Of all the instruments in surveying, the theodolite is the one that measures angles precisely. A compass gives you a rough direction; a theodolite gives you an angle to within seconds of arc.
This post covers what a theodolite does, the two ways it is classified, and how its size is specified.
What a Theodolite Is For
A theodolite is an important instrument used for the measurement of horizontal and vertical angles in surveying.
Its Other Uses
It can also be used for a number of other surveying operations:
- Prolonging a line
- Measuring distances indirectly
- Levelling
Why It Is So Versatile
Look at that list and a pattern emerges. Each of the extra uses is really an angle measurement in disguise.
- Prolonging a line means extending a straight line beyond its end — achieved by sighting along the line and transiting the telescope, which is an exercise in maintaining a direction.
- Measuring distances indirectly is tacheometry — a vertical angle and a staff reading give the distance without touching the ground between.
- Levelling works by setting the line of sight horizontal, which is simply a vertical angle of zero.
Because angle is the most fundamental measurement in surveying, an instrument that measures angles well can be pressed into service for a great deal else.
Classification 1: Transit and Non-Transit
Theodolites can be classified into transit and non-transit theodolites.
Transit Theodolite
A theodolite is said to be a transit one when its telescope can be rotated through 180° in a vertical plane about its horizontal axis, thus directing the telescope in exactly the opposite direction.
Non-Transit Theodolite
A theodolite is said to be non-transit when its telescope cannot be rotated through 180° in a vertical plane about its horizontal axis. Such theodolites are obsolete nowadays.
Why the Ability to Transit Matters So Much
This single capability — flipping the telescope end over end — is far more important than it first sounds, and it explains why non-transit instruments died out.
Transiting allows the face to be changed. And changing face, as the definitions topic shows, eliminates three separate instrumental errors: collimation error, error from the horizontal axis not being perpendicular to the vertical axis, and error from the line of collimation not being parallel to the altitude level axis.
In other words, a transit theodolite can check and cancel its own errors simply by taking a second reading with the telescope flipped. A non-transit instrument cannot do this at all — whatever error it has, it keeps. That is a decisive advantage, and it is why “transit theodolite” is now effectively a synonym for “theodolite”.
Classification 2: Vernier and Precise Optical
Theodolites can also be classified into two types according to how the readings are taken.
1. Vernier Theodolites
- Verniers are used in taking the readings.
- These theodolites are most commonly used in general work.
- Most vernier theodolites can read angles up to 20 seconds — that is, the least count of the theodolite is 20″.
This connects directly back to the vernier topic in the fundamentals chapter. The graduated circle can only be engraved so finely; the vernier then reads the fraction between graduations, giving a least count of s/n — the smallest main scale division divided by the number of vernier divisions.
2. Precise Optical Theodolites
- Fitted with an optical system used to read both horizontal and vertical angles precisely.
- These have a micrometer for taking readings, and are also called micro-optic theodolites.
- Used for precise work.
- Most can read angles up to 1 second or less.
The Difference in Accuracy
| Vernier Theodolite | Precise Optical Theodolite | |
|---|---|---|
| Reading device | Vernier scale | Optical system with micrometer |
| Least count | 20″ | 1″ or less |
| Also called | — | Micro-optic theodolite |
| Used for | General work | Precise work |
The difference is a factor of twenty or more. To appreciate what one second of arc means, it is roughly the angle subtended by a one-rupee coin viewed from about five kilometres away — which is why precise optical theodolites are reserved for work that genuinely justifies them.
How Theodolite Size Is Defined
The size of a theodolite is defined by the size of its lower graduated circle. For example, a 20 cm theodolite means the diameter of the graduated circle of the lower plate is 20 cm.
Generally the size of theodolites varies from 8 cm to 25 cm.
Why Size Is Measured This Way
It seems an odd choice at first — why define an instrument’s size by one internal circle rather than its overall dimensions?
Because that circle is what determines the accuracy. All angular readings come from graduations engraved around the lower plate. A larger circle has a longer circumference, so the same angular division occupies more physical space along it — and a wider gap between graduations can be subdivided more finely and read more precisely.
So the diameter of the graduated circle is not a description of bulk; it is a statement about how accurately the instrument can read. Quoting it as the size is therefore the most informative single number available.
Both Classifications Together
| Basis of Classification | Types | Distinguishing Feature |
|---|---|---|
| Ability to rotate the telescope | Transit / Non-transit | Whether the telescope can be turned through 180° in a vertical plane |
| Method of reading | Vernier / Precise optical | Whether readings are taken by vernier or by optical micrometer |
The two classifications are independent, and a real instrument belongs to one category from each. In modern practice virtually every theodolite is a transit theodolite, and the practical choice is between vernier and precise optical according to the accuracy the job demands.
Quick Revision Notes
- A theodolite measures horizontal and vertical angles.
- It is also used for prolonging a line, measuring distances indirectly, and levelling.
- Transit theodolite: telescope can be rotated through 180° in a vertical plane about its horizontal axis.
- Non-transit theodolite: telescope cannot be so rotated; these are obsolete.
- Transiting matters because it allows changing face, which eliminates three instrumental errors.
- Vernier theodolite: readings by vernier, least count 20″, used for general work.
- Precise optical theodolite: optical system with micrometer, also called micro-optic, reads to 1″ or less, used for precise work.
- Size of a theodolite = diameter of the lower plate’s graduated circle.
- Sizes generally range from 8 cm to 25 cm.
Mistakes Students Commonly Make
- Defining theodolite size by the telescope length or overall height. It is the diameter of the lower graduated circle.
- Swapping the least counts. Vernier reads to 20″; precise optical reads to 1″ or less.
- Saying a transit theodolite rotates 180° in the horizontal plane. It is in a vertical plane about the horizontal axis.
- Forgetting that precise optical theodolites are also called micro-optic theodolites.
- Treating the two classifications as alternatives. They are independent — an instrument has a type from each.
- Giving the size range as 8 to 20 cm. It is 8 to 25 cm.
Conclusion
A theodolite exists to measure angles accurately, and because so much of surveying reduces to angles, it doubles as an instrument for prolonging lines, finding distances indirectly and levelling. It is classified two ways at once: by whether the telescope can be transited through 180 degrees — a capability so useful for cancelling instrumental errors that non-transit instruments have disappeared — and by whether readings are taken on a vernier at 20 seconds or by optical micrometer at one second. And its size is quoted as the diameter of the lower graduated circle, because that circle is what sets the accuracy.
Frequently Asked Questions
What is a theodolite used for?
Primarily for the measurement of horizontal and vertical angles. It can also be used for prolonging a line, measuring distances indirectly and levelling.
What is a transit theodolite?
One whose telescope can be rotated through 180 degrees in a vertical plane about its horizontal axis, thus directing the telescope in exactly the opposite direction.
What is a non-transit theodolite?
One whose telescope cannot be rotated through 180 degrees in a vertical plane about its horizontal axis. Such theodolites are obsolete nowadays.
Why are non-transit theodolites obsolete?
Because the ability to transit the telescope is what allows the face to be changed, and changing face eliminates three separate instrumental errors. A non-transit instrument cannot cancel these errors at all.
What is the least count of a vernier theodolite?
Most vernier theodolites read angles up to 20 seconds, so the least count is 20 seconds.
What is a precise optical theodolite?
A theodolite fitted with an optical system for reading both horizontal and vertical angles precisely, using a micrometer. It is also called a micro-optic theodolite and can generally read to 1 second or less.
How is the size of a theodolite defined?
By the diameter of the graduated circle of its lower plate. A 20 cm theodolite has a lower plate graduated circle of 20 cm diameter.
What is the usual range of theodolite sizes?
Generally from 8 cm to 25 cm.
Why does the graduated circle diameter determine accuracy?
Because a larger circle gives a longer circumference, so each angular division occupies more physical space along it and can therefore be subdivided and read more finely.