The laboratory manual outlines experiments for determining the multiplying and additive constants of a tacheometer for surveying applications. It includes methodologies for calculating distances using horizontal and inclined lines of sight, as well as procedures for experiments focused on gradient determination and curve setting. Additionally, it covers the use of aerial photographs for stereoscopic viewing, providing techniques and formulae relevant to tacheometry and surveying principles.

1. LABORATORY MANUAL
FOR
SURVEYING-II

2. Experiment No- 1
Aim: Determination of the Multiplying and additive constant of given Tacheometer
Apparatus: A tacheometer with tripod, tape, leveling staff, wooden pegs, ranging rods etc.
Figure:
Formulae:
When the line of sight is horizontal, then
D = KS + c
Where,
D = Horizontal distance between instrument station and staff station.
K = Multiplying constant of a tacheometer
S = Staff intersect i.e. difference between top and bottom stadia hair
reading.
When line of sight is inclined and staff vertical then:
D = KS cos2
θ + c cosθ
Where,
D = Horizontal distance between instrument station and staff station.
Site- Time Grades
Date Weather Signature

3. K = Multiplying constant of a tacheometer
S = Staff intersect i.e. difference between top and bottom stadia hair reading.
θ = The inclination of the line of collimation to the horizontal.
c = The additive constant of the tacheometer
Theory:
PRINCIPLE OF STADIA METHOD
The stadia method is based on the principle that the ratio of perpendicular to the base
is Constant in similar isosceles triangles.In fig let two rays OA and OB be equally
inclined to the central ray OC. Let A2B2, A1B1 and AB be staff intercepts.
Evidently
OC2 = OC1 = OC = cons tan tk = 1 Cot β
A2 B2 A1 B1 AB 22
β

4. This constant k entirely depends upon the magnitude of the angle β. If β is made
equal to 34’22”, the constant k=1/2Cot 17’11”=100. In this case the distance between the
staff and the point o will be 100 times the intercept. In actual practice, observation may be
made with inclined line of sight. In the later case, the staff may be kept either vertically or
normal to the line of sight. We shall first derive the distance elevation formulae for the
horizontal sights.
Horizontal Sight: - Considering fig in which o is the optical centre of the objective of an
external focusing telescope.
Let A, C and B= the point cut by the three lines of sight corresponding to the three
wires.
b, c and α (Top, axial and bottom )hairs of the diaphragm.
a b= i= interval between the stadia hairs (stadia interval) AB=s=Staff intercept.
f=focal length of the objective.
f1=Horizontal distance of the staff from the optical centre of the objective.
f2=Horizontal distance of the cross-wires from O.
d= Distance of the vertical axis of the instrument from O.
D= Horizontal distance of the staff from the vertical axis of the instrument.
M= Centre of the instrument, corresponding to the vertical axis.
Since the rays Bob and AOa pass through the optical centre they are straight so that
AOB and aob are similar.

5. f1

s
--------------------------------(1)f
2 i
Again, since f1 and f2 are conjugate focal distances, we have, from lens formula
1  1  1 --------------------------(2)
f f 2f1
Multiplying throughout by ff1, we get
f 
f
1
f

f1
f
2
Substituting the values of
f1

s
in the above, we get
f 2
f
1 
s
f  f -------------------------- (3)
i
The horizontal distance between the axis and the staff is
D  f1  d
D  f s  ( f  d ) ------------------- (4)
i
D  ks  C
Equation (4) is known as the distance equation. In order to get the horizontal distance,
therefore, the staff intercept s is to be found by subtracting the staff reading corresponding
to the top and bottom stadia hairs.
The constant k  f is known as the multiplying constant or stadia interval factor and the
i
constant (f+d) =C is known as the additive stadia if the instrument.
Determination of Constant k and C
The values of the multiplying constant k and the additive constant C can be computed
by the following methods:
1st
Method: - In this method, the additive constant C= (f +d) is measured from the
instruments while the multiplying constant k is computed from field observations.

6. 1) Focus the instruments to a distant object and measure along the telescope the
distance between the objective and crosshair.
1 = 1 + 1
f f1 f 2
Since f1 is very large in this case, f is approximately equal to f2 i.e. equal to the distance
of the diaphragm from the objective.
2) The distance d between the instrument axis and the objective is variable in case of
external focusing telescope, being greater for short sights and smaller for long Sights.
It should, therefore, be measured for average sight. Thus, the additive constant (f +d)
is known.
3) To calculate the multiplying constant k, measure a known distance and take the S1 on
the staff kept at that point, the line of sight being horizontal. Using equation
D1 = KS1 + C
K =
D
1
−C
S1
For the average value, staff intercepts, s2, s3 etc., can be measured corresponding
to distance d2, d3 etc., and mean value can be calculated.
2nd
Method- In this method, both the constants are determined by field observations
as under:
1) Measure a line, about 200 m long on fairly level ground and drive pegs at some
intervals, say 50 meters.
2) Keep the staff on the pegs and observe the corresponding staff intercepts with
horizontal sight.
3) Knowing the values of d and s for different points, a number of simultaneous
equations can be formed by substituting the values of d and s in equation (1.1). The
simultaneous solution of successive pairs of equations will give the values of k and c,
and the average of these can be found.

7. If s1 is the staff intercept corresponding to distance D1 and s2 corresponding to D2, we have,
D1= KS1 + C and----------------------------------------------- (1)
D2= KS 2 + C ---------------------------------------------------- (2)
Subtracting (1) from (2) we get,
K =
D2 − D1
(3)--- --- --- -- --- -- --- -- --- --- -- --- -- --- -- --- --- -- --- -- -
S2 − S1
Substituting the values of k in (1) we get,
C = D1 −
D2 − D1
S1
S 2 − S1
C = D1 S2 − D2 S1 -------------------------------------------------(4)
S2 − S1
Thus, equations 3 and 4 give the values of K and C.
Tacheometry: It is a branch of angular Surveying in which horizontal and vertical distance of
point are obtained by instrumental observation. ) Tacheometer: It is a transit theodolite having
a stadia telescope i.e. telescope fitted with stadia diaphragm
A leveling staff can be used for sighting purpose up to 100m distance.

8. Procedure:
1) Select an instrument station A on a fairly leveled ground and fix a peg.
2) Do the temporary adjustment over A.
3) With vertical circle to the left of the observer and reading 000
00’00” bisect staff held at
10m, 20m, and 30m from A along straight line.
4) Note down the staff reading against top and bottom stadia hair on staff held at 10m, 20,
30m from A.
5) In case of inclined line of sight the same procedure as stated above is followed step by
step with a vertical angle of 050
00’00” in the vertical circle of the theodolite. In this
case, the vertical circle is held to the left of the observer and with the reading 050
00’00”
in the circle the staff is bisected at 10m, 20m, and 30m from A along straight but
inclination line of collimation.
Observation Table:
Instrument Staff Distance Vertical Stadia hair Reading
Remark
station station angle Top Center Bottom
D1
A D2
D3

9. Calculation:
D = Ks + c
For three staff stations,
D1 = Ks1+c ------- (1)
D2 = Ks2+c ------- (2)
D3 = Ks3+c ------- (3)
As ; s1, s2, s3 can be known solving (1) &(2), (2) & (3) , (1) & (3) to get 3 values of m & c
,then average of three values is required answer.
D = Ks cos2
θ + c cosθ
For, three station the equations are;
D
1 = Ks1 cos2
θ1 + C cosθ1 ------- (1)
D
2 = Ks2 cos2
θ2 + C cosθ2-------
(2)
D
3 = Ks3 cos2
θ3 + C cosθ3------- (3)
As ; s1, s2, s3 can be known solving (1) &(2), (2) & (3) , (1) & (3) to get 3 values of K & C
,then average of three values is required answer.
Result: a) For horizontal line of collimation;
1) The additive constant ‘c’ for a given tacheometer is found out to be
2) The multiplying constant ‘m’ for a given tacheometer is found to be ---------
b) For inclination line of collimation;
1) The additive constant ‘c’ for a given tacheometer is found out to be ----------
2) The multiplying constant ‘k’ for a given tacheometer is found to be ---------

10. Qu.1. Explain the necessity of tachometry.
Ans.

11. Experiment No- 2
Aim: Determination of gradient of given length of road by Tachometric survey
(Horizontal distance between two points)
Apparatus: A tacheometer with tripod, tape, leveling staff, wooden pegs, ranging rods
etc.
Figure:
S 1
h 1
V 1
θ
H o r i z o n t a l l i n e
o f
s i g h t
O
θ
S 2
h 2
V 2
B . M .
Formulae:
When the line of sight is horizontal, then
D = Ks + C
Where,
D = Horizontal distance between instrument station and staff station.
K = f/i=100 Multiplying constant of a tacheometer
C= (f+d)=0 additive constant of a tacheometer
S = Staff intersect i.e. difference between top and bottom stadia hair reading.
Site- Time Grades
Date Weather Signature

12. When line of sight is inclined and staff vertical then:
D = KS cos2
θ + C cosθ
Where,
D = Horizontal distance between instrument station and staff station.
K = Multiplying constant of a tacheometer
S = Staff intersect i.e. difference between top and bottom stadia hair reading.
θ = The inclination of the line of collimation to the horizontal. C =
The additive constant of the tacheometer
Distance between P&Q (D)= D12
+ D2 2
− 2D1D2Cosα
Gradient = (RLs of P-RLs of Q)/Length
Theory:
Trigomentrical levelling is the branch of surveying in which the relative elevations of the
points are determined from the observed vertical angles and known horizontal distance.
Whereas in ordinary leveling the difference in elevation is ascertained by running a line
between the given points.
Let P be the point whose reduce level is to determine and M be the reading on bench
mark. The instrument is set up at any convenient point B in the vicinity of the object.
The telescope is kept horizontal and staff reading M on the bench mark is taken. The
point A sighted and the angle of elevation is observed. The reduced level of a point P
can be ascertained as follows
Let D be the horizontal distance between the instrument and the object, H be the height
of point P . ø Be the angle of elevation, then we have H=Dtanø

13. RLs of P=RLs of B.M.+h+V-HI
RLs of Q= RLs of M+HI+V+h
Procedure:
1) Setup the instrument station A and level it carefully with respect to plate bubble tube.
First the centering be done.
2) Select the staff station at a convenient place and held it properly.
3) Release the vertical circle clamping screw and bisect the staff by making the
horizontal line of sight.
4) At the same time the horizontal vernier should read to (00 0’00”) and clamp it in
position.
5) Take three staff readings on the staff station and find the stadia intercept.
6) Release the upper plate clamping screw and bisect the another staff again and
take all three staff readings and then determine the staff intercept
7) Determine the horizontal angle between these two staff station and note the value
ø.
8) Now determine the horizontal distance and vertical distance between staff station
and instrument station respectively.
9) Determine the horizontal distance between two staff station by applying cosine rule.
10) Determine the of two staff station.
11) Finally determine the gradient of given length by given formula

14. Observation Table:
Instrument
Station
Staff
Station
Vertical
Angle
Stadia Hair Reading
Distance RL Remarks
Top Center Bottom
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

15. Sample Calculations:
1. For Distance Calculations-
2. For RL Calculations-

16. Sketch:
Result:
The gradient of given length of two staff station is found to be ___________ by tachometric
survey.

18. Experiment No- 3
Aim:
To determine the gradient of the joining the staff station at d left target of Subtense bar (Study
Experiment)
Instruments Required:
Theodolite, staff, arrow and subtence bar.
Given data:
R.L. of the B.M. = 100.000m
Procedure:
1. Set up the instrument at P, staff at A and the Sub tense Bar at B.
2. Keeping the Vernier A as 00’0”, Note down the axial hair reading of the staff held vertical over the staff
station A.
3. Sight the apex of the left target of the Subtense bar and note down the horizontal angle between the
staff station and left target, and also the vertical angle by Sight the left target.
4. By Sight the other target and from the instrument station note down the horizontal angle between the
left and right target, and also the vertical angle.
5. Find out the benchmark staff readings.
Sketch:
Site- Time Grades
Date Weather Signature

19. Result:

21. Experiment No- 4 [A]
Aim:
To set out the simple curve by Rankin’s method of Deflection angles by using Single theodolite method.
Instruments required:
Theodolite, Ranging rods, Chain, Arrows and pegs.
Principle:
The deflection angle to any point on a circular curve is measured by one – half the angle subtended by
the arc from point of curve to that point. It is assumed that the length of the arc is approximately equal to
its chord.
Given data:
Chainage of curve, angle of intersection () and radius of curve (R)
Procedure:
Site- Time Grades
Date Weather Signature

22. Calculations:
Sketch:

23. Check:
Result:
The given simple curve is thus set out.

24. Experiment No- 4 [B]
Aim:
To set out the transition curve combined with the circular curve by method of deflection angles.
Instruments required:
Theodolite, Ranging rods, Tape or Chain and accessories.
Transition curve:
A transition curve or easement curve is a curve of varying radius introduced between a straight and a
circular curve, or between two branches of a compound curve.
Ideal Transition curve:
The fundamental requirement of a transition curve is that its radius of curvature ‘r’ at any point shall vary
inversely as the distance (l) from the beginning of the curve. Such a curve is the clothed or the Glover’s
spiral and is known as the ideal transition curve.
Procedure:
In order to make the computations for various quantities of the transition and circular curve the data
necessary are
1. The deflection angle () between the original tangents
2. The Radius of the circular curve ( R )
3. The Length of the transition curve (L)
4. The point of intersection (V).
Site- Time Grades
Date Weather Signature

25. Sketch:
Calculations:
Result:
The given transition curve was set out.

26. Experiment No- 5
Aim: Study of Aerial Photographs under Stereoscope.
Stereoscope in an instrument used of viewing stereo pairs. Stereoscopes are
designed for two purposes
1. To assist in presenting to the eyes the images of a pair of photographs so that
the relationship between convergence and accommodation is the same as would
be in natural vision.
2. To magnify the perception of depth.
Apparatus: There are two basic types of stereoscopic for stereoscopic viewing of
Photographs:
A) Mirror stereoscope B) Lens stereoscope.
a b
b '
a
N e g a t i v eN e g a t i v e 1
E Y E E Y E
C a m e r a L e n s C a m e r a L e n s
P H O T O 2
A
P H O T O 2
B
( A ) S t e r e o p a i r o f n a i l
Site- Time Grades
Date Weather Signature

27. R E T I N A R E T I N A
E Y E
E E ' E Y E
M m M '
A
b a a ' b '
P r i n t 1 P r i n t 2
B
A) Mirror stereoscope
The mirror stereoscope shown diagrammatically consist of a pair of small eye-
piece mirrors mirrors m’ and a pair of larger wing mirrors, M and M’ each of which is
oriented at 45% with the place of the photographs. Show a nail mounted on a block of
timber, and is being photographed by two camera position .The camera lens is
placed fist in the position of left eye and then in the position of right eye, and separate
photographs are taken in each position of left eye and then in the position of right eye
and separate photographs are taken in each position. It will be noted that the head of
the nail is to the left in the left film and to the right in the right film. AB are the images
of the nail AB in the two films.
Contact prints from these negatives are placed in the mirror stereoscope as
show in where only images of the nail are drawn.

28. The dour mirrors transfer the light to the eyes exactly (exactly for accommodation) as
if it had come from nail as shown by dotted line. The convergence and retinal
disparity are sufficient for the observer to see the nail in three dimensions.
The total distance b M m E or ‘M’ m’ E’ from the eye to the pane of the
photographs varice 30 cm to 45cm, in order that the unaided eye may comfortably
view the photographs. The angle ϕ is determined by the separation of photographs
that give the most eye comfort, and is compatible with the distance bMme.’ If this
distance is to be reduced, a pair of magnifying lenses is placed at E and E’ each
magnifier has a focal length slightly smaller than the distance bMme. Some types of
mirror stereoscope have a set of removable binoculars which are place at the eye
positions E and E’.
Show a wild ST – 4 mirror stereoscopes with a parallax bar manufactured by
Ms Wild Heerbrugg Ltd. It is used for spatial observation of stereo photographs upon
a maximum model size of approximately 18cm×cm. The distance between the central
points of mirrors is 25cm for all interpupillary distances. The whole model area can be
seen through the two lenses provided for correction of the bundle of rays and for
accommodating. A removable set of eyepieces with 3 X magnification can be swung
in over these lenses for closer examination of parts of the model and study of details.
A pair of eyepieces particularly useful when selecting tie points in aerial triangulation.
The two inclined binocular eyepiece tubes are adjustable for interpupillarly distance of
56 to 74mm and have eye-piece adjustments for focusing the separate images.

29. The greatest single advantage of the mirror stereoscope is the fact that
photographs may be completely separated of the mirror stereoscope is the fact that
the photographs may be completely separated for viewing, and the entire overlap
area may be seen stereoscopically without having to slip the photographs.
B) Lens stereoscope
A lens stereoscope consists of a single magnifying lens for each eye, and
no mirrors. The two magnifying lenses are mounted with a separation equal to the
average interpupillary distances of the human eyes, but provision is made for
changing this separation to suit the individual user.
The distance between the nodal point of the lens and the plane of the
photographs depends upon the focal length of the lens. The two photographs can be
brought so closet the eyes that proper convergence can be maintained without
causing the photographs to interfere with each other as show in since the
photographs are very close to the eyes, the images occupy larger angular
dimensions and therefore appear enlarged show a lens stereoscope.
The lens stereoscope is apt to cause eye strain as accommodation is not in
sympathy with convergence and the axes of the eyes are forced out their normal
conciliation and can be slipped in one’s pocket this type being called a pocket
stereoscope. Because of larger size, mirror stereoscope is not so portable as is the
pocket stereoscope.

30. Experiment No- 6
Site- Time Grades
Date Weather Signature
Aim: Traversing by Total Station.
Equipment:
• Total Station
• Prism Pole
• Mini Prism
• Tripod
• Safety Vest
Procedure:

31. Project- 1
Road Project
Site- Time Grades
Date Weather Signature
Aim: To create a road profile by profile levelling.
Apparatus:
Procedure:
Observations:
Sample Calculations:
Result

32. Observations-
Sr.
No.
Station Distance
Staff Readings
Rise Fall RL Remarks
BS IS FS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Check-

33. Sr.
No.
Station Distance
Staff Readings
Rise Fall RL Remarks
BS IS FS
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Check-

34. Sr.
No.
Station Distance
Staff Readings
Rise Fall RL Remarks
BS IS FS
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Check-

35. Sr.
No.
Station Distance
Staff Readings
Rise Fall RL Remarks
BS IS FS
Check-

37. Project- 2
Radial Contoring
Site- Time Grades
Date Weather Signature
Aim: To analyze the surface with the Radial / Tachometric contouring.
Apparatus:
Procedure:

38. Observation Table:
Station
Staff
Station
Vertical
Angle
Elevation/
Depression
Stadia Hair Reading
RL Distance
Remarks
Top Center Bottom

39. Station
Staff
Station
Vertical
Angle
Elevation/
Depression
Stadia Hair Reading
RL Distance
Remarks
Top Center Bottom

40. Station
Staff
Station
Vertical
Angle
Elevation/
Depression
Stadia Hair Reading
RL Distance
Remarks
Top Center Bottom

41. Instrume
nt Station
Staff
Station
Vertical
Angle
Elevation/
Depression
Stadia Hair Reading
RL Distance
Remarks
Top Center Bottom

42. Sample Calculations:
3. For Distance Calculations-
4. For RL Calculations-
Results:

43. Project- 3
Block Contouring
Aim: To analyze the surface with the Net / Grid / Block contouring.
Apparatus:
Procedure:
Site- Time Grades
Date Weather Signature

44. Observation Table:
Sr. No. Station Distance Staff Readings H.I. R.L. Remarks
Check-

45. Observation Table:
Sr. No. Station Distance Staff Readings H.I. R.L. Remarks
Check-

46. Observation Table:
Sr. No. Station Distance Staff Readings H.I. R.L. Remarks
Check-

47. Observation Table:
Sr. No. Station Distance Staff Readings H.I. R.L. Remarks
Check-

48. Project-4
Theodolite Traversing
Aim: To locate a structure by a Theodolite Traverse and locate the details.
Apparatus:
Procedure:
Observations:
Site- Time Grades
Date Weather Signature

49. Sample Calculations:
Result: