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Interpolating Freiberger Yacht Sextant Arc Errors
Date: 2016 Apr 10, 12:45 -0700

My Freiberger Yacht Sextant (No 111087, dated 19 Dec 1978 ) has considerable arc errors on its calibration curve.

The data nailed to the inside of the sextant box gives corrections (Verbesserung) in arcseconds at every 10 degrees.

Until recently, I never bothered the arc errors, but I’ve done  a little work over the winter to interpolate the corrections

at the intermediate 5 degree points ( perhaps pointless pursuit of tenths of a minute.. ), making a fuller and more useful set of corrections.

The whole thing can be done by graphing the correction curve and using French Curves to interpolate if you wish, but the newish web site ‘mycurvefit.com’ makes it all very easy ...

On the web site, Hit ‘Fit Method’, select 'Polynomial Curve Fit', 'Cubic Regression'.

Delete the demo data and type in (only) four lines of data from the sextant correction table.

The left hand data figure ( which becomes the graph X axis ) is the sextant indicated angle in degrees, the right hand data figure ( Y axis ) is the correction in seconds : in my case  the first run used

0  0

10 -15

20  -20

30  -7

... the calibration curve automatically and instantly appears in the website  graphing window.

Inspecting the graph, I read off the correction value from the middle of the graphed range, so getting the interpolated correction -19" for the sextant angle of 15 degrees.

Encouraged, I repeated succesively up the calibration table, using four successive pairs of values always, the next data set being

10 -15

20 -20

30 -7

40 -6

Out of which can be read the interpolated correction for 25 degrees, -14 " … and so on.

More than four data pairs in the website data window will produce only an approximate curve fit.

After that, I put together a critical table for the sextant's arc correction converted to tenths of a minute, very quick and easy to use.

Definitely a winter type job, no apologies offered to myself or anyone else for producing 0.5' maximum practical difference in my intercepts. It just feels better than throwing away useable data. And it saves peering sideways into the sextant box for a correction, ( in the dark?) ,  converting it to tenths of a minute in my head, with little confidence in the guesstimated interpolation.

Enjoy the coming summer ..

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