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Bill Lionheart you wrote: "I wonder how easily one can machine an accurately pitched thread on the arc of a sextant?"  

You do it using a dividing head, or 'dividing engine' as Jesse Ramsden would have called it, (viewable in the South Kensington Science Museum).  This is a typical video of which there are several similar online.  https://www.bing.com/videos/riverview/relatedvideo?&q=using+a+dividing+head&&mid=52C63021CDDC3AF733D752C63021CDDC3AF733D7&&FORM=VRDGAR although I’d have been happier if the chap had been more careful over hiding his shirt cuffs.  Don't mention 'Sextant' in your searches; they'll only tell you what a sextant is and how to use it.  Search for 'using a dividing head'

When I made my plywood sextant for a PGCE in Design and Technology in 1983, I just started by drilling the hole for the index arm in a quadrant section of half inch ply.  Then I glued an ABS bearing plate close to the outer edge.  Next, I got the lab technician to set it up in the dividing head so that I could take the sextant round one degree at a time to scratch one degree marks into the ABS.  I can't remember what I did about the half degrees.  In the video the chap mills a 14 toothed gear wheel.  You could do the same for a sextant arc. 

The accuracy would depend upon the skill and care of the technician and how much backlash remains in the dividing head and the cutting gear.  The gear obviously wears over time.  Try comparing the calibration certificates in the top of the boxes of a particular sextant using ‘Images’.  My 1941 Hughes Mates Three Circle claims a perfect arc, whereas 1970s models (the ones with the crinkle grey finish) of the same model of sextant have significant arc errors recorded.  If the 'Fake' sextants in question are being made in a garage in the Far East using second, third, or fourth hand machinery, then accuracy and repeatability is bound to suffer.  Don't look too closely at my Vernier.  It's clearly rubbish, I think I must have failed to reset the head, but I was running out of time. DaveP  

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