Engineering

# Source of Error in Theodolite Work

Here in this guide we are going to elaborate the source of error in theodolite work.

These may be classified into three groups:-

## 1. Instrumental Errors

Instrumental errors are classified in following points

• Non-Adjustment of Plate Level: If the plate levels which are not perpendicular to the vertical axis, are centered, the vertical axis of the instrument is not made truly vertical. As a result, the horizontal circle is inclined and the angles are measured in an inclined plane instead of in a horizontal plane. The errors are introduced in the measurement of both horizontal and vertical angles. The errors is serious when the horizontal angles between points at considerably different elevations are to be measured.

The errors can be minimized by leveling the instrument with reference to the altitude bubble.

• The Line of  Collimation not Being perpendicular to the Horizontal Axis: If the line of collimation is not perpendicular to the horizontal axis, it will trace out the surface of a cone instead of a plane when the telescope is revolved in the vertical plane. As a result horizontal angles when measured between points at widely different elevations will be incorrect.

The error can be eliminated by reading angles on both the faces and taking the mean of the observed values.

• The Horizontal Axis not Being Perpendicular to the Vertical Axis: If the horizontal axis is not perpendicular to the vertical axis, the line of collimation will not revolve in a vertical plane when the telescope is raised or lowered. This causes an angular error both in horizontal and vertical angles.

The error can be eliminated by reading angles on both the faces and taking the mean of the two values.

• The Line of Collimation and the Axis of Telescope Level not Being Parallel to Each Other: If the line of collimation and the axis of telescope level are not parallel to each other, the zero line of the vertical verniers is not a true line of the reference and as a result, an error is introduced in the measurement in the measurement of vertical angles.

The error can be eliminated by taking two observation of the angles, one with the telescope normal and the other with the telescope inverted, and taking the mean of the two values.

• The Inner and Outer Axis i.e., The Axis on Both the Upper and Lower Plates not Being Concentric: This makes the angles read on either vernier incorrect. The error is eliminated by reading both verniers and averaging the two values.
• The Graduation Being Unequal: The error is minimized by measuring the angles several times on different parts of the circle and taking the mean of all.
• Verniers Being Eccentric: The zeros of the verniers with not be diametrically opposite to each other. An error will be introduced if only one vernier is read, but it will cancel itself if both verniers are read and the taken mean.
• The Vertical Hair not Being Exactly Vertical: The error is minimized by suing the portion of the hair near the horizontal hair for bisecting the signal.

### 2. Observational and Personal Errors

Observational and personal errors are classified in following points:-

• Inaccurate Centering:  This is very common error and is introduced in all angles measured at a given station. Its magnitude depends upon the length of the sight. It varies inversely as the length. The error is much reduced by carefully centering the instrument over the station-mark.
• Inaccurate Leveling: The effect of this error is similar to that of the error due to non-adjustment of plate levels. The error is serious when horizontal angles between points at considerably different elevations are to be measured. The error can be minimized by leveling the instrument carefully with reference to the altitude level.
• Slip: The slip may occur if the instrument is not firmly screwed to the tripod-head or the shifting head is not sufficiently clamped or the lower clamp is not properly tightened. As a result, the observations will be in errors. This can be prevented by proper care.
• Working Wrong Tangent Screw: This is a common mistake on the part of a beginner. This can be avoided by proper care and experience. Always operate the lower tangent screw for a back sight and the upper tangent screw for a fore-sight.
• Parallax: This error arises due to imperfect focusing. The parallax can be eliminated by proper focusing the eye-piece and the object glass.
• Inaccurate Bisection of the Point Sighted and Non Vertically of the Ranging Rod: Care should be taken to bisect the lowest point visible on the ranging rod. In case of short sights, the point of a pencil or the pulb-line may be used instead of a ranging rod. The errors varies inversely with the length of sight.
• Other Errors: Such as,

(a) Mistake in setting the verniers

(b) Mistake in reading the scales and verniers.

(c) Mistake in reading wrong verniers.

(d) Mistake while booking the readings can be prevented by habitual checks and precautions.

#### 3. Natural Errors

Natural errors are classified in following points:

• High temperature causing irregular refraction.
• Wind storm causing vibration of the instrument.
• The sun shining on the instrument.

These are negligible for ordinary surveys, but the precise work is usually performed under the most favorable atmospheric conditions.