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    Re: averaging
    From: Jim Thompson
    Date: 2004 Oct 24, 07:30 -0300

    > -----Original Message-----
    > From: Bill
    > I wholeheartedly agree as to calculating a slope
    > and fitting data points to it.  Plot the observations. Calculate the slope
    > for that time period. Use that slope to determine your outliers.
    > For those
    > of us who are not mathematicians, surveyors, engineers, historians,
    > astronomers or some combination thereof, I alluded weeks ago to
    > the rational
    > and methods for calculating the slope (which were included in
    > older versions
    > of Bowditch)
    > Drill down in David Burch's site.
    > http://www.starpath.com/online/celestial/sight_average.pdf
    
    Bill, After again reading David's article, I ammended my summary to this:
    
    3. Inspect the set of sights for consistency and discard obvious outliers,
    or sights that fail to increase and decrease in time or altitude reasonably
    smoothly. It helps to plot the sights on a graph of altitude over time; or
    to build a table, and then use arithmetic to calculate the change in time
    and altitude between sights, and then inspect the table for outliers. Beware
    discarding an apparent outlier that might in fact be a good sight: David
    Burch explained a method of using the slope or rate of ascent/descent to
    optimize a run of sights in an article posted at
    http://www.starpath.com/online/celestial/sight_average.pdf.
    
    > -----Original Message-----
    > From: Chuck Taylor
    > When I teach this, I find that students have less
    > trouble if they first convert all altitudes to minutes
    > of arc, and all times to seconds of time, and then do
    > the averaging. Then when they are done, convert back.
    
    Chuck (and George), here is my revision:
    
    4. Average time by adding up the minutes and seconds of either uncorrected
    or corrected sight time, and then dividing by the number of sights, and then
    adding that average to the whole hour. Be careful to note whether whole
    hours change over the run of sights. Learners should convert all the times
    to seconds of time, total those, and convert that total back to hours,
    minutes and seconds. After becoming familiar with the method, they will see
    how to make safe short cuts.
    
    5. Average altitude by adding up the minutes and seconds of uncorrected
    sextant altitude, and then dividing by the number of sights, and then adding
    that average to the whole degrees. Be careful to note whether whole degrees
    change over the run of sights. Learners should convert all the angles to
    decimal minutes of arc, total those, and convert that total back to degrees
    and decimal minutes.
    
    Jim Thompson
    jim2{at}jimthompson.net
    www.jimthompson.net
    Outgoing mail scanned by Norton Antivirus
    -----------------------------------------
    
    
    

       
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