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  • INTRODUCTION OF SURVEYING
    • INTRODUCTION
    • REFERENCE ELLIPSOID
    • BASIC MEASUREMENTS
    • The geoid
    • PROTECTION AND REFERENCING
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    • The ellipsoid
    • BASIC SETTING-OUT PROCEDURES USING COORDINATES
    • LOCATING POSITION
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    • PLOTTING DETAIL
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    • Computer-aided design (CAD)
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    • SIGNIFICANT FIGURES
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    • ERRORS IN MEASUREMENT
    • WEIGHT MATRIX
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    • Deviation of the vertical
    • INDICES OF PRECISION
    • VARIANCE-COVARIANCE MATRIX OF THE PARAMETERS
    • COMPUTATION ON THE ELLIPSOID
    • COMBINATION OF ERRORS
    • Uncertainty of addition or subtraction
    • Eigenvalues, eigenvectors and error ellipses
    • BLUNDER DETECTION
    • RELIABILITY OF THE OBSERVATIONS
    • PRACTICAL CONSIDERATIONS
    • ESTIMATION IN THREE DIMENSIONS

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    • Plan network
    • SOURCES OF ERROR
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    • Direction & Angle equation
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    • Parallel plate micrometer
    • ERROR ELLIPSES
    • Field procedure
    • Booking and computing
    • DIGITAL LEVELLING
    • Factors affecting the measuring procedure
    • TRIGONOMETRICAL LEVELLING

  • CONTOURING
    • TAPES
    • Introduction of Satellite positioning
    • FIELD WORK
    • GPS SEGMENTS
    • Measuring in catenary
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    • DISTANCE ADJUSTMENT
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    • GPS OBSERVING METHODS
    • ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM)
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    • ORDNANCE SURVEY NATIONAL GRID
    • (t – T) correction
    • PRACTICAL APPLICATIONS
    • Contouring
    • HEIGHTING WITH GPS

  • Theodolite Surveying
    • PLANE RECTANGULAR COORDINATES
    • PRINCIPLE OF LEAST SQUARES
    • PRINCIPLE OF LEAST SQUARES
    • TRAVERSING
    • LINEARIZATION
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    • Reconnaissance
    • NETWORKS
    • LINEARIZATION
    • Sources of error
    • Traverse computation
    • TRIANGULATION
    • Resection and intersection
    • Resection
    • NETWORKS
    • INSTRUMENT ADJUSTMENT
    • FIELD PROCEDURE
    • Setting up using the optical plumb-bob
    • MEASURING ANGLES
    • Measurement by directions
    • SOURCES OF ERROR

  • Simple Curves
    • CIRCULAR CURVES
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    • SETTING OUT CURVES
    • PARTITION OF LAND
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    • VOLUMES
    • TRANSITION CURVES
    • Effect of curvature on volumes
    • Centrifugal ratio
    • MASS-HAUL DIAGRAMS
    • CONTROLLING VERTICALITY
    • The equation of motion
    • Coefficient of friction
    • CONTROLLING GRADING EXCAVATION
    • Sources of error
    • SETTING-OUT DATA
    • ROUTE LOCATION
    • LINE AND LEVEL
    • Highway transition curve tables (metric)
    • THE OSCULATING CIRCLE
    • Transitions joining arcs of different radii (compound curves)
    • Coordinates on the transition spiral
    • VERTICAL CURVES
    • Vertical curve design
    • Sight distances
    • Permissible approximations in vertical curve computation

Branch : Civil Engineering
Subject : Surveying-I
Unit : INTRODUCTION OF SURVEYING

Uncertainty of addition or subtraction


Description:

Consider a quantity A = a b where a and b have standard errors σa and σb, then

As subtraction is simply addition with the signs changed, the above also holds for the error in a difference:

Equation should not be confused with equation (2.4) which refers to the mean, not the sum as above.

Uncertainty of a product:


Consider A = (a × b × c) where a, b and c have standard errors σa, σb and σc. The variance

The terms in brackets may be regarded as the relative errors Ra, Rb, Rc giving

Uncertainty of a quotient

Consider A = a/b, then the variance

Uncertainty of powers and roots:
The case for the power of a number must not be confused with the case for multiplication, for example
a3 = a × a × a, with each term being exactly the same.


Thus if A = an, then the variance

Similarly for roots, if the function is A = a1/n, then the variance

The same approach is adapted to general forms which are combinations of the above.

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