NavList:

Or will this instrument irregularity introduce a different error at every possible altitude?

Yes, a different error at each angle, proportional to tan(angle/4), and quadratic in the perpendicularity error.  Chauvenet says that with a perpendicularity error of 5 arcminutes, the sextant-angle error (at 120 degrees measured angle) is 0.5 arcsecond.  If the perpendicularity were out by some much larger amount, say 20 times higher or 1 degree, then the sextant-angle error is 400 times larger or 200 arcseconds (3 arcmin).

So it seems wise to keep the index mirror perpendicular to the arc to better than say 10 arcmin.  Try estimating the error of your Mark 3 by viewing the reflections of two small objects placed on the arc and sighting in the plane of the tops of these objects.  (The mirror is offset a little from the axis of the index bearing, so viewing the arc edge from above is not quite right.)  I too have a Mark 3, but I've never measured the nonperpendicularity.  I'll give that a go just to see what it is.

Incidentally, and this is off-topic to the question, but what is the reasoning behind a horizon mirror with glass in the horizon path?  The Mark 3 has just a mirror on the index-mirror path and empty air on the horizon path.  It seems perfectly usable this way.  Do "normal" sextants provide a split mirror to get the benefit of the 4% reflection from the plain glass?  Or they don't want to expose the edge of the mirror to the elements?  Or is there some other reason?

Cheers,

Peter