CHAPTER 2 TOPOGRAPHICAL SURVEY

Topographicsurveyingistheprocessofdeterminingthepositions,bothontheplanand elevation,ofthenaturalandartificialfeaturesofalocalityforthepurposeofdelineating thembymeansofconventionalsignsuponatopographic map. Topographydefinesthe shape or configuration of the earth’s surface. The basic purpose of a topographic map is to indicate the three-dimensional relationships for the terrain of any given area of land. Thus, on a topographic map, the relative positions of the points are represented both horizontallyas well as vertically.

The main objectives of traversing are:

Tobuildupaframeworkoftraverselegsandtraversestationswiththevisibility of all the features on the ground at least from each station so that it can be locatedfrom the instrument.

To provide control pointsfor chain surveying, plane tablingin flatgrounds

To fix the alignment of roads, canals, rivers, boundaries etc. when better accuracy is required.

Toascertaintheco-ordinatesof boundarypillarsin numericaltermsthatcan be preserved for future reference such as forest boundary pillars, international boundary pillarsetc.

To prepare a topographic map of the surveyed area for future use during different engineeringproject.

To make contours of a ground taking suitable intervals to provide an exact approximation of the nature of terrainand feasibility of a projectinthatarea.

Tomarkthepositionsofvariousimportantdetailsthatcaninduceeffectsonthe forthcoming project.

1.Reconnaissancesurveyoftheareatobesurveyed.Formaclosedtraverse(major andminor)aroundthepremisesoftheareabyfixingormarkingappropriateno. of stations (11-15). In the selection of the traverse stations the leg ratio, i.e. the ratiooflengthofthelongesttraverselegtothelengthofthesmallestleg,should be less than orequal to 1:2 for major traverse and1:3 for the minor traverse.

2.Two-way measurement of the traverse legs by means of a Total Station. Accuracy of two-way measurement in the case of major traverse is 1:2000 and 1:1000inthecaseofminortraverse.(Two-waymeasurement,i.e.measurement of the traverse leg in theforward as wellas in the backward direction.)

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6.Plotting of the traverse stations by co-ordinate method. An appropriate scale is selected, i.e. 1:1000 forthe traverse.

The equipment used forthe topographic survey are listedas follows

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The methodologyis based on the principles of surveying. Theyareas follows:

The different methodologies used forsurveying are explainedbelow.

2.5.1 Reconnaissance

The planning of work is the most important phase required to accomplish the work without any irregularity and difficulty in the scheduled time frame. So, for better planning, detailed inspection of the area is carried out which is known as reconnaissance survey.

Reconnaissance means the exploration or scouting of an area. In survey, it involves walking around the survey area and roughly planning the number of stations and the positions of the traverse stations. Recce is primarily done to get the overall idea of the site. This helps to make the necessary observations regarding the total area, type of land, topography, vegetation, climate, geology and intervisibility conditions that help in detailedplanning.

Roughsketchincludingalltheprincipalfeaturessuchasbuildings,roads,electricpoles, drain,etc.waspreparedwhich wouldhelpfor reference whilecarryingoutthedetailed surveyordetailing.Thisreferencesketchwouldalsohelp duringthe preparationofthe mapas perthe details obtained.

Some of the points which should be kept in mind for appropriate selection of major traverse control points forming the closed traverse around the premises of the area to be surveyed are summedup asfollows:

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2.5.2Traversing

Traversingisatype of surveyinwhichthe frameworkconsists ofaseriesofconnected lines, the directions and lengths of which are measured with the help of an angle measuring instrument and a length measuring instrument, i.e. Total Station (or Theodolite) and anElectronic Distance Measurement(EDM) systemrespectively.

A loop or circuit formed from a number of connected survey lines is known as a traverse. A traverse maybe classed as-

A. Closed traverse

A traverse is said to be closed when a complete circuit is made or when it begins and ends at points whose positions on plan are known. The work may be checked and balanced.

Known point

Known point

Figure1 ClosedTraverse

B. Open traverse

If the traverse ends elsewhere other than at the starting point or at some other point, thenthe traverse is termed as an open traverse.

Unknown point

Figure 2 Open Traverse

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2.5.2.1 Major Traverse

Thewholesitewhichwastobesurveyedwasenclosedbyanumberofinter-connectingsurvey lines forming a closed circuit or a framework joining successive major control points. This was the required major traverse.

Fixing of control points

After the completion of reconnaissance of the area to be surveyed, the major traverse controlpointswerefixedbydrivingpegsintothegroundorbymarkingthepointswith enamelincludingthegroupnameandthepegnumber.Someofthepointsneededtobe kept in the mind while fixing major traverse stations areas follows:

Inter-visibility of the adjacent major traverse stations.

Maintainingof the permissible leg ratioof 1:2.

Measurement oftraverse legs withoutany obstruction.

Fixing of stations with reference pointsas well as a neat sketch.

Fixing of stations driving wooden pegsand marking with enameland marker.

Total Station traversing Total Station

Atotalstationisanopticalinstrument.ItisthecombinationofanelectronicTheodolite, an Electronic Distance Meter (EDM), and software running on an external computer known as data collector.

With a total station one may determine angles and distances from the instrument to points to be surveyed. With the aid of trigonometry and triangulation, the angles and the distances may be used to calculate the coordinates of actual positions of the surveyedpointsorthepositionof theinstrumentfrom knownpoints,inabsoluteterms.

EDM

ElectronicDistanceMeasurement(EDM)isoneof themodernsurveyingequipment’s, whichisveryaccurateandhencepopular.Asitsnamesuggests,itisusedformeasuring the horizontal distance between two places- instrument station and target. Due to the ease of the use of the instrument, it has been usedin many placesand has replaced the conventionalmeasurement methodslike chaining, tapingetc.

ThebasicprincipleofEDMisthatdistancebetweenanytwopointscanbeknownonce the time light takes to travel the distance between the station and the target is known. Then the following relation, which is already programmed in the memory of the instrument along with other correction factors, calculates the required horizontal distance and is displayedon the LCD screen.

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Distance= velocity of light (V) * time (T/2)

Total station traversing is the process involved in the surveying of connecting lines to create a closed circuit or a frame-work and it consists of two tasks viz. two-waymeasurement of the traverse legs by EDM and measurement of traverse angles by makinguse of totalstation forangular measurements.

Measurementof traverselegs

Work on the major traverse should be precise. Thus, after appropriate selection and fixing of major traverse stations, two-way measurements of the traverse legs were carried outmakinguse ofEDMin the totalstation. The distancesbetweenthe adjacent controlpointswereaccuratelymeasuredasfaraspossiblefortheaccuracyofthewhole traverse. The precision of the measurement shouldbe within 1:2000.

Measurementof traverseangles

Theinteriortraverseanglesweremeasuredwiththehelpofanglemeasuringinstrument or the electronic Theodolite. Forachievingtheinternaltraverseangle,0º0’0″ wassetat the preceding station and the telescope was turned in the clockwise direction. In the case of major traverse, two sets of angular measurement were observed having 0º0’0″ and 90º0’0″ setatthe precedingstations. The angles obtained fromthese two sets were averaged to get the mean traverse angle. The difference in two angles and as well in eachof the angular observationcannotexceed 1’as stated earlier.

Sum and the correction of the interior angles Permissible Angular Error for the closed traverse = C√N

Where, N = no. of traverse legs

C=1’

For a closed traverse,

Sum of interior angles =(2n –4) *90°

Closing error = (2n – 4)*90°- ∑ Observed sum of internalangles

If theangularerroriswithin the permissible value of 1′√N,then the errorin the sumof internal angles isequally distributed.

Bearingcomputationof the traverse legs

The bearing of the common line CP1-CP2 was observed with the help of a compass. The bearing of the remaining traverse legs was computed. They were calculated using following relation:

Bearing of successive line = Fore bearing of the previous line + clockwise traverse angle ± 180°or 540°

Note:

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B(x,

L

2.5.2.2 Computation of the co-ordinates

After the computation of bearings and having the average lengths of all traverse legs, the positions or the co-ordinates of the major stations are calculated.

a. Consecutive co-ordinates

The latitude of the survey line is defined as its coordinate length measured parallel to anassumed meridian. Itis also termed as northing.

The departure of the survey line is defined as its coordinate length measured perpendicular to anassumedmeridian. It is also termed as Easting.

Each station point is defined by its latitude and departure with respect to the origin. Latitude of B, (y) = Latitude of A (Y) + L*cosθ

Departure of B, (x) = Departure of A(X) + L*sinθ

Where,

θ = Bearing of the line AB

L = Length of the line AB

b. Independentco-ordinates

The latitude and departure of any line with respect to a common origin of co-ordinatesarecalledindependentco-ordinatesortotalco-ordinates.Theindependentco-ordinates are calculated after the traverse is completely balanced. They are obtained by adding algebraically the latitudes and departures of the traverse legs between that station and origin.

Closing Error

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In a closed traverse, the algebraic sum of the latitudes and departures must be zero if linear as well as angular measurements of the traverse along with their computations are correct. If not, the distance between the starting station & point or position of the samestationobtainedbythecalculationisknownasclosingerror.Thevalueofclosing error is obtainedby the following formula.

Error = √∑(∆ ) + ∑(∆ )

A’

Figure 5 Closing Error AA’

Balancing thetraverse

The processof adjustingthe consecutiveco-ordinates byapplyingthe correctionto the latitudes&departuresofeachofthetraverselegs suchthattheiralgebraic sumisequal to zero is called balancingthe traverse orbalancing the consecutive co-ordinates.

A closedtraverse can be balanced by any one of the following methods.

The method is based on the assumption that errors in the linear measurement are proportional to √L and the errors in the angular measurements are inversely proportionalto√Lwhere‘L’isthelengthofaline.Themethodisapplicablewhenboth the linearas well asangular measurementsare of equal precision.

The Bowditch rule is:

Correction to latitude (or departure) of any side

= Total error in latitude (or departure) *Length of thatside Perimeter of traverse

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Where,

CLat =Correctiontolatitude ofanysideCD =CorrectiontodepartureofanysideΣLat=

Totalerror inlatitude

ΣD = Totalerror in departure

ΣL = Total perimeter of traverse L = Length of any side

2.Transit Method

hemethodismostapplicablewhenangularmeasurementsareofmoreprecisionthanlinear measurement. According to this rule, the total error in latitude and in departure is distributed in proportion to the latitude and departure of the sides. The angles are less affected bythe correctionsapplied bythis method thanbytheBowditchmethod.

The Transit rule is:

Correction in Latitude (or Departure)of any side

= Total error in Latitude (or Departure) * Latitude (or Departure) of that line Arithmetic sumof Latitudes(Departures)

CL =ΣL *L CD = ΣD *D LT DT

Where,CL= Correctiontolatitude ofany side

CD = Correctionto departure ofanyside L = Latitude of any line

D = Departure ofany line

LT = Arithmetic sum oflatitudes DT = Arithmetic sum of departures

Plotting of major traverse stations

After the computation and correction of the coordinates of the major traverse stations, the traverse stations were plotted in the grid sheet. The entire grid should be checked diagonally to avoid the plotting error. The major traverse stations were plotted in the scale of 1:1000to the grid paper. Papermanagementis done so thatthe drawntraverse lies in the centre of the grid sheet which also comforts the detail drawing or the preparation of the topographic map.

2.5.2.3 Minor Traverse

A closed frame-work made within the major traverse for the ease and comfort to carry out detailed survey or detailing is known as minor traverse. The entire vertical as well asthehorizontalcontrolsistransferredfromthemajortraverse.Minortraverselegsare fixedandstretchedinand outthe area tobesurveyed. Minortraverse stationsarefixed in such a way that it covers the maximum details which can be surveyed in the time frame with lesseffortand much ease.

Reconnaissance

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The whole area at the survey camp was divided into two plots of KITC ,kakaniAs in the case of major traverse, reconnaissance was carried out before the selection of the minorcontrolpointsortraversestations.Minorstationswerefixedsuchthattherewere (2 – 6) stations in a loop. One or two loops were formed as per the requirement and easeindetailing.Thestationswerefixedinsuchawaythatmaximumnumberofdetails couldbe controlledfrom a single minor station.

Marking andfixing ofcontrol points

Afterthecompletionofreconnaissance,2minorloopswereformed.Altogether2minor control points were fixed at suitable places considering all the required criteria. A tie- stationwas also fixed to control the details.

Measurement oftraverse legs

Asinthecaseofthemajortraverse,twowaymeasurementsofallthetraverselegswere carried out. The accuracy required for two-way measurement in the case of minor traverse is 1:1000. The leg ratio should be within 1:3.

Measurement ofinteriorangles

Only one set of horizontal angle observation is sufficient for the minor traverse. As in the case of major traverse, the difference of the observed angle in each observation should not exceed 1′. In the same way, 0º0’0″ was set at the preceding station and the telescope wasturned in the clock-wise directionfor the requiredhorizontalangle.

Permissible Angular Error for the closedtraverse = 1′√N

Where,N = no. of traverse leg

For theclosedtraverse,

Sum of interior angles =(2n –4)*90°

Closing error = (2n – 4)*90°- ∑ Observed sum of internal angles

If theangularerroriswithin the permissible value of 1′√N,then the errorin the sumof internalanglesisnotequallydistributedtoalltheanglesasinthecaseofmajortraverse. Here, the major angle cannot be corrected or given correction. Correction is provided for the angles included by minor traverse legs.

Computationof bearingof the traverse legs

As in the case of the major traverse, the bearing of the entire minor traverse legs are obtained from the bearing of the preceding leg (which has already been calculated in themajortraverse)andthe measuredhorizontaltraverse angle.Priorto computationof bearing, correctionforangular misclosure is applied as statedearlier.

Computationof coordinates of minorcontrol points

Using the co-ordinates of the major traverse which are already defined or computed, the co-ordinates of the minor control points are calculated. The co-ordinates of the minor traverse stations are calculated using the bearings and the average length of the minor traverse legs using their latitudes and departures.

Plotting of minortraverse stations

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As in the case of plotting of the major traverse, minor traverse is plotted in the grid sheet. The grid should be checked diagonally in order to avoid the plotting error. The minor traverse is plottedin the scale of 1:500.

Checking forOrientation

The cross check of the orientation of the traverse was done using plane table and its accessories. The traverse plot was placed coinciding the corresponding station and its orientation wascheckedbyresection method.

2.5.3 Leveling

Leveling is definedas the branch of surveyingwhich deals in findingthe elevations of the given points with respect to a given or an assumed datum. It also deals with establishingthepointsatagivenelevationwithrespecttoagivenoranassumeddatum. Itdealswiththemeasurementinaverticalplane.Ithelpstoprovidetheverticalcontrols in a topographic map. The elevations of the relevant points must be known so that complete topography of the area can be explored.

Accuratedeterminationoftheelevationsofdifferentpointsalongthecertainalignment is a necessary part. Hence, it is a subject of prime importance to engineers and the projectas a whole.

figure 6 levelling

Types of leveling

1. Direct Leveling

It isthe branchof levelingin whichthe verticaldistanceswith respecttothe horizontal line (perpendicular to the direction of gravity) may be used to determine the relative differenceinelevationbetweentwoadjacentpoints.Alevelprovideshorizontallineof sight i.e. a line tangential to the level surface at a point where the instrument stands. The difference in the elevation of the two, points is the vertical distance between the two levellines.Withalevelsetupatanyplace, the differenceintheelevationbetween anytwopointswithinproperlengthsofsightisgivenbythedifferencebetweentherod readings taken on these points. By a succession of instrument stations and related readings, the difference in elevation between widely separated points is thus obtained. Following are some special methods of direct leveling:

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a. Simple Leveling

It is the method of leveling which is used to determine the difference of elevation between twopointswhich arevisiblefromasingle point. Thismethod isappliedwhen thedistancebetweentwopointsisnottoolong.Inthistypeofleveling,onlythemiddle wire readingagainst the staff heldis observedandrecorded.

b. Differential Leveling

It is the method of direct leveling the object of which is solely to determine the difference in the elevation of two points regardless of the horizontal positions of the points with respect to each other. This type of leveling is also known as fly leveling. All three wire readings are observed and recorded. This method was employed at the survey camp to transfer the RL to majorandminor traverse stations.

c. Profile leveling

It is the method of leveling the object of which is to determine the elevations of the points at measured intervals along the given line in order to obtain the profile of the surfacealongthat line.

d. Cross- sectioning

It is the process of taking the levels oneach side of the main line at rightangles tothat line, in order to determine a vertical cross- section of the surface of the ground, or of underlying strata, or of both.

e. Reciprocal leveling

It isthe methodof leveling in whichthe difference intheelevation betweentwo points is accurately determined by two sets of reciprocal observations when it is not possible to set up the level between the two points.

2. Indirect leveling

Indirect method of trigonometric leveling is the process of leveling in which the elevations of the points are computed fromthe vertical anglesand horizontal distances measured in the field, just as the length of any side in any triangle can be computed from proper trigonometric relations.

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Adjustmentof level

The adjustment of level that needs to be done before each observation is known as the temporary adjustment of level. The temporary adjustment of the level is done in following steps:

1. Setting up the level

Theoperationof settingup includesthefixingthe instrumentonthe standandleveling the instrumentapproximately.

2. Leveling up

Accurate leveling is done with the help of foot screws and with reference to the plate levels. The purpose of levelingis tomake the verticaland horizontal line of sight truly horizontal.

3. Removal of parallax

Parallax is a condition arising when the image formed by the objective not formed in the plane of cross hairs. Parallax is eliminated by focusing the eyepiece for distinct vision of the cross hairs and by focusing the objective to bring the image of the object in the plane of the cross hairs.

Permanent adjustment of the level is the adjustment of level that is done when the correspondingrelationship between the parts of the instrumentis disturbed.

Booking and reducingof levels

There are two methods of booking and reducing the elevation of points from the observed staff readings. Theyare asfollows:

a. HI Method

Inthismethod,firstlytheheightofinstrumentiscalculatedbybacksightingtoaknown station i.e. adding back sight (BS) to RL of BM or previous known station for each setting of instrument. The RL of the next station is then calculated by subtracting the foresight (FS) to the HI. If any intermediate sights (IS) are taken, then their RL is also calculated by subtracting IS from HI. HI is calculated for every new set up of instrument.

b. Riseand Fall Method

It is the method which was mostly used in the survey camp for fly leveling as well as in the case of transferring RL from TBM to the entire major and the minor traverse stations. In riseand fallmethod, the height of instrument is not atall calculated butthe difference of level or elevation between consecutive points is found by comparing the staff readings on the two points for the same setting of the instrument. The difference between their staff readings indicates a rise or fall according as the staff reading at the

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point is smaller or greater than that at the preceding point. The figures for rise and fall workedoutthusforallthepointsgivetheverticaldistanceofeachpointaboveorbelow the preceding one, and if the level of any one point is known the level of the next will be obtained byaddingits rise or subtracting itsfall, as the case may be.

Arithmetic check

The difference between the sum of back sights and the sum of fore sights should be equaltothe difference betweenthe sum of riseandthesum of falland should be equal to the difference between the RL of last andthefirst points. Thus,

∑B.S. – ∑F.S. = ∑Rise -∑Fall = Last R.L. – First R.L.

This provides a complete check on the intermediate sights also. The arithmetic check would only fail in the unlikely, but possible, case of two more errors occurring in such a mannerasto balance eachother.

Permissible Errorand Correction

Permissible error in leveling is given by the relation Error = ±25√ where, k is the distance in km.

Error is corrected in fly leveling by adding the half of correction in the calculated RL of the endpoint.

In case of transfer of RL to the control points, error is divided according to the length of traverse legs following the f1ormula given below:

Correction in first leg = l

Correction in second leg = l1+l2

Correction in (n-1)th leg = 1+ 2+ + −1

Correction in nth leg = 1+ 2+ + −1+

2.5.4 Detailing

The process of allocating the object position on the map with the help of vertical and horizontal measurements withsufficient accuracyas perjob iscalled detailing.

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Tachometry is a branch of angular surveying in which the horizontal and vertical distances of points are obtained by optical means. Though it has less accuracy, about 1/300 to 1/500, itisfasterandconvenientthanthe measurements bytape orchain. Itis very suitableforsteep orbroken ground, deepravinesandstretchesofwater orswamp where taping is impossible.

The objective of the tachometric survey is the preparation of the topographic map or plaan with both horizontal and vertical controls. For the survey of high accuracy, it provides a check on the distancesmeasured by tape.

The formula for the horizontal distance, for the tachometer with the additive constant 0.00and multiplyingconstant 100.00 is,

H = k*S*cos2Ѳ

The formula forthe vertical distance is,

V = (k*S*Sin2 Ѳ)/2

Where,S = staff intercept = Top reading – Bottom reading K = multiplying constant (Generally=100)

Ѳ = vertical angle on Theodolite

Here the detailing was carried out using a Total Station by measuring the length and bearing of the line of sight of the object from the pre-determined station. The coordinates of the major and minor stations were already calculated and corrected before the detailing work. Thenthe Total stationwas set up at one stationand oriented bybacksightinganothercontrolstation.The totalstationisaninstrumentthatprovides the coordinates (easting, northing and RL) by itself in recorded form with codes to facilitate betterunderstanding. Separate manual booking wasalso done with necessary sketches to facilitate independent checks and for help in plotting. Then the position of the object was plotted with the help of recorded data and a rough sketch made during detailing.

In order to prepare the topographic map of the given area detail survey or detailing is carried out. Detail survey can either be carried out by tachometry, coordinate method using total station or by using plane table survey. Some of the steps followed while carrying out the detail survey are summedup as follows:

Instrument was setat each control pointwithaccurate centering and leveling.

The vertical distance from the center of the trunnion axis to the peg at the ground was measuredasthe height of the instrument.

Theinstrumentwasorientatedwithreferencetoafixedstationwhichisalready well defined.

Target was held verticallyasfaraspossible withproper leveling ofthe bubble forthecasedetailsurveyandinthecase ofRLtransferfrom BMtomajorand minor traverse stations the staff was held vertically as possible.

Hard details were not missed as far as possible and were indicated by numbering in the reference mapfor the future reference of plotting.

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After obtaining the distances and the directions from the extraction of the details from the total station, they were plotted in the grid sheet which already contained the minor traverse stations.

2.5.4 Contouring

Acontourisanimaginarylineofconstantelevation onthegroundsurface.Itisthe line in which the surface of the ground is intersected by the level surface.

Contour interval and Horizontal Equivalent

The vertical distance between any two consecutive contours is called the contour interval. The contour interval is kept constant for a contour plan or the topographic map; otherwise the general appearance of the map will be misleading. The horizontal distance between two points on two consecutive contours is known as horizontal equivalent and it depends upon the steepness of the ground. The choice of the proper contourinterval dependsupon the followingconsiderations:

The nature of the ground

The scale of the map

The purpose and the extent of the survey

Timeandexpense of field and the office work

Characteristics of Contours

The characteristic features of the contour which are used while plotting and reading a contourmapor the topographic mapare summedup as follows:

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7.Contourlinescrossa watershed orthe ridge line atrightangles. TheyformcurvesofU-shapedrounditwiththeconcavesideofthecurvetowardsthehigherground.

Methods of Locating Contours

Thelocationofapointintopographicsurveyinvolvesbothhorizontalaswellasvertical control.Themethodsoflocatingcontours,therefore,dependupontheinstrumentsused.

a. The direct method b. The indirect method

In the direct method, the contour to be plotted is actually traced on the ground. Only thosepointsaresurveyedwhichneedstobeplotted.Afterhavingsurveyedthosepoints, they are plotted and the contours are drawn through them. The method is slow and tediousand is used for the smallareaswhere greataccuracy is required.

In the indirectmethod, some suitable guide pointsare selectedandsurveyed;the guide pointsneednotnecessarilybeonthecontours.Theseguidepoints,havingbeenplotted, serveasbasisfortheinterpolationofcontours.Thisisthemethodmostcommonlyused in engineering surveys.

Interpolation of the Contour lines

Interpolation of the contour is the process of spacing the contours proportionately between the plotted ground points established by indirect methods. The method of interpolation is based on the assumption that the slope of the ground between the two points, which are surveyed, is uniform. There aredifferent methods of interpolation of contours. They are as follows:

By Estimation

This methodis extremely rough and is used for small scale work only. Theposition of the contour points between the guide points are located by estimation.

By Arithmetic Calculations

The method, though accurate, is time consuming. The position of contour points between the guide points are located byarithmetic calculation.

X= (H/V)*Y

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Where,X= Horizontal distance of the point to be located H= Horizontal distance between two guide points V= Vertical distance betweentwo guide points

Y= Vertical distance between the point to be located andlowerelevation point

By Graphical Method

In the graphical method, the interpolation is done with the help of a tracing paper or a tracing cloth.

Hence, the coordinates of the entire Major as well as Minor traverse stations were computed and were plotted in the grid sheet in respective scales. The reduced level of the all the control points were computed by fly leveling. Detailing was carried out by tachometric surveying.

Allcomputationswerecarriedoutwithinthepermissiblerangethough therewerefield obstacles aswell as instrumental errors. The temperaturechange and the inconsistency maybe the common sources of error during the entire work

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