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    Re: Time of meridian passage accuracy
    From: George Huxtable
    Date: 2009 Sep 26, 17:27 +0100

    Posting [9939] concludes with these words-
    
    "There is a vast difference between practical navigation and theoretical 
    astronomy.
    That is the point which you have academically and pedantically missed."
    
    Well, thank you, Douglas Denny, for those few kind words. No doubt they were 
    intended to disparage, but "academic and pedantic" is a badge I will wear 
    with some little pride. It's a standard I hope to maintain...
    
    ===================
    
    When he wrote those words, Douglas was taking the Sun's declination to be 
    changing at 0.8 arc-minutes per day, which he then revised in a suibsequent 
    posting to be 0.8 arc-minutes per hour. Does that factor of 24 lead him to 
    reassess any of the statements he made in [9939], I wonder, or does he still 
    maintain that the effect of changing declination is "very small as to be of 
    no practical concern to practical navigators."? How much, if any, of that 
    posting does he now wish to retract?
    
    This question, of the time-difference between meridian passage and maximum 
    altitude (= culmination) has been discussed in some detail in the "Admialty 
    Manual of Navigation, vol III". My edition is 1938, where it's on pages 146 
    to 156. Thanks to list member Jim Wilson, for pointing that out. Jim has 
    also written about the matter in "Position from observation of a single 
    body", in Navigation, 32(1) Spring 1985. Antoine's posting [9938] explains 
    the matter rather better than I could.
    
    Jim derives the formula for the amount of the correction in time, between 
    meridian passage and culmination, due to changing declination, as-
    correction (in seconds of time) = rate of change of declination (in 
    arc-minutes per hour) x (tan lat - tan dec) x 48 / pi.
    
    For the observations quoted by Douglas Denny, with dec changing at 0.8 
    minutes per hour, lat = 50�, dec = 14.5�, this amounts to a time-error of 
    about 11.3 seconds. That is, indeed, very significantly less than both my 
    earlier rough-guesses. Perhaps, Douglas and I are now starting to 
    converge... Nevertheless, if he is hoping to establish the time of meridian 
    passage with any precision, that correction should certainly be taken into 
    account, and not dismissed out of hand. It amounts to a systematic error in 
    deduced longitude of nearly 3 arc-minutes, in every such observation made at 
    that time of year.
    
    Use of bubble sextant, on land, for such a purpose isn't in itself conducive 
    to high precision, and observations made with a better tool for such a job, 
    sextant or theodolite, would give a more precise result. The better that is, 
    the more necessary it is to take such time-correction into account.
    
    Of course, the same correction would become much larger if the observation 
    was being made from a moving vessel, with a North-South component of speed 
    which can be tens of knots, not limited to a knot as is the motion of Sun 
    declination. That matter has been discussed,  in great detail, in recent 
    postings about longitude-around-noon on Navlist.
    
    Some additional points-
    
    Douglas wrote- "I am aware of the changing declination of the Sun - it is 
    changing constantly, hence a meridian passage curve such as the one I gave 
    is actually skewed - in theory."
    
    Not "skewed", actually. The shape, near noon, is a parabola. It remains a 
    parabola, of just the same shape, when the changing declination is allowed 
    for; but is simply displaced a bit in time from being centred on LAN, as 
    I've indicated.
    
    And he added- "The differences between actual (appareent) max Altitude and 
    true Mer passage of the Sun are so small as to be negligable if max altitude 
    is calculated near to the apparent Mer Passage... ". Which is indeed 
    correct, as far as altitude is concerned. The small difference in altitude 
    between LAN and culmination can often be neglected. However, navigators of 
    vessels that possessed chronometers, particularly if they were steaming fast 
    in a North-South direction, were advised to measure the noon altitude, not 
    at its peak value, but at the moment of calculated LAN, to arrive at a 
    correct latitude..
    
    But that's not what we've been discussing. It's not a change in altitude, 
    but a shift in time-of-peak, to obtain longitude, that concerns us here.
    
    It's not a matter that was much discussed in navigational texts. That's 
    because longitude-around-noon was never a standard tool in the navigator's 
    box, though it has achieved great prominence on Navlist. Navigators were 
    aware of its many drawbacks, as have been discussed by us at length; one of 
    which is the need for such time-corrections to be made. Instead, they relied 
    for longitude on observations made as far as possible from meridian passage, 
    which implied, if their timepiece was good, that longitudes could then be 
    almost as precise as latitudes were.
    
    ==============
    
    In response to my pointing-out that he had made no allowance for 
    time-offset, between LAN and maximum altitude, Douglas wrote, in [9932]-
    
    "The difference is 0.000737068 degrees,  or 0.04422408 minutes,  or 2,6 
    seconds of arc.
    
    Utterly  negligable "
    
    Does he still maintain that statement? Otherwise, I invite him to withdraw 
    it now. I don't know what it was based on; perhaps he will explain. It was 
    on that basis that I wrote that he had missed the point. Was that wrong?
    
    George.
    
    contact George Huxtable, at  george{at}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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