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    Re: Lunar distance measurement in ideal conditions: attainable accuracy.
    From: Bill Morris
    Date: 2013 Jan 7, 20:44 -0800

    Dear Alex

    "Does this mean that the index error was always positive...?"

    Yes, they were all "on the arc".

    "I am still amazed with the difference of accuracy between Lunar 1
    and Lunar 2 spreadsheets. Your Index Error does not show such remarkable
    progress."

    Well the ratio of the variances of the index errors is 2.07, which is nearly 2.12, the f-ratio for significance at the 5% level. I don't really know what I'm talking about - I've mislaid my easy statistics book and don't understand the difficult one - but I think that suggests that the distributions are significantly different. We wouldn't expect the mean of the second lot to be closer to zero with increasing skill, but we could anticipate that the SD would be less, and it is.

    "Was sheet 1 the very first Lunar you ever tried?"

    Thirty three years ago an elderly surveyor explained lunars to me, complete with seven figure log tables. I shot one lunar distance and did the calculations using logs. It hurt my brain so much that until this year I never tried again. I felt it was sufficient to admire people like Cook, Green and Bligh. At the time, my computer had only 3 kB of memory available for use and the www had not been invented.

    "How does Cook describe his position...?

    Cook writes "...Cape St Diego bore at that time SBE (south by east) distant about 4 leagues."

    "...what edition of his journal do you use?

    That of J.C Beaglehole, The Voyage of the Endeavour, Cambridge University Press, 1968, pp 41 - 43. It is a long time since I last read it and have found in Beaglehole's introduction that there was on board "A brass Hadley's sextant bespoke by Mr Maskelyne of Mr Ramsden." I think I saw this instrument or one very like it in the National Maritime Museum, Greenwich, in August 1967. In Cook's footnote he remarks that his _quadrant_ was out of order.

    "...what is the date of the observation?

    Cook's date was Saturday 14 January and was ship's time "At 6, the weather being clear...", but his day began twelve hours before the civil day and ran from noon to noon.

    I had planned to do another series of lunars tomorrow, to see if Lunar 2 was a fluke, but high cloud obscured the moon. Perhaps tomorrow.

    Bill Morris
    Pukenui
    New Zealand
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