the index error is positive, subtract it from each sextant reading. If the in￾dex error is negative, add it to each sextant reading. 1613. Selecting A Sextant Carefully match the selected sextant to its required uses. For occasional small craft or student use, a plastic sextant may be adequate. A plastic sextant may also be appropriate for an emergency navigation kit. Accurate offshore navigation re￾quires a quality metal instrument. For ordinary use in measuring altitudes of celestial bodies, an arc of 90° or slightly more is sufficient. If using a sextant for back sights or deter￾mining horizontal angles, purchase one with a longer arc. If necessary, have an experienced mariner examine the sextant and test it for non adjustable errors before purchase. 1614. The Artificial Horizon Measurement of altitude requires an exact horizontal ref￾erence. At sea, the visible sea horizon normally provides this reference. If the horizon is not clearly visible, however, a dif￾ferent horizontal reference is required. Such a reference is commonly termed an artificial horizon. If it is attached to, or part of, the sextant, altitudes can be measured at sea, on land, or in the air, whenever celestial bodies are available for obser￾vations. Any horizontal reflecting surface will work. A pan of any liquid sheltered from the wind will serve. Foreign material on the surface of the liquid is likely to distort the image and in￾troduce an error in the reading. To use an external artificial horizon, stand or sit in such a position that the celestial body to be observed is reflected in the liquid, and is also visible in direct view. With the sex￾tant, bring the double-reflected image into coincidence with the image appearing in the liquid. For a lower limb obser￾vation of the sun or the moon, bring the bottom of the double-reflected image into coincidence with the top of the image in the liquid. For an upper-limb observation, bring the opposite sides into coincidence. If one image covers the other, the observation is of the center of the body. After the observation, apply the index correction and any other instrumental correction. Then take half the remaining an￾gle and apply all other corrections except dip (height of eye) correction, since this is not applicable. If the center of the sun or moon is observed, omit the correction for semidiameter. 1615. Artificial Horizon Sextants Various types of artificial horizons have been used, in￾cluding a bubble, gyroscope, and pendulum. Of these, the bubble has been most widely used. This type of instrument is fitted as a backup system to inertial and other positioning sys￾tems in a few aircraft, fulfilling the requirement for a self￾contained, non-emitting system. On land, a skilled observer using a 2-minute averaging bubble or pendulum sextant can Figure 1612b. Testing the perpendicularity of the horizon glass. On the left, side error does not exist. At the right, side error does exist

281INSTRUMENTSFORCELESTIALNAVIGATIONigators can sometimes obtainbetterresultswithan artificial-measure altitudes to an accuracy of perhaps 2,(2miles)This, ofcourse,refers to the accuracy ofmeasurement onlyhorizon sextant than with a marine sextant.Some artificial-anddoesnotincludeadditionalerrorssuchasabnormalre-horizon sextantshave provision for making observationsfraction,deflection of thevertical, computing and plottingwiththenatural horizonas a reference,but results arenoterrors,etc.In steadyflight through smooth airtheerror ofagenerally as satisfactory as by marine sextant. Because of2-minuteobservation is increased toperhaps5to 10 miles.theirmorecomplicatedoptical systems,and theneedforpro-At sea, with virtually no rollor pitch,results should ap-viding a horizontal reference,artificial-horizon sextants areproach those on land.However,even a gentle roll causesgenerally much more costly to manufacture than marinelarge errors.Under these conditions observational errors ofsextants10-16 milesarenotunreasonable.Withamoderate sea,erAltitudes observed by artificial-horizon sextants arerors of30milesor morearecommon.Ina heavysea, anysubjectto the same errorsasthose observed bymarinesex-useful observations arevirtually impossibleto obtain.Sin-tant, exceptthat the dip (height ofeye)correction does notgle altitude observations in a moderate sea can be in errorapply. Also, when the center of the sun or moon is ob-byamatterofdegreesWhen the horizon is obscured by ice or haze,polar nav-served,no correction for semidiameter is requiredCHRONOMETERS1616.The Marine Chronometerfrom radio time signals.This eliminates chronometer error(CE)and watch error (WE)corrections.Should the secondhand be in error by a readable amount, it can be resetThe spring-driven marine chronometer is a precisionelectrically.timepiece.Itisusedaboardshiptoprovideaccuratetimefor timing celestial observations.A chronometer differsThe basic element for timegeneration is a quartz crys-from a spring-driven watch principally in that it contains ataloscillator.Thequartzcrystalistemperaturevariable lever device to maintain even pressure on thecompensatedand is hermetically sealed in an evacuateden-mainspring,and a special balance designed to compensatevelope.A calibrated adjustment capabilityis provided tofortemperaturevariationsadjustfor theaging of the crystalA spring-driven chronometeris set approximatelytoThechronometer isdesigned tooperatefora minimumGreenwich mean time (GMT) and is not reset until the in-of1 year on a single set of batteries. A good marine chro-strument is overhauled and cleaned, usually at three-yearnometer has a built-in push button battery test meter.Theintervals.The difference between GMT and chronometermeter face is marked to indicate when thebattery should betime(C)is carefullydetermined andapplied as acorrectionreplaced.The chronometer continues to operate and keepto all chronometer readings.This difference,called chro-thecorrecttimeforatleast5minuteswhilethebatteriesarechanged.The chronometer is designed to accommodatethenometererror(CE),isfast(F)ifchronometertimeislaterthan GMT, and slow (S) if earlier.The amount by whichgradual voltage drop during the life of the batteries whilechronometer error changes in1day is called chronometermaintainingaccuracyrequirements.rate.An erratic rate indicates a defective instrument requir-1618.Watchesingrepair.The principal maintenance requirement is regularwinding at about the same time each day.At maximum in-Achronometershould notbe removed from its casetotervals of about three years, a spring-driven chronometertime sights.Observations maybe timed and ship's clocksshould be sent to a chronometer repair shopfor cleaningset with a comparing watch, which is set to chronometerand overhaul.time(GMT)and taken to thebridge wing for recordingsighttimes.In practice,a wristwatch coordinated to the1617.QuartzCrystalMarineChronometersnearest second with the chronometer will beadequateA stop watch,either spring wound or digital, mayalsoQuartz crystal marine chronometers have replacedbe used for celestial observations. In this case, the watch isspring-driven chronometers aboard many ships becauseofstarted ataknown GMT by chronometer, and theelapsedtheirgreateraccuracy.They aremaintained onGMTdirectlytimeof each sightadded to this to obtain GMT ofthe sight

INSTRUMENTS FOR CELESTIAL NAVIGATION 281 measure altitudes to an accuracy of perhaps 2’, (2 miles). This, of course, refers to the accuracy of measurement only, and does not include additional errors such as abnormal re￾fraction, deflection of the vertical, computing and plotting errors, etc. In steady flight through smooth air the error of a 2-minute observation is increased to perhaps 5 to 10 miles. At sea, with virtually no roll or pitch, results should ap￾proach those on land. However, even a gentle roll causes large errors. Under these conditions observational errors of 10-16 miles are not unreasonable. With a moderate sea, er￾rors of 30 miles or more are common. In a heavy sea, any useful observations are virtually impossible to obtain. Sin￾gle altitude observations in a moderate sea can be in error by a matter of degrees. When the horizon is obscured by ice or haze, polar nav￾igators can sometimes obtain better results with an artificial￾horizon sextant than with a marine sextant. Some artificial￾horizon sextants have provision for making observations with the natural horizon as a reference, but results are not generally as satisfactory as by marine sextant. Because of their more complicated optical systems, and the need for pro￾viding a horizontal reference, artificial-horizon sextants are generally much more costly to manufacture than marine sextants. Altitudes observed by artificial-horizon sextants are subject to the same errors as those observed by marine sex￾tant, except that the dip (height of eye) correction does not apply. Also, when the center of the sun or moon is ob￾served, no correction for semidiameter is required. CHRONOMETERS 1616. The Marine Chronometer The spring-driven marine chronometer is a precision timepiece. It is used aboard ship to provide accurate time for timing celestial observations. A chronometer differs from a spring-driven watch principally in that it contains a variable lever device to maintain even pressure on the mainspring, and a special balance designed to compensate for temperature variations. A spring-driven chronometer is set approximately to Greenwich mean time (GMT) and is not reset until the in￾strument is overhauled and cleaned, usually at three-year intervals. The difference between GMT and chronometer time (C) is carefully determined and applied as a correction to all chronometer readings. This difference, called chro￾nometer error (CE), is fast (F) if chronometer time is later than GMT, and slow (S) if earlier. The amount by which chronometer error changes in 1 day is called chronometer rate. An erratic rate indicates a defective instrument requir￾ing repair. The principal maintenance requirement is regular winding at about the same time each day. At maximum in￾tervals of about three years, a spring-driven chronometer should be sent to a chronometer repair shop for cleaning and overhaul. 1617. Quartz Crystal Marine Chronometers Quartz crystal marine chronometers have replaced spring-driven chronometers aboard many ships because of their greater accuracy. They are maintained on GMT directly from radio time signals. This eliminates chronometer error (CE) and watch error (WE) corrections. Should the second hand be in error by a readable amount, it can be reset electrically. The basic element for time generation is a quartz crys￾tal oscillator. The quartz crystal is temperature compensated and is hermetically sealed in an evacuated en￾velope. A calibrated adjustment capability is provided to adjust for the aging of the crystal. The chronometer is designed to operate for a minimum of 1 year on a single set of batteries. A good marine chro￾nometer has a built-in push button battery test meter. The meter face is marked to indicate when the battery should be replaced. The chronometer continues to operate and keep the correct time for at least 5 minutes while the batteries are changed. The chronometer is designed to accommodate the gradual voltage drop during the life of the batteries while maintaining accuracy requirements. 1618. Watches A chronometer should not be removed from its case to time sights. Observations may be timed and ship’s clocks set with a comparing watch, which is set to chronometer time (GMT) and taken to the bridge wing for recording sight times. In practice, a wrist watch coordinated to the nearest second with the chronometer will be adequate. A stop watch, either spring wound or digital, may also be used for celestial observations. In this case, the watch is started at a known GMT by chronometer, and the elapsed time of each sight added to this to obtain GMT of the sight