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    Re: Lunars: Jupiter's BIG.
    From: Herbert Prinz
    Date: 2003 Dec 20, 16:57 -0500

    Fred,
    
    It would seem that you are applying the least square fit incorrectly. To apply
    it to the plot of distance versus time is to shoot with guns at sparrows. You
    can have this cheaper by averaging the time, averaging the distances, and then
    proceed as if the averaged values where the actual observation - just as you
    are suggesting. This is what was normally done, and what is feasible to the
    navigator without electronic tools. To use this technique does not prevent you
    from plotting the distances versus time to find outlyers. As long as you have
    the individual distances, that is, because from repeating instruments (such as
    the Borda circle), one does not get them.
    
    However, if you really must apply a least square fit to the given data, (and I
    could not argue with you if you claim that this is the only rigorous treatment
    of any set of more than 2 observations), the only correct method is to solve
    for the watch error for which the sum of the square of the distance residuals
    becomes a minimum. Besides from being correct, it has the additional benefit
    that you can combine observations to different objects, in particular
    observations on either side of the moon, which helps to cancel certain
    instrument and observation errors.
    
    It goes without saying that this has no practical value on the boat. But it
    could have been used this way in surveying, right before the telegraph was
    introduced.
    
    Herbert Prinz
    
    Fred Hebard wrote:
    
    > Interestingly, I usually plot the raw distance against the time of
    > observation and use the least squares fit to pick out a point for
    > reduction.
    
    > I think perhaps the old method of using the mean of the observations
    > would be better than using a line of best fit, although plotting the
    > data instantly tells one how good they are.  Using the mean, the time
    > would have been out by 8 seconds, about 2 minutes of longitude.
    
    
    

       
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