If the earth is considered to be a very big gyro that turns around its axis once every 24 hours, and on this big gyro we are operating our small gyro-instrument, the problem of making this small gyro-instrument north-seeking consists of arranging it as a suspended pendulous gyro Fig. With the earth rotating from west to east, the axis of the spinning gyro is directed in an east-west direction position I. When the plumbline has changed 15 degrees, the gyro-axis tends to keep the same position as in I shown in position 11 because of its inertia. But the precession due to the gravity force F compels the gyro-axis to turn to a north-south orientation, which is shown in position If the inertia of the system is great enough, the axis of the gyro-wheel will overshoot the meridian, and therefore cause the axis to precess in the opposite direction.
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This principle was adapted by Max Schuler in to build the first surveying gyro. In , the gyro-theodolite - at that time called a "meridian pointer" or "meridian indicator"  - was first used by the Clausthal Mining Academy underground. Several years later it was improved with the addition of autocollimation telescopes.
In , the Fennel Kassel company produced the first of the KT1 series of gyro-theodolites. The battery-powered gyro wheel is rotated at 20, rpm or more, until it acts as a north-seeking gyroscope. By tracking the spin axis as it oscillates about the meridian, a record of the azimuth of a series of the extreme stationary points of that oscillation may be determined by reading the theodolite azimuth circle.
A mid point can later be computed from these records that represents a refined estimate of the meridian. Careful setup and repeated observations can give an estimate that is within about 10 arc seconds of the true meridian. These errors can be moderated by refining the initial estimate of the meridian to within a few arc minutes and correctly aligning the zero torque of the suspension.
This is because the daily rotation of the Earth is in effect continuously tilting the east-west axis of the station. The spinner axis then accelerates towards and overshoots the meridian, it then slows to a halt at an extreme point before similarly swinging back towards the initial point of release.
This oscillation in azimuth of the spinner axis about the meridian repeats with a period of a few minutes. In practice the amplitude of oscillation will only gradually reduce as energy is lost due to the minimal damping present. The electrically powered gyroscope is started while restrained and then released for operation. During operation the gyroscope is supported within the instrument assembly, typically on a thin vertical tape that constrains the gyroscope spinner axis to remain horizontal.
The alignment of the spin axis is permitted to rotate in azimuth by only the small amount required during operation. An initial approximate estimate of the meridian is needed. This might be determined with a magnetic compass , from an existing survey network or by the use of the gyro-theodolite in an extended tracking mode.
Uses Gyro-theodolites are primarily used in the absence of astronomical star sights. For example, where a conduit must pass under a river, a vertical shaft on each side of the river might be connected by a horizontal tunnel. A gyro-theodolite can be operated at the surface and then again at the foot of the shafts to identify the directions needed to tunnel between the base of the two shafts. Unlike an artificial horizon or inertial navigation system, a gyro-theodolite cannot be relocated while it is operating.
It must be restarted again at each site. When available, astronomical star sights are able to give the meridian bearing to better than one hundred times the accuracy of the gyro-theodolite. Where this extra precision is not required, the gyro-theodolite is able to produce a result quickly without the need for night observations.
This principle was adapted by Max Schuler in to build the first surveying gyro. In , the gyro-theodolite — at that time called a "meridian pointer" or "meridian indicator"  — was first used by the Clausthal Mining Academy underground. Several years later it was improved with the addition of autocollimation telescopes. In , the Fennel Kassel company produced the first of the KT1 series of gyro-theodolites. The battery-powered gyro wheel is rotated at 20, rpm or more, until it acts as a north-seeking gyroscope.