Theodolitetraversing

Theodolite

1. Theodolite Traversing
Unit-V

2. Syllabus
TheodoliteSurveying:
•Objective,variouspartsoftransittheodolite,technical
terms,temporaryandpermanentadjustmentsofa
transit,measuringhorizontalandverticalangles,
methodsofrepetitionandreiteration,computationof
latitudeanddeparture,balancingoftraversebyBow-
Ditch‟stransitrule,thirdruleandmodifiedtransit
rules,missingdataproblems,Precautionsinusing
theodolite,errorsintheodolitesurvey,useoflatitude
anddepartureforareacalculation,Galestraverse
table.

3. Introduction
•Thetheodoliteisanintricateinstrumentused
mainlyforaccuratemeasurementofhorizontal
andverticalangleupto10”or20”,depending
upontheleastcountoftheinstrument.Because
ofitsvarioususes,thetheodoliteissometimes
knownas“UniversalInstrument”.

4. Theodolite

5. Introduction
•Thefollowingarethedifferentpurposeforwhichthe
theodolitecanbeused:
•MeasuringHorizontalAngle
•MeasuringVerticalAngles
•MeasuringDeflectionAngles
•MeasuringMagneticBearing
•Measuringthehorizontaldistancebetweentwopoints
•Findingtheverticalheightofanobject
•Findingdifferenceofelevationbetweenvariouspoints
•Rangingofaline.

6. Introduction

7. Theodolite Traversing
Theodolitesmaybeoftwotypes
•(i)TransitTheodolite
•(ii)Non-Transit
•Inthetransittheodolite,thetelescope,the
telescopecanberevolvedthroughacomplete
revolutionaboutitshorizontalaxisinavertical
plane.
•Inthenontransittheodolite,thetelescope,cannot
berevolvedthroughacompleterevolutioninthe
verticalplane.

8. Transit Theodolite & Non-Transit

9. Definitions
Centring
•Thesettingofatheodoliteexactlyoverastationmarkbymeans
ofaplumbbob.Isknownascentering.
Transiting
•Themethodofturningthetelescopeaboutitshorizontalaxisin
averticalplanethrough180
0
istermedastransiting.Inother
wordstransitingresultsinachangeinface.
Faceleft
•„Faceleft‟meansthattheverticalcircleofthetheodoliteison
theleftoftheobserveratthetimeoftakingreading.

10. Optical Plummet

11. Definitions
Faceright
Thisreferstothesituationwhentheverticalcircleofthe
instrumentisontherightoftheobserverwhenthereadingis
taken
Changingface
Theoperationofbringingtheverticalcirclefromonesideof
theobservertotheotherisknownaschangingface.
Swingingthetelescope
Thisindicatesturningthetelescopeinahorizontalplane.Itis
called„rightswing‟whenthetelescopeisturnedclockwise
and„leftswing‟whenthetelescopeisturnedanticlockwise.

12. The Transit Theodolite

13. Definitions
LineofCollimation
•Itisanimaginarylinepassingthroughoptical
centreoftheobjectiveglassanditscontinuation.
AxisofTelescope
Theaxisisanimaginarylinepassingthroughthe
opticalcentreoftheobjectglassandtheoptical
centreoftheeye-peace.
AxisoftheBubbleTube
•Itisanimaginarylinetangentialtothelongitudinal
curveofthebubbletubeatitsmiddlepoint.

14. Axis of Theodolite

15. Difinitions
VerticalAxis
•itistheaxisofrotationofthetelescopeinthehorizontal
plane
HorizontalAxis
•Itistheaxisofrotationofthetelescopeintheverticalplane.
TemporaryAdjustment
•Thesettingifthetheodoliteoverastationatthetimeof
takinganyobservationiscalledtemporaryadjustment.
PermanentAdjustment
•Whenthedesiredrelationshipbetweenthefundamental
linesofatheodoliteisdisturbed,thensomeproceduresare
adoptedtoestablishthisrelationship.Thisadjustmentis
knownaspermanentadjustment.

16. Difinitions
LeastCountofthevernier
•Thisisthedifferencebetweenthevalueofthesmallest
divisionofthemainscaleandthatofthesmallestdivisionof
thevernierscale.Itisthesmallestvaluethatcanbemeasured
byatheodolite.
•V=d
n
Where,v=ValueofsmallestdivisionofvernierScale
d=Valueofthesmallestdivisionofmainscale
n=noofsmalldivisionsonvernierscale.
Leastcountoftheodolitesaregenerally20”and15”andsoon.

17. Difinitions
TheDiaphragm
•Thediaphragmisabrassringconsistingof
cross-hairs,oronecontainingaglassdiscwith
finelinesengravedonit.Itisplacedinposition
byturningfourcapstan-headedscrews,andcan
bemovedup,downorsidewayswhenrequired.
Itisfixedinfrontoftheeye-piece.Thecross-
hairsmaybemadeoffineplatinumwire.

18. Difinitions

19. The Transit Theodolite
Trivet
•Itisacircularplatehavingacentral,threaded
holeforfixingthetheodoliteonthetripod
standbyawingnut.Itisalsocalledthebase
plate.Threefootscrewsaresecuredtothis
platebymeansofaballandsocket
arrangement.Andtheupperthreadedpart
passesthroughthethreadedholeinthetribrach
plate.

20. The Transit Theodolite

21. The Transit Theodolite
FootScrews
•Thesearemeantforlevelingtheinstrument.Thelowerpart
ofthefootscrewaresecuredinthetrivetbymeansofaball
andsocketarrangementandtheupperthreadedpartpasses
throughthethreadedholeinthetribrachplate.
Tribrach
•Itisatriangularplatecarryingthreefootscrewsatitsends.
Levelinghead
•thetrivet,footscrewsandthetribrachconstitutingabody
whichisknownasthelevelinghead.
Spindles
•Thetheodolitesconsistsoftwospindlesoraxes-oneinner
andtheotherouter.Theinneraxisissolidandconical,and
theouterishollow.Thetwospindlesarecoaxial.

22. The Transit Theodolite

23. The Transit Theodolite
LowerPlate
•Thelowerplateisattachedtotheouteraxis,andisalso
knownasthescaleplateItisbeveledandthescaleis
graduatedfrom0
0
to360
0
.
UpperPlate
•TheupperplatecontainsthevernierscaleAandB.Itis
attachedtotheinneraxis.Itsmotioniscontrolledbythe
upperclampscrewandtheuppertangentscrew.When
theclampscrewistightenedthevernierscalearefixed
withtheinneraxis,andforfineadjustmentofthescale
thetangentscrewisrotated.

24. Upper Plate & Lower Plate

25. The Transit Theodolite
PlateBubble
•Twoplatebubblesaremountedatrightanglestoeachotheron
theuppersurfaceofthevernierplate.Onebubbleiskeptright
paralleltothehorizontalaxisofthetheodolite.Sometimesone
platebubbleisprovidedonthevernierplate.Thebubbleare
meantforlevelingthisinstrumentatthetimeofmeasuringthe
horizontalangle.
Standardor„A‟Frame
•Twoframesareprovidedontheupperplatetosupportthe
telescope,theverticalcircleandthevernierscales.These
framesareknownasstandardA-Frames.

26. The Transit Theodolite

27. The Transit Theodolite
TheTelescope
•Thetelescopeispivotedbetweenthestandardatright
anglestothehorizontalaxis.Itcanberotatedaboutits
horizontalaxisinaverticalplane.Thetelescopeis
providedwithafocusingscrew,clampingscrewand
tangentscrew.
VerticalCircle
•Theverticalcircleisrigidlyfixedwiththetelescopeand
moveswithit.Itisdividedintofourquadrants.Each
quadrantisgraduatedfrom0to90
0
inopposite
directions,withthe„Zero‟markattheendofthe
horizontaldiameteroftheverticalcircle.

28. The Transit Theodolite

29. The Transit Theodolite
IndexbarorT-frame
•Theindexbarisprovidedonthestandardin
frontoftheverticalcircle.Itcarriestwovernier
(CandD)atthetwoendsofthehorizontal
arm.Theverticallegoftheindexbaris
providedwithaclipscrewatthelowerendby
meansofwhichthealtitudebubblecanbe
broughttothecentre.

30. The Transit Theodolite
Altitudebubble
•Alongsensitivetubeisprovidedonthetopof
indexbar.Thisbubbleisbroughttothecentreby
theclipscrewatthetimeofmeasuring.Ofthe
verticalangle.
Compass
•Sometimesacircularboxcompassismountedon
thevernierscalebetweenthestandards.Inmodern
theodolites,anadjustabletroughcompassor
tubularcompasscanbefittedwithascrewtothe
standard.

31. The Transit Theodolite
ReadingofVernierTheodolite
Theleastcountofthevernieristodeterminedfirst.
Letitbe20”.Themaindivisionofthemainscale
isofonedegree.Supposeitisdividedintothree
partstheneachpartaccountsfor20‟(i.e.d=20‟)
Thevernierscalehas20bigand60smalldivisions
LeastCount=d=20x60=20”
n60
Here,Leastcountforonesmalldivisions=20”

32. The Transit Theodolite
Therefore,Leastcountofonebigdivision
=(20”x3)=60”=1‟
Aftermakingthefinaladjustmentformeasuringtheangle,
thepositionofthearrowofthevernierscaleisnoted.
Supposethearrowcrosses10
0
and20‟,whichisthe
directreadingobtainedfromthemainscale.Suppose,
againthatthefirstsmalldivisionafter12bigdivision
exactlycoincideswithanyofthemainscaledivisions.
Thenthevernierreading12‟20”
ThereforeFinalAngle=10
0
20‟+12‟20”=10
0
32‟20”

33. The Transit Theodolite
TemporaryAdjustmentofTheodolite
•Settingthetheodoliteoverthestation
•Thetripodstandisplacedovertherequired
station.Thetheodoliteisthenshiftedfromthe
boxandfixedontopofthestandbymeansofa
wingnutoraccordingtothefixedarrangement
providedalongwiththeinstrument.

34. The Transit Theodolite

35. The Transit Theodolite
ApproximatelevelingbyTripod
•Thelegsofthetripodstandareplacedwell
apartandfirmlyfixedontheground.Then,
approximatelylevelingisdoneusingthisstand,
Todothis,twolegsarekeptfirmlyfixedonthe
groundandthirdismovedinorout,clockwise
oranticlockwise,sothatthebubbleis
approximatelyatthecentreofitsrun.

36. The Transit Theodolite

37. The Transit Theodolite
Centring
•Centringistheprocessofsettingofthe
instrumentsexactlyoverastation.Atthetime
ofapproximatelevelingbymeansofthetripod
stand,itshouldbeensuredthattheplumbbob
suspendedfromthebookunderthevertical
axisliesapproximatelyoverthestationpeg.

38. The Transit Theodolite

39. The Transit Theodolite
Leveling
•Beforestartingthelevelingoperation,allthefoot
screwarebroughttothecentreoftheirrun.Then
thefollowingprocedureisadopted.
•(a)Theplatebubbleisplacedparalleltoanypair
offootscrews.Byturningboththesescrews
equallyinwardsoroutwards.
•Theplatebubbleisturnedthrough90
0
sothatitis
perpendiculartothelinejoiningthefirstand
secondfootscrews.Thenbyturningthethirdfoot
screweitherclockwiseoranticlockwisethebubble
isbroughttothecentre.

40. The Transit Theodolite

41. The Transit Theodolite
•Someinstrumentsmayhavetwoplatebubblesperpendicularto
eachother.Insuchacase,onebubbleiskeptparalleltoanypair
offootscrews;theotherplatybubblewillautomaticallybe
perpendiculartothepositionoffirstbubble.Here,the
instrumentsneednotbeturned.Thefirstbubblecanbebrought
tothecentrebyturningthefirstandsecondfootscrews,andthe
secondbubblecanbebroughttothecentrebyturningthethird
footscrew.
•Theprocessisrepeatedseveraltimes,sothatthebubbleremains
inthecentralpositionoftheplatybubble,bothdirections
perpendiculartoeachother.
•Theinstrumentisrotatedthrough360
0
aboutitsverticalaxis.If
thebubblestillremainsinthecentreposition,theadjustmentof
thebubbleisperfectandtheverticalaxisistrulyvertical.

42. The Transit Theodolite
FocusingoftheEyePiece
•Theeyepieceisfocusedsothatthecross-hairs
canbeseenclearly.Todothis,thetelescopeis
directedtowardstheskyorapieceofwhite
paperisheldinfrontoftheobjectglass,andthe
eye-pieceismovedinoroutbyturningitin
clockwiseoranticlockwiseuntilthecross–hairs
appeardistinctandsharp.

43. The Transit Theodolite
SettingtheVernier
•ThevernierAissetto0
0
andvernierBis180
0
.
Todothisthelowerclampisfixed.Theupper
clampisloosenedandtheupperplateturneduntil
thearrowofvernier.Aapproximatelycoincides
withzero.AndthevernierBapproximately
coincideswiththe180
0
mark.Thentheupper
clampistightened,andbyturningtheupper
tangentscrewthearrowsarebroughttoaposition
ofexactcoincides.

44. The Transit Theodolite

45. Permanent Adjustment of Theodolite
•Atheodoliteconsistsofseveralfundamental
lines.Inorderthereadingstobeaccurate,
certaindesiredrelationshipmustexistbetween
thefundamentallinesoftheinstrument.But
duetoimproperhandlingorexcessiveuse,this
relationshipmaybedisturbedandhencefrom
thetheodolitemayleadtoerroneousresults.

46. Permanent Adjustment of Theodolite
•Forrectifyingadisturbedrelationship,some
procedures,termedpermanentadjustmentsare
adopted.
•Thefundamentallinesofatheodoliteare:
•Theverticalaxis
•Theaxisoftheplatelevel
•Thelineofcollimation
•Thehorizontalaxisortrunnionaxis
•Thebubblelineofthealtitudelevel

47. Permanent Adjustment of Theodolite
Thedesiredrelationshipsbetweenthefundamentallines
areasfollows:
•Theaxisoftheplatelevelmustbeperpendiculartothe
verticalaxis
•Thelineofcollimationshouldcoincidewiththeoptical
axisofthetelescopeandshouldalsobeperpendicularto
theverticalaxis.
•Theaxisoftelescopemustbeparalleltothelineof
collimation.
•Thelineofcollimationmustbeperpendiculartothe
horizontalaxis.Andtheverticalcircleshouldreadzero
whenthelineofcollimationishorizontal.

48. Permanent Adjustment of Theodolite
Tomaketheaxisoftheplatelevelperpendiculartothevertical
axis,thefollowingprocedureisadoptedpriortothefirst
adjustment.
•Thetheodoliteissetuponfirmgroundwithitslegswellapart,and
firmlyfixedontheground.
•Theplatebubbleismadeparalleltoanypairoffootscrews,andbrought
tothecentreofitsrunbyturningtheconcernedfootscrews.
•Thebubbleisturnedthrough90
0
andthenbroughttothecentreby
turningthethirdfootscrew.
•Theprocessisrepeatedseveraltimesuntilthebubbleisperfectly
centeredinthesetwopositions.
•Thebubbleisturnedthrough180
0
abouttheverticalaxis.
•Ifthebubblestillremainsinthecentralposition,theaxisofthebubbleis
perpendiculartotheverticalaxiswhichmaybeassumedtobetruly
vertical.
•Ifthebubbledoesnotremaininthecentralpositiontheamountof
deviationisnoted,sayitis2ndivision.

49. Permanent Adjustment of Theodolite
Adjustment
•Halfofthetotal(i.e.ndivision)isadjustedbymeans
ofthecapstanheadednutprovidedbelowthebubble
tube.
•TheRemaininghalf(i.e.ndivisionisadjustedby
turningtheconcernedfootscrews.
•Theprocessisrepeatedseveraltimesuntilthebubble
remaininthecentralpositionforanydirectionofthe
bubbletube.

50. Permanent Adjustment of Theodolite
Tomakethelineofcollimationcoincidewiththeopticalaxisofthe
telescope,firstthehorizontalandthenverticalhairareadjusted.
•AdjustmentofHorizontalHair.
•ThreepegsaredrivenintothegroundatT,AandBaknown
distanceapart.
•ThetheodoliteissetupatTandafterproperadjustmentstaffare
takenonAandB.SupposethereadingsareAaandBb
1
•BytransistingthetheodolitethestaffreadingaretakenonAandB
•Ifthereadingsofthesecondobservationtallieswiththoseofthefirst
horizontalhairisinadjustment.
•Ifthesecondobservationgivesanewreading,sayBb
2,thenthe
horizontalhairrequiresadjustment.

51. Adjustment of Horizontal Hair.

52. Permanent Adjustment of Theodolite
AdjustmentofVerticalHair
•ThetheodoliteissetupatT.Afterproperleveling,a
rangingrodisfixedatAbylookingthroughthe
telescopekeepingtheupperandlowerclampsfixed.
•BytransistingthetelescopearangingrodisfixedatB
•Theupperclampisloosenedandbyturningthevernier
platetherangingrodatAisagainbisected.
•Iftherangingrodatbisseenbisectedaftertransisting
thetelescope,theverticalhairisperfect.
•Ifnot,theamountoferrorisnoted,letBB
1bethetotal
error.

53. Adjustment of Vertical Hair

54. Permanent Adjustment of Theodolite
Adjustment
•ApositionismarkedbyarangingrodatB‟,where
B
1B‟isonefourthofthetotalerror.
•Theverticalhairisshiftedbyturningthehorizontal
diaphragmscrews,tobisecttherangingrodatB‟
•Duringadjustment,one-fourthofthetotalerroris
takenintoconsiderationbecausetheactualerroris
magnifiedfourtimesasthetelescopewasturned
twiceintheverticalplane.

55. Permanent Adjustment of Theodolite
ThirdAdjustment
•Tomakethehorizontalaxisperpendiculartotheverticalaxis,the
followingprocedureisadoptedbeforemakingthenecessary
adjustment.
•ThetheodoliteissetupatTsomedistanceawayfromapoleP.
•Theplatebubbleisperfectlyleveled.Lookingthroughthetelescope,
awelldefinedpointAismarkedonthepole.Theupperandlower
clampscrewsarekeptfixed.
•ThetelescopeisloweredandanotherpointBismarkednearthe
baseofthepoleinthesamelineofsight.
•Theupperclampisloosenedandtelescopeisturnedthrough180
0
.
bytransistingit,themarkAisbisected.Thetelescopeisthen
lowered.IfthelineofsightbisectthemarkB,thentheadjustmentis
perfect.
•Ifnot,anotherpointB‟ismarkedonarangingrodRatthesame
levelasB

56. Adjustment of Vertical Hair

57. Permanent Adjustment of Theodolite
Adjustment
•ApointCismarked(inasuitableway)mid-waybetween
BandB‟
•ThepointCisbisectedbythetelescopeandtheupper
clampistightened.
•Thetelescopeisnowraised.Thistimethelineofsight
willnotbisectA.
•Theadjustmentendofthehorizontalaxisisraisedor
lowereduntilthelineofsightbisectsthemarkA.
•Theprocedureisrepeatedseveraltimesuntilthe
correctionisperfect.

58. Permanent Adjustment of Theodolite
FourthAdjustment
•Tomaketheaxisofthetelescopelevel(altitude
bubble)paralleltothelineofcollimation,the
procedureofadjustmentisexactlysimilarto
“Two-PegMethod”

59. Permanent Adjustment of Theodolite
FifthAdjustment
•Thisadjustmentismadeinordertoensurethatthevertical
circlereadzerowhenthelineofcollimationishorizontal.
•Thisadjustmentisnotrequiredfortransittheodolite.Thisis
becauseinsuchatheodolitethevernierisadjustableand
clampedatzerowhenthealtitudebubbleiscentered.
•Intheodoliteprovidedwithnon-adjustableverniers,the
readingoftheverniermaynotbezerowiththealtitude
bubbleiscentered.Insuchacase,theamountofangular
error,knownas“indexerror”isnoted.Thesignoftheindex
errorshouldbetakenintoaccount.Necessarycorrectionhas
tobeappliedtotheobservedverticalangleaccordingtothe
signofindexerror.

60. Some Modern Theodolites
•Geodeticandastronomicalsurveysrequireahighdegreeof
precision.Inordertomeetthisneeds,high–precession
theodolitesaremanufacturednowadays.Thecharacteristics
ofmoderntheodolitesareasfollows:
•Theyaremorecompactandlight
•Thegraduationsaremadeonaglasscircleandarefiner.
•Improvedmicrometerusingwhichtheobservercantake
readingsaccuratelytoonesecond,areprovidedalongwith
them.
•Theinstrumentismadewaterproofanddustproof
•Itiselectricallyilluminatedtofacilitateworkatnightorina
tunnel.
•Adjustmentsforthemicrometrearenotnecessary
•Magnificationishigher.

61. Some Modern Theodolites
WattMicro-OpticTheodolite
•Therearethreemodelsofthistype.Thefirstand
thethirdmodelarecapableofreadingupto5”,
andthesecondcanreadupto1”.Thehorizontal
andverticalcirclesofthistheodolitesaremadeup
ofglass.Micrometersformeasuringhorizontaland
verticalanglesareprovided.Theotheraccessories
arethesameasinthetransittheodolite.Butthe
arrangementareverycompact,andwellprotected
fromatmosphericaction.

62. Watt Micro-Optic Theodolite

63. Some Modern Theodolites
WildT-2Theodolite
•Thehorizontalandverticalcirclesofthis
instrumentaremadeofglass.Thediameterofthe
horizontalcircleis90mmandthatofthevertical
circle70mm.Thecirclesareelectrically
illuminatedthroughanadjustablemirror.
•Theinstrumentisautomaticallycenteredbyits
ownweight.Thereadingsaretakenthrougha
micrometrebythecoincidencesystem

64. Wild T-2 Theodolite

65. Some Modern Theodolites
WildT-3PrecessionTheodolite
•Thehorizontalandverticalcirclesaremadeof
glassandfinallygraduated.Theminimumreading
ofthehorizontalcircleis4‟andthatofvertical
circleis8‟.Theangleismeasuredbmeansofan
opticalmicrometerwhichisaccurateupto0.2”.
Theverticalaxisconsistsofanaxisbushandball
bearings.
•Theinstrumentisautomaticallycenteredbyits
ownweight.Itconsistsofonesetofclampand
tangentscrewsforthemotionoftheverticalaxis.

66. Wild T-3 Precession Theodolite

67. Some Modern Theodolites
WildT-4UniversalTheodolite
•Thisinstrumentiswidelyusedinthe
determinationofgeographicalpositions,andfor
takingastronomicalobservationswiththeutmost
precision.Itconsistofahorizontalcircleofdia250
mmandaregraduatedtoaminimumreadingof
2‟.Withtheopticalmicrometre,onecantake
readingaslowas0.1”.Theverticalandhorizontal
circlesoftwodiametricallyoppositereadings
automaticallywhichgivesthearithmeticmeanof
twodiametricallyoppositereadingsautomatically.

68. Wild T-4 Universal Theodolite

69. Some Modern Theodolites
TheTailstockTheodolite
•Thehorizontalandverticalcirclesaremadeof
graduatedthatareadingaslowas1”canbe
taken,anoneof0.25”canbeestimated.A
singleopticalmicrometerisprovidedforboth
thescalesbothcirclesareilluminatedbya
singlemirrorisprovidedwithscaleplummet
forcenteringoverthestation

70. The Tailstock Theodolite

71. Sources of Error in Theodolite
InstrumentErrors
Non-adjustmentofplatebubble
•Theaxisoftheplatebubblemaynotbe
perpendiculartoverticalaxis.So.Whentheplate
levelarecentered,theverticalaxismaynotbetruly
vertical.Insuchacase,thehorizontalcirclewould
beinclinedandtheanglewillbemeasuredinan
inclinedplane.Thiswouldcauseanerrorinangle
measured.
•Thiserrormaybeeliminatedbylevelingthe
instrumentwithreferencetothealtitudebubble.

72. Sources of Error in Theodolite
Lineofcollimationnotbeingperpendicularto
horizontalaxis
•Inthiscase,aconeisformedwhenthe
telescopeisrevolvedintheverticalplane,and
thiscausesanerrorintheobservation.
•Thiserroriseliminatedbyreadingtheangle
fromboththefaces(leftandright)andtakethe
averageofthereading.

73. Sources of Error in Theodolite
Horizontalaxisnotbeingperpendicularto
verticalaxis
•Ifthehorizontalaxisisnotperpendiculartothe
verticalaxis,thereisanangularerror.Thisis
eliminatedbyreadingtheanglefromboththe
faces.

74. Sources of Error in Theodolite
Lineofcollimationnotbeingparalleltoaxisof
telescope.
•Ifthelineofcollimationisnotparalleltothe
axisoftelescope,thereisanerrorinthe
observedverticalangle.Thiserroriseliminated
bytakingreadingfrombothfaces.

75. Sources of Error in Theodolite
EccentricityofInnerandOuteraxes
•Thisconditioncausesanerrorinvernier
readings.Thiserroriseliminatedbytaking
readingfromboththevernierandconsidering
theaveragereadings.

76. Sources of Error in Theodolite
GraduationnotbeingUniform
•Theerrorduetothisconditioniseliminatedby
measuringtheanglesseveraltimesondifferent
partsofthecircle.

77. Sources of Error in Theodolite
VernierbeingEccentric
•Thezerosoftheverniershouldbe
diametricallyoppositetoeachother.When
vernierAissetat0
0
,VernierBshouldbeat
180
0
,Butinsomecases,thisconditionmay
notexist.
•Thiserroriseliminatedbyreadingboth
verniersandtakingtheaverage.

78. Sources of Error in Theodolite
PersonalError
•Thecenteringmaynotbedoneperfectly,dueto
carelessness.Thelevelingmaynotbedonecarefully
accordingtousualprocedure.Iftheclampscrewsare
notproperlyfixed,theinstrumentmayslip.Theproper
tangentscrewmaynotbeoperatedThefocusingin
ordertoavoidparallaxmaynotbeperfectlydone.
•Theobjectofrangingrodmaynotbebisectedaccurately
Theverniermaynotbesetinproperplace.
•Errorwouldalsoresultiftheverniersarenotread
becauseofoversight.

79. Sources of Error in Theodolite
NaturalErrors
•Hightemperaturecauseserrorduetoirregular
refraction.
•Highwindcausesvibrationintheinstrument,
andthismayleadtowrongreadingsonthe
verniers.

80. Direct Method of Measuring
Horizontal Angle
•SupposeanangleAOBistobemeasured.The
followingprocedureisadopted:
•TheinstrumentissetupoverO.Itiscenteredand
leveledperfectlyaccordingtotheproceduredescribed
fortemporaryadjustment.Supposetheinstrumentwas
initiallyinthefaceleftposition.
•Thelowerclampisfixed.Theupperclampisloosened
andbyturningthetelescopeclockwisevernierAissetto
0
0
andvernierBtoapproximately180
0
.Theupper
clampisthentightened.Nowbyturningtheupper
tangentscrew,vernierAandBaresettoexactly0
0
and
180
0
bylookingthroughmagnifyingglass.

81. Direct Method of Measuring
Horizontal Angle

82. Direct Method of Measuring
Horizontal Angle
•Theupperclampistightfixed.Theloweroneis
loosenedandthetelescopeisdirectedtothelefthand
objectA.TherangingrodatAisbisectedapproximately
byproperfocusingthetelescopeandeliminating
parallax.Thelowerclampistightened,andbyturning
thelowertangentscrewtherangingtodatAisaccurately
bisected.
•Thelowerclampiskeptfixed.Theupperclampis
loosenedandthetelescopeisturnedclockwiseto
approximatelybisecttherangingrodatBbyproper
focusingthetelescope.Theupperclampistightened,
andtherangingrodatBbisectedaccuratelybyturning
theupperplatescrew.

83. Direct Method of Measuring
Horizontal Angle
•ThereadingonvernierAandBarenoted.VernierAgives
theangledirectly.ButinthecaseofvernierB,theangleis
obtainedbysubtractingtheinitialreadingfromfinalreading.
•Thefaceoftheinstrumentischangedandtheprevious
procedureisfollowed.Thereadingoftheverniersarenoted
inthetable.
•Themeanoftheobservations(i.e.Faceleftandfaceright)is
theactualangleAOB.Thetwoobservationsaretakento
eliminateanypossibleerrorsduetoimperfectadjustmentof
theinstrument.
•Thetwomethodsofmeasuringhorizontalanglearethoseof
repetitionandreiteration.

84. Direct Method of Measuring
Horizontal Angle
RepetitionMethod
•Inthismethod,theangleisaddedanumberof
times.Thetotalisdividedbythenumberof
readingtogettheangle.Theangleshouldbe
measuredclockwiseinthefaceleftandface
rightpositions,withthreerepetitionateach
face.Thefinalreadingofthefirstobservation
willbetheinitialreadingofthesecond
observation,andsoon.

85. Direct Method of Measuring
Horizontal Angle
•SupposetheangleAOBistobemeasuredbytherepetition
process.ThetheodoliteissetupatO.Theinstrumentis
centeredandleveledproperly.VernierAissetto0
0
and
vernierBto180
0
.
•Theupperclampisfixed,andtheloweroneisloosened.By
turningthetelescope,therangingrodatAisperfectlybisected
withthehelpofthelowerclampscrewandthelowertangent
screw.HeretheinitialreadingofvernierAis0
0
.
•Theupperclampisloosenedandthetelescopeisturned
clockwisetoperfectlybisecttherangingrodatB.Theupper
clampisclamped.SupposethereadingonvernierAis30
0
.
•Thelowerclampisloosenedandthetelescopeturned
anticlockwisetoexactlybisecttherangingrodatA.Here,the
initialreadingis30
0
forthesecondobservation.

86. Direct Method of Measuring
Horizontal Angle
•Thelowerclampistightened.Theupperoneisloosenedand
telescopeisturnedclockwisetoexactlybisecttherangingrodatB.
ThereadingonvernierAis60
0.
•Theinitialreadingforthethirdobservationissetto60
0
.angleAOB
isagainmeasured.LetthefinalreadingonthevernierAis90
0
.
Whichistheaccumulatedangle.
•AngleAOB=AccumulatedAngle
NoofReading
=90
0
=30
0
3
•Thefaceoftheinstrumentischangedandthepreviousprocedureis
followed.
•ThemeanofthetwoobservationgivestheactualangleAOB

87. Repetition Method

88. Direct Method of Measuring
Horizontal Angle

89. Direct Method of Measuring
Horizontal Angle
ReiterationMethod
•Thismethodissuitablewhenseveralanglesare
measuredfromasinglestation.Inthismethodall
theanglearemeasuredsuccessivelyandfinallythe
horizonisclosed(i.e.anglebetweenthelastand
firststationismeasured)So,thefinalreadingof
theleadingvernierisequallydistributedamongall
theobservedangles.Ifitislarge,thereadings
shouldbecancelledandnewsetstaken.
•SupposeitisrequiredtomeasureAOBand
BOCfromO.Theprocedureisasfollows.

90. Direct Method of Measuring
Horizontal Angle
FirstSet
•ThetheodoliteisperfectlycenteredoverOandleveled
properlyintheusualmanner.Suppose,theobservation
istakeninthefaceleftpositionandthetelescopeis
turnedclockwise(rightSwing)
•VernierAissetto0
0
(i.e.360
0
)andvernierBto180
0
.
•Theupperclampisfixedandtheloweroneisloosened.
TherangingrodatAisperfectlybisected.Now,the
lowerclampistightened.
•Theupperclampisloosened,andtherangingrodor
objectatBisbisectedproperlybyturningthetelescope
clockwise.Thereadingsonboththeverniersaretaken
AOBisnoted.

91. Direct Method of Measuring
Horizontal Angle
•Similarly,theobjectCisbisectedproperly,andthe
readingontheverniersarenotedBOCis
recorded.
•Nowthehorizonisclosed,thelastangleCOAis
measured.Thepositionoftheleadingvernieris
noted.Theleadingverniershouldshowtheinitial
readingonwhichitwasset.Ifitdoesnot,the
amountofdiscrepancyisnoted.Ifitissmall,the
errorisdistributedamongtheangle.Ifthe
discrepancylarge,theobservationshouldbetaken
again.

92. Direct Method of Measuring
Horizontal Angle
SecondSet
•Thefaceoftheinstrumentischanged.Againthe
vernieraresetattheirinitialpositions.Thistimethe
anglesaremeasuredanticlockwise(leftSwing)
•Theupperclampisfixed,andtheloweroneloosened.
ThentheobjectAisperfectlybisected.
•Thelowerclampistightened.Thetelescopeisturned
anticlockwise,andtheobjectCbisectedbyloosening
theupperclampScrew.Thereadingonboththe
vernieraretakenCOAisnoted.

93. Direct Method of Measuring
Horizontal Angle
•ThentheobjectedBisbisectedbyturningthe
telescopeanticlockwise,andthereadingsonthe
vernieraretakenBOCisrecorded.
•Finally,thehorizonisclosedi.e.theobjectAis
bisected.Here,theleadingvernierAshouldshow
areading0
0
.ThelastangleAOBisnoted.
•Themeanangleofthetwosetsgivetheactual
valueoftheangle.Ifsomeerrorisfoundafter
arithmeticcheck,itshouldbeequallydistributed
amongtheangles.

94. Reiteration Method

95. Reiteration Method
B
A
C
O
Horizon Closed

96. Measuring Vertical Angle
•Theverticalangleistheonebetweenthehorizontalline(i.e.
lineofcollimation)andtheinclinedlineofsight.Whenitis
abovethehorizontalline,itisknownastheangleofelevation.
Whenthisangleisbelowthehorizontalline,itiscalledthe
angleofdepression.
•ConsiderSupposetheangleofelevationAOCandthatof
depressionBOCaretobemeasured.Thefollowing
procedureisadopted.
•Thetheodoliteissetupat0.Itiscenteredandleveled
properly.Thezerosofthevernier(generallyCandD)areset0
0
0
0
markoftheverticalcircle(whichisfixedtothetelescope)
thetelescopeisthenclamped.

97. Measuring Vertical Angle
•Theplatebubbleisbroughttothecentrewiththehelp
offootscrew.Thenthealtitudeisbroughttothe
centrebymeansofaclipscrew.Atthispositionthe
lineofcollimationisexactlyhorizontal.
•Tomeasuretheangleofelevation,thetelescopeis
raisedslowlytobisectthepointAaccurately.The
readingsonboththeverniersarenoted,andtheangle
ofelevationisrecorded.

98. Measuring Vertical Angle
•Thefaceoftheinstrumentischangedandthe
pointAisagainbisected.Thereadingonthe
vernierarenoted.Themeanoftheangleofthe
observedisassumedtobecorrectangleof
elevation.
•Tomeasuretheangleofdepression,thetelescope
isloweredslowlyandobservations(faceleftand
faceright)(Themeanangleoftheobservationis
takentobecorrectangleofdepression.

99. Measuring Vertical Angle
A
C
B
O
O
i

100. Computation of Latitude and Departure
•Thetheodoliteisnotplottedaccordingtointerior
anglesorbearings.Itisplottedbycomputingthe
latitudeanddepartureofthepointandthen
findingtheindependentcoordinatesofthepoint.
•Thelatitudeofalineisthedistancemeasured
paralleltotheNorth-Southlineandthedeparture
ofalinemeasuredparalleltotheEast-Westline.
•Thelatitudeanddepartureoflinesarealso
expressedinthefollowingways

101. Computation of Latitude and
Departure
•Northing=Latitudetowardsnorth=+L
•Southing=LatitudetowardsSouth=-L
•Easting=DeparturetowardsEast=+D
•Westing=DeparturetowardsWest=-D
•ConversionofWCBtoRB
WCB RB Quadrant
0 to 90
0
RB=WCB NE
90
0
and 180
0
RB= 180 –WCB SE
180
0
and 270
0
RB= WCB-180
0
SW
270
0
and 360
0
RB= 360
0
–WCB NW

102. Computation of Latitude and
Departure
Line Length (L) Reduced
Bearing (Ө)
Latitude
(LCOS Ө)
Departure
(L Sin Ө)
AB L NӨE + L cosӨ + L sin Ө
BC L SӨE -L cos Ө + Lsin Ө
CD L SӨW -L cos Ө -L sin Ө
DA L NӨW + Lcos Ө -L sin Ө
N
B
E
A
S
W
Departure= (L Sin Ө)
Latitude= (L Cos Ө)
Ө

103. Computation of Latitude and
Departure
Line Length Reduced
Bearing
Consecutive Coordinates
(L) (Ө) Northing
(+)
Southing
(-)
Easting
(+)
Westing
(-)
AB L NӨE L cosӨ L sin Ө
BC L SӨE Lcos Ө Lsin Ө
CD L SӨW Lcos Ө Lsin Ө
DA L NӨW L cosӨ Lsin Ө
Check for Closed Traverse
Sum of Northing= Sum of Southing
Sum of Easting= Sum of Westing

104. Computation of Latitude and
Departure
ConsecutiveCoordinates
•Thelatitudeanddepartureofapointcalculated
withreferencetotheprecedingpointforwhatare
calledconsecutivecoordinates.
IndependentCoordinates
•Thecoordinatesofanypointwithrespecttoa
commonoriginaresaidtobetheindependent
coordinatesofthatpoint.Theoriginmaybea
stationofthesurveyorapointentirelyoutsidethe
traverse.

105. Computation of Latitude and
Departure
BalancingofTraverse
•InCaseofClosedTraverse,thealgebraicsumoflatitude
mustbeequaltozeroandthatofdeparturemustalsobe
equaltozerointheidealcondition.Inotherwords,thesum
ofthenorthingmustequalthatofthesouthing,andthesum
oftheeastingmustbethesameasthatofthewesting.
•Butinactualpractice,someclosingerrorisalwaysfoundto
existwhilecomputingthelatitudeanddepartureofthe
traversestation.
•Thetotalerrorsinlatitudeanddeparturearedetermined.
Theseerrorsarethendistributedamongthetraversestations
proportionately,accordingtothefollowingrule.

106. Bowditch‟s Rule
•Bythisrule,thetotalerror(inlatitudeordeparture)is
distributedinproportiontothelengthofthetraverse
legs.Thisisthemostcommonmethodoftraverse
adjustment.
(a)Correctiontolatitudeofanyside
•=LengthofthatSidexTotalErrorinlatitude
PerimeterofTraverse
(b)Correctiontodepartureofanyside
•LengthofthatSidexTotalErrorindeparture
PerimeterofTraverse

107. Transit Rule
(a)CorrectiontolatitudeofanySide
LatitudeofthatSidexTotalErrorinLatitude
ArithmeticalSumofalllatitude
(b)CorrectiontodepartureofanySide
DepartureofthatSidexTotalErrorindeparture
ArithmeticalSumofallDeparture

108. Third Rule
(a)CorrectiontoNorthingofanySide
NorthingofthatSidex½totalerrorinlatitude
SumofNorthing
(b)CorrectiontoSouthingofanySide
Southingofthatsidex½totalerrorinlatitude
SumofSouthing
(c)CorrectiontoEastingofanySide
EastingofthatSidex½totalerrorindeparture
SumofEasting
(d)CorrectiontoWestingofanySide
=WestingofthatSidex½totalerrorindeparture
SumofWesting
Iftheerrorispositive,correctionwillbenegative,andviceversa.

109. References
•“Surveying and Leveling” Vol-I
Kanetkar and Kulkarni (2011)
•“Surveying and Leveling”
N.N.Basak

110. Thanks !