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    Re: Almanac errors
    From: George Huxtable
    Date: 2008 Mar 4, 23:16 -0000

    Thanks to Frank Reed for some really useful information on Almanac accuracy, 
    much of which was quite new to me.
    
    He provided as a reference Souchon's "Treatise on Practical Astronomy", 
    Paris 1883, which I had never even heard of before. Frank, is that in 
    English tramslation, as the given title might imply, or is it in French? My 
    own French is very halting, but even so, I might give it a try if I can find 
    a copy.
    
    Frank's other refence, from J E D Williams "From Sails to Satellites", was 
    actually on my bookshelf, but I hadn't thought to look that one up. In my 
    1992 edition, that table is on page 96 (93 in Frank's). Although it didn't 
    tell me much more than Frank's extract did, it led to another reference, in 
    "Journal of Navigation", vol 18 No.4, October 1965, pages 391 to 401. This 
    was a paper by Eric Forbes, entitled "The foundation and early development 
    of the nautical almanac". I have that on a DVD, and it contains some 
    fascinating insights into early almanac-making. I will retell a few nuggets 
    for anyone interested.
    
    Right at the start of the Nautical Almanac, for 1767, Maskelyne employed a 
    team of human "computers", who were to make the complex calculations in 
    duplicate, quite independently, in secret from each other, and a "comparer", 
    to put their results together and search out errors. And that team had 
    several names which will ring familiar to anyone who knows the lunar story 
    well. They included Israel Lyons (heard of "Lyon's method", for clearing 
    lunars?), George Witchell (Witchell's method), William Wales (who later 
    became Astronomer in Cook's two last voyages), with Dunthorne (Dunthorne's 
    method)  as comparer. In the early days, two computers were instantly 
    dismissed when found to be copying.
    
    By 1789, they team were being paid rather well for the responsible job they 
    were doing, and by "piece-work", in that they each received �100 for each 
    completed years-worth of Almanac they produced. This provided such an 
    incentive that by 1793 they had calculated for ten years ahead! At this 
    point the Board of Longitude cried "stop!", and suspended the calculations 
    for five years, giving the team other tasks.
    
    One of the team in the early 1800s was a lady, Mrs Mary Edwards, who became 
    one of the more experienced computers, and for a short time even acted in 
    the prestigious post of comparator. In her later years, her two daughters 
    were drafted in to help with the calculations.
    
    I was rather surprised to learn that a second Longitude Act, had been passed 
    in 1774, after the first, famous Longitude Prize had been distributed. This 
    stated that the authors of improved solar or lunar tables would be rewarded 
    by �5000 if the tables proved sufficiently exact to yield the distance of 
    the Moon from the Sun and stars to within 15 seconds of arc, corresponding 
    to about 7 minutes of longitude. This would have been a doubling, or 
    thereabouts, of the precision of the Almanac. There's no record of that 
    prize having been awarded before the Board was dissolved in 1828.
    
    Anyway, all this stuff was no more than a distraction from my quest, to 
    discover more about improvements to the precision of lunar distances in the 
    almanac. Forbes provides a bit more detail than did Frank, and quotes from 
    another reference, the Board of Longitude "Confirmed minutes" (2 Nov 1820), 
    VII, 317. This reports on work by the Board's secretary, Dr Thomas Young 
    (not the Young of "Young's method"), who analysed 4000 observations that had 
    been made of the Moon's position over the previous 36 years, and compared 
    them with predictions. Will those minutes contain any detailed infomation? 
    Probably not, but I live in hope. I guess they will be held in the Longitude 
    archive at the Fitzwilliam Library in Cambridge.
    
    One puzzle is that Forbes, and Frank, both refer to "mean error", as well as 
    "greatest error". The divergence can be positive or negative, and one might 
    hope that its mean would be about zero, which is why root-mean-square error, 
    or standard deviation, is a more useful quantity today.. But is that what 
    was meant, before the days of statistical analysis? Or did they change the 
    sign of negative errors to positive, before finding the mean value? I 
    wonder.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 
    
    
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