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    Re: Sun Moon Lunars to 155 degrees
    From: George Huxtable
    Date: 2010 Mar 29, 13:20 +0100

    Kermit asks several relevant questions, and I will offer some "informed 
    guesses", and suggestions.
    
    "1 - We are to assume that all observations are supposed to be made on 
    board a non-moving vessel and at the very same time."
    
    No, they will mostly have been made from a vessel under way, except for 
    those taken in harbour at the foot of that page. However, each 
    corresponding set, of lunat distance and altitudes,  may well have been 
    taken simultaneously, as such vessels were well-manned, with a number of 
    competent observers on board, and  provided with two brass sextants, and 
    most likely a number of wooden octants, good enough for taking altitudes. I 
    imagine the Navy making a bit of a ceremony of the job.
    
    "2 - We are to assume also that all given Angles are "raw data" corrected 
    only for Instrument error. i.e. all remaining corrections remain to be 
    performed as applicable and as follows :
    
    2.1 - All Distances (Column 3 ) are "refracted topocentric from Limb to 
    Limb" (if Moon + Sun)" or - as the case may be - "refracted topocentric 
    from Star/Planet to Moon's Limb". Accordingly if we use 
    'conventional/classical' clearing methods we are to transform such 
    distances into "unrefracted geocentric from Center to Center" distances in 
    order to compare such results to Maskelyne's tabular Lunar Distances, and"
    
    Yes, I would think so, though it isn't obvious whether index error has 
    already been allowed for, or not. My guess is that it probably has.
    
    "2.2 - All heights (Columns 4 and 5) should be corrected for all 
    appreciable effects and in accordance with our well known standard height 
    reduction corrections, i.e. :
    
    2.2.1 - Dip. WHAT IS THE HEIGHT OF EYE ? , and"
    
    Wait, Kermit. It's a bit more complex than that. For the lunar distance 
    itself, that gets corrected for parallax and refraction in the clearing 
    process, so the altitudes to be input to that process won't normally have 
    been corrected for those effects first; just for the dip. Which implies 
    that you can't use a combined-correction, as given in modern almanacs. 
    (though actually, the clearing process would be  little affected affected 
    by any such pre-correction; it's very undemanding of great precision in the 
    altitudes).
    
    Where the normal altitude correction process applies is in getting Local 
    Apparent Time, to compare with the GMT given by the lunar after converting 
    LAT to LMT by applying the equation of time. I presume that in the case of 
    a Sun-lunar, LAT was being calculated from the Sun altitude that was 
    measured as part of that lunar, providing that this job had been 
    deliberately done away from local noon. For a star-lunar, the star altitude 
    would provide LAT, in a similar, but somewhat more complicated way. And for 
    that purpose, all the normal altitude corrections need to be made, in the 
    familiar manner.
    
    As for height-of-eye, Beaglehole's volume 2 provides a draught of 
    Resolution, not of Adventure that concerns us at present but no doubt very 
    similar, and a measurement off that draught shows a nominal poop-deck 
    height of about 18 feet above the water line, which will of course vary 
    with lading. To that, we must add about 5 feet for the observer's eye.
    
    "2.2.2 - Refraction. I can see that Temperatures are given in Column 9 but 
    I fail to see any values given for Atmospheric Pressure, and"
    
    From Beaglehole, the weather seems to have been generally benign over this 
    period, when the two ships were keeping company, so in my view it would be 
    fair to assume a standard value for pressure.
    
    "2.2.3 - As applicable, Parallax and Augmented Semi-diameter."
    
    Yes, and SD can be deduced from the parallax. It could be taken from a 
    modern prediction or from the 1773 almanac.
    
    "4.1 - The 3rd column title should be construed as "Distance from Moon's 
    Limb from Sun's (Limb) or Star (Limb)" . Everybody agrees here ?"
    
    I agree, that's observed distance, as Kermit has described.
    
    "4.2 - At the end of each Lunar Distance given in this 3 rd column, we can 
    read :
    
    - either 2 "  +  " signs on top of one another (such as 05 Jul, 02 Aug, and 
    several other dates), or
    - only one "  +  " sign (such as 12 Jul, 12 Aug and several other dates), 
    or
    - one "  :  " sign (such as 14 Aug) , or even
    - no sign at all, (such as  25 Jul, 13 and 25 Aug, and 8 Sep).
    
    What do these codes mean ?
    
    Obviously they must be (somewhat) related to the use of either the Moon's 
    Near Limb or the Moon's Far Limb in case of Planetary/Stars Observations.
    
    But ... in the case of Sun-Moon Lunars, the Moon's Near Limb is to be used 
    (always). Accordingly such Sun-Moon Distances should then all bear the VERY 
    SAME code. HOWEVER I can see FOUR different such codes : either 2 "  +  " 
    on 09 Jul, or just one " + " on 10 Jul for example, or just nothing on 25 
    Jul, or even a "  :  " sign on 14 Aug.
    
    SO ... What is the exact meaning of all these codes ??? Some kind of 
    reliability scale ??? If so, where are the (required) indications about 
    Near/Far Limb in case of Star/Planetary Lunars ?then "
    
    
    These are common printers' dagger symbols, that refer to a footnote 
    somewhere, on another page. Perhaps Kermit may find it helpful to compare 
    with the publicly-available text for the third voyage, which may offer an 
    analogy, on this matter and perhaps on others..
    
    For stars (I don't think lunar distances to planets were predicted until a 
    later era), except very close to exact full moon, it should be rather easy 
    to work it out. A planetarium program might be useful here (and elsewhere). 
    What's needed is to know whether it's before, or after, full Moon, and 
    whether the star was East or West of the Moon, which the almanac always 
    made clear.
    
    Some things to be aware of-
    
    Lunar distances, then, and everything else, were tabulated in Greenwich 
    Apparent Time, not GMT. So it's convenient to stick with apparent time 
    throughout, especially if you use a digitised copy of the 1773 Nautical 
    Almanac, which would be the most "authentic" way to work this example.. And 
    then, there's no delta-T to worry about. However, users of modern 
    predictions will have to allow for both the equation of time, because 
    modern predictions relate to GMT, and also for the change in delta-T since 
    1773.
    
    Another problem to be aware of is that there were systematic errors in the 
    lunar ephemeris then used, which varied rather cyclically over a month and 
    could amount to 1' in Moon position, or 30' in longitude. These persisted 
    over many years, in such a way that on a particular day, all mariners using 
    these tables, wherever they were in the World, would find their longitudes 
    displaced by the same amount.
    
    The gap in observations, after 25 August, was because the Society Islands 
    had been reached, and the ships were taking various anchrages at Matavai 
    Bay, Tahiti, and other islands.
    
    The position given, at the foot of the page, for "Omahareno" harbour, 
    within Passe Rautoanui at the NW corner of Ulieres (more commonly named 
    Raiatea), can be compared with modern values from Google Earth.
    
    That page is convincing evidence that lunars were not just a mathematical 
    abstraction, but a practical means of navigation, in no way inferior to the 
    timekeeper technology of the day.
    
    George.
    
    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.
    
    ----- Original Message ----- 
    From: "Antoine Couette" 
    To: 
    Sent: Monday, March 29, 2010 9:11 AM
    Subject: [NavList] Re: AW: Sun Moon Lunars to 155 degrees
    
    
    Hello to all,
    
    
    Before we could start doing any reliable and conclusive "re-processing" of 
    this wonderful page 174 of historical ASTRONOMICAL OBSERVATIONS, should we 
    not get first a full understanding of all the data printed ?
    
    This is what I have been able to figure out so far, with still some (BIG) 
    questions unanswered yet.
    
    Your answers, confirmations, corrections are highly desirable and your 
    comments will be highly appreciated.
    
    *******
    
    
    1 - We are to assume that all observations are supposed to be made on board 
    a non-moving vessel and at the very same time.
    
    2 - We are to assume also that all given Angles are "raw data" corrected 
    only for Instrument error. i.e. all remaining corrections remain to be 
    performed as applicable and as follows :
    
    2.1 - All Distances (Column 3 ) are "refracted topocentric from Limb to 
    Limb" (if Moon + Sun)" or - as the case may be - "refracted topocentric 
    from Star/Planet to Moon's Limb". Accordingly if we use 
    'conventional/classical' clearing methods we are to transform such 
    distances into "unrefracted geocentric from Center to Center" distances in 
    order to compare such results to Maskelyne's tabular Lunar Distances, and
    
    2.2 - All heights (Columns 4 and 5) should be corrected for all appreciable 
    effects and in accordance with our well known standard height reduction 
    corrections, i.e. :
    
    2.2.1 - Dip. WHAT IS THE HEIGHT OF EYE ? , and
    
    2.2.2 - Refraction. I can see that Temperatures are given in Column 9 but I 
    fail to see any values given for Atmospheric Pressure, and
    
    2.2.3 - As applicable, Parallax and Augmented Semi-diameter.
    
    
    3 - FIRST COLUMN
    
    3.1 - It gives the dates with codes for the names of week (Sun Figure for 
    Sunday, Moon figure for Monday, ... ).
    
    3.2 - Dates MIGHT possibly be local dates and not Greenwhich dates. This 
    one is fairly simple to sort out with the help of the publihsed distances.
    
    4 - THIRD COLUMN
    
    4.1 - The 3rd column title should be construed as "Distance from Moon's 
    Limb from Sun's (Limb) or Star (Limb)" . Everybody agrees here ?
    
    4.2 - At the end of each Lunar Distance given in this 3 rd column, we can 
    read :
    
    - either 2 "  +  " signs on top of one another (such as 05 Jul, 02 Aug, and 
    several other dates), or
    - only one "  +  " sign (such as 12 Jul, 12 Aug and several other dates), 
    or
    - one "  :  " sign (such as 14 Aug) , or even
    - no sign at all, (such as  25 Jul, 13 and 25 Aug, and 8 Sep).
    
    What do these codes mean ?
    
    Obviously they must be (somewhat) related to the use of either the Moon's 
    Near Limb or the Moon's Far Limb in case of Planetary/Stars Observations.
    
    
    But ... in the case of Sun-Moon Lunars, the Moon's Near Limb is to be used 
    (always). Accordingly such Sun-Moon Distances should then all bear the VERY 
    SAME code. HOWEVER I can see FOUR different such codes : either 2 "  +  " 
    on 09 Jul, or just one " + " on 10 Jul for example, or just nothing on 25 
    Jul, or even a "  :  " sign on 14 Aug.
    
    SO ... What is the exact meaning of all these codes ??? Some kind of 
    reliability scale ??? If so, where are the (required) indications about 
    Near/Far Limb in case of Star/Planetary Lunars ?then
    
    5 - NINTH COLUMN
    
    Temperatures are given here in Farenheit scale. Everybody agrees here ?
    
    
    6 - Apparently missing data :
    
    6.1 - HEIGHT OF EYE. Does anybody have any clue here (Wolgang ?)
    
    6.2 - Atmospheric Pressure. Should we go "standard" 29.92"/1013.25 HPa/Mb ?
    
    
    *******
    
    
    All your answers, confirmations and corrections are highly desirable and 
    all your comments will be highly appreciated.
    
    Again WARMEST THANKS TO WOLFGANG !
    
    
    and Best Regards to you all,
    
    
    Kermit
    
    
    Antoine M. "Kermit" Couëtte
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