# NavList:

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

**Re: "Vernier acuity" of horizon IC tests**

**From:**Douglas Denny

**Date:**2009 Jul 6, 13:42 -0700

Dear Mr. Rudzinski, No confusion. I am interested in the standard deviation figures only, which are a measure of the spread of the results, which is depndent on, and a function of, the resolving power of the eye, and hence what I am interested in. The index error itself is not the valued quantity of interest - the sigma of the results is. The sight tube gives a sigma of:- 1.0' The 4 x 40 " " :- 0.15' The 7 x 35 " " :- 0.28' Using the usual criteria of twice sigma for obtaining 68% of all expected readings which will fall into that spread; and four times sigma for an expected range of 95% of all readings we have:- sight tube twice sigma: 2.0' 4 x 40 scope " : 0.3' 7 x 35 scope " : 0.56' sight tube four times sigma : 4.0' 4 x 40 scope " : 0.6' 7 x 35 " : 1.12' These are very interesting. They illustrate a number of points. Firstly that someone can go out with their sextant, take a number of sights, and with a fairly small sample obtain very consistent results. Secondly, the sight tube only (eye only) gives a spread (measured by sigma) of around one minute of arc. This is exactly the same as standard "letter acuity" as measured by your optometrist with his chart and is the expected recognised average minimum acuity expected for a large sample population. Thirdly, sigma with telescopes used is indeed improved, and better than simple "letter acuity" of one minute of arc (the increase in resolution of course might be expected with the greater resolving power of a telescope) and comes down to that of around the graticule resolution of the eye (black/white bars).. but is not _tremendously_ improved compared to the much greater theoretical resolving power that a magnified image gives with the telescope ... which in turn suggests the eye is still the limiting factor in the resolution achieved. This is to me, very interesting indeed. Fourthly, increasing the magnification from four to seven did not materially affect the resolution very greatly, and in fact degraded it. Gordon found anomalous effects with telescopes too. This is very interesting. Gordon suggests the optical qualities of the telscope are very important; and your own results suggest, as Gordon found, telescopes definitely can improve the quality of sight taking with a sextant, but the results cannot be predicted with particular telescope magnification/aperture combinations. There is scope (pardon pun-can't resit it) for practical research here for people on this forum to go out with their sextants with different telescopes and sextants and obtain a list of results like yours, then using this forum as a central exchange, collecting and analysing the results which might give an interesting insight into the qualities of the different telescopes and their aid to resolving power with practical sextant use. It would be an intersting and useful extension of the work Gordon started in the 1960s. He was acutely aware his results were dependent on only 500 observations; but the power of the internet now brings the possibility of many people around the world with their sextants adding to this simple basic research data started by Gordon. It would be a fitting tribute to Gordon's work. If it were done, all must do the same thing though to try to keep parameters constant - so simple index error check using a horizon would do admirably, with as many sights taken as possible; and with a note of details such as conditions of horizon; sextant, telescope, height above sea level, refraction (glasses prescription) of the individual, if any eye condition present (cataract for example) and suchlike. This would be expected to give results better than simple letter acuity, as a straight line is involved and theoretically can get down to the ultimate resolving power of the eye approaching ten seconds of arc at best. Degrading parameters in the sextant/telescope conmbination are likely to mean this is not achieved of course, but it would be fascinating to get some real hard analytical data on this. Douglas Denny. Chichester. England. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---