Let us first assume your sextant is accurate near 0°. Further, that you have properly decided index error.
The first potential source of error may be abnormal refraction. Refraction affects lower angles more so than larger angles. You should take note of the air temperature and barometric pressure so as to refine your observation.
Another potential source of error is the artificial horizon. You mentioned that it is leveled using a Starrett level and supported by a plastic(!) cutting board. You should be aware that all materials deflect under load, as a function of stiffness and where the load is applied. Further, you do not mention where the level is placed. If you cannot be sure of the parallelism betwixt the cutting board and the front surface, or the back and front surfaces of the mirror, then you should be placing the level on the front surface of the mirror. Ideally, you should have two levels, placed orthagonal to each other and unmoved during the leveling operation. The levels should not be moved during the observation either. Professional horizons have sensitive vial levels, permanently affixed to the instrument. While it is possible, of course, to obtain excellent results with a homemade instrument, extra care must be taken.
'As a relative newcomer to celestial nav., I've experienced a puzzling problem. Using an artificial horizon, my sights at angles of 20 to 15 deg. (40 to 30 deg. sextant) have been significantly in error (40 min. to a full degree). Readings at greater angles have been relatively accurate.
My AH is a first surface miror mounted on a plastic cutting board. The board has three leveling feet and is leveled using a Starrett 98 level. The problem is evident with two different sextants.
Can anyone offer suggestions?
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