## Sources of error

The main sources of error associated with the gyro, other than those errors that apply just to the theodoliteobservations, are:

**(1) The assumed value of 1 scale unit in angular measure:**

There is uncertainty in the value of s of about 5% of its true value. The term s appears twice in equation and once in equation . When the value of C has been determined with equation it may be substituted into equation and rearranged to give:

The effect of an error in s may therefore be minimized by minimizing the size of d. This may be achieved with very careful use of a screwdriver by adjusting the point of suspension of the tape. The resulting value of d can then be found by the amplitude or a transit method. The effect of the error in s upon the computed value of N will be δN = dδs. If δs is assumed to be 20, and this can be no more than an assumption, then its effect will be reduced to 2 if d is reduced to 0.1 of a scale division. This is not easily achieved, but it can be done.

**(2) Other oscillations:**

So far it has been assumed that the suspended gyroscope is a single degree of freedom system. That is, the only way the mast can move is a simple rotation about its own axis. It can be shown that there are in fact five degrees of freedom. The top of the mast may swing like a pendulum both in a north–south and an east–west direction. The bottom of the mast may also swing like a pendulum both in a north–south direction and an east–west one with respect to the top of the mast. In practice, with a well set up gyro these swings should be very small, but when the spinner is spinning the effect upon the moving shadow mark is to add four further damped harmonic motion terms to the equation of motion. Equation now becomes:

This equation is of course quite unmanageable, there are 21 unknowns that need to be solved for. Fortunately the magnitudes of all the oscillations are quite small, and provided the gyro is allowed to settle down before the readings start the effects of the oscillations become negligible. This is because the damping terms associated with the other oscillations are larger than that of the main oscillation. One oscillation has a period of half a second.

This oscillation is often seen on the scale as a 2 Hz wobble when the mast is released. It takes a steady hand to be able to release the mast so that this movement is not significant. If a small 2 Hz wobble is present then it is best to let the gyro oscillate until the 2 Hz wobble has decayed and is not visible to the naked eye.

**(3) Tape zero drift:**

When the GAK1 is in transit, with the clamp tightened, the mast is held in position so that there is no tension in the tape. When the instrument is in operation, in either the spin or nonspin mode, the tape supports the full weight of the mast.

**(4) Change in the spin rate:**

The period of an oscillation depends, among other things, on the angular velocity of the spinner. The spinner is kept at a constant angular velocity by a power/control unit. As the battery in the power/control unit runs down during a set of observations there must be an effect upon the velocity of the spinner. It has been shown that a 0.1 volt change in the power produces a 0.1 second change in the period.

**(5) Irregularities in the engraving of the gyro scale:**

The effect of errors in the engraving of a glass theodolite circle is reduced by comparing opposite sides of the circle in a single observation and by using different parts of the circle in different observations. This is not possible with the gyro and so errors must be assumed to be negligible.

**(6) Dislevelment in the prime vertical:**

When the theodolite is perfectly levelled, the mast in its rest position would hang vertically from its point of suspension. If the theodolite was now dislevelled the mast would still hang vertically but would be in a different spatial position with respect to the body of the gyro housing and thus to the gyro scale.