Errors in tacheometric surveying can be categorized into three main types: instrumental errors, errors due to manipulation and sighting, and errors due to natural causes. Let's discuss each of these types in detail:

1. Instrumental errors:
- These errors occur due to imperfections or malfunctions in the surveying instruments used for tacheometry.
- Instrumental errors can include errors in the levelling of the instrument, errors in the vertical and horizontal circles, errors in the telescope, and errors in the staff readings.
- Levelling errors can arise from incorrect adjustment of the instrument's leveling screws, resulting in an inaccurate horizontal plane.
- Errors in the vertical and horizontal circles can occur due to incorrect graduation or index errors.
- Telescope errors can arise from issues such as imperfect collimation, non-parallelism of the crosshairs, or incorrect adjustment of the diaphragm.
- Errors in staff readings can result from misreading the staff, parallax, or errors in the staff graduation.

2. Errors due to manipulation and sighting:
- These errors occur during the process of manipulating the instrument and taking readings.
- Manipulation errors can include errors in centering the instrument over the station, incorrect focusing, or improper leveling.
- Sighting errors can arise from misalignment of the instrument's line of sight with the target point, parallax, or errors in reading the staff.

3. Errors due to natural causes:
- These errors are caused by environmental factors that affect the accuracy of the surveying measurements.
- Natural causes can include atmospheric refraction, temperature variations, wind, and vibrations.
- Atmospheric refraction can cause the apparent position of the target to differ from its true position, especially when the line of sight passes through different air layers with varying densities.
- Temperature variations can lead to thermal expansion or contraction of the surveying instruments, affecting their measurements.
- Wind can cause the instrument or target to move, resulting in errors in the readings.
- Vibrations from nearby traffic, construction activities, or other sources can also introduce errors in the measurements.

In conclusion, all the mentioned types of errors (instrumental errors, errors due to manipulation and sighting, and errors due to natural causes) can occur in tacheometric surveying. It is essential for surveyors to be aware of these errors and take appropriate measures to minimize their impact on the accuracy of the surveying results.