Theodolite Errors Eliminated by Observations

Taking both left face (FL) and right face (FR) observations in a theodolite is a standard procedure to minimize systematic errors affecting horizontal and vertical angle measurements. This technique leverages the principle that certain errors manifest differently depending on the instrument's orientation.

Eliminating Collimation Error

The error caused by the line of collimation not being perpendicular to the horizontal axis is eliminated by observing in both FL and FR.

• Reason: This error introduces a constant angular deviation in the line of sight. When observations are made with the face left and then face right, this deviation effectively adds in one position and subtracts in the other.
• Calculation: Combining the FL and FR readings, typically by averaging, cancels out the effect of this collimation error. For example, the true horizontal angle is often calculated as $\frac{\text{Reading}_{FL} + \text{Reading}_{FR}}{2}$.

Eliminating Horizontal Axis Error

The error resulting from the horizontal axis not being perpendicular to the vertical axis is also eliminated by using both FL and FR observations.

• Reason: This error causes the vertical circle reading to be incorrect when the instrument is not perfectly leveled in azimuth. Similar to the collimation error, its effect is reversed when switching from FL to FR.
• Calculation: Averaging the readings obtained in both positions helps to balance out and eliminate this error, leading to a more accurate result.

Errors Not Eliminated by FL/FR

The following errors are generally not eliminated solely by taking FL and FR observations:

• Error due to eccentricity of the verniers: This error arises if the vernier is not placed exactly at the center of the graduated circle. FL/FR does not compensate for this inherent bias.
• Error due to imperfect graduations: Inaccurate markings on the instrument's circles represent a fixed error that FL/FR observations cannot correct.