The document discusses the use of theodolites in surveying, detailing types such as transit and non-transit theodolites, and outlining their parts and functions, including the vertical and horizontal axes, telescope, and various scales. It covers methods for measuring horizontal and vertical angles, deflection angles, magnetic bearings, and the closing errors in traverses, while also explaining two common rules for balancing traverse errors. The content serves as a comprehensive guide for understanding and effectively using theodolites in surveying applications.

1. S.R.E.S. SANJIVANI COLLEGE OF ENGINEERING,
KOPARGAON
(An Autonomous Institute)
DEPARTMENT OF STRUCTURAL ENGINEERING
SURVEYING (ST306)
UNIT NO-03 [STUDY OF 20 SECOND VERNIER TRANSIT
THEODOLITE]

2. INTRODUCTION OF THEODOLITE SURVEY
▶ Theodolite surveying is that branch of surveying in which theodolite is used to measure the
horizontal
and vertical angles.
▶ There are generally two types of Theodolites:
1. Transit Theodolite: A transit Theodolite is the one in which the telescope mounted in the instrument
can be revolved through a complete revolution about its horizontal axis, in a vertical plane.
2.Non-Transit Theodolite: It is the opposite of Transit Theodolite. In this type of Theodolite, the
telescope can not be revolved through a complete revolution about its horizontal axis, in a vertical
plane. It can be rotated to a certain extent to take vertical angles.
▶ Theodolites can also be classified into two categories on the basis of the Scale used in theodolite as:
1.Vernier Theodolite: it is fitted with a Vernier Scale. Vernier Theodolites are most commonly used
in normal Surveying operations
2. Micrometre Theodolite: Fitted with a micro micrometre scale
▶ The size of Theodolites is defined according to the diameter of its main scale, such as a 10 cm
theodolite means that the diameter of its main scale is 10cm.

3. IMPORTANT PARTS OF THE THEODOLITE &
THEIR FUNCTIONS
▶ A Theodolite is said to be transit when its telescope can be revolved through 180° in a
vertical plane about its horizontal axis, thus directing the telescope in exactly opposite
direction.
▶ The various parts of theodolite are shown in following figure-

4. ▶ Vertical Circle:- The vertical circle is rigidly fixed with the telescope, and moves along with it. It
is subdivided into four quadrants, each quadrants having a reading of 0° to 90° in proper directions.
▶ Plate Level:-These plate levels are mounted horizontally at right angles to each other on the upper
plate.
▶ Horizontal Axis:-The horizontal axis of a theodolite about which the telescope and the vertical
circle rotate
in a vertical plane is also called the ‘trunnion’ axis.
▶ Vernier Arm:-It is also known as a T-frame or a vernier frame. It has two arms, one vertical and one
horizontal. The vertical arm assists in locking the telescope at the desired level, while the horizontal arm
is useful for measuring vertical angles.
▶ Plate Bubble:- Two plate bubbles are mounted at the upper surface of the Vernier plate at right angles. One
plate bubble is kept parallel to the horizontal axis of the Theodolite and is used for horizontal levelling of
the instrument.
▶ Levelling Head:-The leveling head consists of two parallel triangular plates called tribrach plates. The
upper one is called as upper tribrach plate and is used to level the upper plate and telescope with the help of
equalizing screws provided at its three ends. The lower one is called a lower tribrach plate and is connected
FUNCTIONS OF DIFFERENT PARTS

5. ▶ Clamping Nut:- These are situated in the lower plate of the instrument mostly and are used in rotating
the instrument about its horizontal axis.
▶ Vertical Axis:- It is the axis about which the instrument rotates in the horizontal plane.
▶ Telescope:-The telescope of theodolite is mounted on the horizontal spindle. It can be rotated about the
horizontal axis to sight the objects. The telescope is internal focusing type i.e. the objective lens is fixed
in the position and an additional double concave (focusing lens) is moved between the diaphragm and the
objective.
▶ Standards:-Standards look like 'A' shaped and for that, it is known as A-frame. The standards’
frames support the telescope and allow it to spin about the vertical axis.
▶ Line of Sight:- The line of collimation or line of sight should coincide with axis of the telescope. The line
of sight should also be perpendicular to the horizontal axis at its intersection with the vertical axis .
▶ Axis of plate bubble:-It is horizontal when the bubble is center. Plate level axis: It is perpendicular to
the vertical axis when the bubble is at the center.
▶ Upper plate:- It is the bottom on that standard and vertical settled.
FUNCTIONS OF DIFFERENT PARTS (CONT.)

6. ▶ Lower Plate:- The lower plate is that the base of the entire instrument. It homes the foot screws and the
carrying for the vertical axis. it is strictly connected to the tripod-escalating assembly and does not
modifier or shift. Horizontal angles are measured with this plate.
▶ Tribrach:-A tribrach is a special plate that can be used to attach any type of surveying equipment
▶ Foot screws:- These are also termed as levelling screws, and are used to properly level the instrument in
the ground. There is three number of foot Screws, which are rotated in a certain direction, to level the
instrument.
▶ Trivet:-The lower plate with a large threaded hole in its center is called trivet or foot plate. It provides
a means to place the instrument on (tripod) stand and get it screwed.
▶ Plumb Bob:- To center the instrument precisely over a station mark, a plumb bob is suspended from
the hook fitted to the rock bottom of the central vertical axis.
FUNCTIONS OF DIFFERENT PARTS (CONT.)

7. As we know that the Theodolite is an evolved instrument used mainly for accurate measurements of
horizontal and vertical angles upto 10’’ to 20’’.
There are various uses of Theodolite as mentioned below :-
▶ Measuring Horizontal angles.
▶ Measuring Vertical angles.
▶ Measuring deflection angles.
▶ Measuring magnetic bearings.
▶ Measuring horizontal distance between two points.
▶ Finding the vertical height of an object.
▶ Finding the difference of elevation between various points.
▶ Ranging a line.
USES OF THEODOLITE

8. ▶ Centring:- The setting of theodolite exactly over a station marked by means of plumb bob is
known as Centring.
▶ Transiting :- The method of turning the telescope about the horizontal axis in a vertical
plane
through 180° is termed as transiting.
▶ Face left :- It means the vertical circle of theodolite is at the left of observer at the time of taking
reading.
▶ Face right :- It means the vertical circle of theodolite is at the right of observer at the time of
taking reading.
▶ Swinging the telescope:- It indicates turning of telescope in horizontal plane. It is called right
swing when telescope is turned clockwise and left swing when telescope is turned anticlockwise.
▶ Line of collimation:- It is an imaginary line passing through the intersection of cross hairs with
the diaphragm in optical center of the object glass and its continuation.
IMPORTANT TERMINOLOGIES (DEFINATIONS)

9. As given in fig. Suppose ∠AOB is to be measured. The following procedure is adopted.
▶ The instrument is set up at ‘O’ and it is centred and levelled properly.
▶ The lower clamp is kept fixed while upper clamp is kept loosened and by
turning the telescope clockwise vernier A is set 0° and B is 180°.
▶ Upper clamp is tightened by turning the upper tangent screw, verniers A & B
are set to exactly 0° and 180° by looking through magnifying glass.
▶ The upper clamp is fixed tightly. The lower one is loosened and telescope is directed to left-hand
object ‘A’. Then ranging rod at ‘A’ is bisected.
▶ The lower clamp is then tightened and by turning lower tangent screw, the ranging rod at ‘A’ is
accurately bisected.
▶ The lower clamp is kept fixed. The upper clamp is loosened and the telescope is turned clockwise
to approximately to bisect ranging rod at ‘B’ similarly by tightening upper clamp ranging rod at ‘B’
is accurately bisected by turning upper tangent screw.
DIRECT METHOD OF MEASURING HORIZONTAL
ANGLE

10. ▶ The readings on verniers A and B are noted. Vernier A gives angle directly whereas vernier at B,
the angle is obtained by subtracting the initial reading from final reading.
▶ Then readings are noted in tabular standard format.
▶ The face of instrument is changed and previous procedure is followed and again readings of verniers
are noted in table.
▶ The mean of observations (i.e. Face left & Face right) is the actual ∠AOB.
▶ The two observations are taken to eliminate any possible error due to improper instrument
adjustments or any manual error.
DIRECT METHOD OF MEASURING HORIZONTAL
ANGLE (CONT.)

11. In this method, the angle is added number of times. The total is divided by the number of readings
to get the angle. The angle should be measured clockwise in face left and face right position, with
three repetitions at each face. The final reading of first observation will be initial reading of second
observation and so on. The procedure for the same is as follows:-
▶ Suppose ∠AOB is measured by repetition process. The theodolite is set
up at ‘O’ and instrument is centered and levelled properly.
▶ Vernier A is set to 0° and vernier B to 180°.
▶ The upper clamp is fixed, lower one Is loosened. By turning the telescope
the ranging rod at ‘A’ is perfectly bisected with the help of lower clamp
screw and lower tangent screw, here initial reading at vernier A is 0°.
▶ The upper clamp is loosened and telescope is turned clockwise to perfectly bisect the ranging rod
at ‘B’. The upper clamp is then clamped.
▶ Suppose the reading on vernier A is 30°.
REPETATION METHOD FOR MEASURING
HORIZONTAL ANGLE

12. ▶ The lower clamp is loosened and the telescope is turned anticlockwise to exactly bisect ranging rod
at ‘A’. Here initial reading is 30° for second observation.
▶ The lower clamp is tightened, upper one is loosened and telescope is turned clockwise to exacly
bisect ranging rod at ‘B’. Let reading on vernier A is 60°.
▶ The initial reading for third observation is set to 60°, ∠AOB again measured. Let the final
reading on vernier A be 90° which is accumulated angle.
∠AOB=
𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑒𝑑 𝑎𝑛𝑔𝑙𝑒
=
90
= 30°
𝑁𝑜.𝑜𝑓 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 3
▶ The face of instrument is changed and previous method is followed.
▶ The mean of two observations gives the actual angle ∠AOB. The results then tabulated.
REPETATION METHOD FOR MEASURING
HORIZONTAL ANGLE (CONT.)

13. 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 called angle of elevation. When this angle is below
the horizontal line, it is called angle if depression.
▶ Consider fig. Suppose angle of elevation ∠AOC & depression
∠BOC are to be measured, then following procedure is as:-
▶ The theodolite is set up at ‘O’ and centred and levelled properly.
▶ The zeros of vernier are set to 0°-0° mark of the vertical circle and
telescope is then clamped.
▶ The plate bubble is brought to center with the help of foot screws. Then the altitude bubble
is brought to centre by means of 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.
MEASUREMENT OF VERTICAL ANGLES

14. ▶ The face of instrument is changed and point A is again bisected. The readings on verniers
are noted.
▶ The mean of the angles of the observed is assumed to be correct angle of elevation.
▶ To measure the angle of depression, the telescope is lowered slowly and point B is bisected. The
readings on the verniers are noted for two observations.
▶ The mean of observations are taken to be correct angle of depression & results are noted in a
tabular format.
MEASUREMENT OF VERTICAL ANGLES
(CONT.)

15. The deflection angle is the angle by which a line is deflected from its original direction. The
deflection may be towards right or left, depending upon whether angle is measured in clockwise
or
anticlockwise direction from extension of proceeding line.
▶ Consider fig. let AB be the general direction of survey. Suppose it is
deflected in direction BC, the line AB is extended up to P, then ∠PBC
(Ø) is known as angle of deflection. The procedure as adopted below:-
▶ The theodolite is set up at B and centred & levelled properly. Vernier A
is set at 0° and B at 180 °.
▶ The upper clamp is tightened and lower one loosened. By turning the telescope, the ranging rod
at
A is perfectly bisected. The lower clamp is then fixed.
▶ The telescope is transited and ranging rod at P is fixed along the prolongation of AB.
▶ The upper clamp is loosened. By turning the telescope clockwise, ranging rod at C is perfectly
MEASUREMENT OF DEFLECTION ANGLES

16. ▶ The upper clamp is tightened, now the verniers give the deflection angle (Ø).
▶ The lower clamp is loosened and by turning the telescope clockwise the ranging rod at A is again
bisected. The lower clamp is then fixed.
▶ The telescope is transited. The upper clamp is loosened and by turning the telescope clockwise
the ranging rod at C is bisected once more. The readings on vernier are taken.
▶ Thus the deflection angle is doubled. The average of two verniers is taken. One-half of average
value will give correct value of deflection angle.
Note:- Deflection angle is doubled in order to eliminate errors at wrong adjustment if instrument or
manual error if any.
MEASUREMENT OF DEFLECTION ANGLES
(CONT.)

17. MEASUREMENT OF MAGNETIC BEARING
▶ Consider fig. Supose the magnetic bearing of line AB is to be measured,
following procedure is adopted:-
▶ Theodolite is set up at A, and centered and levelled properly. Vernier A is
0° and vernier B is set to 180° & upper clamp is fixed.
▶ Now, a trough compass or tubular compass is fixed on the left hand
standard (A-frame) with fixing screw.
▶ By loosening the lower clamp, the telescope is rotated until it points to the north (i.e.
magnetic needle coincides with 0-0 mark).
▶ The lower clamp is fixed and upper clamp is loosened. Then by turning the telescope clockwise,
ranging rod at B is bisected with help of upper tangent screw.
▶ The readings of both verniers A & B area taken. Mean of these two readings will be
magnetic bearing of AB.
▶ The face is changed and similarly magnetic bearing of AB is measured. Mean of twoobservations
will give correct magnetic bearing of that line.

18. PROLONGING A STRAIGHT LINE
▶ Suppose line AB is to be prolonged as In fig.
▶ Set up instrument at A and level it carefully.
▶ Bisect station B accurately by means of lower clamp and
tangent screws.
▶ Look over from the telescope through the pin and hole arrangement and direct the surveyor with
a ranging rod near C, to be in line with A & B.
▶ See through the telescope and exactly bisect ranging rod at C.
▶ Move the instrument to B and repeat same above procedure.
▶ Continue the procedure until the last point E is established.

19. Closing Error :-
▶ In a closed traverse, the algebraic sum of latitudes and departures must be equal to zero.
▶ But due to errors in field measurements of angles and lengths, sometimes finishing point may not
coincide with the starting points of closed traverse.
▶ The distance by which a traverse fails to close is known as closing error.
▶ In fig. traverse ABCDA1 fails to close by distance AA1 which is the closing
error of this traverse.
▶ Closing error AA1 = ∑𝐿2 + ∑𝐷2
where, L = Latitude & D = Departure.
PART B UNIT I
I
I
THEODOLITE TRAVERSING

20. ▶ The theodolite traverse is not plotted according to interior angles or bearings, it is plotted
by computing latitudes and departures of the points.
▶ The latitude of a line is the distance measured parallel to north-south line and the departures
of a
line is measured parallel to east-west line.
▶ The latitudes and departures of line are expressed as below-
Northing= latitude towards north= +L
Southing= latitude towards south= -L
Easting= departure towards east= +D
Westing= departure towards west= -D
COMPUTATION OF LATITUDE AND DEPARTURE

21. In case of closed traverse, the algebraic sum of latitudes must be equal to zero and that of departures
must also be equal to zero in ideal condition.
In actual practice, some closing error is always found to exist while computing the latitude and
departures of traverse station.
The total errors in latitude and departures are determined. These errors are then distributed among the
traverse stations proportionately according to following rules.
▶ Bowditch’s Rule :-
By this rule, the total error is distributed in proportions to lengths of traverse legs.
a) Correction to latitude of any side
=
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓
𝑡ℎ𝑎𝑡 𝑠𝑖𝑑𝑒
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓
𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒
x total error in latitude
b) Corrections to departure of any side =
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓
𝑡ℎ𝑎𝑡 𝑠𝑖𝑑𝑒
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓
𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒
x total error in departure.
This is one of the most common method of traverse adjustment.
BALANCING OF TRAVERSE

22. ▶ Transit Rule :-
a) Correction to latitude of any side
=
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓
𝑡ℎ𝑎𝑡 𝑠𝑖𝑑𝑒
𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙
𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒𝑠
x total error in latitude
b) Corrections to departure of any side
=
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓
𝑡ℎ𝑎𝑡 𝑠𝑖𝑑𝑒
𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙
𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒𝑠
x total error in departure.
▶ Third rule :-
a) Correction to northing of any side
=
𝑁𝑜𝑟𝑡ℎ𝑖𝑛𝑔 𝑜𝑓 𝑡ℎ𝑎𝑡
𝑠𝑖𝑑𝑒
1
𝑆𝑢𝑚 𝑜𝑓 𝑛𝑜𝑟𝑡ℎ𝑖𝑛𝑔𝑠
2
x (total error in latitude)
b) Correction to southing of any side
=
𝑆𝑜𝑢𝑡ℎ𝑖𝑛𝑔 𝑜𝑓 𝑡ℎ𝑎𝑡
𝑠𝑖𝑑𝑒
1
𝑆𝑢𝑚 𝑜𝑓 𝑠𝑜𝑢𝑡ℎ𝑖𝑛𝑔𝑠
2
x (total error in latitude)
c) Correction to easting of any side
=
𝑆𝑢𝑚 𝑜𝑓
𝑒𝑎𝑠𝑡𝑖𝑛𝑔𝑠
𝐸𝑎𝑠𝑡𝑖𝑛𝑔 𝑜𝑓 𝑡ℎ𝑎𝑡
𝑠𝑖𝑑𝑒 1
2
x (total error in departure)
d) Correction to westing of any side
=
𝑊𝑒𝑠𝑡𝑖𝑛𝑔 𝑜𝑓 𝑡ℎ𝑎𝑡
𝑠𝑖𝑑𝑒
1
𝑆𝑢𝑚 𝑜𝑓 𝑤𝑒𝑠𝑡𝑖𝑛𝑔𝑠
2
x (total error in departure)
Note:- if the errors are positive, correction will be negative, and vice versa
BALANCING OF TRAVERSE (CONT.)

23. Traverse computations are usually done in tabular forms. One such form is Gale’s Tabular traverse
table & it is widely used because of its simplicity. As shown in fig. followings steps are illustrated.
▶ In case of theodolite traversing, included angle are adjusted
to satisfy geometric conditions while in case of compass
traversing, the observed bearings are adjusted for local attraction.
▶ From observed bearing of a line, Line AB, the WCB of all other
lines are calculated and then these bearings are reduced to those
in quadrantal system.
▶ From the lengths and RB of lines, latitudes and departures are
worked out.
▶ A check is done to find whether algebraic sum of latitudes and
departures are zero.
▶ The independent coordinates are the worked out. The origin is so selected that entire traverse lies
in North-East quadrant.
GALE’S TRAVERSE TABLE