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    Re: Impossible lunar example. was: Short-cut lunars. was: Clearing lunars
    From: George Huxtable
    Date: 2010 Aug 28, 21:48 +0100

    Antoine asked a simple-looking question about that "impossible lunar 
    example", attached to my mailing of 28 August as "moore p45.jpg"-
    "Just one question now : by to-day date/UT time reckoning standards, what 
    would be the day and time of this Lunar. Should we read it as : 20 Nov 
    1796, 18h46 UT ???"
    Oh, dear. This is going to be complicated. I often get confused by this 
    business, but I'll do my best.
    I presume that Moore was following Maskelyne and using the Astronomer's 
    day, the time-scale which was used for the Almanac.This, for Greenwich, 
    starts at Greenwich noon in the middle of the corresponding civil 
    (midnight-to midnight) day. So afternoons had the same date in both scales. 
    In the morning, the astronomer's date was 1 day less, but his hour-count 
    during the morning ran from 12h (at midnight) to 24 hr (at noon). I hope 
    that's clear. So in this case, the time being given as "6H. 10M. P.M. per 
    watch well regulated", on the 10th November 1796, being PM, the civil date 
    and the astronomical date will both be 10 Nov.
    However, at sea there's an extra complication. Mariners tended to make up 
    their logs and journals, at sea, in terms of the nautical day, which ended 
    at noon of the corresponding civil date, so it corresponded in hour to the 
    astronomical day, but it was always 1 day ahead; the day number being one 
    greater. To make it more complex still, during the time of a vessel's stay 
    in harbour, the log would generally switch to the civil date.
    How these different dates related to the day-of-the-week name has long 
    puzzled me. Presumably, that day-name had to change at local midnight.
    To make it more complex still, round about the period we are talking about, 
    the nautical day was being disparaged, and gradually phased out in favour 
    of the astronomical day, so on a particular vessel, depending on her 
    master, it's hard to be sure which was being used. I will presume, unless 
    it's shown to be otherwise, that in the examples given by Maskelyne and 
    Moore, the Astronomical day and date are being referred to throughout.
    When I'm examining old ship's logs, I usually look out for a recorded value 
    of Sun declination, which then can be worked backwards to check on the 
    date-system in use. That's usually pretty foolproof.
    But there's yet another complication, which means that the answer to 
    Antoine's question has to be "no".
    Until 1834, the basis for all the predictions in the Almanac was not 
    Greenwich mean time, but Greenwich apparent time. Because as everything was 
    calculated on that consistent basis, it all worked together well. A lunar 
    provided Greenwich apparent time; a time-sight from the Sun provided local 
    apparent time; the difference gave the longitude, with no call to invoke 
    the equation of time.
    But the bugbear was the chronometer, which had to keep mean time. From 
    1834, when a lunar then provided Greenwich mean time, the equation of time 
    had to come in somewhere to compare it with a Sun time-sight.
    So if Antoine plans to apply modern predictions, based on UT, to that era, 
    he has to apply the equation of tme (of about 15m 51 sec) accordingly. I'll 
    leave it to him to get the sign right..
    What isn't clear to me (perhaps it is to others) is what time scale is 
    being kept by the on-board timekeeper, referred to as "per watch well 
    regulated". Would it be regulated to keep to Greenwich mean time, as a 
    chronometer would be. Or, does well-regulated mean that it's readjusted 
    day-by-day to correspond with the vagaries of apparent Greenwich time? Not 
    that it matters, in the context.
    I suspect that Antoine plans to compare the stated Sun and Moon altitudes 
    with those computed by a modern almanac. Perhaps I can help here, just by 
    some crude measurements using a blow-up globe and a piece of string.
    At a time of 6 h 10 m pm, the Sun will have reached a longitude of roughly 
    90º West. Being 10 November, it must be well South, at around 17º South 
    declination. The Sun's altitude being observed to be about 19º, the zenith 
    angle, and so the distance from the Sun's position, must be around 71º. 
    We're told that the longitude (by account, presumably) is 9º West, but not 
    told the latitude, so we can draw on the globe a line down the meridian of 
    9º West, on which the vessel must lie. And it must also be at a radius of 
    71º from that estimated position of the Sun. Trouble is, that arc fails to 
    intersect the 9º West meridian, by quite a long way. There's nowhere on 
    that meridian at which the Sun could possibly be so high at that time.
    So, unless I've made an error, that's a second impossibility in that 
    example. Does it bear any relation at all to real-life, then, or have the 
    numbers been simply dreamed up, and then dressed up with implausible dates 
    and times to make it "look real"? It seems like that to me. I know little 
    about Moore, but I would have expected better of Maskelyne.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 

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