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    Re: Lunar Distances
    From: George Huxtable
    Date: 2002 Feb 5, 12:12 +0000

    This is a response to mailings by Greg Gilbert and Bill Noyce, and also
    many others.
    Greg Gilbert writes-
    >I've been trying to work through the example given by George Huxtable in
    >"About Lunars".  It's a great way to try to understand the subject, and get
    >a feel of the calculations done by early navigators.
    >I've had a problem however, in that I think there is a typo in one
    >I've followed the calculation for Predicted Lunar Distances - OK.
    >I've followed the calculations for observed and corrected Sun and Moon
    >altitudes - OK.
    >However, correcting the Observed Lunar Distance (105 degrees 50.5 minutes)
    >by adding the semi-diameters of Sun and Moon (16 minutes for the Sun and
    >16.4 minutes for the Moon) gives me an answer of d = 106 degrees 22.9
    >minutes, not 107 degrees 22.9 minutes.
    >Putting this into the formula for clearing the Lunar Distance gives me an
    >answer for D of 105 degrees 50.2 minutes.
    >I don't think this is correct because this gives me a GMT time for the
    >observations of 15:53:04, which doesn't tally with the estimated time of
    >"something between 1700 and 1800 GMT", and the watch time of 17:36:43.
    >Could the watch be incorrect by 1 hour, 43 minutes and 39 seconds?
    >Can someone help me here?
    >Greg Gilbert,
    >35o10' S, 138o42' E.
    George Huxtable responds-
    Sorry, Greg. You are absolutely right: it's a typo. Steven's figure for the
    sextant reading of the lunar distance, corrected for index errors, was
    106deg 50.5, NOT 105deg 50.5. I transcribed it wrong. Entirely my fault.
    Thank you for bringing it to our attention.
    I wonder how many others have been hampered by this error. Please, would
    any list members, who have plans to work through that example from 2001
    April 2, correct the Sun-Moon distance, before semidiameter correction,
    from 105deg 50.5 to 106deg 50.5.
    This brings me to another point raised earlier by Greg, who asked-
    >Some suggestions which would help me, and probably others, are:
    >1.      Pictures and diagrams always make life easier for me, so I was
    >wondering if some could be included at a later date.
    >2.      The trig formulae are a little bit hard to visualise with the
    >notation used, and would be better written down with an Equation Editor or
    I have much sympathy with Greg. I always believe that a picture is worth a
    thousand words: or each word corresponds to 1 millipicture.
    One reason why the text that was sent out became so damn wordy is the
    result of an attempt to avoid adding graphic attachments.
    I disliked having to write out those complex trig formulae all on one line
    so that they would fit in with emailese. They are expressed in a sort of
    Bastard Basic, which might make sense to those that are familiar with
    computer languages, but are distinctly off-putting to anyone that has to
    remember back to their high-school maths.
    I have a scanner, and could write the equations down longhand on paper in
    high-school format, add some diagrams, and send to the list as an graphics
    attachment. Would that help?
    My problem is this. I run an old Mac, and have endless trouble with
    incompatible attachments which come from those in thrall to Microsoft. And
    no doubt they would have similar troubles with attachments sent by me. I
    wonder if any list member, familiar with both Mac and PC platforms, might
    recommend a suitable encoding method that others could unravel without
    problems. Mentioning no names, of course, but Dan Allen springs to mind. I
    am not at all skilled in handling graphics. My Mac can handle GIF, TIFF,
    and JPEG, I understand.
    There is a mailing on the stocks which should shortly answer Bill Noyce's
    request, if he will allow me a few more days.
    I wrote, in "About Lunars, part 2, about Young's method for clearing the
    lunar distance-
    "If readers find the need to do this clearance longhand using logs, my
    suggestion is to use Borda's method, to be found in Cotter. On request, I
    will spell it out for the list."
    Bill Noyce responded by saying-
    >And I would like to take him up on his offer to spell out Borda's
    >method for clearing the distance longhand.  Young's formula seems
    >to require converting out of logs to do additions.
    It's coming, Bill.
    Finally, I would like to acknowledge the kind messages that have arrived,
    off-list and on-list, from many members, about parts 1 and 2 which have
    gone out so far. It's been a great surprise, that there was such widespread
    interest in lunar distances. I hope you find the stuff to be useful.
    Part 3 will come later, but it will be weeks rather than days, I fear.
    George Huxtable.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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