Theodolite
Traversing
Theodolite Surveying:-
Ø Objective,
various parts of transit theodolite, technical terms, temporary and permanent adjustments of a transit,measuring horizontal and
vertical angles, methods of repetition and reiteration, computation of latitude and departure,
balancing of traverse by Bow-Ditch’s transit rule, third rule and modified
transit rules, missing data problems, Precautions in using theodolite, errors in theodolite survey, use of latitude
and departure for area calculation, Gales traverse table.
Ø The
theodolite is an intricate instrument used mainly for accurate measurement of
horizontal and vertical angle up to 10” or 20”, depending upon the least count
of the instrument. Because of its various uses, the theodolite is sometimes
known as “Universal Instrument”.
The following are the different purpose for which the theodolite can be
used:
Ø Measuring
Horizontal Angle
Ø Measuring
Vertical Angles
Ø Measuring
Deflection Angles
Ø Measuring
Magnetic Bearing
Ø Measuring
the horizontal distance between two points
Ø Finding
the vertical height of an object
Ø Finding
difference of elevation between various points
Ø Ranging
of a line.
Theodolite Traversing:
Theodolites
may be of two types
Ø
(i) Transit Theodolite
Ø
(ii) Non-Transit
Ø
In the transit theodolite,
the telescope, the telescope can be revolvedthrough a complete revolution
about its horizontal axis in a vertical plane.
Ø
In the non transit theodolite,
the telescope, cannot be revolved through a complete revolution in the vertical
plane.
Definitions:-
Centering:-
•
The setting of a theodolite exactly
over a station mark by means of a plumb bob. Is known as centering.
Transiting:-
•
The method of turning the
telescope about its horizontal axis in a vertical plane through 180 0 is termed as transiting. In other words
transiting results in a change in face.
Face left :-
•
‘Face
left’ means that the vertical circle of the theodolite is on the left of the observer at the time of taking
reading.
Face right:-
•
This refers to the situation
when the vertical circle of the instrument is on the right of the observer when
the reading is taken
Changing face:-
•
The operation of bringing the vertical circle from one side of the
observer to the other is known as changing face.
Swinging
the telescope:-
•
This indicates turning the telescope in a horizontal plane. It is called
‘right swing’ when the telescope is turned clockwise and ‘left swing’ when the
telescope is turned anticlockwise.
Line of Collimation:-
•
It is an imaginary line
passing through optical centre of the objective glass and its continuation.
Axis of Telescope :-
The axis is an imaginary line passing through the
optical centre of the object glass and the optical centre of the eye-peace.
Axis of the Bubble Tube:-
•
It is an imaginary line
tangential to the longitudinal curve of the bubble tube at its middle
point.
Vertical Axis:-
•
it is the axis of rotation of
the telescope in the horizontal plane
Horizontal Axis:-
•
It is the axis of rotation of
the telescope in the vertical plane.
Temporary Adjustment:-
•
The setting if the theodolite over
a station at the time of taking any observation is called temporary
adjustment.
Permanent Adjustment:-
•
When the desired relationship
between the fundamental lines of a theodolite is disturbed, then some
procedures are adopted to establish this relationship. This adjustment is
known as permanent adjustment.
Least Count of the vernier:-
•
This is the difference between
the value of the smallest division of the main scale and that of the smallest
division of the Vernier scale. It is the smallest value that can be measured by
a theodolite.
•
V= d/n
Where, v= Value of smallest division of Vernier
Scale
d=
Value of the smallest division of main scale
n=
no of small divisions on Vernier scale.
Least count of theodolites are generally 20” and 15”
and so on.
The Diaphragm:-
•
The diaphragm is a brass ring
consisting of cross-hairs, or one containing a glass disc with fine lines
engraved on it. It is placed in position by turning four capstan-headed
screws, and can be moved up, down or sideways when required. It is fixed in
front of the eye-piece. The cross-hairs may be made of fine platinum wire.
Axis of Theodolite:-
The Transit Theodolite:
Trivet:-
Ø It is a circular plate having a central, threaded
hole for fixing the theodolite on the tripod stand by a wing nut. It is
also called the base plate. Three foot screws are secured to this plate by
means of a ball and socket arrangement. And the upper threaded part
passes through the threaded hole in the tribrach plate.
Foot Screws:-
Ø These are meant for leveling the instrument.
The lower part of the foot screw are secured in the trivet by means of a ball
and socket arrangement and the upper threaded part passes through the
threaded hole in the tribrach plate.
Tribrach:-
Ø It is a triangular
plate carrying three foot screws at its ends.
Ø The trivet, foot screws and the tribrach
constituting a body which is known as the leveling head.
Spindles:-
Ø The theodolites consists of two spindles or axes- one
inner and the other outer. The inner axis is solid and conical, and the
outer is hollow. The two spindles are coaxial.
Lower Plate:-
Ø The lower plate is attached to the outer axis, and
is also known as the scale plate It is beveled and the scale is graduated
from 0 0
to 360 0.
Upper Plate:-
Ø The upper plate contains the Vernier scale A
and B. It is attached to the inner axis. Its motion is controlled by the upper
clamp screw and the upper tangent screw. When the clamp screw is tightened
the Vernier scale are fixed with the inner axis, and for fine adjustment of the
scale the tangent screw is rotated.
Upper Plate & Lower Plate:
Plate Bubble
•
Two plate bubbles are mounted
at right angles to each other on the upper surface of the Vernier plate. One
bubble is kept right parallel to the horizontal axis of the theodolite.
Sometimes one plate bubble is provided on the Vernier plate. The bubble are
meant for leveling this instrument at the time of measuring the horizontal
angle.
Standard or ‘A’ Frame
•
Two frames
are provided on the upper plate to support the telescope, the vertical circle and the Vernier scales. These
frames are known as standard A-Frames.
The Telescope
•
The telescope is pivoted
between the standard at right angles to the horizontal axis. It can be
rotated about its horizontal axis in a vertical plane. The telescope is
provided with a focusing screw, clamping screw and tangent screw.
Vertical Circle
•
The vertical circle is rigidly
fixed with the telescope and moves with it. It is divided into four quadrants.
Each quadrant is graduated from 0 to 90 0in opposite directions, with
the ‘Zero’ mark at the end of the horizontal diameter of the vertical
circle.
Index bar or T-frame
• The
index bar is provided on the standard in front of the vertical circle. It
carries two Vernier (C and D) at the two ends of the horizontal arm. The
vertical leg of the index bar is provided with a clip screw at the lower end by
means of which the altitude bubble can be brought to the centre.
Altitude bubble:-
•
A long sensitive tube is
provided on the top of index bar. This bubble is brought to the centre by
the clip screw at the time of measuring. Of the vertical angle.
Compass:-
•
Sometimes
a circular box compass is mounted on the Vernier scale between the standards. In modern theodolites, an adjustable trough compass
or tubular compass can be fitted with a screw to the standard.
Reading of Vernier Theodolite
The least count of the Vernier
is to determined first. Let it be 20”. The main division of the main scale is
of one degree. Suppose it is divided into three parts then each part accounts
for 20’ (i.e. d= 20’)
•
The Vernier scale has 20 big and 60 small divisions
•
Least Count= d/n= (20 x 60)/60= 20”
Here, Least count for one small divisions= 20”
Therefore, Least count of one big division
= (20” x 3) = 60” = 1’
After making the final adjustment for measuring
the angle, the position of the arrow of the Vernier scale is noted. Suppose the
arrow crosses 10 0 and 20’, which is
the direct reading obtained from the
main scale. Suppose, again that the first small division after 12 big
division exactly coincides with any of the main scale divisions. Then the Vernier
reading 12’ 20”
Therefore Final
Angle= 10 0 20’ + 12’ 20”= 10 0 32’ 20”
Temporary Adjustment of Theodolite:-
•
Setting the theodolite over the station
The tripod stand is placed over the required
station. The theodolite is then shifted from the box and fixed
on top of the stand by means of a wing nut or according to the fixed
arrangement provided along with the instrument
Approximate leveling by Tripod:-
• The
legs of the tripod stand are placed well apart and firmly fixed on the ground.
Then, approximately leveling is done using this stand, To do this, two legs are
kept firmly fixed on the ground and third is moved in or out, clockwise or
anticlockwise, so that the bubble is approximately at the centre of its run.
Centering:-
• Centering
is the process of setting of the instruments exactly over a station. At the
time of approximate leveling by means of the tripod stand, it should be ensured
that the plumb bob suspended from the book under the vertical axis lies
approximately over the station peg.
Leveling:-
•
Before starting the leveling
operation, all the foot screw are brought to the center of their run. Then the
following procedure is adopted.
•
(a) The plate bubble is placed
parallel to any pair of foot screws. By turning both these screws equally
inwards or outwards.
•
The plate bubble is turned
through 90 0
so that it is perpendicular to the line joining the first and
second foot screws. Then by turning the third foot screw either clockwise
or anticlockwise the bubble is brought to the center.
Ø Some instruments may have two plate bubbles
perpendicular to each other. In such a case, one bubble is kept parallel to any
pair of foot screws; the other platy bubble will automatically be perpendicular
to the position of first bubble. Here, the instruments need not be turned.
The first bubble can be brought to the centre by turning the first and second
foot screws, and the second bubble can be brought to the centre by turning the
third foot screw.
Ø The process is repeated several times, so
that the bubble remains in the central position of the platy bubble, both
directions perpendicular to each other.
Ø The instrument is rotated through 360 0 about its vertical axis. If the bubble
still remains in the centre position, the adjustment of the bubble is
perfect and the vertical axis is truly vertical.
Focusing of the Eye Piece:-
Ø The eye piece is focused so that the cross-hairs can be
seen clearly. To do this, the telescope is directed towards the sky or a
piece of white paper is held in front of the object glass, and the eye-piece is
moved in or out by turning it in
clockwise or anticlockwise until the cross –hairs appear distinct and sharp.
Setting the Vernier:-
•
The Vernier A is
set to 0 0 and Vernier B is 180 0. To
do this the lower clamp is fixed. The upper clamp is loosened and
the upper plate turned until the arrow of Vernier. A approximately
coincides with zero. And the Vernier B approximately coincides with the 180 0 mark. Then the upper clamp is tightened,
and by turning the upper tangent screw the arrows are brought to a position of
exact coincides.
Permanent Adjustment of Theodolite:-
A theodolite consists of several fundamental
lines. In order the readings to be accurate, certain desired
relationship must exist between the fundamental lines of the instrument.
But due to improper handling or excessive use, this relationship may be
disturbed and hence from the theodolite may lead to erroneous results.
For rectifying a
disturbed relationship, some procedures, termed permanent adjustments are
adopted.
The fundamental lines
of a theodolite are:
Ø The vertical
axis
Ø The axis
of the plate level
Ø The line
of collimation
Ø The horizontal
axis or trunnion axis
Ø The bubble
line of the altitude level
Ø The desired
relationships between the fundamental lines are as follows:
Ø The axis
of the plate level must be perpendicular to the vertical axis
Ø The line
of collimation should coincide with the optical axis of the telescope and
should also be perpendicular to the vertical axis.
Ø The axis
of telescope must be parallel to the line of collimation.
Ø The line
of collimation must be perpendicular to the horizontal axis. And the vertical
circle should read zero when the line of collimation is horizontal.
To make the axis of the plate level
perpendicular to the vertical axis, the following procedure is adopted prior to
the first adjustment.
Ø
The
theodolite is set up on firm ground with its legs well apart, and firmly
fixed on the ground.
Ø
The
plate bubble is made parallel to any pair of foot screws, and brought to the
centre of its run by turning the concerned foot screws.
Ø
The
bubble is turned through 90 0 and then brought to the centre
by turning the third foot screw.
Ø
The
process is repeated several times
until the bubble is perfectly centered in these two positions.
Ø
The
bubble is turned through 180 0about the vertical axis.
Ø
If
the bubble still remains in the central position, the axis of the bubble is
perpendicular to the vertical axis which may be assumed to be truly
vertical.
Ø If the bubble
does not remain in the central position the amount of deviation is noted, say
it is 2n division.
Adjustment:-
Ø Half of the total (i.e. n division) is adjusted by means of the capstan headed
nut provided below the bubble tube.
Ø
The Remaining half
(i.e. n division is adjusted by turning the concerned foot screws.
Ø The process is repeated several times until
the bubble remain in the central position for any direction of the bubble
tube.
To make the line of
collimation coincide with the optical axis of the telescope, first the
horizontal and then vertical hair are adjusted.
Adjustment
of Horizontal Hair.
Ø Three pegs are driven
into the ground at T, A and B a known distance apart.
Ø The theodolite is set
up at T and after proper adjustment staff are taken on A and B. Suppose the
readings are Aa and Bb1
Ø By transisting the
theodolite the staff reading are taken on A and B
Ø If the readings of
the second observation tallies with those of the first horizontal hair is in
adjustment.
Ø If the second
observation gives a new reading, say Bb2, then the horizontal hair
requires adjustment.
Adjustment of
Vertical Hair
• The theodolite is set up at T. After proper
leveling, a ranging rod is fixed at A by looking through the telescope keeping
the upper and lower clamps fixed.
• By transisting the telescope a ranging rod is
fixed at B
• The upper clamp is loosened and by turning the
vernier plate the ranging rod at A is again bisected.
• If the ranging rod at b is seen bisected after
transisting the telescope, the vertical hair is perfect.
• If not, the amount of error is noted, let BB1 be the total error.
Adjustment
•
A position is marked
by a ranging rod at B’, where B1B’ is one fourth of the total error.
•
The vertical hair is
shifted by turning the horizontal diaphragm screws, to bisect the ranging rod
at B’
•
During adjustment,
one-fourth of the total error is taken into consideration because the actual
error is magnified four times as the telescope was turned twice in the vertical
plane.
Third Adjustment
•
To
make the horizontal axis perpendicular to the vertical axis, the following
procedure is adopted before making the necessary adjustment.
•
The
theodolite is set up at T some distance away from a pole P.
•
The
plate bubble is perfectly leveled. Looking through the telescope, a well
defined point A is marked on the pole. The upper and lower clamp screws are
kept fixed.
•
The
telescope is lowered and another point B is marked near the base of the pole in
the same line of sight.
•
The
upper clamp is loosened and telescope is turned through 180 0.
bytransisting it, the mark A is bisected. The telescope is then lowered. If the
line of sight bisect the mark B, then the adjustment is perfect.
•
If
not, another point B’ is marked on a ranging rod R at the same level as B
Adjustment
•
A point C is marked
(in a suitable way) mid-way between B and B’
•
The point C is
bisected by the telescope and the upper clamp is tightened.
•
The telescope is now
raised. This time the line of sight will not bisect A.
•
The adjustment end of
the horizontal axis is raised or lowered until the line of sight bisects the
mark A.
•
The procedure is
repeated several times until the correction is perfect.
Fourth Adjustment
•
To
make the axis of the telescope level (altitude bubble) parallel to the line of
collimation, the procedure of adjustment is exactly similar to “Two-Peg
Method”
Fifth Adjustment
•
This
adjustment is made in order to ensure that the vertical circle read zero when
the line of collimation is horizontal.
•
This
adjustment is not required for transit theodolite. This is because in such
a theodolite the vernier is adjustable and clamped at zero when the
altitude bubble is centered.
•
In
theodolite provided with non-adjustable verniers, the reading of the vernier
may not be zero with the altitude bubble is centered. In such a case, the
amount of angular error, known as “ index error” is noted. The sign of
the index error should be taken into account. Necessary correction has to be
applied to the observed vertical angle according to the sign of index error.
Some
Modern Theodolites:-
Watt
Micro-Optic Theodolite
•
There
are three models of this type. The first and the third model are capable of
reading up to 5”, and the second can read up to 1”. The horizontal and vertical
circles of this theodolites are made up of glass. Micrometers for measuring
horizontal and vertical angles are provided. The other accessories are the
same as in the transit theodolite. But the arrangement are very compact, and
well protected from atmospheric action.
Wild T-2 Theodolite:-
} The horizontal and
vertical circles of this instrument are made of glass. The diameter of the
horizontal circle is 90 mm and that of the vertical circle 70 mm. The
circles are electrically illuminated through an adjustable mirror.
} The instrument is
automatically centered by its own weight. The readings are taken through
a micrometer by the coincidence system
Wild T-3 Precession
Theodolite:-
•
The
horizontal and vertical circles are made of glass and finally graduated.
The minimum reading of the horizontal circle is 4’ and that of vertical circle
is 8’. The angle is measured b means of an optical micrometer which is
accurate up to 0.2”. The vertical axis consists of an axis bush and ball bearings.
•
The
instrument is automatically centered
by its own weight. It consists of one set of clamp and tangent screws for
the motion of the vertical axis.
Wild
T-4 Universal Theodolite:-
This
instrument is widely used in the
determination of geographical positions , and for taking astronomical
observations with the utmost precision. It consist of a horizontal circle of dia
250 mm and are graduated to a minimum reading of 2’. With the optical micrometer,
one can take reading as low as 0.1”. The vertical and horizontal circles of
two diametrically opposite readings automatically which gives the arithmetic
mean of two diametrically opposite readings automatically.
The
Tailstock Theodolite:-
} The horizontal and
vertical circles are made of graduated that a reading as low as 1” can be
taken, an one of 0.25” can be estimated. A single optical micrometer is
provided for both the scales both
circles are illuminated by a single mirror is provided with scale
plummet for centering over the station
Sources of Error in Theodolite:-
Instrument Errors:-
Non-adjustment
of plate bubble:-
} The axis of the plate bubble
may not be perpendicular to vertical axis. So. When the plate level are
centered, the vertical axis may not be truly vertical. In such a case, the
horizontal circle would be inclined and the angle will be measured in an
inclined plane. This would cause an error in angle measured.
} This error may be
eliminated by leveling the instrument with reference to the altitude bubble.
Line of collimation
not being perpendicular to horizontal axis:-
} In this case, a cone is
formed when the telescope is revolved in the vertical plane, and this
causes an error in the observation.
} This error is eliminated
by reading the angle from both the faces (left and right) and take the
average of the reading.
Horizontal
axis not being perpendicular to vertical axis:-
} If the horizontal axis is
not perpendicular to the vertical axis, there is an angular error. This
is eliminated by reading the angle from both the faces.
Line of
collimation not being parallel to axis of telescope:-
} If the line of
collimation is not parallel to the axis of telescope, there is an error in
the observed vertical angle. This error is eliminated by taking reading from
both faces.
Eccentricity of Inner and Outer
axes:-
} This condition causes an error in Vernier readings. This error is
eliminated by taking reading from both the Vernier and considering the average
readings.
Graduation not being Uniform:-
} The error due to this condition is eliminated by measuring the angles
several times on different parts of the circle.
Vernier
being Eccentric:-
} The
zeros of the vernier should be diametrically opposite to each other. When
vernier A is set at 0 0, Vernier B should be at 180 0,
But in some cases, this condition may not exist.This error is eliminated
by reading both verniers and taking the average.
Personal Error:-
} The
centering may not be done perfectly, due to carelessness. The leveling may not
be done carefully according to usual procedure. If the clamp screws are not
properly fixed, the instrument may slip. The proper tangent screw may not
be operated The focusing in order to avoid parallax may not be perfectly
done.
} The object
of ranging rod may not be bisected accurately The vernier may not be
set in proper place.
} Error
would also result if the verniers are not read because of oversight.
Natural Errors:-
} High
temperature causes error due to irregular refraction.
} High
wind causes vibration in the instrument, and this may lead to wrong
readings on the verniers.
Direct Method of Measuring
Horizontal Angle:-
} Suppose
an angle AOB is to be measured. The following procedure is adopted:
} The instrument
is set up over O. It is centered and leveled perfectly according to the
procedure described for temporary adjustment. Suppose the instrument was
initially in the face left position.
} The lower
clamp is fixed. The upper clamp is loosened and by turning the telescope
clockwise vernier A is set to 0 0 and vernier B to approximately
180 0. The upper clamp is then tightened. Now by turning the
upper tangent screw, vernier A and B are set to exactly 0 0 and 180 0
by looking through magnifying glass.
} The upper
clamp is tight fixed. The lower one is loosened and the telescope is
directed to the left hand object A. The ranging rod at A is bisected
approximately by proper focusing the telescope and eliminating parallax. The
lower clamp is tightened, and by turning the lower tangent screw the ranging
tod at A is accurately bisected.
} The lower clamp is kept fixed. The upper clamp is loosened and
the telescope is turned clockwise to approximately bisect the ranging rod at B
by proper focusing the telescope. The upper clamp is tightened, and the
ranging rod at B bisected accurately by turning the upper plate screw.
} The
reading on vernier A and B are noted. Vernier A gives the angle
directly. But in the case of vernier B, the angle is obtained by subtracting
the initial reading from final reading.
} The
face of the instrument is changed and the previous procedure is followed. The
reading of the verniers are noted in the table.
} The
mean of the observations (i.e. Face left and face right) is the actual
angle AOB. The two observations are
taken to eliminate any possible errors due to imperfect adjustment of the
instrument.
} The two
methods of measuring horizontal angle are those of repetition and reiteration.
Repetition Method:-
} In this
method, the angle is added a number of times. The total is divided by the
number of reading to get the angle. The angle should be measured clockwise
in the face left and face right positions, with three repetition at each
face. The final reading of the first observation will be the initial
reading of the second observation, and so on.
} Suppose
the angle AOB is to be measured
by the repetition process. The theodolite is set up at O. The instrument is
centered and leveled properly. Vernier A is set to 0 0 and
vernier B to 180 0.
} The upper
clamp is fixed, and the lower one is loosened. By turning the telescope,
the ranging rod at A is perfectly bisected with the help of the lower clamp
screw and the lower tangent screw. Here the initial reading of vernier A is
0 0.
} The upper
clamp is loosened and the telescope is turned clockwise to perfectly bisect the
ranging rod at B. The upper clamp is clamped. Suppose the reading on vernier
A is 30 0.
} The
lower clamp is loosened and the telescope turned anticlockwise to exactly
bisect the ranging rod at A. Here, the initial reading is 30 0 for
the second observation.
} The
lower clamp is tightened. The upper one is loosened and telescope is turned
clockwise to exactly bisect the ranging rod at B. The reading on vernier A is
60 0.
} The
initial reading for the third observation is set to 60 0. angle AOB
is again measured. Let the final reading on the vernier A is 90 0.
Which is the accumulated angle.
} Angle
AOB= Accumulated Angle
No
of Reading
= 90 = 30 0
3
} The
face of the instrument is changed and the previous procedure is followed.
} The
mean of the two observation gives the actual angle <AOB
Reiteration
Method:-
} This method is suitable when
several angles are measured from a single station. In this
method all the angle are measured successively and finally the horizon is
closed (i.e. angle between the last and first station is measured) So, the
final reading of the leading vernier is equally distributed among all the
observed angles. If it is large, the readings should be cancelled and new sets
taken.
} Suppose
it is required to measure AOB and BOC
from O. The procedure is as follows.
First Set:-
} The theodolite
is perfectly centered over O and leveled properly in the usual manner. Suppose,
the observation is taken in the face left position and the telescope is turned
clockwise (right Swing)
} Vernier
A is set to 0 0 (i.e. 360 0) and vernier B to 180 0.
} The upper
clamp is fixed and the lower one is loosened. The ranging rod at A is perfectly
bisected. Now, the lower clamp is tightened.
} The upper
clamp is loosened, and the ranging rod or object at B is bisected properly by
turning the telescope clockwise. The readings on both the verniers are
taken AOB
is noted.
} Similarly,
the object C is bisected properly, and the reading on the verniers are noted
BOC is recorded.
} Now the
horizon is closed, the last angle COA is
measured. The position of the leading vernier is noted. The leading vernier
should show the initial reading on which it was set. If it does not, the amount
of discrepancy is noted. If it is small, the error is distributed among the
angle. If the discrepancy large, the observation should be taken again.
Second Set:-
} The
face of the instrument is changed. Again the vernier are set at their initial
positions. This time the angles are measured anticlockwise (left Swing)
} The upper
clamp is fixed, and the lower one loosened. Then the object A is
perfectly bisected.
} The lower
clamp is tightened. The telescope is turned anticlockwise, and the
object C bisected by loosening the upper clamp Screw. The reading on
both the vernier are taken COA is
noted.
} Then
the objected B is bisected by turning the telescope anticlockwise, and the
readings on the vernier are taken
BOC is recorded.
} Finally,
the horizon is closed i.e. the object A is bisected. Here, the leading vernier
A should show a reading 0 0.
The last angle AOB is noted.
} The mean
angle of the two sets give the actual value of the angle. If some error is
found after arithmetic check, it should be equally distributed among the
angles.
Measuring Vertical Angle:-
} The
vertical angle is the one between the horizontal line (i.e. line of
collimation) and the inclined line of sight. When it is above the
horizontal line, it is known as the angle of elevation. When this angle is
below the horizontal line, it is called the angle of depression.
} Consider Suppose the angle of elevation AOC and that of depression BOC are to be measured. The following
procedure is adopted.
} The
theodolite is set up at 0. It is centered and leveled properly. The zeros of
the vernier (generally C and D) are set 0 0 0 0
mark of the vertical circle (which is fixed to the telescope) the telescope
is then clamped.
} The plate
bubble is brought to the centre with the help of foot screw. Then the altitude
is brought to the centre by means of a clip screw. At this position
the line of collimation is exactly horizontal.
} To
measure the angle of elevation, the telescope is raised slowly to bisect
the point A accurately. The readings on both the verniers are noted, and the
angle of elevation is recorded.
} The face
of the instrument is changed and the point A is again bisected. The reading
on the vernier are noted. The mean of the angle of the observed is assumed
to be correct angle of elevation.
} To
measure the angle of depression, the telescope is lowered slowly and
observations (face left and face right)( The mean angle of the observation
is taken to be correct angle of depression.
Computation
of Latitude and Departure:-
} The theodolite
is not plotted according to interior angles or bearings. It is plotted
by computing the latitude and departure of the point and then finding the
independent coordinates of the point.
} The latitude
of a line is the distance measured parallel to the North-South line and the
departure of a line measured parallel to the East-West line.
} The
latitude and departure of lines are also expressed in the following ways
} Northing=
Latitude towards north= + L
} Southing=
Latitude towards South= -L
} Easting=
Departure towards East= + D
} Westing=
Departure towards West= -D
}
Conversion of WCB to RB
Check for Closed Traverse
Sum of Northing= Sum of Southing
Sum of Easting= Sum of Westing
Consecutive Coordinates:-
} The
latitude and departure of a point calculated with reference to the preceding
point for what are called consecutive coordinates.
Independent Coordinates:-
} The coordinates
of any point with respect to a common origin are said to be the independent
coordinates of that point. The origin may be a station of the survey or a point entirely outside the traverse.
Balancing of Traverse:-
} In Case
of Closed Traverse, the algebraic sum of latitude must be equal to zero and
that of departure must also be equal to zero in the ideal condition. In
other words, the sum of the northing must equal that of the southing, and
the sum of the easting must be the same as that of the westing.
} But in
actual practice, some closing error is always found to exist while computing
the latitude and departure of the traverse station.
The total errors in
latitude and departure are determined. These errors are then distributed
among the traverse stations proportionately, according to the following rule.
Bowditch’s Rule
•
By
this rule, the total error (in latitude or departure) is distributed in
proportion to the length of the traverse legs. This is the most common method
of traverse adjustment.
(a) Correction to
latitude of any side
= Length of that Side x Total Error in
latitude
Perimeter of Traverse
(b) Correction to
departure of any side
Length of that Side x
Total Error in departure
Perimeter of Traverse
Transit Rule:-
(a) Correction to
latitude of any Side
Latitude of that Side x
Total Error in Latitude
Arithmetical Sum of all latitude
(b) Correction to
departure of any Side
Departure of that Side x
Total Error in departure
Arithmetical Sum of all Departure
Third Rule:-
(a) Correction to
Northing of any Side
Northing of that Side x ½ total
error in latitude
Sum of Northing
(b) Correction to
Southing of any Side
Southing of that side x ½ total error in latitude
Sum of Southing
(c) Correction to Easting of any Side
Easting of that Side x ½ total error in departure
Sum of Easting
(d) Correction to
Westing of any Side
= Westing
of that Side x½ total error
in departure
Sum of Westing
If the error is
positive, correction will be negative, and vice versa.
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