《航海学》课程参考文献（地文资料）CHAPTER 26 EMERGENCY NAVIGATION

CHAPTER 26EMERGENCYNAVIGATIONINTRODUCTION2600.Planning For Emergency Navigationmethod.He should be ableto construct aplotting sheet withaprotractorand improvisea sextant.Forthenavigatorpre-With a complete set of emergency equipment, emer-pared with such knowledge the situation is never hopelessgency navigation differs little from traditional shipboardSome method of navigation is aways available.This wasrecently proven by a sailor who circumnavigated the earthnavigationroutine.Increasingrelianceoncomplexelec-using no instruments ofanykind,notevena compass.Basictronic systems has changed the perspectiveof emergencynavigation.Todayitismorelikelythatanavigatorwill suf-knowledgecansuffice.ferfailureofelectronicdevicesandbe left with littlemoreThemodern ship's regular navigationgear consists ofthanasextant withwhichtonavigatethanthathewill bemanycomplexelectronicsystems.Thoughtheymaypossesforced to navigate a lifeboat. In the event offailure or de-a limited backup power supply,most depend on an uninter-structionofelectronicsystems,navigationalequipmentandrupted supplyof electrical power.Thefailureof thatpowermethods may need tobe improvised.Theofficer who regu-due to hostile action, fire, or breakdown can instantly ren-larly navigates by blindly“filling in the blanks"or readingder the unprepared navigator helpless. This discussion isthe coordinatesfrom“black boxes"will notbeprepared tointended to provide the navigator withthe informationusebasicprinciplestoimprovisesolutionsinanneeded to navigate a vessel in the absence of the regularemergencysuite ofnavigation gear.Training and preparation for a nav-For offshore voyaging, the professional navigator mustigation emergency are essential. This should consist ofbecome thoroughlyfamiliar withthe theory of celestialregularpractice inthetechniques discussedherein whilethenavigation.He should be ableto identifythemost usefulregular navigation routine is in effect, so that confidence instars andknowhowto solvehis sights by any widely usedemergencyprocedures is establishedBASICTECHNIOUESOFEMERGENCYNAVIGATION2601.Emergency Navigation Kitseasons should be included.Plotting sheets areuseful but not essential if charts are available.The navigator should assemble akit containing equip-Universal plottingsheetsmaybepreferred,partic-ment for emergency navigation. Even with no expectationularly if the latitude coverage is large. Includeofdanger, it is good practiceto have sucha kitpermanentlymaneuvering boards andgraph paper.3. Plotting equipment. Pencils, erasers, a straight-locatedinthechartroomoronthebridgesothatitcanbequickly broken out if needed.It can be used on the bridgeedge, protractor or plotter, dividers and compasses,intheeventofdestructionorfailureofregularnavigationand aknife orpencil sharpenershould beincluded.systems, or taken to a lifeboat if the“abandon ship"call isAruleris also useful.made4.Timepiece.A good watch is needed iflongitude is toIf practical.full navigational equipment shouldbeprobe determined astronomically.It should be water-vided inthe emergencykit.As many as possible of theproof or kept in a waterproof container whichitems in thefollowing list should be includedpermits reading and winding ofthe watch if necessary without exposing it to the elements.The1.A notebook or journal suitable for use as a deck logoptimumtimepieceisa quartzcrystalchronometerbut any high-quality digital wristwatch will suffice ifandforperformingcomputationsit is synchronized with the ship's chronometer. A2Charts and plotting sheets. A pilot chart is ex-portable radio capable ofreceiving time signals,to-cellent for emergency use. It can be used forgether with a good wristwatch, will also suffice.plottingand asasourceof informationoncom-5.Sextant.A marine sextant should be included.Ifthispass variation, shipping lanes, currents, winds,is impractical,an inexpensive plastic sextantwill suf-andweather.Chartsforbothsummerandwinter379

379 CHAPTER 26 EMERGENCY NAVIGATION INTRODUCTION 2600. Planning For Emergency Navigation With a complete set of emergency equipment, emer￾gency navigation differs little from traditional shipboard navigation routine. Increasing reliance on complex elec￾tronic systems has changed the perspective of emergency navigation. Today it is more likely that a navigator will suf￾fer failure of electronic devices and be left with little more than a sextant with which to navigate than that he will be forced to navigate a lifeboat. In the event of failure or de￾struction of electronic systems, navigational equipment and methods may need to be improvised. The officer who regu￾larly navigates by blindly “filling in the blanks” or reading the coordinates from “black boxes” will not be prepared to use basic principles to improvise solutions in an emergency. For offshore voyaging, the professional navigator must become thoroughly familiar with the theory of celestial navigation. He should be able to identify the most useful stars and know how to solve his sights by any widely used method. He should be able to construct a plotting sheet with a protractor and improvise a sextant. For the navigator pre￾pared with such knowledge the situation is never hopeless. Some method of navigation is always available. This was recently proven by a sailor who circumnavigated the earth using no instruments of any kind, not even a compass. Basic knowledge can suffice. The modern ship’s regular navigation gear consists of many complex electronic systems. Though they may posses a limited backup power supply, most depend on an uninter￾rupted supply of electrical power. The failure of that power due to hostile action, fire, or breakdown can instantly ren￾der the unprepared navigator helpless. This discussion is intended to provide the navigator with the information needed to navigate a vessel in the absence of the regular suite of navigation gear. Training and preparation for a nav￾igation emergency are essential. This should consist of regular practice in the techniques discussed herein while the regular navigation routine is in effect, so that confidence in emergency procedures is established. BASIC TECHNIQUES OF EMERGENCY NAVIGATION 2601. Emergency Navigation Kit The navigator should assemble a kit containing equip￾ment for emergency navigation. Even with no expectation of danger, it is good practice to have such a kit permanently located in the chart room or on the bridge so that it can be quickly broken out if needed. It can be used on the bridge in the event of destruction or failure of regular navigation systems, or taken to a lifeboat if the “abandon ship” call is made. If practical, full navigational equipment should be pro￾vided in the emergency kit. As many as possible of the items in the following list should be included. 1. A notebook or journal suitable for use as a deck log and for performing computations. 2. Charts and plotting sheets. A pilot chart is ex￾cellent for emergency use. It can be used for plotting and as a source of information on com￾pass variation, shipping lanes, currents, winds, and weather. Charts for both summer and winter seasons should be included. Plotting sheets are useful but not essential if charts are available. Universal plotting sheets may be preferred, partic￾ularly if the latitude coverage is large. Include maneuvering boards and graph paper. 3. Plotting equipment. Pencils, erasers, a straight￾edge, protractor or plotter, dividers and compasses, and a knife or pencil sharpener should be included. A ruler is also useful. 4. Timepiece. A good watch is needed if longitude is to be determined astronomically. It should be water￾proof or kept in a waterproof container which permits reading and winding of the watch if neces￾sary without exposing it to the elements. The optimum timepiece is a quartz crystal chronometer, but any high-quality digital wristwatch will suffice if it is synchronized with the ship’s chronometer. A portable radio capable of receiving time signals, to￾gether with a good wristwatch, will also suffice. 5. Sextant. A marine sextant should be included. If this is impractical, an inexpensive plastic sextant will suf-

380EMERGENCYNAVIGATIONupdated with a DR position will be adequate. But whenfice.Several types are availablecommercially.Theemergencysextantshouldbeusedperiodicallyinac-conflicting information or information ofquestionablereli-tualdailynavigationsoitslimitationsandcapabilitiesability is received, the navigator must determine an MPParefully understood.Plastic sextants havebeen usedWhen completepositional information is lacking,orsafely onextensive ocean voyages.Do not hesitate towhentheavailable information is questionable,the mostuse them in an emergency.probable position mightbedetermined fromtheintersec-tionof a single line of position anda DR, from a line of6.Almanac.A currentNautical Almanac containssoundings, from lines of position which are somewhat in-ephemeral data and concise sight reduction tables.Anothervear'salmanaccanbeusedforstarsandconsistent, or from a dead reckoning position with athe sun without serious error by emergency stan-correction for current or wind.Continuea dead reckoningdards.Someform of long-term almanacmight beplotfromonefixtoanotherbecausetheDRplotoftenpro-vides the best estimate of theMPP.copied or pasted in the notebook7.Tables.Someformof tablewill be neededfor re-A series of estimated positions may not be consistentducing celestial observations.The Nauticalbecause of thecontinual revisionof the estimateas addi-Almanac produced by the U.S.Naval Observatorytional information is received.However,it isgood practicetoplotallMPP's,and sometimestomaintaina separateEPcontains detailed procedures forcalculator sight re-duction and a compact sight reduction table.plot based upon thebest estimateoftrack and speed madegood over the ground.This could indicate whether the8Compass.Each lifeboat must carry a magneticpresent course is a safe one.See Chapter 23.compass.For shipboard use,makea deviationtablefor each compass with magnetic material in its nor-2603.Plotting Sheetsmal place.The accuracy of each table should becheckedperiodicallyIf plotting sheets are not availablea Mercator plotting9.Flashlight.A flashlight isrequired in each lifeboat.Check the batteries periodically and include extrasheet can be constructed through either of two alternativemethods based upon agraphical solution ofthe secantofthebatteriesandbulbsinthekitlatitude,which approximates the expansion of latitude10.Portableradio.Atransmitting-receiving set ap-provedbytheFederalCommunicationsFirstmethod (Figure 2603a)Commissionforemergencyusecanestablishcom-munications with rescueauthorities.A smallStep one.Drawa series of equally spacedverticalportable radio may be used as a radio directionlines at any spacing desired.These arefinder or for receiving time signals.the meridians; label them at any desired11.An Emergency Position Indicating Radiobeaconinterval, suchas1,2',5',10',30,1etc.(EPIRB)is essential.When activated, this deviceSteptwo.Drawand label a horizontal line throughemits a signal which will be picked up by theCOSPAS/SARSAT satellitesystem and automati-thecenter of the sheetto represent theparallel of the mid-latitude of the area.cally relayed to a ground station. It is then routedStep three.Through any convenientpoint,suchasdirectlyto rescueauthorities.Thelocation of thedistress can be determined very accurately.De-the intersection of the central meridianand theparallel ofthemid-latitude,drawpendingon thetypeofEPIRB,thesignalmayevenidentify the individual vessel in distress, thus al-a line making an angle with the horizon-lowingrescuerstodeterminehowmanypeoplearetal equal to the mid-latitude. In Figurein danger, the type of emergency gear they may2603athisangleis35°have,and otherfacts to aid in therescue.BecauseStep four.Draw in and label additional parallels.of this system,thenavigator must question thewis-The length of the oblique line betweendom of navigating away from the scene of themeridians is the perpendicular distancedistress.It may well be easier for rescue forces tobetween parallels,as shown by the bro-find him if heremains inoneplace.SeeChapter28ken arc.The number of minutes of arcThe Global MaritimeDistress and Safety Systembetween parallels is the same as that be-(GMDSS).tweenthemeridiansStep five.Graduate the oblique line into conve-2602.MostProbablePositionnient units. If I' is selected, this scaleservesasbothalatitudeandmilescale.ItInthe eventoffailureof primaryelectronic navigationcan also be used as a longitude scale bymeasuring horizontallyfrom ameridiansystems,thenavigatormayneed to establishthemostprobable position (MPP)of the vessel.Usually there isinstead of obliquelyalong the lineThe meridians may be shown at the desired interval and theusuallylittledoubtas to theposition.Themost recent fix

380 EMERGENCY NAVIGATION fice. Several types are available commercially. The emergency sextant should be used periodically in ac￾tual daily navigation so its limitations and capabilities are fully understood. Plastic sextants have been used safely on extensive ocean voyages. Do not hesitate to use them in an emergency. 6. Almanac. A current Nautical Almanac contains ephemeral data and concise sight reduction tables. Another year’s almanac can be used for stars and the sun without serious error by emergency stan￾dards. Some form of long-term almanac might be copied or pasted in the notebook. 7. Tables. Some form of table will be needed for re￾ducing celestial observations. The Nautical Almanac produced by the U. S. Naval Observatory contains detailed procedures for calculator sight re￾duction and a compact sight reduction table. 8. Compass. Each lifeboat must carry a magnetic compass. For shipboard use, make a deviation table for each compass with magnetic material in its nor￾mal place. The accuracy of each table should be checked periodically. 9. Flashlight. A flashlight is required in each lifeboat. Check the batteries periodically and include extra batteries and bulbs in the kit. 10. Portable radio. A transmitting-receiving set ap￾proved by the Federal Communications Commission for emergency use can establish com￾munications with rescue authorities. A small portable radio may be used as a radio direction finder or for receiving time signals. 11. An Emergency Position Indicating Radiobeacon (EPIRB) is essential. When activated, this device emits a signal which will be picked up by the COSPAS/SARSAT satellite system and automati￾cally relayed to a ground station. It is then routed directly to rescue authorities. The location of the distress can be determined very accurately. De￾pending on the type of EPIRB, the signal may even identify the individual vessel in distress, thus al￾lowing rescuers to determine how many people are in danger, the type of emergency gear they may have, and other facts to aid in the rescue. Because of this system, the navigator must question the wis￾dom of navigating away from the scene of the distress. It may well be easier for rescue forces to find him if he remains in one place. See Chapter 28, The Global Maritime Distress and Safety System (GMDSS). 2602. Most Probable Position In the event of failure of primary electronic navigation systems, the navigator may need to establish the most probable position (MPP) of the vessel. Usually there is usually little doubt as to the position. The most recent fix updated with a DR position will be adequate. But when conflicting information or information of questionable reli￾ability is received, the navigator must determine an MPP. When complete positional information is lacking, or when the available information is questionable, the most probable position might be determined from the intersec￾tion of a single line of position and a DR, from a line of soundings, from lines of position which are somewhat in￾consistent, or from a dead reckoning position with a correction for current or wind. Continue a dead reckoning plot from one fix to another because the DR plot often pro￾vides the best estimate of the MPP. A series of estimated positions may not be consistent because of the continual revision of the estimate as addi￾tional information is received. However, it is good practice to plot all MPP’s, and sometimes to maintain a separate EP plot based upon the best estimate of track and speed made good over the ground. This could indicate whether the present course is a safe one. See Chapter 23. 2603. Plotting Sheets If plotting sheets are not available, a Mercator plotting sheet can be constructed through either of two alternative methods based upon a graphical solution of the secant of the latitude, which approximates the expansion of latitude. First method (Figure 2603a): Step one. Draw a series of equally spaced vertical lines at any spacing desired. These are the meridians; label them at any desired interval, such as 1', 2', 5', 10', 30', 1°, etc. Step two. Draw and label a horizontal line through the center of the sheet to represent the parallel of the mid-latitude of the area. Step three. Through any convenient point, such as the intersection of the central meridian and the parallel of the mid-latitude, draw a line making an angle with the horizon￾tal equal to the mid-latitude. In Figure 2603a this angle is 35°. Step four. Draw in and label additional parallels. The length of the oblique line between meridians is the perpendicular distance between parallels, as shown by the bro￾ken arc. The number of minutes of arc between parallels is the same as that be￾tween the meridians. Step five. Graduate the oblique line into conve￾nient units. If 1' is selected, this scale serves as both a latitude and mile scale. It can also be used as a longitude scale by measuring horizontally from a meridian instead of obliquely along the line. The meridians may be shown at the desired interval and the

381EMERGENCYNAVIGATION*tsfrfes2WrE(Steps)36*N36*MA5)Tsrep新(Step2)35N35'Nrdsidors)ds)34N(Stepa)34°W15E1sofe1sewaft14gfeFigure2603a.Small area plotting sheet with selected longitude scalemid-parallel may be printed and graduated in units of lon-Step four.Draw in and label the meridians.Thegitude.In using the sheet it is necessary only to label thefirstisavertical linethroughthecenterofmeridians and draw the oblique line. From it determine thethe circle. The second is a vertical lineinterval usedtodraw in and label additional parallels.Ifthethrough the intersection of the obliqueline and the circle.Additional meridianscentral meridian is graduated, the oblique line need notbe.aredrawnthesamedistanceapartastheSecond method (Figure 2603b)firsttwo.Step five.Graduate the oblique line into conve-Step one. At the center of the sheet draw a circlenient units. If I'is selected, this scalewith a radius equal to 1o (or any otherserves as a latitude and mile scale.It canconvenient unit) of latitude at the desiredalso be used as a longitude scale by mea-scale.If a sheet with a compass rose issuring horizontally from a meridian,available, as in Figure 2603b, the com-instead of obliquelyalong the line.pass rose can beused as thecircle and willprove useful for measuring directions.ItIn the second method, theparallels may be shown atneed not limit the scale of the chart, as anthe desired interval, and the central meridian may be printedand graduated in units of latitude. In using the sheet it isadditional concentriccirclecanbedrawn,and desired graduations extended to it.necessary only to label the parallels, draw the oblique line,Step two.Drawhorizontal lines throughthe centerand from itdetermine the interval and draw in and label ad-of the circle and tangent at the top andditional meridians. If the central meridian is graduated, asbottom. These are parallels of latitude;shown in Figure 2603b, the oblique line need not be.label them accordingly,at the selected in-The same result is produced by either method. The firstterval (as every 1°, 30, etc.)method, starting with the selection ofthe longitude scale, isStep three.From the center of the circle draw aparticularly useful when the longitude limits of the plottinglinemaking an anglewith the horizontalsheet determine the scale. When the latitude coverage isequal to the mid-latitude. In Figuremore important, the second method may bepreferable.In2603bthisangleis40°eithermethod a central compassrosemightbeprinted

EMERGENCY NAVIGATION 381 mid-parallel may be printed and graduated in units of lon￾gitude. In using the sheet it is necessary only to label the meridians and draw the oblique line. From it determine the interval used to draw in and label additional parallels. If the central meridian is graduated, the oblique line need not be. Second method (Figure 2603b). Step one. At the center of the sheet draw a circle with a radius equal to 1° (or any other convenient unit) of latitude at the desired scale. If a sheet with a compass rose is available, as in Figure 2603b, the com￾pass rose can be used as the circle and will prove useful for measuring directions. It need not limit the scale of the chart, as an additional concentric circle can be drawn, and desired graduations extended to it. Step two. Draw horizontal lines through the center of the circle and tangent at the top and bottom. These are parallels of latitude; label them accordingly, at the selected in￾terval (as every 1°, 30’, etc.). Step three. From the center of the circle draw a line making an angle with the horizontal equal to the mid-latitude. In Figure 2603b this angle is 40°. Step four. Draw in and label the meridians. The first is a vertical line through the center of the circle. The second is a vertical line through the intersection of the oblique line and the circle. Additional meridians are drawn the same distance apart as the first two. Step five. Graduate the oblique line into conve￾nient units. If 1’ is selected, this scale serves as a latitude and mile scale. It can also be used as a longitude scale by mea￾suring horizontally from a meridian, instead of obliquely along the line. In the second method, the parallels may be shown at the desired interval, and the central meridian may be printed and graduated in units of latitude. In using the sheet it is necessary only to label the parallels, draw the oblique line, and from it determine the interval and draw in and label ad￾ditional meridians. If the central meridian is graduated, as shown in Figure 2603b, the oblique line need not be. The same result is produced by either method. The first method, starting with the selection of the longitude scale, is particularly useful when the longitude limits of the plotting sheet determine the scale. When the latitude coverage is more important, the second method may be preferable. In either method a central compass rose might be printed. Figure 2603a. Small area plotting sheet with selected longitude scale

382EMERGENCYNAVIGATION60626rw59w58wE(Step 2)4fN4r'N10350TTTS20-0eul83RtepES?(Step 2)40N40°N3(tdans)1国(r dous)( dais)(tdais)mainiaa10S民lE店8ulw:.20E20C(Step 2)Fe39'NO'NE58w62w60y61°w59wFigure2603b.SmallareaplottingsheetwithselectedlatitudescaleBothmethods usea constantrelationshipoflatitudetosheet. If this proves too difficult, or if an independent check islongitudeover the entire sheet and both fail to allowfor thedesired,someform ofmathematical reckoning maybe useful.ellipticity ofthe earth.For practical navigation these are notTable 2604,a simplified traverse table, can be usedfor this pur-importantconsiderations.pose. This is a critical-type table, various factors being given forlimitingvalues of certainangles.Tofindthedifferenceor2604.DeadReckoningchange of latitude in minutes, enter thetable with course anglereckoned fromnorth or southtowardthe east orwest.MultiplyOfthevarioustypesofnavigation,deadreckoningaloneisthe distance run, in miles, by the factor. To find the departure inalways available in someform.In an emergency it is of moremiles, enter the table with the complement of the course angle.thanaverageimportance.Withelectronicsystemsoutofservice,Multiply the distance run in miles by the factor.To convert de-keepaclosecheckon speed,direction,and distancemadegoodparture to difference oflongitude in minutes, enter the table withCarefullyevaluatetheeffects ofwind and current.Long voyagmid-latitude and divide the departure by thefactor.es with accurate landfalls have been successfully completed bythismethodalone.ThisisnotmeanttominimizetheimportanceExample:Avesseltravels26milesoncourse205°ofother methods ofdetermining position.However,dead reckfromLat.41°44N,Long.56°21WoningpositionsmaybemoreaccuratethanthosedeterminedbyRequired:Latitudeand longitudeofthepointofarrival.other methods.If the means of determining direction and dis-tance (the elements of dead reckoning)are accurate, it maybeSolution: The course angle is 205°-1800= S25°W, andbestto adjustthedeadreckoningonlyaftera confirmedfixthecomplement is900-25°=65°.ThefactorscorrespondingPlotting canbedone directlyon apilot chart orplottingto these angles are 0.9and 0.4,respectively.The diference of75018314149566369818790Angle1.00.90.50.30.2Factor0.80.70.60.40.10.0Table 2604. Simplified traverse table

382 EMERGENCY NAVIGATION Both methods use a constant relationship of latitude to longitude over the entire sheet and both fail to allow for the ellipticity of the earth. For practical navigation these are not important considerations. 2604. Dead Reckoning Of the various types of navigation, dead reckoning alone is always available in some form. In an emergency it is of more than average importance. With electronic systems out of service, keep a close check on speed, direction, and distance made good. Carefully evaluate the effects of wind and current. Long voyag￾es with accurate landfalls have been successfully completed by this method alone. This is not meant to minimize the importance of other methods of determining position. However, dead reck￾oning positions may be more accurate than those determined by other methods. If the means of determining direction and dis￾tance (the elements of dead reckoning) are accurate, it may be best to adjust the dead reckoning only after a confirmed fix. Plotting can be done directly on a pilot chart or plotting sheet. If this proves too difficult, or if an independent check is desired, some form of mathematical reckoning may be useful. Table 2604, a simplified traverse table, can be used for this pur￾pose. This is a critical-type table, various factors being given for limiting values of certain angles. To find the difference or change of latitude in minutes, enter the table with course angle, reckoned from north or south toward the east or west. Multiply the distance run, in miles, by the factor. To find the departure in miles, enter the table with the complement of the course angle. Multiply the distance run in miles by the factor. To convert de￾parture to difference of longitude in minutes, enter the table with mid-latitude and divide the departure by the factor. Example: A vessel travels 26 miles on course 205°, from Lat. 41°44’N, Long. 56°21’W. Required: Latitude and longitude of the point of arrival. Solution: The course angle is 205° - 180° = S25°W, and the complement is 90° - 25° = 65°. The factors corresponding to these angles are 0.9 and 0.4, respectively. The difference of Figure 2603b. Small area plotting sheet with selected latitude scale. Angle 0 18 31 41 49 56 63 69 75 81 87 90 Factor 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Table 2604. Simplified traverse table

EMERGENCYNAVIGATION383latitudeis26×0.9=23'(tothenearestminute)andthedepar-Meridian transit:Any celestial body bears due northtureis26x0.4=10mi.Sincethecourseisinthesouthwesternor southatmeridiantransit,eitherupperorlower.This isthequadrant,intheNorthernHemisphere,thelatitudeofthepointmomentofmaximum(orminimum)altitudeof thebodyof arrival is 41°44'N-23'= 41°21 N.The factor correspond-However, since the altitude at this time is nearly constanting to the mid-latitude 41°32N is 0.7.The difference ofduringa considerablechangeof azimuth,the instantofme-longitude is10+0.7=14:The longitude of the pointofarrivalridian transit may be difficult to determine. If time and anis5621W+14=56°35Walmanac are available, and the longitude isknown,the timeAnswer:Lat.41°21 N,Long.56°35W.oftransitcan be computed.It can alsobegraphed as a curveongraphpaper and thetimeofmeridiantransitdeterminedwith sufficient accuracyfor emergencypurposes.2605.Deck LogBody on prime vertical:If any method is available forAt the beginning of anavigation emergency a naviga-determiningwhen abodyis on theprime vertical (dueeastorwest),thecompassazimuthatthistimecanbeobserved.Tabletionlogshouldbestarted.Thedateandtimeofthecasualtyshould bethefirstentry,followed bynavigational informa-20, Meridian Angle and Altitude ofa Body on the Prime Ver-tionsuchas ship'sposition,status ofallnavigationsystems,tical Circle provides this information Any body on thethe decisions made, and the reasons for themcelestial equator (declination oo)is on the prime vertical at theThebestdetermination of theposition of the casualtytime of rising or setting.Forthe sun this occurs at the time ofthe equinoxes.The star Mintaka (Orionis),the leading star ofshould be recorded,followedbya full account of courses,distances,positions,winds,currents,and leeway.Noim-Orion'sbelt,hasadeclinationofapproximately0.3°sandcanportant navigational information should be left to memorybe consideredon thecelestial equator.For an observer neartheequator,such a body is always nearly east or west.Because ofif itcanberecorded.refractionanddip,theazimuthshould benoted when thecen-2606.Directionter of the sun ora star is a littlemorethan one sun diameter(half adegree)abovethehorizon.Themoon should beob-servedwhen its upper limb is on the horizon.Direction is one of the elements ofdead reckoning.Adeviationtableforeach compass,including lifeboat comBody at rising or setting: Except for themoon, the az-passes, should already have been determined.In the eventimuthangleofabodyisalmostthesameatrising as atof destruction or failure of the gyrocompass and bridgesetting,exceptthattheformer is toward theeast and thelat-magnetic compass, lifeboat compasses can be used.tertoward the west.Iftheazimuth is measured both at risingIf analmanac,accurateGreenwich time,and theneces-and setting,true south (or north)is midwaybetween the twosarytablesareavailable,the azimuthofanycelestial body canobservedvalues,and the difference between this value and180°(or0000)isthecompasserror.Thus,ifthecompassaz-becomputedandthisvaluecomparedwithanazimuthmea-imuth of a body is073°at rising,and277°at setting,truesured bythe compass.If it isdifficult toobservethe compassazimuth,selectabodydead aheadandnotethecompasshead-073°+277°= 175 by compass, and thesouth(180°)ising.The difference between the computed and observed2azimuths is compass error on thatheading.This is of more im+compass error is 5°E.This method may be in error ifthe ves-mediate value than deviation, but if thelatter is desired, it cansel is moving rapidly in a north or south direction. If thebedeterminedbyapplyingvariationtothecompass error.declination and latitudeareknown,thetrueazimuth of anySeveral unique astronomical situations occur,permit-body atrising or setting can bedetermined bymeans ofadi-tingdeterminationofazimuthwithout computation:agram on theplaneof the celestial meridianor byPolaris: Polaris is always within 2°of true north for ob-computation.Forthispurpose,thebody(exceptthemoon)servers between the equator and latitude 60°N.When this starshould be considered as rising or setting when its center is ais directly above or belowthe celestial pole, its azimuth is ex-littlemore than one sun diameter (halfa degree)above theactly north at any latitude. This occurs approximately when thehorizon,because of refraction anddip.trailing star of either Cassiopeia or the Big Dipper (Alkaid) isFinding directionbytherelationship of the suntothedirectly above or directly below Polaris (Figure 2611). Whenhands of a watch is sometimes advocated, butthelimita-a line through the trailing stars and Polaris is horizontal,thetions of this method prevent its practical use at seamaximumcorrection should beapplied.Belowlatitude50othiscanbeconsidered1°;andbetween50°and65°,2IfCas-A simple technique can be usedfor determining devia-siopeia is to the right of Polaris,theazimuth is 001°(or0020)tion.An object that will float but not driftrapidlybefore theand ifto theleft.359°(or358°).Thesouthcelestial pole islo-wind is thrown overboard.Thevessel is then steered steadilycated approximatelyat the intersection of a line through thein theoppositedirectiontothatdesired.Atadistanceof per-longer axis of the Southern Cross with a linefrom the north-hapshalfa mile,ormore ifthefloating objectis still clearlyernmost star of Triangulum Australe perpendicular to the linein view,the vessel is turned around in the smallest practicaljoiningtheothertwo stars ofthetriangle.Noconspicuousstarradius, and headed back toward the floating object. Themarksthisspot(SeestarchartsinChapter15)magnetic course ismidwaybetweenthe coursetowardthe

EMERGENCY NAVIGATION 383 latitude is 26 × 0.9 = 23’ (to the nearest minute) and the depar￾ture is 26 × 0.4 = 10 mi. Since the course is in the southwestern quadrant, in the Northern Hemisphere, the latitude of the point of arrival is 41°44’ N -23’ = 41°21’N. The factor correspond￾ing to the mid-latitude 41°32’N is 0.7. The difference of longitude is 10 ÷ 0.7 = 14’. The longitude of the point of arrival is 56°21’W + 14 = 56°35’W. Answer: Lat. 41°21’N, Long. 56°35’W. 2605. Deck Log At the beginning of a navigation emergency a naviga￾tion log should be started. The date and time of the casualty should be the first entry, followed by navigational informa￾tion such as ship’s position, status of all navigation systems, the decisions made, and the reasons for them. The best determination of the position of the casualty should be recorded, followed by a full account of courses, distances, positions, winds, currents, and leeway. No im￾portant navigational information should be left to memory if it can be recorded. 2606. Direction Direction is one of the elements of dead reckoning. A deviation table for each compass, including lifeboat com￾passes, should already have been determined. In the event of destruction or failure of the gyrocompass and bridge magnetic compass, lifeboat compasses can be used. If an almanac, accurate Greenwich time, and the neces￾sary tables are available, the azimuth of any celestial body can be computed and this value compared with an azimuth mea￾sured by the compass. If it is difficult to observe the compass azimuth, select a body dead ahead and note the compass head￾ing. The difference between the computed and observed azimuths is compass error on that heading. This is of more im￾mediate value than deviation, but if the latter is desired, it can be determined by applying variation to the compass error. Several unique astronomical situations occur, permit￾ting determination of azimuth without computation: Polaris: Polaris is always within 2° of true north for ob￾servers between the equator and latitude 60°N. When this star is directly above or below the celestial pole, its azimuth is ex￾actly north at any latitude. This occurs approximately when the trailing star of either Cassiopeia or the Big Dipper (Alkaid) is directly above or directly below Polaris (Figure 2611). When a line through the trailing stars and Polaris is horizontal, the maximum correction should be applied. Below latitude 50° this can be considered 1°; and between 50° and 65°, 2°. If Cas￾siopeia is to the right of Polaris, the azimuth is 001° (or 002°), and if to the left, 359° (or 358°). The south celestial pole is lo￾cated approximately at the intersection of a line through the longer axis of the Southern Cross with a line from the north￾ernmost star of Triangulum Australe perpendicular to the line joining the other two stars of the triangle. No conspicuous star marks this spot (See star charts in Chapter 15). Meridian transit: Any celestial body bears due north or south at meridian transit, either upper or lower. This is the moment of maximum (or minimum) altitude of the body. However, since the altitude at this time is nearly constant during a considerable change of azimuth, the instant of me￾ridian transit may be difficult to determine. If time and an almanac are available, and the longitude is known, the time of transit can be computed. It can also be graphed as a curve on graph paper and the time of meridian transit determined with sufficient accuracy for emergency purposes. Body on prime vertical: If any method is available for determining when a body is on the prime vertical (due east or west), the compass azimuth at this time can be observed. Table 20, Meridian Angle and Altitude of a Body on the Prime Ver￾tical Circle provides this information. Any body on the celestial equator (declination 0°) is on the prime vertical at the time of rising or setting. For the sun this occurs at the time of the equinoxes. The star Mintaka (δ Orionis), the leading star of Orion’s belt, has a declination of approximately 0.3°S and can be considered on the celestial equator. For an observer near the equator, such a body is always nearly east or west. Because of refraction and dip, the azimuth should be noted when the cen￾ter of the sun or a star is a little more than one sun diameter (half a degree) above the horizon. The moon should be ob￾served when its upper limb is on the horizon. Body at rising or setting: Except for the moon, the az￾imuth angle of a body is almost the same at rising as at setting, except that the former is toward the east and the lat￾ter toward the west. If the azimuth is measured both at rising and setting, true south (or north) is midway between the two observed values, and the difference between this value and 180° (or 000°) is the compass error. Thus, if the compass az￾imuth of a body is 073° at rising, and 277° at setting, true south (180°) is by compass, and the compass error is 5°E. This method may be in error if the ves￾sel is moving rapidly in a north or south direction. If the declination and latitude are known, the true azimuth of any body at rising or setting can be determined by means of a di￾agram on the plane of the celestial meridian or by computation. For this purpose, the body (except the moon) should be considered as rising or setting when its center is a little more than one sun diameter (half a degree) above the horizon, because of refraction and dip. Finding direction by the relationship of the sun to the hands of a watch is sometimes advocated, but the limita￾tions of this method prevent its practical use at sea. A simple technique can be used for determining devia￾tion. An object that will float but not drift rapidly before the wind is thrown overboard. The vessel is then steered steadily in the opposite direction to that desired. At a distance of per￾haps half a mile, or more if the floating object is still clearly in view, the vessel is turned around in the smallest practical radius, and headed back toward the floating object. The magnetic course is midway between the course toward the 073° + 277° 2 - 175 =

384EMERGENCY NAVIGATIONobject and the reciprocal of the course away from theob-directionofthewind,themovementoftheclouds.thedi-jectThus,if theboatisoncompasscourse151whilerection ofthewaves,or bywatchingthewake of thevessel.heading awayfrom theobject,and337°whilereturning,theThe angle between the centerline and the wake is an indica-magneticcourse ismidwaybetween337°and151°+180tion of the amount of leeway.337 + 331Abody having a declination the same as the latitude of=331°,or=334°2thedestinationisdirectlyoverthedestinationonceeachday,when its hour angle equals the longitude, measuredSince334°magneticisthe sameas 337bycompass,thedeviation on this heading is 3°W.westward through360o.AtthistimeitshouldbedeadIfa compass is not available,any celestial body can beahead if the vessel is following thegreat circle leading di-used to steer by,ifits diurnal apparent motion is considered.rectly to the destination.The Nautical Almanac can beAreasonably straight course can be steered by noting theinspected tofind a bodywith a suitabledeclinationEMERGENCYCELESTIALNAVIGATION2607.AlmanacsThefactorfromTable2604is0.5.Thedeclinationis23.45°×0.5=11.70Weknowit isnorthbecauseofthedateAlmanac information,particularlydeclination andAnswer:Dec.11.7oN.Greenwich hour angleofbodies,is importanttocelestialnavigation.If the currentNautical Almanac is available,there is no problem.If the only copyavailable isfor apre-Theaccuracyofthis solutioncanbe improved bycon-vious year, it can be used for the sun, Aries, and starssidering the factor of Table2604 as the valuefor themid-without serious error, by emergency standards.However,anglebetweenthetwo limiting ones (exceptthat 1.00 isforgreater accuracy,proceed asfollows:correctfor0°and 0.00is correctfor90),and interpolat-For declination of the sun,enterthe almanac with a timeing to one additional decimal. In this instance theinterpolationwould bebetween0.50at59.5and0.40atthat is earlier than the correcttime by 5h 49m times the number66.The interpolated value is 0.47,giving a declinationofof years between thedate of the almanac and the correct date,11.0°N. Still greater accuracy can be obtained by using aadding24hoursforeachFebruary29thatoccursbetweenthedates. If the date is February 29, use March 1 and reduce by onetableofnatural cosinesinsteadof Table2604.Bynaturalcosine the value is 11.3°Nthenumberof24hourperiodsadded.ForGHAofthesunorAr-ies, detemine the value for the correct time, adjusting theIfthelatitude isknown, the declination ofany body canminutes andtenths ofarc to agree with that at thetimefor whichbe determinedby observinga meridian altitude.It is usuallythe declination is determined. Since the adjustment never ex-bestto makeanumberof observations shortlybefore andceeds halfa degree, care should be used when the value is nearafter transit,plotthe values ongraphpaper,letting theordi-nate (vertical scale) represent altitude, and the abscissaa wholedegree,to prevent thevalue from being in error by10(horizontal scale)the time.The altitude is found by fairingIfnoalmanacisavailable,aroughapproximationofthea curve or drawing an arc ofa circlethrough thepoints,anddeclination of the sun can be obtained as follows:Count thetaking the highest value.A meridian altitude problem isdavsfromthegivendatetothenearersolstice(June21orDe-then solved in reverse.cember22).Dividethis bythenumber of days from thatsolstice to theequinox (March21 or September 23),using theExample 2:The latitude ofa vessel is 40016 S.The sumequinox that will result in the given date being between it andthe solstice.Multiplythe resultby90°.EnterTable2604withis observed on themeridian, bearing north.The observedthe angle so found and extract the factor. Multiply this byaltitudeis36°29:23.45°to find the declination.Required: Declination of the sun.Solution:Thezenithdistanceis90°-36°29'=53°31:Examplel:ThedateisAugust24.The sun is 5331'north of the observer, or 13°15'north oftheequator.Hence,thedeclinationis13°15'N.Required:The approximate declination of the sun.Solution: The number of days from the given date to theAnswer:Dec.13°15'N.nearer solstice (June21)is 64.There are94daysbetwveenJune21andSeptember23.Dividingandmultiplyingby90°The GHA of Aries can be determined approximately64by considering it equal to GMT (in angular units) on Sep-4 × 90° = 61.3'tember23.TofindGHAAries onanyother date,add1°for

384 EMERGENCY NAVIGATION object and the reciprocal of the course away from the ob￾ject. Thus, if the boat is on compass course 151° while heading away from the object, and 337° while returning, the magnetic course is midway between 337° and 151° + 180° Since 334° magnetic is the same as 337° by compass, the deviation on this heading is 3°W. If a compass is not available, any celestial body can be used to steer by, if its diurnal apparent motion is considered. A reasonably straight course can be steered by noting the direction of the wind, the movement of the clouds, the di￾rection of the waves, or by watching the wake of the vessel. The angle between the centerline and the wake is an indica￾tion of the amount of leeway. A body having a declination the same as the latitude of the destination is directly over the destination once each day, when its hour angle equals the longitude, measured westward through 360°. At this time it should be dead ahead if the vessel is following the great circle leading di￾rectly to the destination. The Nautical Almanac can be inspected to find a body with a suitable declination. EMERGENCY CELESTIAL NAVIGATION 2607. Almanacs Almanac information, particularly declination and Greenwich hour angle of bodies, is important to celestial navigation. If the current Nautical Almanac is available, there is no problem. If the only copy available is for a pre￾vious year, it can be used for the sun, Aries, and stars without serious error, by emergency standards. However, for greater accuracy, proceed as follows: For declination of the sun, enter the almanac with a time that is earlier than the correct time by 5h 49m times the number of years between the date of the almanac and the correct date, adding 24 hours for each February 29 that occurs between the dates. If the date is February 29, use March 1 and reduce by one the number of 24 hour periods added. For GHA of the sun or Ar￾ies, determine the value for the correct time, adjusting the minutes and tenths of arc to agree with that at the time for which the declination is determined. Since the adjustment never ex￾ceeds half a degree, care should be used when the value is near a whole degree, to prevent the value from being in error by 1°. If no almanac is available, a rough approximation of the declination of the sun can be obtained as follows: Count the days from the given date to the nearer solstice (June 21 or De￾cember 22). Divide this by the number of days from that solstice to the equinox (March 21 or September 23), using the equinox that will result in the given date being between it and the solstice. Multiply the result by 90°. Enter Table 2604 with the angle so found and extract the factor. Multiply this by 23.45° to find the declination. Example 1: The date is August 24. Required: The approximate declination of the sun. Solution: The number of days from the given date to the nearer solstice (June 21) is 64. There are 94 days between June 21 and September 23. Dividing and multiplying by 90°, The factor from Table 2604 is 0.5. The declination is 23.45° × 0.5 = 11.7°. We know it is north because of the date. Answer: Dec. 11.7°N. The accuracy of this solution can be improved by con￾sidering the factor of Table 2604 as the value for the mid￾angle between the two limiting ones (except that 1.00 is correct for 0° and 0.00 is correct for 90°), and interpolat￾ing to one additional decimal. In this instance the interpolation would be between 0.50 at 59.5 and 0.40 at 66°. The interpolated value is 0.47, giving a declination of 11.0°N. Still greater accuracy can be obtained by using a table of natural cosines instead of Table 2604. By natural cosine the value is 11.3°N. If the latitude is known, the declination of any body can be determined by observing a meridian altitude. It is usually best to make a number of observations shortly before and after transit, plot the values on graph paper, letting the ordi￾nate (vertical scale) represent altitude, and the abscissa (horizontal scale) the time. The altitude is found by fairing a curve or drawing an arc of a circle through the points, and taking the highest value. A meridian altitude problem is then solved in reverse. Example 2: The latitude of a vessel is 40°16’S. The sun is observed on the meridian, bearing north. The observed altitude is 36°29’. Required: Declination of the sun. Solution: The zenith distance is 90° - 36°29’ = 53°31’. The sun is 53°31’ north of the observer, or 13°15’ north of the equator. Hence, the declination is 13°15’ N. Answer: Dec. 13°15’ N. The GHA of Aries can be determined approximately by considering it equal to GMT (in angular units) on Sep￾tember 23. To find GHA Aries on any other date, add 1° for = 331° , or 337 331 + 2 - = 334° . 64 94- × 90° = 61.3′

385EMERGENCYNAVIGATIONeach day following September 23.The value is approxi-eraged, the accuracy can be improved.A measurement,mately90°onDecember22,180°onMarch21,and2700however approximate,isbetterthan anestimate.Twogen-on June21.Thevalues so found canbe in error byas mucheral types of improvisation are available:as several degrees,and so should not beused if better infor-1. Circle. Any circular degree scale, such as a maneu-mation is available.An approximate check is provided byveringboard,compassrose,protractor,orplottercanbeusedthe great circle through Polaris, Caph (the leading star ofto measure altitude or zenith distance directly.This is theCassiopeia),and the eastern sideof the squareof Pegasus.principle of the ancient astrolabe.A maneuvering board orWhen this great circle coincides with the meridian, LHAcompass rosecanbemounted onaflatboard.Aprotractoror is approximately 0°The hour angle of a body is equalplottermaybeuseddirectly.Thereareanumberofvariationsofthetechniqueofusingsuchadevice.Someofthemareto its SHAplus the hourangle of Aries.A peg or nail is placed at the center of the circle. Aweight is hung from the 90graduation, and a string forIfanerrorofupto4,oralittlemore,isacceptable,theGHA of the sun can be considered equal to GMT ± 1800holding thedevice is attached at the270°graduation.Whenit is held with the weight acting as a plumb bob, the 00 .(12h).Formoreaccurateresults,onecanmakeatableofthe18oline is horizontal.In this position the board is turnedequationof timefromtheNauticalAlmanacperhapsatin azimuth until it is in line with the sun.The intersection offive-or ten-day intervals,and include this in the emergencythe shadow of the center peg with the arc of the circle indi-navigationkit.Theequation oftime is appliedaccordingtocates the altitude ofthe center of the sun.its sign to GMT±180°to find GHA.Theweightand loopcanbeomitted andpegsplaced atthe 0° and 180°points of the circle.While one observer2608.AltitudeMeasurementsights along the line of pegs to the horizon, an assistantnotes thealtitude.Witha sextant, altitudes are measured in the usual mannerIfina smallboatorlifeboat,it isagood ideatomakeanumberThe weight can be attached to the center pin, and theofobservations andaverageboththealtitudes and times,orplotthreepins (0°,center,1800)aligned with the celestial bodyongraphpaperthe altitudesversus time.Therougherthe sea,theThe reading is made at the point where the string holdingmore important isthisprocess,whichtendsto averageouterrorsthe weight crosses the scale. The reading thus obtained isthe zenith distance unless the graduations are labeled to in-causedbyheavyweatherobservationsdicate altitude.This method, illustrated in Figure 2608b, isThe improvisations whichmay bemadein the absenceused for bodies other than the sun.ofa sextantare sovariedthat invirtuallyanycircumstancesa little ingenuity will produce a device to measure altitudeWhatever the technique, reverse the device for half theTheresultsobtainedwithanyimprovisedmethodwillbereadings of a series,to minimize errors of construction.approximateatbest,but ifanumberofobservationsareav-Generally,thecirclemethodproducesmoreaccurateresultsCF STRINGPESaPEG型STRINGPETSTRINGAEICHSEGHFigure2608a.Improvisedastrolabe,shadowmethodFigure2608b.Improvised astrolabedirect sighting method

EMERGENCY NAVIGATION 385 each day following September 23. The value is approxi￾mately 90° on December 22, 180° on March 21, and 270° on June 21. The values so found can be in error by as much as several degrees, and so should not be used if better infor￾mation is available. An approximate check is provided by the great circle through Polaris, Caph (the leading star of Cassiopeia), and the eastern side of the square of Pegasus. When this great circle coincides with the meridian, LHA is approximately 0°. The hour angle of a body is equal to its SHA plus the hour angle of Aries. If an error of up to 4°, or a little more, is acceptable, the GHA of the sun can be considered equal to GMT ± 180° (12h). For more accurate results, one can make a table of the equation of time from the Nautical Almanac perhaps at five- or ten-day intervals, and include this in the emergency navigation kit. The equation of time is applied according to its sign to GMT ± 180° to find GHA. 2608. Altitude Measurement With a sextant, altitudes are measured in the usual manner. If in a small boat or lifeboat, it is a good idea to make a number of observations and average both the altitudes and times, or plot on graph paper the altitudes versus time. The rougher the sea, the more important is this process, which tends to average out errors caused by heavy weather observations. The improvisations which may be made in the absence of a sextant are so varied that in virtually any circumstances a little ingenuity will produce a device to measure altitude. The results obtained with any improvised method will be approximate at best, but if a number of observations are av￾eraged, the accuracy can be improved. A measurement, however approximate, is better than an estimate. Two gen￾eral types of improvisation are available: 1. Circle. Any circular degree scale, such as a maneu￾vering board, compass rose, protractor, or plotter can be used to measure altitude or zenith distance directly. This is the principle of the ancient astrolabe. A maneuvering board or compass rose can be mounted on a flat board. A protractor or plotter may be used directly. There are a number of variations of the technique of using such a device. Some of them are: A peg or nail is placed at the center of the circle. A weight is hung from the 90° graduation, and a string for holding the device is attached at the 270° graduation. When it is held with the weight acting as a plumb bob, the 0° - 180° line is horizontal. In this position the board is turned in azimuth until it is in line with the sun. The intersection of the shadow of the center peg with the arc of the circle indi￾cates the altitude of the center of the sun. The weight and loop can be omitted and pegs placed at the 0° and 180° points of the circle. While one observer sights along the line of pegs to the horizon, an assistant notes the altitude. The weight can be attached to the center pin, and the three pins (0°, center, 180°) aligned with the celestial body. The reading is made at the point where the string holding the weight crosses the scale. The reading thus obtained is the zenith distance unless the graduations are labeled to in￾dicate altitude. This method, illustrated in Figure 2608b, is used for bodies other than the sun. Whatever the technique, reverse the device for half the readings of a series, to minimize errors of construction. Generally, the circle method produces more accurate results Figure 2608a. Improvised astrolabe; shadow method. Figure 2608b. Improvised astrolabe; direct sighting method

386EMERGENCYNAVIGATIONhorizon.The rule is held vertically.The length of rule abovethan the righttrianglemethod,described below.thethumb,dividedbythedistancefromtheeyetothetopof2.Righttriangle.Across-staff can beusedto establishthe thumb, is the tangent ofthe angle observed.The cosineone or more right triangles, which can be solved by mea-canbefound by dividingthedistancefrom theeyetothetopsurement of the angle representing the altitude, eitherof thethumb bythedistancefrom theeyeto thetopof thedirectly or by reconstructing the triangle.Another way ofrule.Iftheruleistiltedtowardtheeyeuntiltheminimumofdetermining the altitude is tomeasure two ofthe sides oftherule is used, thedistance from the eye to themiddle of thetriangle and divide onebythe otherto determine one of therule is substituted for the distance from the eye to thetop oftrigonometricfunctions.Thisprocedure,ofcourse,requiresthethumb.halfthelengthoftheruleabovethethumbisusedasourceofinformationonthevaluesoftrigonometricfunc-andtheanglefoundis multiplied by2.Graduations consistoftions corresponding to various angles. If the cosine ismarksontheruleorstickindicatingvariousaltitudes.Forthefound,Table2604canbeused.Thetabulatedfactorscanbeaverageobservereachinchof rulewill subtend anangleofconsidered correctto oneadditional decimal for thevalueabout2.3°,assuming an eye-to-ruler distance of25inchesmidwaybetweenthe limited values (exceptthat1.00is theThisrelationship is goodtoamaximumaltitudeofabout200correctvaluefor0and0.00 isthecorrectvaluefor900)The accuracy of this relationship can be checked bywithout serious errorby emergencystandards.Interpolationcomparing the measurement against known angles in thecan then bemadebetween suchvalues.sky.Angular distances between stars can be computed byByeitherprotractorortable,mostdevices can begrad-sight reduction methods, including Pub. No. 229, by usinguated in advance so that angles can be read directly.Therethedeclinationofone star as the latitude ofthe assumed po-are many variations of the right triangle method. Some ofsition, and the difference between the hour angles (orthese are described below.SHA's)of the two bodies as the local hour angle.The angu-Two straight pieces of wood can be attached to each oth-lardistance is thecomplementofthecomputed altitude.Theer in sucha waythattheshorter onecanbemoved along theangulardistancesbetweensomewell-knownstarpairsarelonger, thetwoalways beingperpendicular toeach otherend starsofOrion'sbelt,2.7o:pointersoftheBigDipper.The shorter piece is attached at its center. One end of the5.4°,Rigel to Orion'sbelt, 9.0,eastem side of the greatlonger arm is held to the eye.The shorter arm is moved untilsquare ofPegasus, 14.0°, Dubhe (the pointer nearer Polaris)itstopedgeisinlinewiththecelestialbody,anditsbottomand Mizar (the second star in theBig Dipper, counting fromedge is in line with the horizon. Thus, two right triangles aretheend of the handle),19.3°formed,eachrepresentinghalfthealtitude.Forlowaltitudes.The angle between the lines of sight from each eye is,atonlyoneofthetrianglesisused.thelongarmbeingheldinarm's length,about 6°.By holdinga pencil or finger horizontal-linewith thehorizon.The length of half theshort arm,divid-ly,andplacingthehead on itsside,onecanestimateanangleofed by the length of that part of the long arm between the eyeabout 6°by closingfirst one eye and then the other,and notingand the intersection with the short arm, is the tangent of halfhowmuchthepencilorfingerappearstomove inthesky.the altitude (the whole altitude if only one right triangle isThelengthofthe shadowofapegor nail mounted perpen-used).The cosine can befound by dividing that part of thedicular to a horizontal board can be used as one side of anlong arm between the eye and the intersection with the shortaltitude triangle. The other sides are the height ofthe peg and thearmbytheslantdistancefromtheeyetooneendoftheshortslantdistancefromthetopofthepegtotheendoftheshadowarm.GraduationsconsistofaseriesofmarksalongthelongThe height ofthe peg, divided by thelength ofthe shadow, is thearm indicating settings for various angles.ThedeviceshouldtangentofthealtitudeofthecenterofthesunThelengthofthebe invertedforalternatereadings ofaseries.shadow,dividedbytheslantdistance,isthecosine.GraduationsA rule or any stick can be held at arm's length. The topconsist of a series of concentric circles indicating various alti-of the rule is placed in line with the celestial body being ob-tudes, the peg being at the common center.The device is keptserved, and thetop ofthethumb isplaced in linewiththehorizontal byfloating it in a bucketof water.Half the readingsofa seriesare taken withthe board turned 180°in azimuth.Two pegs or nails can be mounted perpendicular to aboard, witha weight hung from the onefarther from the eye.The board is held vertically and the two pegs aligned with theTOBODYbody being observed. A finger is then placed over the stringholdingthe weight,tokeep it inposition astheboard isturnedon its side. A perpendicular line is dropped from the peg near-er the eye,to the string.The body's altitude is the acute anglenearer the eye.For alternate readings of a series, the boardshould be inverted.Graduations consist of a series of marksTO HORIZONindicating the position ofthe string at various altitudes.As the altitudedecreases,thetrianglebecomes smaller.Figure2608c.Improvisedcross-staff.Atthe celestial horizon it becomes a straight line.No instru-

386 EMERGENCY NAVIGATION than the right triangle method, described below. 2. Right triangle. A cross-staff can be used to establish one or more right triangles, which can be solved by mea￾surement of the angle representing the altitude, either directly or by reconstructing the triangle. Another way of determining the altitude is to measure two of the sides of the triangle and divide one by the other to determine one of the trigonometric functions. This procedure, of course, requires a source of information on the values of trigonometric func￾tions corresponding to various angles. If the cosine is found, Table 2604 can be used. The tabulated factors can be considered correct to one additional decimal for the value midway between the limited values (except that 1.00 is the correct value for 0° and 0.00 is the correct value for 90°) without serious error by emergency standards. Interpolation can then be made between such values. By either protractor or table, most devices can be grad￾uated in advance so that angles can be read directly. There are many variations of the right triangle method. Some of these are described below. Two straight pieces of wood can be attached to each oth￾er in such a way that the shorter one can be moved along the longer, the two always being perpendicular to each other. The shorter piece is attached at its center. One end of the longer arm is held to the eye. The shorter arm is moved until its top edge is in line with the celestial body, and its bottom edge is in line with the horizon. Thus, two right triangles are formed, each representing half the altitude. For low altitudes, only one of the triangles is used, the long arm being held in line with the horizon. The length of half the short arm, divid￾ed by the length of that part of the long arm between the eye and the intersection with the short arm, is the tangent of half the altitude (the whole altitude if only one right triangle is used). The cosine can be found by dividing that part of the long arm between the eye and the intersection with the short arm by the slant distance from the eye to one end of the short arm. Graduations consist of a series of marks along the long arm indicating settings for various angles. The device should be inverted for alternate readings of a series. A rule or any stick can be held at arm’s length. The top of the rule is placed in line with the celestial body being ob￾served, and the top of the thumb is placed in line with the horizon. The rule is held vertically. The length of rule above the thumb, divided by the distance from the eye to the top of the thumb, is the tangent of the angle observed. The cosine can be found by dividing the distance from the eye to the top of the thumb by the distance from the eye to the top of the rule. If the rule is tilted toward the eye until the minimum of rule is used, the distance from the eye to the middle of the rule is substituted for the distance from the eye to the top of the thumb, half the length of the rule above the thumb is used, and the angle found is multiplied by 2. Graduations consist of marks on the rule or stick indicating various altitudes. For the average observer each inch of rule will subtend an angle of about 2.3°, assuming an eye-to-ruler distance of 25 inches. This relationship is good to a maximum altitude of about 20°. The accuracy of this relationship can be checked by comparing the measurement against known angles in the sky. Angular distances between stars can be computed by sight reduction methods, including Pub. No. 229, by using the declination of one star as the latitude of the assumed po￾sition, and the difference between the hour angles (or SHA’s) of the two bodies as the local hour angle. The angu￾lar distance is the complement of the computed altitude. The angular distances between some well-known star pairs are: end stars of Orion’s belt, 2.7°; pointers of the Big Dipper, 5.4°, Rigel to Orion’s belt, 9.0°; eastern side of the great square of Pegasus, 14.0°; Dubhe (the pointer nearer Polaris) and Mizar (the second star in the Big Dipper, counting from the end of the handle), 19.3°. The angle between the lines of sight from each eye is, at arm’s length, about 6°. By holding a pencil or finger horizontal￾ly, and placing the head on its side, one can estimate an angle of about 6° by closing first one eye and then the other, and noting how much the pencil or finger appears to move in the sky. The length of the shadow of a peg or nail mounted perpen￾dicular to a horizontal board can be used as one side of an altitude triangle. The other sides are the height of the peg and the slant distance from the top of the peg to the end of the shadow. The height of the peg, divided by the length of the shadow, is the tangent of the altitude of the center of the sun. The length of the shadow, divided by the slant distance, is the cosine. Graduations consist of a series of concentric circles indicating various alti￾tudes, the peg being at the common center. The device is kept horizontal by floating it in a bucket of water. Half the readings of a series are taken with the board turned 180° in azimuth. Two pegs or nails can be mounted perpendicular to a board, with a weight hung from the one farther from the eye. The board is held vertically and the two pegs aligned with the body being observed. A finger is then placed over the string holding the weight, to keep it in position as the board is turned on its side. A perpendicular line is dropped from the peg near￾er the eye, to the string. The body’s altitude is the acute angle nearer the eye. For alternate readings of a series, the board should be inverted. Graduations consist of a series of marks indicating the position of the string at various altitudes. As the altitude decreases, the triangle becomes smaller. Figure 2608c. Improvised cross-staff. At the celestial horizon it becomes a straight line. No instru-

387EMERGENCYNAVIGATIONment is needed to measurethe altitude when either the(-)34Planet/star:upper or lower limb is tangent to the horizon, as the sextantaltitude is then00Dip should be added algebraicallyto thesevalues.Since the“sextant"altitude is zero, the“observed"al-2609.SextantAltitudeCorrectionstitude is equal to the total correction.Ifaltitudes are measured byamarine sextant,the usual2610.SightReductionsextant altitude corrections apply.If the center ofthe sun ormoon is observed, either by sighting at the center or bySight reduction tables should be used, if available. If not,shadow,the lower-limb corrections should beapplied, asusethe compact sightreductiontables found intheNautical Al-usual,andan additional correctionofminus16applied.Ifmanac.Iftrigonometrictables andthenecessaryformulas arethe upper limb is observed, use minus 32' If a weight isavailable, they will serve the purpose. Speed in solution is sel-used as a plumb bob, or if the length of a shadow is mea-domafactor in a lifeboat,butmightbe important aboard ship,sured, omit thedip (height ofeye)correction.particularly in hostile areas.Iftables but no formulas are avail-Ifanalmanacis not available forcorrections,eachable,determinethemathematical knowledgepossessedbythesource oferrorcanbecorrected separatelyasfollowscrew.Someonemaybeabletoprovidethemissing informationIftheformulas are available,but no tables, approximatenaturalIf a sextant is used, the index correction should be de-termined and applied to all observations, or the sextantvalues of thevarioustrigonometric functions canbeobtainedadjusted to eliminate index error.graphically.Graphical solution of the navigational triangle canbe made by theorthographic methodexplained in the chapter onRefraction is given to the nearest minute of arc in Ta-ble2609.The value fora horizon observation is 34If theNavigational Astronomy.Amaneuveringboard mightprovehelpful in the graphical solution for either trigonometric func-nearest 0.1°is sufficiently accurate,as with an improvisedtions or altitude and azimuth.Very careful work will be neededmethod ofobserving altitude,acorrectionofo.j°shouldbeappliedforaltitudesbetween5°and18°,andnocorrectionfor useful results by either method Unless full navigationalequipment is available,betterresultsmightbeobtainedbymakappliedforgreateraltitudes.Refractionappliestoall obser-vations,and isalwaysminusing separate determinations of latitude and longitude.Dip,inminutesofarc,isapproximatelyequaltothesquare2611.LatitudeDeterminationrootoftheheightofeye,infeet.Thedipcorrectionappliestoallobservations in whichthe horizon isused asthe horizontal refer-ence.It is always aminus.If0.1°accuracy is acceptable,no dipSeveral methods are availablefor determininglatitude,correction is needed for small boat heights of eye.nonerequires accurate time.The semidiameter of the sun and moon is approxi-Latitudecanbedetermined usingameridian altitudemately16'of arc.The correction does not applyto otherof anybody,if itsdeclination isknown.If accuratetime.bodies ortoobservations ofthe center of the sun andmoon,knowledgeofthelongitude,andanalmanacareavailable.by whatever method,including shadow.The correction isthe observation can be made at the correct moment, as de-positive if the lower limb is observed, and negative if thetermined inadvance.However,ifanyofthese is lacking,orupperlimbisobservedifanaccuratealtitude-measuring instrument is unavailableFor emergency accuracy, parallax is applied to obser-abetterprocedure istomakeanumber ofaltitudeobserva-vationsofthemoononly.Anapproximatevalue,inminutestionsbefore and aftermeridiantransit.Thenplotaltitudeofarc,canbefoundbymultiplying57'bythefactorfromversustime on graph paper, and thehighest (or lowest, forTable 2604,entering that table with altitude.For moreac-lower transit)altitude is scaledfroma curvefaired throughthe plotted points. At small boat speeds, this procedure iscurateresults,thefactorscanbeconsideredcorrecttooneadditionaldecimalfor the altitudemidwaybetween thelim-not likely to introduce a significant error.The time used foritingvalues(exceptthat1.00 is correctfor0°and 0.00 isplotting the observations need not be accurate, as elapsedcorrectfor 90°),and thevalues for other altitudes can betimebetweenobservationsisall thatisneeded,andthisisfound by interpolation.This correction is always positive.notofcriticalaccuracy.Anyaltitudesthatarenotconsistentwith others of the series should be discarded.For observations of celestial bodiesonthehorizon,thetotal correctionfor zeroheight ofeye is:Latitude byPolaris is explained in Chapter 20, SightSun:Lower limb: (-)18", upper limb: (-)50Reduction.In an emergency,only the first correction is ofMoon:Lower limb: (+)39', upper limb: (+)7.practical significance. If suitable tables are not available,50708°12015021°3306010°63°90°Altitude275'3'198'6'4'0RefractionTable2609.Refraction

EMERGENCY NAVIGATION 387 ment is needed to measure the altitude when either the upper or lower limb is tangent to the horizon, as the sextant altitude is then 0°. 2609. Sextant Altitude Corrections If altitudes are measured by a marine sextant, the usual sextant altitude corrections apply. If the center of the sun or moon is observed, either by sighting at the center or by shadow, the lower-limb corrections should be applied, as usual, and an additional correction of minus 16’ applied. If the upper limb is observed, use minus 32’. If a weight is used as a plumb bob, or if the length of a shadow is mea￾sured, omit the dip (height of eye) correction. If an almanac is not available for corrections, each source of error can be corrected separately, as follows: If a sextant is used, the index correction should be de￾termined and applied to all observations, or the sextant adjusted to eliminate index error. Refraction is given to the nearest minute of arc in Ta￾ble 2609. The value for a horizon observation is 34’. If the nearest 0.1° is sufficiently accurate, as with an improvised method of observing altitude, a correction of 0.1° should be applied for altitudes between 5° and 18°, and no correction applied for greater altitudes. Refraction applies to all obser￾vations, and is always minus. Dip, in minutes of arc, is approximately equal to the square root of the height of eye, in feet. The dip correction applies to all observations in which the horizon is used as the horizontal refer￾ence. It is always a minus. If 0.1° accuracy is acceptable, no dip correction is needed for small boat heights of eye. The semidiameter of the sun and moon is approxi￾mately 16’ of arc. The correction does not apply to other bodies or to observations of the center of the sun and moon, by whatever method, including shadow. The correction is positive if the lower limb is observed, and negative if the upper limb is observed. For emergency accuracy, parallax is applied to obser￾vations of the moon only. An approximate value, in minutes of arc, can be found by multiplying 57’ by the factor from Table 2604, entering that table with altitude. For more ac￾curate results, the factors can be considered correct to one additional decimal for the altitude midway between the lim￾iting values (except that 1.00 is correct for 0° and 0.00 is correct for 90°), and the values for other altitudes can be found by interpolation. This correction is always positive. For observations of celestial bodies on the horizon, the total correction for zero height of eye is: Dip should be added algebraically to these values. Since the “sextant” altitude is zero, the “observed” al￾titude is equal to the total correction. 2610. Sight Reduction Sight reduction tables should be used, if available. If not, use the compact sight reduction tables found in the Nautical Al￾manac. If trigonometric tables and the necessary formulas are available, they will serve the purpose. Speed in solution is sel￾dom a factor in a lifeboat, but might be important aboard ship, particularly in hostile areas. If tables but no formulas are avail￾able, determine the mathematical knowledge possessed by the crew. Someone may be able to provide the missing information. If the formulas are available, but no tables, approximate natural values of the various trigonometric functions can be obtained graphically. Graphical solution of the navigational triangle can be made by the orthographic method explained in the chapter on Navigational Astronomy. A maneuvering board might prove helpful in the graphical solution for either trigonometric func￾tions or altitude and azimuth. Very careful work will be needed for useful results by either method. Unless full navigational equipment is available, better results might be obtained by mak￾ing separate determinations of latitude and longitude. 2611. Latitude Determination Several methods are available for determining latitude; none requires accurate time. Latitude can be determined using a meridian altitude of any body, if its declination is known. If accurate time, knowledge of the longitude, and an almanac are available, the observation can be made at the correct moment, as de￾termined in advance. However, if any of these is lacking, or if an accurate altitude-measuring instrument is unavailable, a better procedure is to make a number of altitude observa￾tions before and after meridian transit. Then plot altitude versus time on graph paper, and the highest (or lowest, for lower transit) altitude is scaled from a curve faired through the plotted points. At small boat speeds, this procedure is not likely to introduce a significant error. The time used for plotting the observations need not be accurate, as elapsed time between observations is all that is needed, and this is not of critical accuracy. Any altitudes that are not consistent with others of the series should be discarded. Latitude by Polaris is explained in Chapter 20, Sight Reduction. In an emergency, only the first correction is of practical significance. If suitable tables are not available, Sun: Lower limb: (–)18', upper limb: (–)50'. Moon: Lower limb: (+)39', upper limb: (+)7'. Planet/star: (–)34'. Altitude 5° 6° 7° 8° 10° 12° 15° 21° 33° 63° 90° Refraction 9' 8' 7' 6' 5' 4' 3' 2' 1' 0 Table 2609. Refraction

388EMERGENCYNAVIGATIONhalf-interval method is of insufficientaccuracy,and allow-this correction can be estimated.The trailing star of Cassi-opeia(eCassiopeiae)andPolarishavealmostexactlytheance should be madefor the longitude correction.same SHA. The trailing star of the Big Dipper (Alkaid) isThe declination of a body in zenith is equal to the lat-nearly oppositePolarisand eCassiopeiae.Thesethreeitude of theobserver.If no means are availabletomeasurestars,e Cassiopeiae,Polaris, and Alkaid, form a linealtitude, the position of the zenith can be determined bythrough the pole (approximately).When this lineishori-holding a weighted string overhead.zontal, there is no correction. When it is vertical,themaximumcorrectionof 56applies.It shouldbeaddedto2612.LongitudeDeterminationtheobserved altitude if Alkaid is at thetop,and subtractedif e Cassiopeiae is at the top.For any other position, esti-Unlike latitude,determining longitude requires accuratemate the angle this line makes with the vertical, andGreenwich time.All such methods consist of notingthemultiplythemaximumcorrection(56)bythefactorfromGreenwich time at which a phenomenon occurs locally. InTable 2604,adding if Alkaid is higher than e Cassiopeiae,addition,a table indicating thetimeofoccurrenceofthesameand subtracting if it is lower.For more accurate results,thephenomenon at Greenwich,or equivalent information,isfactorfromTable2604canbeconsideredaccuratetooneneededThreemethodsmaybeusedtodeterminelongitudeadditionaldecimalfor the mid-value between thosetabulat-Whena body is on the local celestial meridian,its GHAed(exceptthat1.00iscorrectfor0°and0.00for90°).Otheristhe same as thelongitude of the observer if in west longi-valuescanbefoundbyinterpolationtude, or 360- in east longitude. Thus, ifthe GMT of localThe length of the day varies with latitude.Hence, lat-time oftransit is determined and atableofGreenwich houritude can be determined ifthe elapsed time between sunriseangles(ortime of transitof theGreenwichmeridian)isand sunset can be accurately observed.Correct the ob-available,longitude can be computed.If only theequationserved length of dayby adding 1minutefor each 15ofoftime is available,the method can be used withthe sunlongitudetraveledtowardtheeastandsubtractinglminuteThis is thereverse of theproblem of finding thetime offor each15'of longitude traveled toward thewest.The lat-transit ofa body.The timeoftransit is notalways apparentitudedetermined bylength of day is the value for the timeIfa curve is made ofaltitude versus time,as suggestedpre-of meridian transit.Since meridian transit occurs approxi-viously,the time corresponding to the highest altitude ismatelymidwaybetween sunrise and sunset, half theusedinthedeterminationoflongitude.Undersomecondi-intervalmaybe observed and doubled.If a sunrise and sun-tions, it may be preferableto observe an altitude beforemeridiantransit,and then again after meridian transit, whensettable isnot available,the lengthof daylight can bedeterminedgraphically using a diagram on the plane of thethebodyhas returnedtothesamealtitudeas atthefirstob-servation.Meridian transit occurs midway between thesecelestialmeridian,as explained in Chapter15.Amaneuver-two times.Abody in the zenith is on the celestial meridian.ing board is useful for this purpose.This method cannot beIfaccurateazimuthmeasurementisavailable,notethetimeused near the time of the equinoxes and is of little valuewhentheazimuthis000°or180°near the equator.The moon can be used if moonrise andmoonsettables areavailable.However,withthemoon,theThedifferencebetween theobserved GMT of sunriseorsunset and the LMT tabulated in the almanac is the longitude in-time units, which can then be converted to angular measure.IfECassiopeiaetheNautical Almanac isused,this information is tabulatedforeachthirddayonly.Greateraccuracy canbeobtained ifinterpo★★★*lation is used for determining intermediate values.Moonrise or★moonsetcanbeused ifthetabulated LMT is correctedforlongitude.Planets and stars can be used if thetime of risingorsetting can be determined. This can be computed, or approxi-N.CELESTIALPOLEPolarismated using a diagram on theplane of the celestial meridian★★(See Chapter 15, Navigational Astronomy)-***TOAEither of thesemethods can beused in reverse to setawatchthat hasrun downortocheck the accuracyofawatch+ifthe longitudeis known.In the case of a meridian transitAlkaidthetimeneednot bedetermined at the instantoftransit.The---watch is started.and thealtitudeisthenmeasured severaltimes beforeand after transit, or at equal altitudes beforeand after.The times of these observations arenoted,andfrom them the time of meridian transit is determined.TheFigure2611.RelativepositionsofeCassiopeiae,PolarisdifferencebetweenthistimeandthecorrecttimeoftransitandAlkaidwithrespecttothenorthcelestial polecan then beused as a correctiontoresetthe watch

388 EMERGENCY NAVIGATION this correction can be estimated. The trailing star of Cassi￾opeia (∈ Cassiopeiae) and Polaris have almost exactly the same SHA. The trailing star of the Big Dipper (Alkaid) is nearly opposite Polaris and ∈ Cassiopeiae. These three stars, ∈ Cassiopeiae, Polaris, and Alkaid, form a line through the pole (approximately). When this line is hori￾zontal, there is no correction. When it is vertical, the maximum correction of 56’ applies. It should be added to the observed altitude if Alkaid is at the top, and subtracted if ∈ Cassiopeiae is at the top. For any other position, esti￾mate the angle this line makes with the vertical, and multiply the maximum correction (56’) by the factor from Table 2604, adding if Alkaid is higher than ∈ Cassiopeiae, and subtracting if it is lower. For more accurate results, the factor from Table 2604 can be considered accurate to one additional decimal for the mid-value between those tabulat￾ed (except that 1.00 is correct for 0° and 0.00 for 90°). Other values can be found by interpolation. The length of the day varies with latitude. Hence, lat￾itude can be determined if the elapsed time between sunrise and sunset can be accurately observed. Correct the ob￾served length of day by adding 1 minute for each 15’ of longitude traveled toward the east and subtracting 1 minute for each 15’ of longitude traveled toward the west. The lat￾itude determined by length of day is the value for the time of meridian transit. Since meridian transit occurs approxi￾mately midway between sunrise and sunset, half the interval may be observed and doubled. If a sunrise and sun￾set table is not available, the length of daylight can be determined graphically using a diagram on the plane of the celestial meridian, as explained in Chapter 15. A maneuver￾ing board is useful for this purpose. This method cannot be used near the time of the equinoxes and is of little value near the equator. The moon can be used if moonrise and moonset tables are available. However, with the moon, the half-interval method is of insufficient accuracy, and allow￾ance should be made for the longitude correction. The declination of a body in zenith is equal to the lat￾itude of the observer. If no means are available to measure altitude, the position of the zenith can be determined by holding a weighted string overhead. 2612. Longitude Determination Unlike latitude, determining longitude requires accurate Greenwich time. All such methods consist of noting the Greenwich time at which a phenomenon occurs locally. In addition, a table indicating the time of occurrence of the same phenomenon at Greenwich, or equivalent information, is needed. Three methods may be used to determine longitude. When a body is on the local celestial meridian, its GHA is the same as the longitude of the observer if in west longi￾tude, or 360 - λ in east longitude. Thus, if the GMT of local time of transit is determined and a table of Greenwich hour angles (or time of transit of the Greenwich meridian) is available, longitude can be computed. If only the equation of time is available, the method can be used with the sun. This is the reverse of the problem of finding the time of transit of a body. The time of transit is not always apparent. If a curve is made of altitude versus time, as suggested pre￾viously, the time corresponding to the highest altitude is used in the determination of longitude. Under some condi￾tions, it may be preferable to observe an altitude before meridian transit, and then again after meridian transit, when the body has returned to the same altitude as at the first ob￾servation. Meridian transit occurs midway between these two times. A body in the zenith is on the celestial meridian. If accurate azimuth measurement is available, note the time when the azimuth is 000° or 180°. The difference between the observed GMT of sunrise or sunset and the LMT tabulated in the almanac is the longitude in time units, which can then be converted to angular measure. If the Nautical Almanac is used, this information is tabulated for each third day only. Greater accuracy can be obtained if interpo￾lation is used for determining intermediate values. Moonrise or moonset can be used if the tabulated LMT is corrected for lon￾gitude. Planets and stars can be used if the time of rising or setting can be determined. This can be computed, or approxi￾mated using a diagram on the plane of the celestial meridian (See Chapter 15, Navigational Astronomy). Either of these methods can be used in reverse to set a watch that has run down or to check the accuracy of a watch if the longitude is known. In the case of a meridian transit, the time need not be determined at the instant of transit. The watch is started, and the altitude is then measured several times before and after transit, or at equal altitudes before and after. The times of these observations are noted, and from them the time of meridian transit is determined. The difference between this time and the correct time of transit can then be used as a correction to reset the watch. Figure 2611. Relative positions of ∈ Cassiopeiae, Polaris, and Alkaid with respect to the north celestial pole