Sycamore
the latitude nut caters for `transport drift` ,not Earth rotation.
The latitude nut is simply a metal nut mounted on a threaded stud which protrudes from the inner gimbal. Altering the position of the nut creates an imbalance of the gimbal. This in turn creates a wander rate which compensates for (part of) the wander of the gyro.
The latitude nut is not accessible to the pilot, so it can be adjusted only in the instrument workshop........................1
Earth rate wander (in degrees per hour) = 15 x Sin latitude. So for a given latitude it is constant.
Transport wander = West - East Ground speed x Tan Latitude / 60.
The west-east ground speed can be adjusted (within limits) at will by the pilot................2
If you look at statements 1 and 2 you should see that the
(constant) position of the latitude nut cannot compensate for the
(non constant) transport wander, but it can compensate for the
(constant) earth rate wander.