A theodolite reads to 20 seconds, or with a good optical instrument to one second. But an instrument’s stated precision means nothing if the reading itself is wrong for some other reason.
Errors in theodolite work fall into three categories, and knowing which category an error belongs to tells you how — or whether — it can be dealt with.
The Three Categories
- Instrumental errors
- Personal errors
- Errors due to natural causes
The distinction is essentially about where the fault lies — in the instrument, in the observer, or in the environment.
1. Instrumental Errors
These arise from imperfections in the instrument itself.
| No. | Instrumental Error |
|---|---|
| a | Maladjustment of the plate level |
| b | Line of sight not perpendicular to the trunnion axis |
| c | Horizontal axis not perpendicular to the vertical axis |
| d | Eccentricity of inner and outer axes |
| e | Axis of altitude level not parallel to the line of sight |
| f | Faulty circle graduation |
| g | Eccentric vernier |
The Pattern in the First Five
Errors (a) to (e) are all failures of perpendicularity or parallelism between the instrument’s axes. None of them concerns the target, the ground or the observer — they are faults in how the instrument is assembled and adjusted.
That shared nature is what makes them treatable, as we shall see.
Eccentricity of the Inner and Outer Axes
This one deserves explanation, since it follows directly from the twin-spindle design.
The upper plate turns on the inner spindle and the lower plate on the outer spindle. Ideally the two share exactly the same centre. If they do not — if one is slightly off-centre relative to the other — the verniers no longer sit symmetrically on the graduated circle.
The result is that the two verniers give different readings. This is precisely why theodolites carry two verniers set 180° apart, and why the mean of both verniers is taken: an eccentricity that makes one vernier read high makes the other read low by the same amount, so the mean is correct.
Faulty Graduation and Eccentric Vernier
Errors (f) and (g) are different in kind from the others. They are manufacturing defects in the scales themselves rather than misalignments of axes.
Because they are built into the engraving, they cannot be adjusted out in the field. They are dealt with by taking readings on different parts of the circle — since a graduation error at one position will differ from that at another, distributing observations around the circle averages the defect away.
Errors Eliminated by Changing Face
Recall from the basic definitions that changing face eliminates three specific errors. Comparing that list with the instrumental errors above shows the overlap directly:
| Instrumental Error | Eliminated by Changing Face? |
|---|---|
| (b) Line of sight not perpendicular to trunnion axis | Yes |
| (c) Horizontal axis not perpendicular to vertical axis | Yes |
| (e) Axis of altitude level not parallel to line of sight | Yes |
| (a) Maladjustment of plate level | No |
| (d) Eccentricity of axes | No — use the mean of both verniers |
| (f) Faulty graduation | No — read different parts of the circle |
| (g) Eccentric vernier | No — use the mean of both verniers |
Why Changing Face Cannot Fix Everything
Changing face works because a geometric misalignment reverses its effect when the instrument is reversed, so the two errors cancel in the mean.
But this only helps for errors that actually reverse. Maladjustment of the plate level tilts the vertical axis itself, and a tilted vertical axis stays tilted the same way no matter which face you observe on — so flipping the telescope changes nothing. That error must be removed by careful levelling, which is why levelling is one of the temporary adjustments.
Similarly, a fault engraved into the circle is present on both faces identically.
2. Personal Errors
These arise from the observer.
| No. | Personal Error |
|---|---|
| a | Inaccurate centering |
| b | Slip |
| c | Inaccurate levelling |
| d | Inaccurate bisection of the target |
| e | Displacement of the target |
| f | Parallax |
| g | Mistakes in setting and reading verniers |
Three of These Are Failures of Temporary Adjustment
Errors (a), (c) and (f) map directly onto the five temporary adjustments:
- Inaccurate centering — the vertical axis is not exactly over the station mark, so the angle is measured from the wrong point.
- Inaccurate levelling — the vertical axis is not truly vertical, so horizontal angles are not measured in a truly horizontal plane.
- Parallax — the target image does not lie in the plane of the cross-hairs, caused by focusing the objective before the eyepiece.
This is why temporary adjustments matter. Skipping or rushing them does not merely delay the work — it introduces named errors into every reading.
Slip
Slip means the instrument or one of its plates moves unintentionally between observations — perhaps a clamp was not tightened, or the tripod shifted.
It is particularly dangerous in the repetition method, where readings are accumulated over many turns without resetting. A slip partway through corrupts the accumulated total, and since there is no intermediate zero to check against, it may go unnoticed.
Errors versus Mistakes
Item (g) — mistakes in setting and reading verniers — is different from the rest. As noted in the chaining errors topic, a mistake is a blunder, not an error. It follows no statistical law, has no consistent magnitude, and cannot be reduced by averaging.
A mistake can only be caught by a check — which is exactly why the reiteration method closes the horizon at 360°, and why a closed traverse must sum to (2n − 4) × 90°.
3. Errors Due to Natural Causes
The third category covers influences from the environment rather than from the instrument or the observer — conditions such as wind, temperature, refraction of the line of sight and unstable ground.
These share an important property: they are outside anyone’s control. You cannot adjust the atmosphere. They are managed by choosing when and how to observe — avoiding the heat of the day when refraction and shimmer are worst, shielding the instrument from wind, and setting the tripod on firm ground.
One natural condition has already appeared in the temporary adjustments: wind causing the plumb bob to swing, which is why an optical plummet is used instead in windy weather.
How Each Category Is Handled
| Category | Source | How It Is Dealt With |
|---|---|---|
| Instrumental | The instrument | Changing face, mean of both verniers, reading different parts of the circle, permanent adjustment |
| Personal | The observer | Careful temporary adjustments, careful observation, and checks to catch mistakes |
| Natural | The environment | Choosing suitable conditions and timing; cannot be adjusted away |
The Underlying Principle
Look across the “how it is dealt with” column and one idea recurs throughout theodolite work:
Observe the same thing twice in opposite senses, and any error that reverses will cancel in the mean.
Both faces cancel collimation error. Both verniers cancel eccentricity. Left and right swings cancel friction and backlash. Different parts of the circle average out graduation defects.
It is the same principle behind fore and back bearings in compass surveying and behind double sighting — build redundancy into the observation, and errors reveal or remove themselves.
Quick Revision Notes
- Three categories: instrumental, personal, and natural errors.
- Seven instrumental errors: maladjustment of plate level; line of sight not perpendicular to trunnion axis; horizontal axis not perpendicular to vertical axis; eccentricity of inner and outer axes; axis of altitude level not parallel to line of sight; faulty circle graduation; eccentric vernier.
- Seven personal errors: inaccurate centering; slip; inaccurate levelling; inaccurate bisection of target; displacement of target; parallax; mistakes in setting and reading verniers.
- Changing face eliminates three instrumental errors — those involving perpendicularity of collimation to the trunnion axis, of the horizontal axis to the vertical axis, and parallelism of collimation to the altitude level.
- Eccentricity is dealt with by taking the mean of both verniers.
- Faulty graduation is dealt with by reading different parts of the circle.
- Maladjustment of the plate level cannot be removed by changing face — it requires careful levelling.
- Parallax is prevented by focusing the eyepiece before the objective.
- Natural errors are managed by choice of conditions, not by adjustment.
Mistakes Students Commonly Make
- Assuming changing face removes all instrumental errors. It removes three of the seven.
- Placing parallax among instrumental errors. It is a personal error, caused by incorrect focusing.
- Placing inaccurate centering and levelling among instrumental errors. Both are personal.
- Forgetting that eccentricity is why two verniers are provided and why their mean is taken.
- Treating mistakes in reading verniers as an ordinary error. A mistake is a blunder, removable only by a check.
- Listing fewer than seven instrumental or seven personal errors.
- Thinking natural errors can be corrected by formula. They are managed by observing under suitable conditions.
Conclusion
Theodolite errors sort into three groups by where the fault lies. Instrumental errors come from misaligned axes and imperfect scales, and the best of them — three of the seven — are removed simply by changing face, while eccentricity is handled by meaning both verniers. Personal errors come from the observer, and three of them are nothing more than temporary adjustments done badly. Natural errors come from the environment and can only be avoided, not corrected. Running through all of it is one method: observe twice in opposite senses, and let the errors cancel themselves.
Frequently Asked Questions
What are the three categories of error in theodolite work?
Instrumental errors, personal errors, and errors due to natural causes.
What are the instrumental errors?
Maladjustment of the plate level; line of sight not perpendicular to the trunnion axis; horizontal axis not perpendicular to the vertical axis; eccentricity of the inner and outer axes; axis of the altitude level not parallel to the line of sight; faulty circle graduation; and eccentric vernier.
What are the personal errors?
Inaccurate centering, slip, inaccurate levelling, inaccurate bisection of the target, displacement of the target, parallax, and mistakes in setting and reading the verniers.
Which instrumental errors are eliminated by changing face?
Those due to the line of collimation not being perpendicular to the horizontal axis, the horizontal axis not being perpendicular to the vertical axis, and the line of collimation not being parallel to the axis of the altitude level.
Why can changing face not remove maladjustment of the plate level?
Because that error tilts the vertical axis itself, and a tilted vertical axis remains tilted the same way on both faces, so nothing reverses and nothing cancels. It must be removed by careful levelling.
What is eccentricity of the inner and outer axes?
A condition in which the two concentric spindles do not share exactly the same centre, so the verniers sit asymmetrically on the graduated circle and give different readings.
How is eccentricity dealt with?
By taking the mean of both verniers, which are set 180 degrees apart, since an eccentricity that makes one read high makes the other read low by the same amount.
How are faulty graduations dealt with?
By taking readings on different parts of the graduated circle, so that graduation errors at different positions average out.
Is parallax an instrumental or personal error?
Personal. It arises when the objective is focused before the eyepiece, leaving the target image out of the plane of the cross-hairs.
How are natural errors handled?
By choosing suitable observing conditions and timing, since environmental influences such as wind, temperature and refraction are outside the surveyor’s control and cannot be adjusted away.