On Thu, 3 May 2001, Peter Smaardijk wrote:
> You mean that along loxodromes the magnetic north is in exactly the
> same direction, or do you mean true north? I thought it was true
> north, actually, but I'm not sure now.
True north. A loxodrome by definition maintains the same angle relative to
true north.
> And do you know whether a great circle is measured along the earths
> surface being a perfect sphere? I remember vaguely there is also an
> approximated "earth surface", not the actual one with mountains on
> it, but rather one that takes into account the fact that the earth is
> not a perfect sphere but more "pear-shaped". I can't think of the
> name now though. (And I remember vaguely (lots of vague memories)
> that there is an earths surface based on a level of equal gravity.
> But that would have to take into account the different matter inside
> the earth. This is probably beside the point here.)
Earth is approximately an oblate spheroid, i.e. flattened pole-to-pole
relative to the diameter of the equator. I don't know the answer to the
great circle on the oblate spheroid question. Of course the meridians are
not circles but ellipes, but they are still shortest paths. Equator is a
shortest path and the greatest circle (tangent to the earth) of them all.
But I don't know how if at all the oblateness effects the length of great
'circle' paths.
David
> Peter S.
>
> --- In BoundaryPoint@y..., David Mark <dmark@g...> wrote:
> >
> > The CA-US border (Lake of the Woods to Point Robers) consists of a
> number
> > of "straight" segments between boundary markers, it is sometimes as
> far as
> > 1/4 mile north or south of the 49th parallel.
> >
> > I put "straight" in quotes because of the issue of what constitutes
> a
> > straight line on the earth's surface. The usual definition of the
> > equivalent of a straight line is a great circle. But great circles
> other
> > than meridians and the equator have costantly changing bearings
> (compass
> > directions). Lines of constant compass bearing, known as
> loxodromes, are
> > not shortest paths unless they run north-south or are along the
> equator.
> >
> > David
> >
> > On Thu, 3 May 2001, michael donner wrote:
> >
> > > actually brian has filed the ultimate dissertation on this topic
> > > but it would take a search or a chase goose to get us back to it
> > >
> > > i think one basic point of his tho was that the lines between
> each pair of
> > > monuments are unique great circles
> > > & thus actually none of them ever aligns perfectly with any other
> > >
> > > & this is apart from the slight local irregularities that
> necessarily occur
> > > everywhere a monument is placed
> > >
> > > whether there are more egregious zigzags or offsets than these i
> dont know
> > >
> > > m
> > >
> > >
> > > >
> > > >Interesting about Iraq-Jordan.
> > > >
> > > >My newest atlas show a straight line, but expedia.com shows a
> zig zag.
> > > >
> > > >Is the caus border between Point Roberts and Lake Wood 100%
> straight, or
> > > >are the local irregularities?
> > > >
> > > >Jesper
> > > >----- Original Message -----
> > > >From: "michael donner" <m@...>
> > > >To: <BoundaryPoint@y...>
> > > >Sent: Thursday, May 03, 2001 12:38 AM
> > > >Subject: Re: [BoundaryPoint] Re: Fiat boundaries
> > > >
> > > >
> > > >> peter mentioned
> > > >>
> > > >> >
> > > >> >--- In BoundaryPoint@y..., michael donner <m@d...> wrote:
> > > >> >> & jesper
> > > >> >> of these 5 or 3 singular fiat boundaries we have found
> > > >> >> your chad nigeria line is probably the truest & purest in
> the world
> > > >> >> by virtue of being totally wet as well as probably unmarked
> > > >> >> & therefore almost certainly absolutely undeflected by so
> much as a
> > > >> >single
> > > >> >> subatomic particle
> > > >> >>
> > > >> >> m
> > > >> >
> > > >> >Not deflected, but Lake Chad being a very salty one with
> fluctuating
> > > >> >amounts of water (+salt) in it, there are possibly (also
> fluctuating)
> > > >> >amounts of land that are cut by the boundary.
> > > >>
> > > >> actually it is now a completely dry line
> > > >> as recent photos clearly show in
> > > >>
> <http://www.afrol.com/Categories/Environment/env062_lake_chad.htm>
> > > >>http://www.afrol.com/Categories/Environment/env062_lake_chad.htm
> > > >> if you can mentally supply where the border is
> > > >>
> > > >> still being legal but indefinite it remains the most
> pristine of all the
> > > >> singular fiats
> > > >>
> > > >>
> > > >> btw i also just noticed that the iraq jordan boundary
> > > >> 1 of the 2 other best claimants of singular fiathood
> > > >> has recently lapsed into a rather messy de facto zigzag
> > > >> vaguely suggestive of the egypt sudan administrative line
> > > >>
> > > >> so it may well have bitten the dust for any playful purposes
> > > >> & we could now be looking at a world class set with only 2
> members
> > > >> both dry
> > > >> one marked
> > > >>
> > > >> >>
> > > >> >> still cresting on my brendan waves
> > > >> >> & so wishing for the perfect moment point of happy landing
> > > >> >>
> > > >> >
> > > >> >Yes I know what you mean. The viscosity of these waves is
> huge, I
> > > >> >think. What substance is this? No salt water...
> > > >>
> > > >> i think it must be aurora australis concentrate
> > > >>
> > > >> responds shimmeringly to your every thought
> > > >>
> > > >> still dancing across the empyrian on it here too
> > > >>
> > > >> excelsior
> > > >> m
> > > >>
> > > >>
> > > >>
> > > >>
> > > >>
> > > >>
> > > >>
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