In Vernier Theodolites, vernier are used for taking the readings.
These theodolites are most commonly used in the general works.
Most of the general Theodolites can read upto 20"
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Transit and non-transit theodolite.
Varies according to instrument. There are differing scales and degrees of precision. Look up any catalog on surveying instruments and you will get some information, maybe more than you need, but you will get an idea. There are all different types, some heavily electronic
A theodolite is used to measure angles of a plane. This can be both vertical or horizontal, and it is used with high precision.
How much error is allowed in a digital vernier
A vernier caliper.