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    Re: Navigating Around Hills and Dips in the Ocean
    From: George Huxtable
    Date: 2003 Aug 17, 13:37 +0100

    George Istok wrote->
    Mr. Huxtable,
    >Though I am now in agreement with you, I came to that position by a slightly
    >different argument (that may or may not be valid).
    I'm delighted that we now agree, though I fear that George Istok's argument
    is indeed invalid, even though it gives what I believe to be correct
    To digress slightly beforehand, when discussing gravity, one has to
    distinguish carefully between upper-case G, and lower-case g, which by
    convention mean very different things. G is the Universal Constant of
    Gravitation, defining the force between any two masses at a distance apart,
    and takes the same value anywhere in the Universe (or so our observations
    indicate). On the other hand, g is the acceleration due to gravity, a local
    matter that defines the force on a certain mass, caused by the pull of the
    Earth with all its irregularities, and varying with position and height or
    depth. It's an unfortunate choice of symbols which causes much confusion.
    Where George refers to changes in G, I think we should take it that he
    really means changes in g.
    George goes on to say-
    >I assumed a completely
    >isolated sphere of a light matter covered with water, a distance from the
    >center of the sphere to the surface of the water, a value (G) for the
    >gravitational attraction at the surface of the water, and that the surface
    >of the water at any point must always be at a distance from the center of
    >the sphere such that the value of G is constant.
    And there's the problem. The water surface (or a spirit-level) adjusts
    itself so that it's everywhere at a right-angle to the local direction of
    gravity, but that does NOT imply that over the sea surface the value of g
    is constant. There's no reason why it should be. Indeed, in an earlier
    mailing, I pointed out that g varied (at sea-level) between 978 and 983 cm
    per square second, between the equator and the poles. So, the basic
    assumption being wrong, that argument fails.
    He goes on to say-
    >I do not claim that the argument above is whole or that it is valid, but it
    >did convince me that there will be a mound over an anomaly where the
    >attraction is stronger and a dip where it is weaker.  Your argument is much
    >simpler and even more convincing.
    Thank you. We are in accord. Sorry I didn't get it right first time round;
    it would hace saved some trouble.
    George Huxtable.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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