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Lars,

Many thanks for your message.  To get a better feeling for the behavior of the eccentricity formula you described, I calculated correction values using your data for R (303°) and E (38”) and plotted them.  The black circles in the figure are the values listed in the sextant’s certificate, the white circles are the values calculated with your formula, and the distance between them are the residual errors. This shows that the function would reach a maximum at approximately 65° and return to 0 at approximately 125°.  I see now why the statement that correction values increase systematically from 0° to 120°,  as stated by Krasavcev in the page posted by Modris Fersters, does not hold for this value of E.

 I don't know how the Freiberger manufacturers calculate the correction values listed in their certificates either, or how they can measure error values as small as 1”.  The assumption that these are the measurements taken at 10° increments seems reasonable.  Their drum sextant does not come with a vernier, although one may be obtained as an accessory. I plan to send them an email message to ask if they would be able to give some information about their calibration techniques and report back.  They are still at the same location in Freiberg (Saxony) listed in the 1984 calibration certificate, and do answer requests.  For example, I was able to purchase an 8x30 prism telescope directly from them. It fits in my sextant, as the basic design of the Trommelsextant has not changed much since the 1980s.

Regards, Rafael