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    Re: Bowditch and the tides.
    From: Herbert Prinz
    Date: 2003 Sep 25, 02:17 -0400

    Hello George,
    
    I hope you had a good summer and nice sailing.
    
    George Huxtable wrote:
    
    > Bowditch and the tides.
    >
    > Following Trevor Kenchington's recent recommendation, I've just invested in
    > B E Cartwright's "Tides - A Scientific History".(Cambridge University press
    > 1999), which exists in hardback and paperback.
    
    > [...]
    > One disappointment is that nowhere does Cartwright seem to provide an easy
    > answer to the natural question that everyone asks- "Why are there two tides
    > a day when there's only one Moon to attract the water?"
    
    I think Cartwright does address this question as far as it concerns his topic.
    The book is about the history of tidal theory, not an exposition of tidal
    theory itself. Therefore, he can take the physics of it for granted. The
    historical question is: How did various pre-Newton theories account for
    semi-diurnal tides?  After Newton, however, the situation turned around: The
    problem became to account for the absence of semi-diurnal tides or the
    dominance of diurnal tides in certain waters.
    
    The answer to the second question had to wait for Laplace and Cartwright deals
    with it extensively.
    
    On his treatment of the first question, which is related to the one you asked,
    I have a few comments.
    
    Galileo largely ignored semi-diurnal tides and Cartwright duly comments on this
    (p. 29). He points to the strong diurnal tides in Venice that would make it
    doubtful that there really was a semi-diurnal tide everywhere. And he discusses
    Galileo's opinion that each sea basin responds to external disturbances with
    its own natural frequency. I would stress that Galileo never bothered with
    observational details when they did not fit his pre-conceived ideas. The mere
    existence of tides seemed to give evidence of a moving earth (revolving around
    the sun!). This was more important to Galileo than to derive the exact pattern
    of tides from a moving earth.
    
    By contrast, Kepler did offer an explanation for the semi-diurnal period. This
    fact has escaped even as thorough a scholar as Stillman Drake. I find it indeed
    disappointing that Cartwright passes over this as well. His short passage on
    Kepler leaves to be desired. Cartwright quotes from the "Astronomia nova",
    1609, but mistakenly gives as his reference "De fundamentis astrologiae
    certioribus", 1602. This does not prevent him from mis-dating Kepler's first
    ideas on tides to 1609, although Kepler already alluded to the semi-diurnal
    virtue of the moon in thesis 16 of the earlier treatise from 1602. I admit that
    it is only in the work of 1609 that Kepler elaborates somewhat on his idea, and
    what he offers there is far from what we could call a theory.
    
    If Kepler's interest, as Cartwright remarks, lay not in the tides, then
    Cartwright's interest lay not in Kepler. But ironically, Kepler -  sleepwalking
    as usual ? - offered a strikingly modern hydrodynamic explanation involving the
    rotating earth: Since the moon passes so fast over the zenith, the water cannot
    follow as fast. The received impetus keeps the water in motion, it ebbs and
    then sloshes back like in a water bottle. This causes the second flood while
    the moon is away.  When the moon comes back during the next cycle, it takes the
    reigns again. Doesn't this look like an anticipation of what we call
    'resonance'?
    
    
    >
    > On reaching page 69 I came to a passage which may interest Bowditch
    > enthusiasts. It refers to a translation from the French of Laplace's great
    > work, his "Treatise on Celestial Mechanics", published in 1799, in several
    > "books", Book IV dealing with the dynamic effect on water masses of the
    > gravitational forces that give rise to the tides-
    >
    > Cartwright says-
    > "Book IV is included in the second volume of the abundantly annotated
    > English translation of the Mecanique Celeste by the Americam mathematician
    > Nathaniel Bowditch. (Bowditch, who also authored a famous treatise on
    > navigation, did not live to translate Laplace's fifth volume, containing
    > Book XIII.)
    >
    > Another notorious feature of Laplace's writing is his frequent omission of
    > derivatory exposition obvious to him, leaving the reader to fill in the
    > gaps. In the preface to his translation of Mecanique Celeste, Bowditch
    > writes: 'Whenever I meet in LA PLACE (sic) with the words "Thus it plainly
    > appears... [Ainsi il est clair que...]", I am sure that hours, perhaps days
    > of hard study will alone enable to discover HOW it plainly appears.'
    > Fortunately for the present discussion, these lacunae do not often occur in
    > the sections dealing with tides."
    >
    
    Cartwright's quote is inaccurate as he skips one level of indirection. It was
    Henry Ingersoll Bowditch who said in the Memoir (originally attached to Vol. 4,
    but now in Vol 1 of the reprint) that his father "was accustomed" (?) to make
    this remark. Nathaniel himself never wrote a preface to his translation. Apart
    from this, such a comment in published writing would be atypical for his sober
    and modest style. He may have said it en famille. This is not to deny that the
    comment is right on target. As we say in German: "Und wenn es nicht wahr ist,
    so ist es gut erfunden!" (Even if it is not true, it's a good story.)
    
    Best regards
    
    Herbert Prinz
    
    
    

       
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