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I seem to remember this came up a while back.  My solution (theory only never tried), which came up as an offshoot of some work I was doing on the effects of tilt errors on a mirror AH, was that if, you could set the mirror accurately to any angle, you could get rid of 20 degrees of height sextant required for every 10 degrees of mirror tilt.  It did rather look as if you might possibly have to place your body in a rather unusual position in order to do the shot.  Appologies if I,ve use this photo before.  Dave P

I decided to carry out a proof of concept test. I suspected that I would be unpopular if I spent  noon tomorrow staring at the Sun (remember Xmas in the southern hemisphere is usually hot and sunny). I saw no reason why the test had to be carried out at noon so could do it this afternoon. I could not find a mirror but decided that the glass cover of the AH would do. See the photo.

Both sun images were clear in the glass. I had to kneel down but it was not an impossible position.

I calculated Hc then measured  x & y of the mirror to the nearest mm or three. See attached worksheet.

Hc - Ho  = 21° 03'. The mirror angle was tan-1(38/106) = 19° 43'.  Changing the y value  to 41mm gives tan-1(41/106) =21° 08' which is getting close to Hc - Ho.

Given the VERY rough way in which I performed the test I believe that this proves the concept. The difficulty is in setting up an accurately aligned mirror. Until about a year ago there was a second hand tool shop near me. I am sure the owner would know what a sine bar is. Unfortunately the shop was closed and replaced with an expensive cafe more in "keeping" with the area. Maybe I should look on Ebay?

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