A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2017 Nov 13, 14:30 -0800
It's different at each angle, but in a simple way: the error from lack of perpendicularity is directly proportional to the observed angle. So if you have a strong reason to believe that your sextant has a perpendicularity error, and there is no means to eliminate it, you can measure it at some numerically convenient angle --like 100°-- and then apply a proportional amount at any other angle. Example: if you find a 20' error at 100°, you would apply a 12' correction at 60°, or a 6' correction at 30°, and so on. Easy! Note that the exact analysis from Chauvenet yields an error proportional to tan(angle/4), but Chauvenet did not always provide the practical versions of his results. It's very close to a simple linear proportionality for any normal case (in the example here, the worst case is at 60°, where the correction would be 5.75' by the tangent rule instead of 6.0' as the linear rule implies. He does, at least, point out that the error from perpendicularity can be eliminated easily in a common sextant.
Getting back to the case of a Davis Mk 3 plastic sextant, suppose the index arm isn't quite centered... Or suppose the scale isn't quite uniform... These factors and others will yield some variation in measured angle along the arc. We can call that "arc error", and in a sextant that has a non-adjustable index mirror, like the Davis Mk III, the perpendicularity error would be inseparably combined with these other errors. For each angle on the arc, there is some reasonably stable, fixed error. You would need to generate a calibration table for your sextant. There's no real need to focus on that single source of error from perpendicularity. Needless to say, this might be overkill for that type of sextant, but it's good clean fun testing it out, right?