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    Re: Averaging
    From: Alexandre Eremenko
    Date: 2004 Oct 22, 17:36 -0500

    Dear Bill
    
    > I am having trouble with the concept that non-linearity
    > increases as the
    > body approaches the meridian in all cases.
    >
    > In the case of the being on the equator at an equinox,
    > the rate of change
    > throughout the day would be an almost uniform 1d per 4 minutes.
    
    Yes, in this example (given earlier bu Herbert Prinz)
    the altitude changes linearly all the day... Excedpt at
    the very moment of noon.
    Just think of the moment of noon.
    Before noon the altitude increases at constant rate, but
    after noon it DECREASES at the same constant rate.
    
    In other words the rate suddenly jumps from positive
    to negative.
    Just make the graph of altitude near noon, to see how
    very much non-linear it is.
    It is a broken line consisting of two with the corner in the middle.
    
    This is the best example to understand non-linearity
    without any formulas.
    
    Similar phenomenon occurs when the Sun passes the meridian
    close to zenith. The graph is now smooth but has a big hump
    in the middle. Closer to zenith, sharper the hump.
    
    As we found by computer experiments in our discussion this is
    the ONLY case when substantial non-linearity occurs.
    
    Alex.
    
    
    

       
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