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Re: Problem with a sextant
From: George Huxtable
Date: 2006 Apr 25, 20:55 +0100
From: George Huxtable
Date: 2006 Apr 25, 20:55 +0100
Alex quoted Wales, Cook's astronomer on his second voyage, as follows- | | "It must be owned there is yet something | in the constitution of this Quadrant very disagreable, | and not easily to be accounted for. Sometimes, many months | together, the longitudes deduced from observations made about the same | time with my two sextants would not differ more than 10 | or 15 miles, and very seldom so much; after which | the longitudes, so deduced, would begin to differ, and the difference | would gradually increase, sometimes more than a degree and an half: | In little time it would again decrease, and soon after the observations | would agree as well as ever. | It will be readily supposed, that no means were left untried by me | to discover the ause of this strange aberration; but all | my endeavours were ineffectual; | and I mention the circumstance to induce some person, | more skilful in mechanics, to attempt it". ================= It seems like he had a serious problem. A degree and a half of longitude corresponds to about 3 arc-minutes of divergence between the two instruments. That's a lot. A possible explanation might be collimation error. If the telescope of one sextant was badly aligned, to be out of the plane of the instrument, that would give rise to an error which became greater at greater lunar distances. And the sign of the resulting longitude error would switch, between a waxing moon and a waning one. In that way one might expect a divergence between longitudes taken by the two instruments, which varied systematically over the month. Could that be what's behind Wales' observations? How could he be sure which of the two was in error? Presumably he could take a long series of observations from a static known location. A likely place would be at Ship Cove in Queen Charlotte Sound, at the North end of New Zealand's South Island, to which Cook would return again and again. And then one might expect that a good instrument would give a constant longitude when lunars were taken, and a bad instrument would give a varying answer. But it wasn't quite that simple. The Almanac itself could be significantly in error, by rather more than half an arc-minute, an error that would vary cyclically over a lunar month. This problem was investigated, for a voyage made a few years later, by Nicholas A Doe in the "Journal of Navigation", vol 48 no3, Sept 1995, pages374-388, in a paper "Captain Vancouver's longitudes 1792". In which case, even a perfect instrument would show cyclic variations in the resulting longitude. ===================== That question, of systematic errors in the lunar distances in the Almanac, could be of some interest to maritime history. At a particular moment, all navigators using lunar distance, wherever they might be, would be similarly affected: even those using the French "Connaissance du Temps", which took its predictions from Greenwich.. So, in retrospect, positions recorded by those navigators could now be corrected to some extent for those known errors. The Moon's predicted ecliptic latitude and longitude were recorded in the almanac, to the nearest arc-second, at 12-hour intervals. From these, the lunar distances to chosen fixed stars were deduced, at 3-hour intervals by interpolation, and we can probably assume that that part of the operation was done precisely. With modern precise knowledge of the Moon's orbit, its ecliptic lat and long can now be predicted, and is readily available from several sources. It would be a service if someone would survey the almanacs of the lunar-distance era, and tabulate the day-by-day errors in those predictions. That would, until recently, have presented problems, in getting access to those old and precious almanacs. But now, scanned copies have recently become available on line, and would provide an interesting and useful exercise for any student to correlate modern predictions with the contemporary ones, without even stirring from his keyboard. Anyone interested in such a project? George. ============== contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.