# 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:**Bill Morris

**Date:**2009 Jul 6, 22:51 -0700

I have now made the appeal to experiment that I suggested in post 8984, I used a SNO-T sextant whose silky smooth micrometer has well under 6 seconds of error. (Those interested can find a calibration chart for its micrometer in a blog on my web site www.sextantbook.com under "Interesting overhaul problems" Look at "A worm turns"). A prelimary experiment showed that the arm-ache coefficient was going to be substantially exceeded if I made the thirty observations beloved by statisticians, so I clamped the sextant in the soft jaws of a small vice held on top of a theodolite tripod. I used a land horizon about 6 km away and the viewing was very good. At one point, a small insect crept across the landscape near the horizon and with the x 6 'scope I was able to make out that it was a person on a 4-wheel farm bike. Starting with the naked eye at arms length, the first thing I noticed was that there was in fact a very tiny area of overlap of the images, so that I may not in fact have been testing naked eye vernier acuity at all. In the SNO-T horizon mirror, there is a narrow band of paint overlap, about half a millimetre, on the back of the mirror extending on to the clear glass. This is true ( or should be true) of most sextants, as the paint protects the edge of the silvering. Exceptions might be those instruments with sealed mirror cells.Its relevance is not clear to me. For those who are totally ignorant of statistics, rather than 90 percent ignorant like me, standard deviation is a measure of the spread of results about their mean and assumes a "normal", "Gaussian" or "bell-shaped" distribution. Variance is the square of the standard deviatoon. A series of 30 naked eye observations had a mean of 1.467 minutes and a standard deviation of 0.458. After I had done the two telescope series, I did another 30 naked eye observations. This time the mean was 1.30 and the SD was 0.415. A variance ratio test gave an F value of 1.218 against a tabular value for 29 degrees of freedom of 1.85, so we may infer that the SDs are not significantly different at the 10 percent level. A series of 30 observations with a x 4 Galilean telescope gave a mean of 0.743 minutes with an SD of 0.187. The figures with a x 6 Keplerian telescope were a mean of 0.593 and and SD 0.129. Comparing these two series, the variance ratio F was 2.10, which exceeds the tabulated value at the 10 percent level, but not at 2 percent. For our purposes, we can say that the telescope SDs are significantly different from each other and it is clear just on inspection that both differ significantly (F exceeds 4)from the naked eye results. It seems that if using the horizon, we should check index error with the same means that we plan to use for the observations and that in general we will get better results by using the highest magnification that suits the circumstances. This latter may well be open to argument. We'll see... Bill Morris Pukenui New Zealand --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---