NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Old style lunar
From: George Huxtable
Date: 2004 Dec 10, 15:41 +0000
From: George Huxtable
Date: 2004 Dec 10, 15:41 +0000
Alex wrote- >Is it his almanach that is responsible for this >scattering of measurements, >as Frank suggested? A 1800 almanac probably was not >very good in its Moon part. > >But this is probably easy to check. If anyone has a 1800 >(or around) almanach. Just compare it with Frank's online >lunar dist predictor. As I understand it gives accurate results >for the XIX century. ================ This has been done for a limited period, around the time of George Vancouver's arrival from across the Pacific in 1792: I have mentioned the paper before, on Nav-l. "Captain Vancouver's longitudes 1792", by Nicholas A Doe, appeared in The Journal of Navigation (of London, not the American journal with a similar name), vol 48 No 3 (September 1995), pages 374 to 388. Maskelyne's lunar distances, given at 3-hour intervals in the Almanac, were derived by second-order interpolation (so allowing for curvature) from the distance between the ecliptic lat / long of the Moon, and that of the other body, predicted at 12-hour intervals. Of the many steps in this calculation process, the most error-prone was obtaining the ecliptic longitude of the Moon, because of defects in the prediction theory. Doe, comparing almanac predictions with the modern JPL ephemeris, and also comparing with actual Moon observations made at the same period from Greenwich, shows that from mid-March to early May 1782 there was a strong cyclic monthly error in the predicted Moon's longitude. The average error was about 25 arc-seconds, and the variation was about 23.5 arc-seconds either side of that average, with a period of 29 days. So, in that period, there was no time when the error was zero, the error was always in the range 2 to 50 arc-seconds, always in the sense that made Vancouver's calculated Westerly longitudes less than they should have been. There's a useful project waiting out there for someone prepared to put a bit of effort into it. From 1767 on, when mariners started to work lunar distances from the Nautical Almanac, whatever errors occurred in the lunar predictions would put the longitudes of all mariners using lunars, anywhere in the World, out by the same amount on the same day. If we knew what those almanac errors were, a present historian, following a journal account of any lunar navigator from Cook's day on, would be able to correct for almanac errors, retrospectively, any recorded positions based on those lunars. To do that needs some dedicated soul to first extract the appropriate Moon ecliptic-longitudes, noted at noon and midnight, from the Almanacs, and compare them with modern predictions, for (say) the century following 1767. Perhaps less-frequent comparisons than two per day would be acceptable. The comparison with modern predictions could readily be automated, no doubt, once the extraction from the early almanacs had been done. As almanacs have been digitised from 1804 by the Mystic museum, someone that's handy with OCR (optical character recognition) software might be able to automate much of the data-extraction process from that date onward. For the years from 1767 to 1803, there seems no alternative but to scan through old library volumes, transcribing lots of numbers into a laptop. If someone were to create such a useful tool, we would now know the longitudes of those mariners, better than they knew then themselves.. Of course, their own measurement errors and inaccuracies would remain. Eric Forbes' monograph, "The birth of navigationl science", states (ref. 63)- "Dr Thomas Young's "Report on the progressive improvents of the lunar tables", preserved among the Board of Longitude Confirmed Minutes for 2 November 1820, , contains a synopsis of more than 4000 observations of the moon's celestial position over a period of 36 years (RGO MSS, PRO Ref 535, p 317). This summary indicates which sets of lunar tables had been used in comparing the lunar computations throughout that time, as well as the respective errors thought to have been inherent in each...." I haven't seen Young's report, but it looks as if it might provide a good starting point for any such modern study-project as I am advocating here. George. ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================