A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Precision of sextant observations: taken from How many chronometers?
From: Bill Morris
Date: 2009 May 9, 22:24 -0700
From: Bill Morris
Date: 2009 May 9, 22:24 -0700
George Huxtable wrote: "We need to consider the instruments that were being used, throughout the lunar era, which would all be Vernier sextants, not micrometer types. I have such a sextant, which I haven't taken to sea. Using it on land, my old eyes have great difficulty, even with a good magnifier, perceiving which of three adjacent lines on the Vernier makes the best fit, even with really good illumination." and Henry wrote of "well calibrated modern instruments" For most of the period in which lunars were used in earnest, no calibration service was available, at least in Britain. Kew Observatory offered the service from about 1870 onwards, but calibrated only 49 instruments in the first twenty years. Even then, the precision of the calibration could be no better than the precision of the instrument itself. For example, an instrument divided to 20 seconds could be calibrated only to that precision. George has mentioned the difficulty in actually reading the verniers and since it is a rainy day, I have done some simple investigations to try to get some idea of the reliability of a vernier reading in ideal circumstances. The set-up is as shown in the attachment. The sextant sits on a levelling jig on a surface table and an autocollimator is directed at the index mirror so that its axis is at right angles to the mirror. A lamp and low power stereo microscope are used to read the vernier at a magnification of x 20. I won't go into many details of the autocollimator. It is an optical device that can measure the deviation of a projected light ray when it is reflected back from a mirror. The instrument shown has a least division of 0.2 seconds and in expert hands is said to be reliable to 0.3 seconds, given a high class reflector and perfect viewing conditions. For my own part, I can very easily detect a deviation of 3 seconds and I think it is safe to say that the repeatability of a single reading would always fall inside that range. Using first the microscope and then the magnifier provided with the instrument to set the vernier, I reset the sextant thirty times to the same reading and took readings with the autocollimator on the index mirror to study the amount of variation. The results do not depend on mirror adjustments, bearing eccentricity and the like, though both instruments had recently been fully stripped down, rebuilt and adjusted. The first sextant was a ladder framed one by Brandis and Son Inc. The "Inc" places it after 1916 and its serial number places its manufacturing date around the First World War. The vernier is divided to 20 seconds and its simple plano-convex magnifier has a focal length of 25 mm, giving a nominal magnification of x 10. The second sextant was a high class ladder frame sextant by Hughes and Son and has a 1920 calibration certificate from the National Physical Laboratory revealing no error across its range. The vernier is divided to 10 seconds and the Ramsden magnifier magnifies x 7.5. Like the Brandis, its graduations are sharp and easy to read, but are rather finer than the former's. The standard deviation is a measure of dispersion of the results around the mean and in this context we can expect them to be normally distributed. That is to say, about 68 percent of results will be found within 1 SD each side of the mean and 95 percent within 1.96 SDs each side of the mean. In the results that follow, I give the rounded 68 and 95 percent ranges when using the magnifier provided. SD Microscope SD Magnifier 2 SD range 3.92 x SD range (68%) (95%) Brandis 4 11.7 23 46 Hughes 4.3 4.0 8 16 The better results of the Hughes instrument are probably due to the finer graduations and possibly also to the colour correction and flatter field of the magnifier. While repeatability of setting is not quite the same as accuracy of reading of the vernier, this little experiment does give us some insight into the latter. We could perhaps agree that when the Hughes sextant is set to a nominal reading, there is a seventy percent chance that the setting lies within 10 seconds of that chosen reading, and a ninety-five percent chance that it lies within 16 seconds of it. When it comes to reading a sextant, the results are critically dependent on obtaining a correct index error. As I have shown in a previous post, whichever method of ascertaining index error is used, there is quite a lot of dispersion of the results, at least with micrometer instruments. For my own part, I doubt that observations could be reliably and consistently made to within 10 arcseconds. Bill Morris Pukenui New Zealand --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavListfirstname.lastname@example.org -~----------~----~----~----~------~----~------~--~---