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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Centring Error Detector
From: Frank Reed
Date: 2014 Jan 21, 19:55 -0800

You wrote:
"Here's a 7 year old post that caught my eye.
It describes a method that permits you to measure the arc error. It all makes sense to me but I'm trying to figure out how the prism is aligned to the optical path assigned to the horizon."

And you included the link to that post from early 2007 in a follow-up:
http://fer3.com/arc/m2.aspx/Centring-Error-Detector-FrankReed-jan-2007-g2047

Yes, even without the link, I knew exactly what you were referring to! In fact I have implemented that system, and I use to calibrate sextants on a regular basis. However... my implementation does look a LITTLE different from the description...

To answer your specific question, the prism (or equivalent) is mounted or held above the index mirror, assuming the sextant is held vertically. It feeds an image of the horizon deflected so that it appears to be coming from some exact angle, say 45° 00.0' high, in the sky. The observer looking through the instrument then sees a direct and reflected image of the horizon. Make them coincide just like in a common IC test, and then check the instrument reading. Correct for previously determined index error. If the sextant reads 45° 00.5', then the arc error is 0.5' at 45°. You write that down in your correction tables, switch to the next prism, and repeat. Easy, huh?

Back in 2007, we (Alex, me, George H., and a few others) set aside the idea in the patent because it appeared to depend on expensive prisms manufactured to bend light at certain specific angles. But a couple of years after that, I pulled it off the shelf in the back of my head and started considering cheaper alternatives. I realized that the optical system only uses the reflecting properties of the interior faces of the prisms. That means that the prisms could be replaced by pairs of small mirrors rigidly mounted in frames. Now it was starting to look do-able. I would still have to make a dozen of these framed mirror pairs for reasonable coverage of all sextant angles, so not yet actually cheap. At that point, it occurred to me that I could keep one mirror rigidly mounted on the frame and attach the other mirror to some sort of rotating component. Instead of building a dozen fixed-angle pairs, I would have one adjustable pair of mirrors! If I could reliably read off the rotation of that mirror from some calibrated scale, then I could feed ANY angle of light to an un-calibrated sextant just by placing this device (with its two mirrors, a rotating arm, and an angular scale) above the index mirror of that sextant. Do you see it yet?? I had invented a sextant. That is, the optical system of a set of a dozen of these various prisms is identical to a previously calibrated sextant set to a dozen specified angles. I can calibrate an unknown sextant with a known, calibrated sextant. The calibrated sextant "feeds" an image with a known angular deflection to the un-calibrated sextant. And rather than placing the calibrated sextant awkwardly "above" the other (and upside down) to look at a distant horizon, you place the two on their sides on a table to look at a distant vertical target, like a mast. The rest is just like an index correction test, as before. The devil is in the details, of course. But I want to emphasize that as far as the optics are concerned, this is identical to that old patent involving prisms.

Finally, the inevitable question: is this a better method of testing arc error than shooting lunars? Sometimes yes. This test with two sextants works when it's cloudy, which is a big advantage. And I can test ten angles up and down the arc in a single afternoon. But it's cumbersome to set up, and there may be orientation issues that I haven't resolved yet. I feel that it could be cleaned up and streamlined easily enough. It's one of those things that I would like to do if time and money (=time) were infinite.

-FER

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