NavList:

Frank,

The index arm relative to the vertical is fixed independent of the altitude of the body when observed with an artificial horizon and the sextant is used in the orientation such that the horizon mirror transmitted image is the AH.

Proof:

View the sextant from the side where, as the body rises, the sextant frame is rotated ccw to keep the the horizon mirror transmitted image of the AH in view.  A one degree rise in the body requires an equal one dgree ccw frame rotation.

Observe the scale on the sextant arc.  It is well known and obvious that one degree of the scale is half a degree rotation of the index arm.  This arises from the reflection.  Similarly the reflection of the artificial horizon means that when a body rises by one degree, the direct body image and reflected AH image of the body diverge by two degrees.

Note that the index arm is rotated cw as a body rises.

The doubling of the angle by the AH and the halving of the index arm coupled coupled with the frame rotation in the opposite direction as the index arm means the the index arm is stationary relative to the vertical.

DaveF