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    Re: Time of meridian passage accuracy
    From: Douglas Denny
    Date: 2009 Sep 26, 11:39 -0700

    No need for retractions I think. You know full well the reference to change of 
    Dec of 0.8 minutes per hour mentioned as being 24 was a simple error - and  
    corrected within minutes of my posting it and re-reading it. Mentioning that 
    _is_ pedantry. 
    Nor is there any implied 'disparagement' in the words:  "There is a vast 
    difference between practical navigation and theoretical astronomy. That is 
    the point which you have academically and pedantically missed."  
    You are too sensitive. (I believe I was accused of that once).
    There is indeed a huge difference between the two - practical and theoretical 
    navigation - you are focussing however, on the finer academic aspects yet the 
    question was about a practical point of one minute in time leeway at Mer 
    Passage observation.
    Practical sea navigators have been calculating exactly when Mer Passage of the 
    Sun is for centuries, and taking their sight at that time - or rather within 
    one minute - and is quite accurate enough for practical use at sea.
    In post 9948. You continue to miss the practical aspects of the point.
    The question was about a one minute time limit on Mer Passage observation.
    I take it this means taking an observation within one minute of the  
    _calculated Mer Passage_  for the Sun,  not that is necessarly observing the 
    Maximum altitude (which you seem to think I am implying, probably because I 
    gave a series of observations showing that) - and in which case the 
    observation is well within reasonable limits of accuracy for practical use.
    If stationary - as I was with my observations (and which you ignored) - then 
    culmination of the apparent (true) Sun is by definition Local Apparent Time 
    of the (true) Sun.
    The Equation of Time and correction for longitude gives this time with respect 
    to UTC exactly enough alright. 
    In my graph example given, I calculated the former accurately and already know the latter accurately.
    In a moving observer this is different. Then it is agreed culmination, or 
    'dip' of the Sun, max altitude whatever you wish to call it,  and true 
    meridian passage are not necessarily the same... "subtly different" is how 
    you put it, and it is indeed of greater importance in a North / South moving 
    It remains nevertheless that the original request was for opinon as to the 
    accuracy of the Bowditch declaration of taking a sight within one minute of 
    Mer passage, and I have no hesitation in continuing to suggest taking a sight 
    within one minute of time of calculated Mer Passage of the Sun is quite 
    satisfactory in practical navigation.
    You have also ignored my observations and graph; the conclusions regarding 
    that graph with respect to the question posed, (especially that it takes 
    nearly 20 minutes of time to change within a minute of altitude at 
    culmination); the fact it was made as a stationary observer;  and made with 
    exact calculation of when exact Mer Passage of the Apparent Sun actually is 
    at my location - (which is why it is symetrical about the calculated time).
    For a stationary observer, theoretically very slight distortion would be 
    present as declination is changing in the 30 minutes or so of the 
    observation. Negligable though. Max altitude can still give accurate Latitude 
    with culmination, which is what I was doing.
    The change in Declination as a parameter in Meridian Passage is of more 
    significance if the observer is moving North/South, but is not dramatic - a 
    few minutes of arc. The graph of the curve will also then be more 
    significantly distorted in symetry.
    A stationary  observer or one moving East or West will have practically no 
    distortion of symetry of the curve, but an observer moving East/West will 
    have error in time of apparent culmination - a shift of the curve.
    This is all treated with rigor in Charles H. Cotter's book 'The Complete 
    Nautical Astronomer' with full formulae for calculation of these effects and 
    full derivations.
    Douglas Denny.
    Chichester. England.
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