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    Re: Navigating Around Hills and Dips in the Ocean
    From: George Huxtable
    Date: 2003 Aug 16, 14:26 +0100

    On 15 August, I wrote-
    
    >In an earlier mailing today, replying to Sharon Casey, I said-
    
    >Above an underwater sea-mount made of lead, there would be an increase in
    >gravity, and >the sea-level would be a bit lower there than it would be if
    >the lump of lead was absent.
    
    >Thinking about it a bit harder, and perhaps a bit more clearly, it now
    >seems to me that I >got the last bit quite wrong and should really have
    >said-
    
    >"Above an underwater sea-mount made of lead, there would be an increase in
    >gravity, and >the sea-level would be a bit higher there than it would be
    >if the lump of lead was absent."
    
    >That error doesn't affect anything else in the argument, but it's better
    >to get these >things right rather than wrong.
    
    George.
    
    ==========================
    
    George Istok  has since written-
    
    >Mr. Huxtable,
    >
    >The gravitational anomaly caused by the lead sea-mount may cause the
    >sea-level to be higher if the volume of water attracted toward the sea-mount
    >collects in such a way around the sea-mount that it causes a "mound" of
    >water that is "higher" than the total depression of the water surface over
    >the sea-mount.  However, it seems to be asking a lot of gravity, even from a
    >lead sea-mount, to create a "mound" of water.  The rapid decrease in
    >gravitational attraction (inversely proportional to the square of the
    >distance) and the insignificant difference between the vector sum of the
    >attraction towards the sea-mount and the earth and the vector of attraction
    >towards the center of the earth would both seem to make mound building
    >difficult.
    >
    >Therefore, I think your original statement was correct, even for a
    >sea-mount.
    >
    >George Istok
    
    ==================
    
    Let's see if I can persuade George Istok otherwise. What has to be
    considered is the direction of the gravitational force, rather than its
    strength. I hope we will agree that a pendulum will point in the direction
    of the local gravity vector, and the plane of the local sea-surface
    (horizon) will be exactly at right-angles to that direction.
    
    If we had a spherically uniform earth the gravity vector would point
    exactly toward its centre. Assume we are in a shallow sea into which we
    plop a mass of lead: let's say, a mile to our South. That mass will attract
    the pendulum bob toward it and it will then point slightly Southward of
    that original downward direction, in the direction of the vector-sum of the
    two attractions. The local sea-surface will be at exactly 90 deg from that
    new plum-bob direction so it will be tilted slightly, up to the Southward.
    If we now shift position to be directly over the lead mass, although the
    total strength of gravity will be enhanced, its direction will be exactly
    the same as it was before the mass of lead was added, so there's no tilt in
    the sea surface caused by the lead mass. If we go a mile futher South, the
    plumb bob will now be deflected the opposite way by the lead, and the
    sea-surface will now tilt slightly, up to the North.
    
    So it's clear that surrounding the lead mass is an area where the
    sea-surface is everywhere tilted, sloping increasingly upward as we near
    the lead mass. That's a description of a mound in the sea surface, not a
    dip. I ask George Istok to please respond by saying whether he now agrees
    with that statement, or remains unconvinced.
    
    Celestial navigation relies on the plane of the local horizon remaining
    undistorted by local gravitation anomalies, so in theory this could be a
    serious matter. In general, however, the amount of such distortion is not
    enough to affect navigation, to the accuracy that seamen require and are
    able to measure. The biggest effects, I understand, are to be found off the
    Pacific coasts of South America, where the Andes range falls steeply into
    the ocean.
    
    Deflection of the local vertical can have a more serious effect on land
    surveying, which is often done to a much higher precision than we poor
    sailors can manage.
    
    There's an interesting navigational connection in that it was Nevil
    Maskelyne, the celebrated "seaman's astronomer" and producer of the first
    Nautical Almanac in 1767, who set off to measure the local deflection of
    gravity caused by a Scottish mountain, chosen because it was such a regular
    shape that its effects could be roughly estimated. This was a successful
    attempt to estimate G ("big G"), the Universal Gravitational Constant.
    Knowing G, it was then possible to deduce the size of the Solar system (the
    same goal as for the Transit of Venus). Knowing that size, it was then
    possible to determine better the parallax corrections for objects in the
    Solar System. Everything connects...
    
    =====================
    
    Referring to my comment-
    
    >> Geophysics isn't really my subject, so I hope I've got things about right.
    >> If not, someone please tell me.
    
    David Hoyte wrote, inter alia-
    
    >I have difficulty in distinguishing which of George's statements he feels are
    >100% certain, and which he rates as 10% or 1% certain.
    
    George responds-
    
    Well, yes, so do I, and so do most of us, I reckon. Indeed, I've just
    acknowledged that one of my deductions was indeed 100% mistaken (about the
    sign of the surface deflection caused by an underwater seamount).
    
    Science is, or ought to be, somewhat tentative; a theory remains valid only
    until another comes along that fits the facts better. A degree of humility
    is called for, all the time.
    
    When David says-
    
    >George seems to be making the same fundamental error as those centuries
    >of "School Men" in the Roman Catholic institutions of learning, who accepted
    >the statements of Aristotle on scientific matters as unquestionable Truth.
    >
    >These are the bright boys, remember, who threatened Galileo with torture
    >unless
    >he stopped asserting that the Earth went round the Sun . . . because it
    >contradicted Aristotle.
    
    and likens my role to the inquisition; well, my back is broad. But if he
    wishes to cast himself as Galileo, he should remember that Galileo had some
    hard evidence to offer. An observer had only to look at Jupiter's
    satellites in the telescope to see the light.
    
    What evidence is David Hoyte offering to support his assertion that
    different routes around the ocean's peaks and troughs involve different
    expenditure of energy? None at all. For all we can tell, it's just a notion
    that's come into his mind, backed by a hearsay memory from an anonymous
    source at a meeting 30 years ago, who may or may not have known what he was
    talking about. Any inquisition would certainly give him the thumbs-down on
    that basis.
    
    As I said in an earlier mailing, "...an attempt to change the basic laws of
    science by asking for the opinions of mariners will be futile. To support
    his case he needs either contrary numerical observation or contrary logical
    argument, but presents neither." That still stands.
    
    Equally, one could ask mariners whether they are reluctant to start a
    voyage on a Friday-the-13th, and even in these days, there will be some
    superstitious skippers who agree; but that would hardly, in itself, be
    scientific evidence that there was in fact any extra danger involved in
    doing so.
    
    However, David is welcome to glean such evidence where he can, if he can,
    and offer it for what it's worth.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george---.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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