# Determine Horizontal angles of Survey Scheme Using Theodolite

**Objective – Survey Scheme**

The main objective of the survey scheme is to measure the horizontal angles of the scheme using the theodolite so that these values can be used for the traverse computations of the scheme.

**Apparatus**

- Theodolite
- Tripod Stand
- Ranging Rod

**Scheme**

The scheme of which we are going to measure the horizontal angles is following:

**Methods of Measuring Horizontal Angles**

There are two methods:

- Repetition
- Reiteration

**Repetition Method**

A single angle *<AOB *is measured usually four times and then its average value is taken.

**Procedure**

- To measure the angle
*<AOB*, the theodolite is set at point O and then repetition mode of the theodolite is turned on and the Face of the theodolite is taken as left. - Bisect the ranging rod placed at the station point A and set the Theodolite angle as (zero).
- Now turn the theodolite and bisect the ranging rod at station point B. Press the
**Hold**button (a reading will be shown on the display screen). - Now again bisect the station Point A and Press
**R\L**button. - Bisect Point B again, and Press
**Hold**button. - Repeat this process 4 times and take the average value of angle by dividing the
**Accumulated angle**by number of readings taken.

Now repeat this process by taking the Theodolite as Face Right.

Face Left readings and Face Right Readings are taken to ensure the Correctness of the Angle, thus measured.

**Re-iteration Method**

This method is used when two or more angles are to be measured at one Station point.

**Procedure**

- Set the theodolite at station Point
**O**. - Bisect the point A measure the
*<AOB*by turning the theodolite and bisecting the point**B**. - Now Measure the
*<BOC*by bisecting the point**C** - The
**Horizon**is closed by measuring the external angle*<COA* - The sum of all angles must be equal to
**36**.

### Comparison

Repetition Method | Re-iteration Method |

1. When only one angle is to be measured at one station point2. It is comparatively more accurate.3. Horizon is not closed at the instrument station.4. When the precision of measurement of a horizontal angle is desired to be more than the least count of the instrument, this method is used.5. In this method, an angle is measured four times and the average is taken. | 1. When two or more angles are to be measured at one station point.2. Horizon is closed at the instrument station and sum of all angles must be equal to 360^{o} .3. In this method, sub-angles at one station point are measured.The sum of angles after closing the horizon should be equal to 360 ^{o} . |

### Scheme

The horizontal angles of the above-mentioned scheme are measured by using the Re-Iteration method.

**Observation and Calculations**

The angle measurements for different angles at different stations by reiteration method are following:

I.S | Angle Observed | Face | Observed Value | Mean Value | Error | Corrected Mean Value | Remarks |

B | ABC | L | 34⁰03’50” | 34⁰03’50” | +05” | 34⁰03’45” | —- |

R | 34⁰03’50” | ||||||

CBD | L | 56⁰09’25” | 56⁰09’15” | 56⁰09’15” | |||

R | 56⁰09’05” | ||||||

DBA | L | 269⁰47’00” | 269⁰47’00” | 269⁰47’00” | |||

R | 269⁰47’00” | ||||||

A | CAD | L | 60⁰30’35” | 60⁰30’37.5” | -15” | 60⁰30’42.5” | —- |

R | 60⁰30’40” | ||||||

DAB | L | 39⁰31’30” | 39⁰31’35” | 39⁰31’40” | |||

R | 39⁰31’40” | ||||||

BAC | L | 259⁰57’30” | 259⁰57’32.5” | 259⁰57’37.5” | |||

R | 259⁰57’35” | ||||||

G | DGE | L | 18⁰26’00” | 18⁰25’55” | -2.5” | 18⁰25’56.5” | —- |

R | 18⁰25’50” | ||||||

FGE | L | 47⁰04’50” | 47⁰04’50” | 47⁰04’50” | |||

R | 47⁰04’55” | ||||||

EGF | L | 294⁰29’10” | 294⁰29’12.5” | 294⁰29’14” | |||

R | 294⁰29’15” | ||||||

C | ACB | L | 45⁰52’40” | 45⁰52’40” | -25” | 45⁰52’50” | —- |

R | 45⁰52’40” | ||||||

BCD | L | 37⁰05’30” | 37⁰05’25” | 37⁰05’30” | |||

R | 37⁰05’20” | ||||||

DCA | L | 277⁰01’30” | 277⁰01’30” | 277⁰01’40” | |||

R | 277⁰01’30” | ||||||

F | GFE | L | 14⁰19’35” | 14⁰19’32.5” | +25” | 14⁰19’22.5” | —- |

R | 14⁰19’30” | ||||||

EFG | L | 345⁰40’50” | 345⁰40’52.5” | 345⁰40’37.5” | |||

R | 345⁰40’55” | ||||||

E | DEF | L | 85⁰59’10’’ | 85⁰59’05’’ | +10’’ | 85⁰59’02’’ | —– |

R | 85⁰59’10’’ | ||||||

FEG | L | 118⁰40’0’’ | 118⁰40’0’’ | 118⁰39’56’’ | |||

R | 118⁰40’0’’ | ||||||

GED | L | 155⁰21’10’’ | 155⁰21’05’’ | 155⁰21’02’’ | |||

R | 155⁰21’00’’ |

D | BDA | L | 50⁰12’20” | 50⁰12’50” | 00” | 50⁰12’50” | —- |

R | 50⁰13’40” | ||||||

ADC | L | 36⁰31’20” | 36⁰31’17.5” | 36⁰31’17.5” | |||

R | 36⁰31’15” | ||||||

CDE | L | 92⁰42’25” | 92⁰41’17.5” | 92⁰41’17.5” | |||

R | 92⁰42’10” | ||||||

EDB | L | 180⁰34’30” | 180⁰34’35” | 180⁰34’35” | |||

R | 180⁰34’40” |

### Learning Outcomes

**1.** **What is a transit theodolite?**

**Ans: **The theodolite in which telescope can be rotated about its horizontal axis in the vertical plane through 180^{o} is called as the transit theodolite.

**2.** What are fundamental lines of theodolite?

**Ans: **Vertical axis, Horizontal axis, axis of the bubble tube, Line of collimation.

**3. ****What are temporary adjustments of a theodolite?**

**Ans: **Fixing ,Centering, Leveling and focusing.

**4. What are the different methods of finding the horizontal angles?**

**Ans: **1- Repetition

2- Reiteration

**5.**** Define repetition method?**

A**ns: **When only one angle is measured from a point four times then this method is called repetition method.

**6.**** In which condition is reiteration method used?**

**Ans: **This method is used if there is more than one an

**7.**** What is meant by face left and face right observations?**

**Ans: **When the vertical circle is on the left side of the observer then it is called face left obsevation and when the vertical circle is at right side of the observer then this position is called face right position

**8.**** What is another name for circular bubble?**

**Ans: **Bull’s eye bubble , pill box bubble.

**9.**** Which arithmetic check is applied for reiteration method?**

**Ans: **The sum of all angles measured at a point should be equal to 360^{o} .

**10. What does closed horizon means in reiteration method?**

**Ans: **It means after measuring all the angles at the particular station the sum of all these angles should be equal to 360^{o} .