NavList:

Tony you said:  the horizon is too near to do checks
The height difference between the mirrors of my Mate’s sextant is 1.5 inches.  For a height of eye of five feet, the distance of the sea horizon is about 2.6nm.  Therefore, we’re talking about an angular difference of 1.5 in 6080x2.6x12 or tan-1 0.00000791.  That is 0.00453 degrees or 0.027 minutes of arc.  Thinks! Would the error induced be ‘on’ or ‘off’ the arc.

You also said:  The most accurate I.E. check/measurement is measuring Sun's diameter - across - in horizontal direction; with left-right limbs. This excludes any effects of the atmospheric refraction - which are there if the upper-lower limbs are used.

Just how much change in atmospheric refraction would you expect in half a degree change in altitude at medium altitudes?  Between approximately 21 and 33 degrees of altitude, the change in atmospheric refraction is one minute of arc.  That’s 1/12 minutes per degree change of altitude, so 32 minutes change of altitude must equate to roughly 1/24^th minutes change in refraction.  A further one minute refraction difference lies between 33degrees and 63 degrees altitude, so at higher altitudes the change in refraction will be roughly 1/60 minute change in refraction.  How close can you put the Sun’s edges together, especially in muggy weather?

To my mind, continuity of the horizontal is the key, so what’s wrong with picking any old horizontal line a decent distance away?  There’s no clever maths involved, and you can do a quick check every time you take your sextant out of the box.  You can also get within one minute of arc merging any bright star or merging the Moon with a couple of slightly different weak to medium shades in.  I just tried it.  DaveP